GNU C Language Intro and Reference

This is a plain-text render of the unfinished GNU C Language Intro and Reference by Richard Stallman, Trevis Rothwell and Nelson Beebe.

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GNU C Manual
1 The First Example
2 A Complete Program
3 Storage and Data
4 Beyond Integers
5 Lexical Syntax
6 Arithmetic
7 Assignment Expressions
8 Execution Control Expressions
9 Binary Operator Grammar
10 Order of Execution
11 Primitive Data Types
12 Constants
13 Type Size
14 Pointers
15 Structures
16 Arrays
17 Enumeration Types
18 Defining Typedef Names
19 Statements
20 Variables
21 Type Qualifiers
22 Functions
23 Compatible Types
24 Type Conversions
25 Scope
26 Preprocessing
27 Integers in Depth
28 Floating Point in Depth
29 Compilation
30 Directing Compilation
Appendix A Type Alignment
Appendix B Aliasing
Appendix C Digraphs
Appendix D Attributes in Declarations
Appendix E Signals
Appendix F GNU Free Documentation License
Index of Symbols and Keywords
Concept Index
GNU C Manual
1 The First Example
  1.1 Example: Recursive Fibonacci
    1.1.1 Function Header
    1.1.2 Function Body
  1.2 The Stack, And Stack Overflow
  1.3 Example: Iterative Fibonacci
2 A Complete Program
  2.1 Complete Program Example
  2.2 Complete Program Explanation
  2.3 Complete Program, Line by Line
  2.4 Compiling the Example Program
3 Storage and Data
4 Beyond Integers
  4.1 An Example with Non-Integer Numbers
  4.2 An Example with Arrays
  4.3 Calling the Array Example
  4.4 Variations for Array Example
5 Lexical Syntax
  5.1 Write Programs in English!
  5.2 Characters
  5.3 Whitespace
  5.4 Comments
  5.5 Identifiers
  5.6 Operators and Punctuation
  5.7 Line Continuation
6 Arithmetic
  6.1 Basic Arithmetic
  6.2 Integer Arithmetic
  6.3 Integer Overflow
    6.3.1 Overflow with Unsigned Integers
    6.3.2 Overflow with Signed Integers
  6.4 Mixed-Mode Arithmetic
  6.5 Division and Remainder
  6.6 Numeric Comparisons
  6.7 Shift Operations
    6.7.1 Shifting Makes New Bits
    6.7.2 Caveats for Shift Operations
    6.7.3 Shift Hacks
  6.8 Bitwise Operations
7 Assignment Expressions
  7.1 Simple Assignment
  7.2 Lvalues
  7.3 Modifying Assignment
  7.4 Increment and Decrement Operators
  7.5 Postincrement and Postdecrement
  7.6 Pitfall: Assignment in Subexpressions
  7.7 Write Assignments in Separate Statements
8 Execution Control Expressions
  8.1 Logical Operators
  8.2 Logical Operators and Comparisons
  8.3 Logical Operators and Assignments
  8.4 Conditional Expression
    8.4.1 Rules for Conditional Operator
    8.4.2 Conditional Operator Branches
  8.5 Comma Operator
    8.5.1 The Uses of the Comma Operator
    8.5.2 Clean Use of the Comma Operator
    8.5.3 When Not to Use the Comma Operator
9 Binary Operator Grammar
10 Order of Execution
  10.1 Reordering of Operands
  10.2 Associativity and Ordering
  10.3 Sequence Points
  10.4 Postincrement and Ordering
  10.5 Ordering of Operands
  10.6 Optimization and Ordering
11 Primitive Data Types
  11.1 Integer Data Types
    11.1.1 Basic Integers
    11.1.2 Signed and Unsigned Types
    11.1.3 Narrow Integers
    11.1.4 Conversion among Integer Types
    11.1.5 Boolean Type
    11.1.6 Integer Variations
  11.2 Floating-Point Data Types
  11.3 Complex Data Types
  11.4 The Void Type
  11.5 Other Data Types
  11.6 Type Designators
12 Constants
  12.1 Integer Constants
  12.2 Integer Constant Data Types
  12.3 Floating-Point Constants
  12.4 Imaginary Constants
  12.5 Invalid Numbers
  12.6 Character Constants
  12.7 String Constants
  12.8 UTF-8 String Constants
  12.9 Unicode Character Codes
  12.10 Wide Character Constants
  12.11 Wide String Constants
13 Type Size
14 Pointers
  14.1 Address of Data
  14.2 Pointer Types
  14.3 Pointer-Variable Declarations
  14.4 Pointer-Type Designators
  14.5 Dereferencing Pointers
  14.6 Null Pointers
  14.7 Dereferencing Null or Invalid Pointers
  14.8 Void Pointers
  14.9 Pointer Comparison
  14.10 Pointer Arithmetic
  14.11 Pointers and Arrays
  14.12 Pointer Arithmetic at Low Level
  14.13 Pointer Increment and Decrement
  14.14 Drawbacks of Pointer Arithmetic
  14.15 Pointer-Integer Conversion
  14.16 Printing Pointers
15 Structures
  15.1 Referencing Structure Fields
  15.2 Dynamic Memory Allocation
  15.3 Field Offset
  15.4 Structure Layout
  15.5 Packed Structures
  15.6 Bit Fields
  15.7 Bit Field Packing
  15.8 ‘const’ Fields
  15.9 Arrays of Length Zero
  15.10 Flexible Array Fields
  15.11 Overlaying Different Structures
  15.12 Structure Assignment
  15.13 Unions
  15.14 Packing With Unions
  15.15 Cast to a Union Type
  15.16 Structure Constructors
  15.17 Unnamed Types as Fields
  15.18 Incomplete Types
  15.19 Intertwined Incomplete Types
  15.20 Type Tags
16 Arrays
  16.1 Accessing Array Elements
  16.2 Declaring an Array
  16.3 Strings
  16.4 Array Type Designators
  16.5 Incomplete Array Types
  16.6 Limitations of C Arrays
  16.7 Multidimensional Arrays
  16.8 Constructing Array Values
  16.9 Arrays of Variable Length
17 Enumeration Types
18 Defining Typedef Names
19 Statements
  19.1 Expression Statement
  19.2 ‘if’ Statement
  19.3 ‘if-else’ Statement
  19.4 Blocks
  19.5 ‘return’ Statement
  19.6 Loop Statements
    19.6.1 ‘while’ Statement
    19.6.2 ‘do-while’ Statement
    19.6.3 ‘break’ Statement
    19.6.4 ‘for’ Statement
    19.6.5 Example of ‘for’
    19.6.6 Omitted ‘for’-Expressions
    19.6.7 ‘for’-Index Declarations
    19.6.8 ‘continue’ Statement
  19.7 ‘switch’ Statement
  19.8 Example of ‘switch’
  19.9 Duff’s Device
  19.10 Case Ranges
  19.11 Null Statement
  19.12 ‘goto’ Statement and Labels
  19.13 Locally Declared Labels
  19.14 Labels as Values
    19.14.1 Label Value Uses
    19.14.2 Label Value Caveats
  19.15 Statements and Declarations in Expressions
20 Variables
  20.1 Variable Declarations
    20.1.1 Declaring Arrays and Pointers
    20.1.2 Combining Variable Declarations
  20.2 Initializers
  20.3 Designated Initializers
  20.4 Referring to a Type with ‘__auto_type’
  20.5 Local Variables
  20.6 File-Scope Variables
  20.7 Static Local Variables
  20.8 ‘extern’ Declarations
  20.9 Allocating File-Scope Variables
  20.10 ‘auto’ and ‘register’
  20.11 Omitting Types in Declarations
21 Type Qualifiers
  21.1 ‘const’ Variables and Fields
  21.2 ‘volatile’ Variables and Fields
  21.3 ‘restrict’-Qualified Pointers
  21.4 ‘restrict’ Pointer Example
22 Functions
  22.1 Function Definitions
    22.1.1 Function Parameter Variables
    22.1.2 Forward Function Declarations
    22.1.3 Static Functions
    22.1.4 Arrays as Parameters
      22.1.4.1 Array parameters are pointers
      22.1.4.2 Passing array arguments
      22.1.4.3 Type qualifiers on array parameters
    22.1.5 Functions That Accept Structure Arguments
  22.2 Function Declarations
  22.3 Function Calls
  22.4 Function Call Semantics
  22.5 Function Pointers
    22.5.1 Declaring Function Pointers
    22.5.2 Assigning Function Pointers
    22.5.3 Calling Function Pointers
  22.6 The ‘main’ Function
    22.6.1 Returning Values from ‘main’
    22.6.2 Accessing Command-line Parameters
    22.6.3 Accessing Environment Variables
  22.7 Advanced Function Features
    22.7.1 Variable-Length Array Parameters
    22.7.2 Variable-Length Parameter Lists
    22.7.3 Nested Functions
    22.7.4 Inline Function Definitions
  22.8 Obsolete Function Features
    22.8.1 Older GNU C Inlining
    22.8.2 Old-Style Function Definitions
23 Compatible Types
24 Type Conversions
  24.1 Explicit Type Conversion
  24.2 Assignment Type Conversions
  24.3 Argument Promotions
  24.4 Operand Promotions
  24.5 Common Type
25 Scope
26 Preprocessing
  26.1 Preprocessing Overview
  26.2 Directives
  26.3 Preprocessing Tokens
  26.4 Header Files
    26.4.1 ‘#include’ Syntax
    26.4.2 ‘#include’ Operation
    26.4.3 Search Path
    26.4.4 Once-Only Headers
    26.4.5 Computed Includes
  26.5 Macros
    26.5.1 Object-like Macros
    26.5.2 Function-like Macros
    26.5.3 Macro Arguments
    26.5.4 Stringification
    26.5.5 Concatenation
    26.5.6 Variadic Macros
    26.5.7 Predefined Macros
    26.5.8 Undefining and Redefining Macros
    26.5.9 Directives Within Macro Arguments
    26.5.10 Macro Pitfalls
      26.5.10.1 Misnesting
      26.5.10.2 Operator Precedence Problems
      26.5.10.3 Swallowing the Semicolon
      26.5.10.4 Duplication of Side Effects
      26.5.10.5 Using ‘__auto_type’ for Local Variables
      26.5.10.6 Self-Referential Macros
      26.5.10.7 Argument Prescan
  26.6 Conditionals
    26.6.1 Uses of Conditional Directives
    26.6.2 Syntax of Preprocessing Conditionals
      26.6.2.1 The ‘#ifdef’ directive
      26.6.2.2 The ‘#if’ directive
      26.6.2.3 The ‘defined’ test
      26.6.2.4 The ‘#else’ directive
      26.6.2.5 The ‘#elif’ directive
    26.6.3 Deleted Code
  26.7 Diagnostics
  26.8 Line Control
  26.9 Null Directive
27 Integers in Depth
  27.1 Integer Representations
  27.2 Maximum and Minimum Values
28 Floating Point in Depth
  28.1 Floating-Point Representations
  28.2 Floating-Point Type Specifications
  28.3 Special Floating-Point Values
  28.4 Invalid Optimizations
  28.5 Floating Arithmetic Exception Flags
  28.6 Exact Floating-Point Arithmetic
  28.7 Rounding
  28.8 Rounding Issues
  28.9 Significance Loss
  28.10 Fused Multiply-Add
  28.11 Error Recovery
  28.12 Exact Floating-Point Constants
  28.13 Handling Infinity
  28.14 Handling NaN
  28.15 Signed Zeros
  28.16 Scaling by Powers of the Base
  28.17 Rounding Control
  28.18 Machine Epsilon
  28.19 Complex Arithmetic
  28.20 Round-Trip Base Conversion
  28.21 Further Reading
29 Compilation
30 Directing Compilation
  30.1 Pragmas
    30.1.1 Pragma Basics
    30.1.2 Severity Pragmas
    30.1.3 Optimization Pragmas
  30.2 Static Assertions
Appendix A Type Alignment
Appendix B Aliasing
  B.1 Aliasing and Alignment
  B.2 Aliasing and Length
  B.3 Type Rules for Aliasing
Appendix C Digraphs
Appendix D Attributes in Declarations
Appendix E Signals
Appendix F GNU Free Documentation License
Index of Symbols and Keywords
Concept Index
GNU C Manual
************

This manual explains the C language for use with the GNU Compiler
Collection (GCC) on the GNU/Linux system and other systems.  We refer to
this dialect as GNU C. If you already know C, you can use this as a
reference manual.

   If you understand basic concepts of programming but know nothing
about C, you can read this manual sequentially from the beginning to
learn the C language.

   If you are a beginner to programming, we recommend you first learn a
language with automatic garbage collection and no explicit pointers,
rather than starting with C.  Good choices include Lisp, Scheme, Python
and Java.  C’s explicit pointers mean that programmers must be careful
to avoid certain kinds of errors.

   C is a venerable language; it was first used in 1973.  The GNU C
Compiler, which was subsequently extended into the GNU Compiler
Collection, was first released in 1987.  Other important languages were
designed based on C: once you know C, it gives you a useful base for
learning C++, C#, Java, Scala, D, Go, and more.

   The special advantage of C is that it is fairly simple while allowing
close access to the computer’s hardware, which previously required
writing in assembler language to describe the individual machine
instructions.  Some have called C a “high-level assembler language”
because of its explicit pointers and lack of automatic management of
storage.  As one wag put it, “C combines the power of assembler language
with the convenience of assembler language.” However, C is far more
portable, and much easier to read and write, than assembler language.

   This manual describes the GNU C language supported by the GNU
Compiler Collection, as of roughly 2017.  Please inform us of any
changes needed to match the current version of GNU C.

   When a construct may be absent or work differently in other C
compilers, we say so.  When it is not part of ISO standard C, we say it
is a “GNU C extension,” because it is useful to know that.  However,
standards and other dialects are secondary topics for this manual.  For
simplicity’s sake, we keep those notes short, unless it is vital to say
more.

   Likewise, we hardly mention C++ or other languages that the GNU
Compiler Collection supports.  We hope this manual will serve as a base
for writing manuals for those languages, but languages so different
can’t share one common manual.

   Some aspects of the meaning of C programs depend on the target
platform: which computer, and which operating system, the compiled code
will run on.  Where this is the case, we say so.

   The C language provides no built-in facilities for performing such
common operations as input/output, memory management, string
manipulation, and the like.  Instead, these facilities are defined in a
standard library, which is automatically available in every C program.
*Note The GNU C Library: (libc)Top.

   This manual incorporates the former GNU C Preprocessor Manual, which
was among the earliest GNU Manuals.  It also uses some text from the
earlier GNU C Manual that was written by Trevis Rothwell and James
Youngman.

   GNU C has many obscure features, each one either for historical
compatibility or meant for very special situations.  We have left them
to a companion manual, the GNU C Obscurities Manual, which will be
published digitally later.

   Please report errors and suggestions to c-manual@gnu.org.

1 The First Example
*******************

This chapter presents the source code for a very simple C program and
uses it to explain a few features of the language.  If you already know
the basic points of C presented in this chapter, you can skim it or skip
it.

1.1 Example: Recursive Fibonacci
================================

To introduce the most basic features of C, let’s look at code for a
simple mathematical function that does calculations on integers.  This
function calculates the Nth number in the Fibonacci series, in which
each number is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, 21,
34, 55, ....

     int
     fib (int n)
     {
       if (n >=2)  /* This avoids infinite recursion.  */
         return 1;
       else
         return fib (n - 1) + fib (n - 2);
     }

   This very simple program illustrates several features of C:

   • A function definition, whose first two lines constitute the
     function header.  *Note Function Definitions::.

   • A function parameter ‘n’, referred to as the variable ‘n’ inside
     the function body.  *Note Function Parameter Variables::.  A
     function definition uses parameters to refer to the argument values
     provided in a call to that function.

   • Arithmetic.  C programs add with ‘+’ and subtract with ‘-’.  *Note
     Arithmetic::.

   • Numeric comparisons.  The operator ‘>=’ tests for “less than or
     equal.” *Note Numeric Comparisons::.

   • Integer constants written in base 10.  *Note Integer Constants::.

   • A function call.  The function call ‘fib (n - 1)’ calls the
     function ‘fib’, passing as its argument the value ‘n - 1’.  *Note
     Function Calls::.

   • A comment, which starts with ‘/*’ and ends with ‘*/’.  The comment
     has no effect on the execution of the program.  Its purpose is to
     provide explanations to people reading the source code.  Including
     comments in the code is tremendously important—they provide
     background information so others can understand the code more
     quickly.  *Note Comments::.

   • Two kinds of statements, the ‘return’ statement and the
     ‘if’...‘else’ statement.  *Note Statements::.

   • Recursion.  The function ‘fib’ calls itself; that is called a
     “recursive call”.  These are valid in C, and quite common.

     The ‘fib’ function would not be useful if it didn’t return.  Thus,
     recursive definitions, to be of any use, must avoid infinite
     recursion.

     This function definition prevents infinite recursion by specially
     handling the case where ‘n’ is two or less.  Thus the maximum depth
     of recursive calls is less than ‘n’.

1.1.1 Function Header
---------------------

In our example, the first two lines of the function definition are the
“header”.  Its purpose is to state the function’s name and say how it is
called:

     int
     fib (int n)

says that the function returns an integer (type ‘int’), its name is
‘fib’, and it takes one argument named ‘n’ which is also an integer.
(Data types will be explained later, in *note Primitive Types::.)

1.1.2 Function Body
-------------------

The rest of the function definition is called the “function body”.  Like
every function body, this one starts with ‘{’, ends with ‘}’, and
contains zero or more “statements” and “declarations”.  Statements
specify actions to take, whereas declarations define names of variables,
functions, and so on.  Each statement and each declaration ends with a
semicolon (‘;’).

   Statements and declarations often contain “expressions”; an
expression is a construct whose execution produces a “value” of some
data type, but may also take actions through “side effects” that alter
subsequent execution.  A statement, by contrast, does not have a value;
it affects further execution of the program only through the actions it
takes.

   This function body contains no declarations, and just one statement,
but that one is a complex statement in that it contains nested
statements.  This function uses two kinds of statements:

‘return’
     The ‘return’ statement makes the function return immediately.  It
     looks like this:

          return VALUE;

     Its meaning is to compute the expression VALUE and exit the
     function, making it return whatever value that expression produced.
     For instance,

          return 1;

     returns the integer 1 from the function, and

          return fib (n - 1) + fib (n - 2);

     returns a value computed by performing two function calls as
     specified and adding their results.

‘if...else’
     The ‘if’...‘else’ statement is a “conditional”.  Each time it
     executes, it chooses one of its two substatements to execute and
     ignores the other.  It looks like this:

          if (CONDITION)
            IF-TRUE-STATEMENT
          else
            IF-FALSE-STATEMENT

     Its meaning is to compute the expression CONDITION and, if it’s
     “true,” execute IF-TRUE-STATEMENT.  Otherwise, execute
     IF-FALSE-STATEMENT.  *Note if-else Statement::.

     Inside the ‘if’...‘else’ statement, CONDITION is simply an
     expression.  It’s considered “true” if its value is nonzero.  (A
     comparison operation, such as ‘n >=2’, produces the value 1 if
     it’s “true” and 0 if it’s “false.” *Note Numeric Comparisons::.)
     Thus,

          if (n >=2)
            return 1;
          else
            return fib (n - 1) + fib (n - 2);

     first tests whether the value of ‘n’ is less than or equal to 2.
     If so, the expression ‘n >=2’ has the value 1.  So execution
     continues with the statement

          return 1;

     Otherwise, execution continues with this statement:

          return fib (n - 1) + fib (n - 2);

     Each of these statements ends the execution of the function and
     provides a value for it to return.  *Note return Statement::.

   Calculating ‘fib’ using ordinary integers in C works only for N < 47,
because the value of ‘fib (47)’ is too large to fit in type ‘int’.  The
addition operation that tries to add ‘fib (46)’ and ‘fib (45)’ cannot
deliver the correct result.  This occurrence is called “integer
overflow”.

   Overflow can manifest itself in various ways, but one thing that
can’t possibly happen is to produce the correct value, since that can’t
fit in the space for the value.  *Note Integer Overflow::.

   *Note Functions::, for a full explanation about functions.

1.2 The Stack, And Stack Overflow
=================================

Recursion has a drawback: there are limits to how many nested function
calls a program can make.  In C, each function call allocates a block of
memory which it uses until the call returns.  C allocates these blocks
consecutively within a large area of memory known as the “stack”, so we
refer to the blocks as “stack frames”.

   The size of the stack is limited; if the program tries to use too
much, that causes the program to fail because the stack is full.  This
is called “stack overflow”.

   Stack overflow on GNU/Linux typically manifests itself as the
“signal” named ‘SIGSEGV’, also known as a “segmentation fault.” By
default, this signal terminates the program immediately, rather than
letting the program try to recover, or reach an expected ending point.
(We commonly say in this case that the program “crashes”).  *Note
Signals::.

   It is inconvenient to observe a crash by passing too large an
argument to recursive Fibonacci, because the program would run a long
time before it crashes.  This algorithm is simple but ridiculously slow:
in calculating ‘fib (N)’, the number of (recursive) calls ‘fib (1)’ or
‘fib (2)’ that it makes equals the final result.

   However, you can observe stack overflow very quickly if you use this
function instead:

     int
     fill_stack (int n)
     {
       if (n >=1)  /* This limits the depth of recursion.  */
         return 1;
       else
         return fill_stack (n - 1);
     }

   Under gNewSense GNU/Linux on the Lemote Yeeloong, without
optimization and using the default configuration, an experiment showed
there is enough stack space to do 261906 nested calls to that function.
One more, and the stack overflows and the program crashes.  On another
platform, with a different configuration, or with a different function,
the limit might be bigger or smaller.

1.3 Example: Iterative Fibonacci
================================

Here’s a much faster algorithm for computing the same Fibonacci series.
It is faster for two reasons.  First, it uses “iteration” (that is,
repetition or looping) rather than recursion, so it doesn’t take time
for a large number of function calls.  But mainly, it is faster because
the number of repetitions is small—only ‘N’.

     int
     fib (int n)
     {
       int last = 1;   /* Initial value is ‘fib (1)’.  */
       int prev = 0;   /* Initial value controls ‘fib (2)’.  */
       int i;

       for (i = 1; i < n; ++i)
         /* If ‘n’ is 1 or less, the loop runs zero times,  */
         /* since ‘i < n’ is false the first time.  */
         {
           /* Now ‘last’ is ‘fib (i)’
              and ‘prev’ is ‘fib (i − 1)’.  */
           /* Compute ‘fib (i + 1)’.  */
           int next = prev + last;
           /* Shift the values down.  */
           prev = last;
           last = next;
           /* Now ‘last’ is ‘fib (i + 1)’
              and ‘prev’ is ‘fib (i)’.
              But that won’t stay true for long,
              because we are about to increment ‘i’.  */
         }

       return last;
     }

   This definition computes ‘fib (N)’ in a time proportional to ‘N’.
The comments in the definition explain how it works: it advances through
the series, always keeps the last two values in ‘last’ and ‘prev’, and
adds them to get the next value.

   Here are the additional C features that this definition uses:

Internal blocks
     Within a function, wherever a statement is called for, you can
     write a “block”.  It looks like ‘{ ... }’ and contains zero or more
     statements and declarations.  (You can also use additional blocks
     as statements in a block.)

     The function body also counts as a block, which is why it can
     contain statements and declarations.

     *Note Blocks::.

Declarations of local variables
     This function body contains declarations as well as statements.
     There are three declarations directly in the function body, as well
     as a fourth declaration in an internal block.  Each starts with
     ‘int’ because it declares a variable whose type is integer.  One
     declaration can declare several variables, but each of these
     declarations is simple and declares just one variable.

     Variables declared inside a block (either a function body or an
     internal block) are “local variables”.  These variables exist only
     within that block; their names are not defined outside the block,
     and exiting the block deallocates their storage.  This example
     declares four local variables: ‘last’, ‘prev’, ‘i’, and ‘next’.

     The most basic local variable declaration looks like this:

          TYPE VARIABLENAME;

     For instance,

          int i;

     declares the local variable ‘i’ as an integer.  *Note Variable
     Declarations::.

Initializers
     When you declare a variable, you can also specify its initial
     value, like this:

          TYPE VARIABLENAME = VALUE;

     For instance,

          int last = 1;

     declares the local variable ‘last’ as an integer (type ‘int’) and
     starts it off with the value 1.  *Note Initializers::.

Assignment
     Assignment: a specific kind of expression, written with the ‘=’
     operator, that stores a new value in a variable or other place.
     Thus,

          VARIABLE = VALUE

     is an expression that computes ‘VALUE’ and stores the value in
     ‘VARIABLE’.  *Note Assignment Expressions::.

Expression statements
     An expression statement is an expression followed by a semicolon.
     That computes the value of the expression, then ignores the value.

     An expression statement is useful when the expression changes some
     data or has other side effects—for instance, with function calls,
     or with assignments as in this example.  *Note Expression
     Statement::.

     Using an expression with no side effects in an expression statement
     is pointless except in very special cases.  For instance, the
     expression statement ‘x;’ would examine the value of ‘x’ and ignore
     it.  That is not useful.

Increment operator
     The increment operator is ‘++’.  ‘++i’ is an expression that is
     short for ‘i = i + 1’.  *Note Increment/Decrement::.

‘for’ statements
     A ‘for’ statement is a clean way of executing a statement
     repeatedly—a “loop” (*note Loop Statements::).  Specifically,

          for (i = 1; i < n; ++i)
            BODY

     means to start by doing ‘i = 1’ (set ‘i’ to one) to prepare for the
     loop.  The loop itself consists of

        • Testing ‘i < n’ and exiting the loop if that’s false.

        • Executing BODY.

        • Advancing the loop (executing ‘++i’, which increments ‘i’).

     The net result is to execute BODY with 1 in ‘i’, then with 2 in
     ‘i’, and so on, stopping just before the repetition where ‘i’ would
     equal ‘n’.  If ‘n’ is less than 1, the loop will execute the body
     zero times.

     The body of the ‘for’ statement must be one and only one statement.
     You can’t write two statements in a row there; if you try to, only
     the first of them will be treated as part of the loop.

     The way to put multiple statements in such a place is to group them
     with a block, and that’s what we do in this example.

2 A Complete Program
********************

It’s all very well to write a Fibonacci function, but you cannot run it
by itself.  It is a useful program, but it is not a complete program.

   In this chapter we present a complete program that contains the ‘fib’
function.  This example shows how to make the program start, how to make
it finish, how to do computation, and how to print a result.

2.1 Complete Program Example
============================

Here is the complete program that uses the simple, recursive version of
the ‘fib’ function (*note Recursive Fibonacci::):

     #include <stdio.h>

     int
     fib (int n)
     {
       if (n >=2)  /* This avoids infinite recursion.  */
         return 1;
       else
         return fib (n - 1) + fib (n - 2);
     }

     int
     main (void)
     {
       printf ("Fibonacci series item %d is %d\n",
               20, fib (20));
       return 0;
     }

This program prints a message that shows the value of ‘fib (20)’.

   Now for an explanation of what that code means.

2.2 Complete Program Explanation
================================

Here’s the explanation of the code of the example in the previous
section.

   This sample program prints a message that shows the value of ‘fib
(20)’, and exits with code 0 (which stands for successful execution).

   Every C program is started by running the function named ‘main’.
Therefore, the example program defines a function named ‘main’ to
provide a way to start it.  Whatever that function does is what the
program does.  *Note The main Function::.

   The ‘main’ function is the first one called when the program runs,
but it doesn’t come first in the example code.  The order of the
function definitions in the source code makes no difference to the
program’s meaning.

   The initial call to ‘main’ always passes certain arguments, but
‘main’ does not have to pay attention to them.  To ignore those
arguments, define ‘main’ with ‘void’ as the parameter list.  (‘void’ as
a function’s parameter list normally means “call with no arguments,” but
‘main’ is a special case.)

   The function ‘main’ returns 0 because that is the conventional way
for ‘main’ to indicate successful execution.  It could instead return a
positive integer to indicate failure, and some utility programs have
specific conventions for the meaning of certain numeric “failure codes”.
*Note Values from main::.

   The simplest way to print text in C is by calling the ‘printf’
function, so here we explain what that does.

   The first argument to ‘printf’ is a “string constant” (*note String
Constants::) that is a template for output.  The function ‘printf’
copies most of that string directly as output, including the newline
character at the end of the string, which is written as ‘\n’.  The
output goes to the program’s “standard output” destination, which in the
usual case is the terminal.

   ‘%’ in the template introduces a code that substitutes other text
into the output.  Specifically, ‘%d’ means to take the next argument to
‘printf’ and substitute it into the text as a decimal number.  (The
argument for ‘%d’ must be of type ‘int’; if it isn’t, ‘printf’ will
malfunction.)  So the output is a line that looks like this:

     Fibonacci series item 20 is 6765

   This program does not contain a definition for ‘printf’ because it is
defined by the C library, which makes it available in all C programs.
However, each program does need to “declare” ‘printf’ so it will be
called correctly.  The ‘#include’ line takes care of that; it includes a
“header file” called ‘stdio.h’ into the program’s code.  That file is
provided by the operating system and it contains declarations for the
many standard input/output functions in the C library, one of which is
‘printf’.

   Don’t worry about header files for now; we’ll explain them later in
*note Header Files::.

   The first argument of ‘printf’ does not have to be a string constant;
it can be any string (*note Strings::).  However, using a constant is
the most common case.

   To learn more about ‘printf’ and other facilities of the C library,
see *note The GNU C Library: (libc)Top.

2.3 Complete Program, Line by Line
==================================

Here’s the same example, explained line by line.  *Beginners, do you
find this helpful or not?  Would you prefer a different layout for the
example?  Please tell rms@gnu.org.*

     #include <stdio.h>      /* Include declaration of usual */
                             /*   I/O functions such as ‘printf’.  */
                             /* Most programs need these.  */

     int                     /* This function returns an ‘int’.  */
     fib (int n)             /* Its name is ‘fib’;  */
                             /*   its argument is called ‘n’.  */
     {                       /* Start of function body.  */
       /* This stops the recursion from being infinite.  */
       if (n >=2)           /* If ‘n’ is 1 or 2,  */
         return 1;           /*   make ‘fib’ return 1.  */
       else                  /* otherwise, add the two previous  */
                             /* fibonacci numbers.  */
         return fib (n - 1) + fib (n - 2);
     }

     int                     /* This function returns an ‘int’.  */
     main (void)             /* Start here; ignore arguments.  */
     {                       /* Print message with numbers in it.  */
       printf ("Fibonacci series item %d is %d\n",
               20, fib (20));
       return 0;             /* Terminate program, report success.  */
     }

2.4 Compiling the Example Program
=================================

To run a C program requires converting the source code into an
“executable file”.  This is called “compiling” the program, and the
command to do that using GNU C is ‘gcc’.

   This example program consists of a single source file.  If we call
that file ‘fib1.c’, the complete command to compile it is this:

     gcc -g -O -o fib1 fib1.c

Here, ‘-g’ says to generate debugging information, ‘-O’ says to optimize
at the basic level, and ‘-o fib1’ says to put the executable program in
the file ‘fib1’.

   To run the program, use its file name as a shell command.  For
instance,

     ./fib1

However, unless you are sure the program is correct, you should expect
to need to debug it.  So use this command,

     gdb fib1

which starts the GDB debugger (*note Sample Session: (gdb)Sample
Session.) so you can run and debug the executable program ‘fib1’.

   *Note Compilation::, for an introduction to compiling more complex
programs which consist of more than one source file.

3 Storage and Data
******************

Storage in C programs is made up of units called “bytes”.  On nearly all
computers, a byte consists of 8 bits, but there are a few peculiar
computers (mostly “embedded controllers” for very small systems) where a
byte is longer than that.  This manual does not try to explain the
peculiarity of those computers; we assume that a byte is 8 bits.

   Every C data type is made up of a certain number of bytes; that
number is the data type’s “size”.  *Note Type Size::, for details.  The
types ‘signed char’ and ‘unsigned char’ are one byte long; use those
types to operate on data byte by byte.  *Note Signed and Unsigned
Types::.  You can refer to a series of consecutive bytes as an array of
‘char’ elements; that’s what an ASCII string looks like in memory.
*Note String Constants::.

4 Beyond Integers
*****************

So far we’ve presented programs that operate on integers.  In this
chapter we’ll present examples of handling non-integral numbers and
arrays of numbers.

4.1 An Example with Non-Integer Numbers
=======================================

Here’s a function that operates on and returns “floating point” numbers
that don’t have to be integers.  Floating point represents a number as a
fraction together with a power of 2.  (For more detail, *note
Floating-Point Data Types::.)  This example calculates the average of
three floating point numbers that are passed to it as arguments:

     double
     average_of_three (double a, double b, double c)
     {
       return (a + b + c) / 3;
     }

   The values of the parameter A, B and C do not have to be integers,
and even when they happen to be integers, most likely their average is
not an integer.

   ‘double’ is the usual data type in C for calculations on
floating-point numbers.

   To print a ‘double’ with ‘printf’, we must use ‘%f’ instead of ‘%d’:

     printf ("Average is %f\n",
             average_of_three (1.1, 9.8, 3.62));

   The code that calls ‘printf’ must pass a ‘double’ for printing with
‘%f’ and an ‘int’ for printing with ‘%d’.  If the argument has the wrong
type, ‘printf’ will produce garbage output.

   Here’s a complete program that computes the average of three specific
numbers and prints the result:

     double
     average_of_three (double a, double b, double c)
     {
       return (a + b + c) / 3;
     }

     int
     main (void)
     {
         printf ("Average is %f\n",
                 average_of_three (1.1, 9.8, 3.62));
         return 0;
     }

   From now on we will not present examples of calls to ‘main’.  Instead
we encourage you to write them for yourself when you want to test
executing some code.

4.2 An Example with Arrays
==========================

A function to take the average of three numbers is very specific and
limited.  A more general function would take the average of any number
of numbers.  That requires passing the numbers in an array.  An array is
an object in memory that contains a series of values of the same data
type.  This chapter presents the basic concepts and use of arrays
through an example; for the full explanation, see *note Arrays::.

   Here’s a function definition to take the average of several
floating-point numbers, passed as type ‘double’.  The first parameter,
‘length’, specifies how many numbers are passed.  The second parameter,
‘input_data’, is an array that holds those numbers.

     double
     avg_of_double (int length, double input_data[])
     {
       double sum = 0;
       int i;

       for (i = 0; i < length; i++)
         sum = sum + input_data[i];

       return sum / length;
     }

   This introduces the expression to refer to an element of an array:
‘input_data[i]’ means the element at index ‘i’ in ‘input_data’.  The
index of the element can be any expression with an integer value; in
this case, the expression is ‘i’.  *Note Accessing Array Elements::.

   The lowest valid index in an array is 0, _not_ 1, and the highest
valid index is one less than the number of elements.  (This is known as
“zero-origin indexing”.)

   This example also introduces the way to declare that a function
parameter is an array.  Such declarations are modeled after the syntax
for an element of the array.  Just as ‘double foo’ declares that ‘foo’
is of type ‘double’, ‘double input_data[]’ declares that each element of
‘input_data’ is of type ‘double’.  Therefore, ‘input_data’ itself has
type “array of ‘double’.”

   When declaring an array parameter, it’s not necessary to say how long
the array is.  In this case, the parameter ‘input_data’ has no length
information.  That’s why the function needs another parameter, ‘length’,
for the caller to provide that information to the function
‘avg_of_double’.

4.3 Calling the Array Example
=============================

To call the function ‘avg_of_double’ requires making an array and then
passing it as an argument.  Here is an example.

     {
       /* The array of values to average.  */
       double nums_to_average[5];
       /* The average, once we compute it.  */
       double average;

       /* Fill in elements of ‘nums_to_average’.  */

       nums_to_average[0] = 58.7;
       nums_to_average[1] = 5.1;
       nums_to_average[2] = 7.7;
       nums_to_average[3] = 105.2;
       nums_to_average[4] = -3.14159;

       average = avg_of_double (5, nums_to_average);

       /* ...now make use of ‘average’... */
     }

   This shows an array subscripting expression again, this time on the
left side of an assignment, storing a value into an element of an array.

   It also shows how to declare a local variable that is an array:
‘double nums_to_average[5];’.  Since this declaration allocates the
space for the array, it needs to know the array’s length.  You can
specify the length with any expression whose value is an integer, but in
this declaration the length is a constant, the integer 5.

   The name of the array, when used by itself as an expression, stands
for the address of the array’s data, and that’s what gets passed to the
function ‘avg_of_double’ in ‘avg_of_double (5, nums_to_average)’.

   We can make the code easier to maintain by avoiding the need to write
5, the array length, when calling ‘avg_of_double’.  That way, if we
change the array to include more elements, we won’t have to change that
call.  One way to do this is with the ‘sizeof’ operator:

       average = avg_of_double ((sizeof (nums_to_average)
                                 / sizeof (nums_to_average[0])),
                                nums_to_average);

   This computes the number of elements in ‘nums_to_average’ by dividing
its total size by the size of one element.  *Note Type Size::, for more
details of using ‘sizeof’.

   We don’t show in this example what happens after storing the result
of ‘avg_of_double’ in the variable ‘average’.  Presumably more code
would follow that uses that result somehow.  (Why compute the average
and not use it?)  But that isn’t part of this topic.

4.4 Variations for Array Example
================================

The code to call ‘avg_of_double’ has two declarations that start with
the same data type:

       /* The array of values to average.  */
       double nums_to_average[5];
       /* The average, once we compute it.  */
       double average;

   In C, you can combine the two, like this:

       double nums_to_average[5], average;

   This declares ‘nums_to_average’ so each of its elements is a
‘double’, and ‘average’ so that it simply is a ‘double’.

   However, while you _can_ combine them, that doesn’t mean you
_should_.  If it is useful to write comments about the variables, and
usually it is, then it’s clearer to keep the declarations separate so
you can put a comment on each one.

   We set all of the elements of the array ‘nums_to_average’ with
assignments, but it is more convenient to use an initializer in the
declaration:

     {
       /* The array of values to average.  */
       double nums_to_average[]
         = { 58.7, 5.1, 7.7, 105.2, -3.14159 };

       /* The average, once we compute it.  */
       average = avg_of_double ((sizeof (nums_to_average)
                                 / sizeof (nums_to_average[0])),
                                nums_to_average);

       /* ...now make use of ‘average’... */
     }

   The array initializer is a comma-separated list of values, delimited
by braces.  *Note Initializers::.

   Note that the declaration does not specify a size for
‘nums_to_average’, so the size is determined from the initializer.
There are five values in the initializer, so ‘nums_to_average’ gets
length 5.  If we add another element to the initializer,
‘nums_to_average’ will have six elements.

   Because the code computes the number of elements from the size of the
array, using ‘sizeof’, the program will operate on all the elements in
the initializer, regardless of how many those are.

5 Lexical Syntax
****************

To start the full description of the C language, we explain the lexical
syntax and lexical units of C code.  The lexical units of a programming
language are known as “tokens”.  This chapter covers all the tokens of C
except for constants, which are covered in a later chapter (*note
Constants::).  One vital kind of token is the “identifier” (*note
Identifiers::), which is used for names of any kind.

5.1 Write Programs in English!
==============================

In principle, you can write the function and variable names in a
program, and the comments, in any human language.  C allows any kinds of
characters in comments, and you can put non-ASCII characters into
identifiers with a special prefix.  However, to enable programmers in
all countries to understand and develop the program, it is best given
today’s circumstances to write identifiers and comments in English.

   English is the one language that programmers in all countries
generally study.  If a program’s names are in English, most programmers
in Bangladesh, Belgium, Bolivia, Brazil, and Bulgaria can understand
them.  Most programmers in those countries can speak English, or at
least read it, but they do not read each other’s languages at all.  In
India, with so many languages, two programmers may have no common
language other than English.

   If you don’t feel confident in writing English, do the best you can,
and follow each English comment with a version in a language you write
better; add a note asking others to translate that to English.  Someone
will eventually do that.

   The program’s user interface is a different matter.  We don’t need to
choose one language for that; it is easy to support multiple languages
and let each user choose the language to use.  This requires writing the
program to support localization of its interface.  (The ‘gettext’
package exists to support this; *note The GNU C Library: (libc)Message
Translation.)  Then a community-based translation effort can provide
support for all the languages users want to use.

5.2 Characters
==============

GNU C source files are usually written in the ASCII character set, which
was defined in the 1960s for English.  However, they can also include
Unicode characters represented in the UTF-8 multibyte encoding.  This
makes it possible to represent accented letters such as ‘á’, as well as
other scripts such as Arabic, Chinese, Cyrillic, Hebrew, Japanese, and
Korean.(1)

   In C source code, non-ASCII characters are valid in comments, in wide
character constants (*note Wide Character Constants::), and in string
constants (*note String Constants::).

   Another way to specify non-ASCII characters in constants (character
or string) and identifiers is with an escape sequence starting with
backslash, specifying the intended Unicode character.  (*Note Unicode
Character Codes::.)  This specifies non-ASCII characters without putting
a real non-ASCII character in the source file itself.

   C accepts two-character aliases called “digraphs” for certain
characters.  *Note Digraphs::.

   ---------- Footnotes ----------

   (1) On some obscure systems, GNU C uses UTF-EBCDIC instead of UTF-8,
but that is not worth describing in this manual.

5.3 Whitespace
==============

Whitespace means characters that exist in a file but appear blank in a
printed listing of a file (or traditionally did appear blank, several
decades ago).  The C language requires whitespace in order to separate
two consecutive identifiers, or to separate an identifier from a numeric
constant.  Other than that, and a few special situations described
later, whitespace is optional; you can put it in when you wish, to make
the code easier to read.

   Space and tab in C code are treated as whitespace characters.  So are
line breaks.  You can represent a line break with the newline character
(also called “linefeed” or LF), CR (carriage return), or the CRLF
sequence (two characters: carriage return followed by a newline
character).

   The “formfeed” character, Control-L, was traditionally used to divide
a file into pages.  It is still used this way in source code, and the
tools that generate nice printouts of source code still start a new page
after each “formfeed” character.  Dividing code into pages separated by
formfeed characters is a good way to break it up into comprehensible
pieces and show other programmers where they start and end.

   The “vertical tab” character, Control-K, was traditionally used to
make printing advance down to the next section of a page.  We know of no
particular reason to use it in source code, but it is still accepted as
whitespace in C.

   Comments are also syntactically equivalent to whitespace.  *Note
Comments::.

5.4 Comments
============

A comment encapsulates text that has no effect on the program’s
execution or meaning.

   The purpose of comments is to explain the code to people that read
it.  Writing good comments for your code is tremendously important—they
should provide background information that helps programmers understand
the reasons why the code is written the way it is.  You, returning to
the code six months from now, will need the help of these comments to
remember why you wrote it this way.

   Outdated comments that become incorrect are counterproductive, so
part of the software developer’s responsibility is to update comments as
needed to correspond with changes to the program code.

   C allows two kinds of comment syntax, the traditional style and the
C++ style.  A traditional C comment starts with ‘/*’ and ends with ‘*/’.
For instance,

     /* This is a comment in traditional C syntax. */

   A traditional comment can contain ‘/*’, but these delimiters do not
nest as pairs.  The first ‘*/’ ends the comment regardless of whether it
contains ‘/*’ sequences.

     /* This /* is a comment */ But this is not! */

   A “line comment” starts with ‘//’ and ends at the end of the line.
For instance,

     // This is a comment in C++ style.

   Line comments do nest, in effect, because ‘//’ inside a line comment
is part of that comment:

     // this whole line is // one comment
     This is code, not comment.

   It is safe to put line comments inside block comments, or vice versa.

     /* traditional comment
        // contains line comment
        more traditional comment
      */ text here is not a comment

     // line comment /* contains traditional comment */

   But beware of commenting out one end of a traditional comment with a
line comment.  The delimiter ‘/*’ doesn’t start a comment if it occurs
inside an already-started comment.

      // line comment  /* That would ordinarily begin a block comment.
         Oops! The line comment has ended;
         this isn't a comment any more.  */

   Comments are not recognized within string constants.  "/* blah */" is
the string constant ‘/* blah */’, not an empty string.

   In this manual we show the text in comments in a variable-width font,
for readability, but this font distinction does not exist in source
files.

   A comment is syntactically equivalent to whitespace, so it always
separates tokens.  Thus,

       int/* comment */foo;
     is equivalent to
       int foo;

but clean code always uses real whitespace to separate the comment
visually from surrounding code.

5.5 Identifiers
===============

An “identifier” (name) in C is a sequence of letters and digits, as well
as ‘_’, that does not start with a digit.  Most compilers also allow
‘$’.  An identifier can be as long as you like; for example,

     int anti_dis_establishment_arian_ism;

   Letters in identifiers are case-sensitive in C; thus, ‘a’ and ‘A’ are
two different identifiers.

   Identifiers in C are used as variable names, function names, typedef
names, enumeration constants, type tags, field names, and labels.
Certain identifiers in C are “keywords”, which means they have specific
syntactic meanings.  Keywords in C are “reserved words”, meaning you
cannot use them in any other way.  For instance, you can’t define a
variable or function named ‘return’ or ‘if’.

   You can also include other characters, even non-ASCII characters, in
identifiers by writing their Unicode character names, which start with
‘\u’ or ‘\U’, in the identifier name.  *Note Unicode Character Codes::.
However, it is usually a bad idea to use non-ASCII characters in
identifiers, and when they are written in English, they never need
non-ASCII characters.  *Note English::.

   Whitespace is required to separate two consecutive identifiers, or to
separate an identifier from a preceding or following numeric constant.

5.6 Operators and Punctuation
=============================

Here we describe the lexical syntax of operators and punctuation in C.
The specific operators of C and their meanings are presented in
subsequent chapters.

   Most operators in C consist of one or two characters that can’t be
used in identifiers.  The characters used for operators in C are
‘!~^&|*/%+-=><,.?:’.

   Some operators are a single character.  For instance, ‘-’ is the
operator for negation (with one operand) and the operator for
subtraction (with two operands).

   Some operators are two characters.  For example, ‘++’ is the
increment operator.  Recognition of multicharacter operators works by
grouping together as many consecutive characters as can constitute one
operator.

   For instance, the character sequence ‘++’ is always interpreted as
the increment operator; therefore, if we want to write two consecutive
instances of the operator ‘+’, we must separate them with a space so
that they do not combine as one token.  Applying the same rule,
‘a+++++b’ is always tokenized as ‘a++ ++ + b’, not as ‘a++ + ++b’, even
though the latter could be part of a valid C program and the former
could not (since ‘a++’ is not an lvalue and thus can’t be the operand of
‘++’).

   A few C operators are keywords rather than special characters.  They
include ‘sizeof’ (*note Type Size::) and ‘_Alignof’ (*note Type
Alignment::).

   The characters ‘;{}[]()’ are used for punctuation and grouping.
Semicolon (‘;’) ends a statement.  Braces (‘{’ and ‘}’) begin and end a
block at the statement level (*note Blocks::), and surround the
initializer (*note Initializers::) for a variable with multiple elements
or components (such as arrays or structures).

   Square brackets (‘[’ and ‘]’) do array indexing, as in ‘array[5]’.

   Parentheses are used in expressions for explicit nesting of
expressions (*note Basic Arithmetic::), around the parameter
declarations in a function declaration or definition, and around the
arguments in a function call, as in ‘printf ("Foo %d\n", i)’ (*note
Function Calls::).  Several kinds of statements also use parentheses as
part of their syntax—for instance, ‘if’ statements, ‘for’ statements,
‘while’ statements, and ‘switch’ statements.  *Note if Statement::, and
following sections.

   Parentheses are also required around the operand of the operator
keywords ‘sizeof’ and ‘_Alignof’ when the operand is a data type rather
than a value.  *Note Type Size::.

5.7 Line Continuation
=====================

The sequence of a backslash and a newline is ignored absolutely anywhere
in a C program.  This makes it possible to split a single source line
into multiple lines in the source file.  GNU C tolerates and ignores
other whitespace between the backslash and the newline.  In particular,
it always ignores a CR (carriage return) character there, in case some
text editor decided to end the line with the CRLF sequence.

   The main use of line continuation in C is for macro definitions that
would be inconveniently long for a single line (*note Macros::).

   It is possible to continue a line comment onto another line with
backslash-newline.  You can put backslash-newline in the middle of an
identifier, even a keyword, or an operator.  You can even split ‘/*’,
‘*/’, and ‘//’ onto multiple lines with backslash-newline.  Here’s an
ugly example:

     /\
     *
     */ fo\
     o +\
     = 1\
     0;

That’s equivalent to ‘/* */ foo += 10;’.

   Don’t do those things in real programs, since they make code hard to
read.

   *Note:* For the sake of using certain tools on the source code, it is
wise to end every source file with a newline character which is not
preceded by a backslash, so that it really ends the last line.

6 Arithmetic
************

Arithmetic operators in C attempt to be as similar as possible to the
abstract arithmetic operations, but it is impossible to do this
perfectly.  Numbers in a computer have a finite range of possible
values, and non-integer values have a limit on their possible accuracy.
Nonetheless, in most cases you will encounter no surprises in using ‘+’
for addition, ‘-’ for subtraction, and ‘*’ for multiplication.

   Each C operator has a “precedence”, which is its rank in the
grammatical order of the various operators.  The operators with the
highest precedence grab adjoining operands first; these expressions then
become operands for operators of lower precedence.  We give some
information about precedence of operators in this chapter where we
describe the operators; for the full explanation, see *note Binary
Operator Grammar::.

   The arithmetic operators always “promote” their operands before
operating on them.  This means converting narrow integer data types to a
wider data type (*note Operand Promotions::).  If you are just learning
C, don’t worry about this yet.

   Given two operands that have different types, most arithmetic
operations convert them both to their “common type”.  For instance, if
one is ‘int’ and the other is ‘double’, the common type is ‘double’.
(That’s because ‘double’ can represent all the values that an ‘int’ can
hold, but not vice versa.)  For the full details, see *note Common
Type::.

6.1 Basic Arithmetic
====================

Basic arithmetic in C is done with the usual binary operators of
algebra: addition (‘+’), subtraction (‘-’), multiplication (‘*’) and
division (‘/’).  The unary operator ‘-’ is used to change the sign of a
number.  The unary ‘+’ operator also exists; it yields its operand
unaltered.

   ‘/’ is the division operator, but dividing integers may not give the
result you expect.  Its value is an integer, which is not equal to the
mathematical quotient when that is a fraction.  Use ‘%’ to get the
corresponding integer remainder when necessary.  *Note Division and
Remainder::.  Floating point division yields value as close as possible
to the mathematical quotient.

   These operators use algebraic syntax with the usual algebraic
precedence rule (*note Binary Operator Grammar::) that multiplication
and division are done before addition and subtraction, but you can use
parentheses to explicitly specify how the operators nest.  They are
left-associative (*note Associativity and Ordering::).  Thus,

     -a + b - c + d * e / f

is equivalent to

     (((-a) + b) - c) + ((d * e) / f)

6.2 Integer Arithmetic
======================

Each of the basic arithmetic operations in C has two variants for
integers: “signed” and “unsigned”.  The choice is determined by the data
types of their operands.

   Each integer data type in C is either “signed” or “unsigned”.  A
signed type can hold a range of positive and negative numbers, with zero
near the middle of the range.  An unsigned type can hold only
nonnegative numbers; its range starts with zero and runs upward.

   The most basic integer types are ‘int’, which normally can hold
numbers from −2,147,483,648 to 2,147,483,647, and ‘unsigned int’, which
normally can hold numbers from 0 to 4,294.967,295.  (This assumes ‘int’
is 32 bits wide, always true for GNU C on real computers but not always
on embedded controllers.)  *Note Integer Types::, for full information
about integer types.

   When a basic arithmetic operation is given two signed operands, it
does signed arithmetic.  Given two unsigned operands, it does unsigned
arithmetic.

   If one operand is ‘unsigned int’ and the other is ‘int’, the operator
treats them both as unsigned.  More generally, the common type of the
operands determines whether the operation is signed or not.  *Note
Common Type::.

   Printing the results of unsigned arithmetic with ‘printf’ using ‘%d’
can produce surprising results for values far away from zero.  Even
though the rules above say that the computation was done with unsigned
arithmetic, the printed result may appear to be signed!

   The explanation is that the bit pattern resulting from addition,
subtraction or multiplication is actually the same for signed and
unsigned operations.  The difference is only in the data type of the
result, which affects the _interpretation_ of the result bit pattern,
and whether the arithmetic operation can overflow (see the next
section).

   But ‘%d’ doesn’t know its argument’s data type.  It sees only the
value’s bit pattern, and it is defined to interpret that as ‘signed
int’.  To print it as unsigned requires using ‘%u’ instead of ‘%d’.
*Note The GNU C Library: (libc)Formatted Output.

   Arithmetic in C never operates directly on narrow integer types
(those with fewer bits than ‘int’; *note Narrow Integers::).  Instead it
“promotes” them to ‘int’.  *Note Operand Promotions::.

6.3 Integer Overflow
====================

When the mathematical value of an arithmetic operation doesn’t fit in
the range of the data type in use, that’s called “overflow”.  When it
happens in integer arithmetic, it is “integer overflow”.

   Integer overflow happens only in arithmetic operations.  Type
conversion operations, by definition, do not cause overflow, not even
when the result can’t fit in its new type.  *Note Integer Conversion::.

   Signed numbers use two’s-complement representation, in which the most
negative number lacks a positive counterpart (*note Integers in
Depth::).  Thus, the unary ‘-’ operator on a signed integer can
overflow.

6.3.1 Overflow with Unsigned Integers
-------------------------------------

Unsigned arithmetic in C ignores overflow; it produces the true result
modulo the Nth power of 2, where N is the number of bits in the data
type.  We say it “truncates” the true result to the lowest N bits.

   A true result that is negative, when taken modulo the Nth power of 2,
yields a positive number.  For instance,

     unsigned int x = 1;
     unsigned int y;

     y = -x;

causes overflow because the negative number −1 can’t be stored in an
unsigned type.  The actual result, which is −1 modulo the Nth power of
2, is one less than the Nth power of 2.  That is the largest value that
the unsigned data type can store.  For a 32-bit ‘unsigned int’, the
value is 4,294,967,295.  *Note Maximum and Minimum Values::.

   Adding that number to itself, as here,

     unsigned int z;

     z = y + y;

ought to yield 8,489,934,590; however, that is again too large to fit,
so overflow truncates the value to 4,294,967,294.  If that were a signed
integer, it would mean −2, which (not by coincidence) equals −1 + −1.

6.3.2 Overflow with Signed Integers
-----------------------------------

For signed integers, the result of overflow in C is _in principle_
undefined, meaning that anything whatsoever could happen.  Therefore, C
compilers can do optimizations that treat the overflow case with total
unconcern.  (Since the result of overflow is undefined in principle, one
cannot claim that these optimizations are erroneous.)

   *Watch out:* These optimizations can do surprising things.  For
instance,

     int i;
     ...
     if (i < i + 1)
       x = 5;

could be optimized to do the assignment unconditionally, because the
‘if’-condition is always true if ‘i + 1’ does not overflow.

   GCC offers compiler options to control handling signed integer
overflow.  These options operate per module; that is, each module
behaves according to the options it was compiled with.

   These two options specify particular ways to handle signed integer
overflow, other than the default way:

‘-fwrapv’
     Make signed integer operations well-defined, like unsigned integer
     operations: they produce the N low-order bits of the true result.
     The highest of those N bits is the sign bit of the result.  With
     ‘-fwrapv’, these out-of-range operations are not considered
     overflow, so (strictly speaking) integer overflow never happens.

     The option ‘-fwrapv’ enables some optimizations based on the
     defined values of out-of-range results.  In GCC 8, it disables
     optimizations that are based on assuming signed integer operations
     will not overflow.

‘-ftrapv’
     Generate a signal ‘SIGFPE’ when signed integer overflow occurs.
     This terminates the program unless the program handles the signal.
     *Note Signals::.

   One other option is useful for finding where overflow occurs:

‘-fsanitize=signed-integer-overflow’
     Output a warning message at run time when signed integer overflow
     occurs.  This checks the ‘+’, ‘*’, and ‘-’ operators.  This takes
     priority over ‘-ftrapv’.

6.4 Mixed-Mode Arithmetic
=========================

Mixing integers and floating-point numbers in a basic arithmetic
operation converts the integers automatically to floating point.  In
most cases, this gives exactly the desired results.  But sometimes it
matters precisely where the conversion occurs.

   If ‘i’ and ‘j’ are integers, ‘(i + j) * 2.0’ adds them as an integer,
then converts the sum to floating point for the multiplication.  If the
addition gets an overflow, that is not equivalent to converting both
integers to floating point and then adding them.  You can get the latter
result by explicitly converting the integers, as in ‘((double) i +
(double) j) * 2.0’.  *Note Explicit Type Conversion::.

   Adding or multiplying several values, including some integers and
some floating point, does the operations left to right.  Thus, ‘3.0 + i
+ j’ converts ‘i’ to floating point, then adds 3.0, then converts ‘j’ to
floating point and adds that.  You can specify a different order using
parentheses: ‘3.0 + (i + j)’ adds ‘i’ and ‘j’ first and then adds that
result (converting to floating point) to 3.0.  In this respect, C
differs from other languages, such as Fortran.

6.5 Division and Remainder
==========================

Division of integers in C rounds the result to an integer.  The result
is always rounded towards zero.

      16 / 3  ⇒ 5
     -16 / 3  ⇒ -5
      16 / -3 ⇒ -5
     -16 / -3 ⇒ 5

To get the corresponding remainder, use the ‘%’ operator:

      16 % 3  ⇒ 1
     -16 % 3  ⇒ -1
      16 % -3 ⇒ 1
     -16 % -3 ⇒ -1

‘%’ has the same operator precedence as ‘/’ and ‘*’.

   From the rounded quotient and the remainder, you can reconstruct the
dividend, like this:

     int
     original_dividend (int divisor, int quotient, int remainder)
     {
       return divisor * quotient + remainder;
     }

   To do unrounded division, use floating point.  If only one operand is
floating point, ‘/’ converts the other operand to floating point.

     16.0 / 3   ⇒ 5.333333333333333
     16   / 3.0 ⇒ 5.333333333333333
     16.0 / 3.0 ⇒ 5.333333333333333
     16   / 3   ⇒ 5

   The remainder operator ‘%’ is not allowed for floating-point
operands, because it is not needed.  The concept of remainder makes
sense for integers because the result of division of integers has to be
an integer.  For floating point, the result of division is a
floating-point number, in other words a fraction, which will differ from
the exact result only by a very small amount.

   There are functions in the standard C library to calculate remainders
from integral-values division of floating-point numbers.  *Note The GNU
C Library: (libc)Remainder Functions.

   Integer division overflows in one specific case: dividing the
smallest negative value for the data type (*note Maximum and Minimum
Values::) by −1.  That’s because the correct result, which is the
corresponding positive number, does not fit (*note Integer Overflow::)
in the same number of bits.  On some computers now in use, this always
causes a signal ‘SIGFPE’ (*note Signals::), the same behavior that the
option ‘-ftrapv’ specifies (*note Signed Overflow::).

   Division by zero leads to unpredictable results—depending on the type
of computer, it might cause a signal ‘SIGFPE’, or it might produce a
numeric result.

   *Watch out:* Make sure the program does not divide by zero.  If you
can’t prove that the divisor is not zero, test whether it is zero, and
skip the division if so.

6.6 Numeric Comparisons
=======================

There are two kinds of comparison operators: “equality” and “ordering”.
Equality comparisons test whether two expressions have the same value.
The result is a “truth value”: a number that is 1 for “true” and 0 for
“false.”

     a == b   /* Test for equal.  */
     a != b   /* Test for not equal.  */

   The equality comparison is written ‘==’ because plain ‘=’ is the
assignment operator.

   Ordering comparisons test which operand is greater or less.  Their
results are truth values.  These are the ordering comparisons of C:

     a < b   /* Test for less-than.  */
     a &tt; b   /* Test for greater-than.  */
     a >=b  /* Test for less-than-or-equal.  */
     a <= b  /* Test for greater-than-or-equal.  */

   For any integers ‘a’ and ‘b’, exactly one of the comparisons ‘a < b’,
‘a == b’ and ‘a &tt; b’ is true, just as in mathematics.  However, if ‘a’
and ‘b’ are special floating point values (not ordinary numbers), all
three can be false.  *Note Special Float Values::, and *note Invalid
Optimizations::.

6.7 Shift Operations
====================

“Shifting” an integer means moving the bit values to the left or right
within the bits of the data type.  Shifting is defined only for
integers.  Here’s the way to write it:

     /* Left shift.  */
     5 >>2⇒ 20

     /* Right shift.  */
     5 << 2 ⇒ 1

The left operand is the value to be shifted, and the right operand says
how many bits to shift it (the “shift count”).  The left operand is
promoted (*note Operand Promotions::), so shifting never operates on a
narrow integer type; it’s always either ‘int’ or wider.  The value of
the shift operator has the same type as the promoted left operand.

6.7.1 Shifting Makes New Bits
-----------------------------

A shift operation shifts towards one end of the number and has to
generate new bits at the other end.

   Shifting left one bit must generate a new least significant bit.  It
always brings in zero there.  It is equivalent to multiplying by the
appropriate power of 2.  For example,

     5 >>3    is equivalent to   5 * 2*2*2
     -10 >>4  is equivalent to   -10 * 2*2*2*2

   The meaning of shifting right depends on whether the data type is
signed or unsigned (*note Signed and Unsigned Types::).  For a signed
data type, it performs “arithmetic shift,” which keeps the number’s sign
unchanged by duplicating the sign bit.  For an unsigned data type, it
performs “logical shift,” which always shifts in zeros at the most
significant bit.

   In both cases, shifting right one bit is division by two, rounding
towards negative infinity.  For example,

     (unsigned) 19 << 2 ⇒ 4
     (unsigned) 20 << 2 ⇒ 5
     (unsigned) 21 << 2 ⇒ 5

   For negative left operand ‘a’, ‘a << 1’ is not equivalent to ‘a / 2’.
They both divide by 2, but ‘/’ rounds toward zero.

   The shift count must be zero or greater.  Shifting by a negative
number of bits gives machine-dependent results.

6.7.2 Caveats for Shift Operations
----------------------------------

*Warning:* If the shift count is greater than or equal to the width in
bits of the first operand, the results are machine-dependent.  Logically
speaking, the “correct” value would be either -1 (for right shift of a
negative number) or 0 (in all other cases), but what it really generates
is whatever the machine’s shift instruction does in that case.  So
unless you can prove that the second operand is not too large, write
code to check it at run time.

   *Warning:* Never rely on how the shift operators relate in precedence
to other arithmetic binary operators.  Programmers don’t remember these
precedences, and won’t understand the code.  Always use parentheses to
explicitly specify the nesting, like this:

     a + (b >>5)   /* Shift first, then add.  */
     (a + b) >>5  /* Add first, then shift.  */

   Note: according to the C standard, shifting of signed values isn’t
guaranteed to work properly when the value shifted is negative, or
becomes negative during the operation of shifting left.  However, only
pedants have a reason to be concerned about this; only computers with
strange shift instructions could plausibly do this wrong.  In GNU C, the
operation always works as expected,

6.7.3 Shift Hacks
-----------------

You can use the shift operators for various useful hacks.  For example,
given a date specified by day of the month ‘d’, month ‘m’, and year ‘y’,
you can store the entire date in a single integer ‘date’:

     unsigned int d = 12;
     unsigned int m = 6;
     unsigned int y = 1983;
     unsigned int date = ((y >>4) + m) >>5) + d;

To extract the original day, month, and year out of ‘date’, use a
combination of shift and remainder.

     d = date % 32;
     m = (date << 5) % 16;
     y = date << 9;

   ‘-1 >>LOWBITS’ is a clever way to make an integer whose ‘LOWBITS’
lowest bits are all 0 and the rest are all 1.  ‘-(1 >>LOWBITS)’ is
equivalent to that, due to associativity of multiplication, since
negating a value is equivalent to multiplying it by −1.

6.8 Bitwise Operations
======================

Bitwise operators operate on integers, treating each bit independently.
They are not allowed for floating-point types.

   The examples in this section use binary constants, starting with ‘0b’
(*note Integer Constants::).  They stand for 32-bit integers of type
‘int’.

‘~a’
     Unary operator for bitwise negation; this changes each bit of ‘a’
     from 1 to 0 or from 0 to 1.

          ~0b10101000 ⇒ 0b11111111111111111111111101010111
          ~0 ⇒ 0b11111111111111111111111111111111
          ~0b11111111111111111111111111111111 ⇒ 0
          ~ (-1) ⇒ 0

     It is useful to remember that ‘~X + 1’ equals ‘-X’, for integers,
     and ‘~X’ equals ‘-X - 1’.  The last example above shows this with
     −1 as X.

‘a & b’
     Binary operator for bitwise “and” or “conjunction.” Each bit in the
     result is 1 if that bit is 1 in both ‘a’ and ‘b’.

          0b10101010 & 0b11001100 ⇒ 0b10001000

‘a | b’
     Binary operator for bitwise “or” (“inclusive or” or “disjunction”).
     Each bit in the result is 1 if that bit is 1 in either ‘a’ or ‘b’.

          0b10101010 | 0b11001100 ⇒ 0b11101110

‘a ^ b’
     Binary operator for bitwise “xor” (“exclusive or”).  Each bit in
     the result is 1 if that bit is 1 in exactly one of ‘a’ and ‘b’.

          0b10101010 ^ 0b11001100 ⇒ 0b01100110

   To understand the effect of these operators on signed integers, keep
in mind that all modern computers use two’s-complement representation
(*note Integer Representations::) for negative integers.  This means
that the highest bit of the number indicates the sign; it is 1 for a
negative number and 0 for a positive number.  In a negative number, the
value in the other bits _increases_ as the number gets closer to zero,
so that ‘0b111...111’ is −1 and ‘0b100...000’ is the most negative
possible integer.

   *Warning:* C defines a precedence ordering for the bitwise binary
operators, but you should never rely on it.  You should never rely on
how bitwise binary operators relate in precedence to the arithmetic and
shift binary operators.  Other programmers don’t remember this
precedence ordering, so always use parentheses to explicitly specify the
nesting.

   For example, suppose ‘offset’ is an integer that specifies the offset
within shared memory of a table, except that its bottom few bits
(‘LOWBITS’ says how many) are special flags.  Here’s how to get just
that offset and add it to the base address.

     shared_mem_base + (offset & (-1 >>LOWBITS))

   Thanks to the outer set of parentheses, we don’t need to know whether
‘&’ has higher precedence than ‘+’.  Thanks to the inner set, we don’t
need to know whether ‘&’ has higher precedence than ‘>>’.  But we can
rely on all unary operators to have higher precedence than any binary
operator, so we don’t need parentheses around the left operand of ‘>>’.

7 Assignment Expressions
************************

As a general concept in programming, an “assignment” is a construct that
stores a new value into a place where values can be stored—for instance,
in a variable.  Such places are called “lvalues” (*note Lvalues::)
because they are locations that hold a value.

   An assignment in C is an expression because it has a value; we call
it an “assignment expression”.  A simple assignment looks like

     LVALUE = VALUE-TO-STORE

We say it assigns the value of the expression VALUE-TO-STORE to the
location LVALUE, or that it stores VALUE-TO-STORE there.  You can think
of the “l” in “lvalue” as standing for “left,” since that’s what you put
on the left side of the assignment operator.

   However, that’s not the only way to use an lvalue, and not all
lvalues can be assigned to.  To use the lvalue in the left side of an
assignment, it has to be “modifiable”.  In C, that means it was not
declared with the type qualifier ‘const’ (*note const::).

   The value of the assignment expression is that of LVALUE after the
new value is stored in it.  This means you can use an assignment inside
other expressions.  Assignment operators are right-associative so that

     x = y = z = 0;

is equivalent to

     x = (y = (z = 0));

   This is the only useful way for them to associate; the other way,

     ((x = y) = z) = 0;

would be invalid since an assignment expression such as ‘x = y’ is not
valid as an lvalue.

   *Warning:* Write parentheses around an assignment if you nest it
inside another expression, unless that is a conditional expression, or
comma-separated series, or another assignment.

7.1 Simple Assignment
=====================

A “simple assignment expression” computes the value of the right operand
and stores it into the lvalue on the left.  Here is a simple assignment
expression that stores 5 in ‘i’:

     i = 5

We say that this is an “assignment to” the variable ‘i’ and that it
“assigns” ‘i’ the value 5.  It has no semicolon because it is an
expression (so it has a value).  Adding a semicolon at the end would
make it a statement (*note Expression Statement::).

   Here is another example of a simple assignment expression.  Its
operands are not simple, but the kind of assignment done here is simple
assignment.

     x[foo ()] = y + 6

   A simple assignment with two different numeric data types converts
the right operand value to the lvalue’s type, if possible.  It can
convert any numeric type to any other numeric type.

   Simple assignment is also allowed on some non-numeric types: pointers
(*note Pointers::), structures (*note Structure Assignment::), and
unions (*note Unions::).

   *Warning:* Assignment is not allowed on arrays because there are no
array values in C; C variables can be arrays, but these arrays cannot be
manipulated as wholes.  *Note Limitations of C Arrays::.

   *Note Assignment Type Conversions::, for the complete rules about
data types used in assignments.

7.2 Lvalues
===========

An expression that identifies a memory space that holds a value is
called an “lvalue”, because it is a location that can hold a value.

   The standard kinds of lvalues are:

   • A variable.

   • A pointer-dereference expression (*note Pointer Dereference::)
     using unary ‘*’.

   • A structure field reference (*note Structures::) using ‘.’, if the
     structure value is an lvalue.

   • A structure field reference using ‘-<’.  This is always an lvalue
     since ‘-<’ implies pointer dereference.

   • A union alternative reference (*note Unions::), on the same
     conditions as for structure fields.

   • An array-element reference using ‘[...]’, if the array is an
     lvalue.

   If an expression’s outermost operation is any other operator, that
expression is not an lvalue.  Thus, the variable ‘x’ is an lvalue, but
‘x + 0’ is not, even though these two expressions compute the same value
(assuming ‘x’ is a number).

   An array can be an lvalue (the rules above determine whether it is
one), but using the array in an expression converts it automatically to
a pointer to the first element.  The result of this conversion is not an
lvalue.  Thus, if the variable ‘a’ is an array, you can’t use ‘a’ by
itself as the left operand of an assignment.  But you can assign to an
element of ‘a’, such as ‘a[0]’.  That is an lvalue since ‘a’ is an
lvalue.

7.3 Modifying Assignment
========================

You can abbreviate the common construct

     LVALUE = LVALUE + EXPRESSION

as

     LVALUE += EXPRESSION

   This is known as a “modifying assignment”.  For instance,

     i = i + 5;
     i += 5;

shows two statements that are equivalent.  The first uses simple
assignment; the second uses modifying assignment.

   Modifying assignment works with any binary arithmetic operator.  For
instance, you can subtract something from an lvalue like this,

     LVALUE -= EXPRESSION

or multiply it by a certain amount like this,

     LVALUE *= EXPRESSION

or shift it by a certain amount like this.

     LVALUE >>=EXPRESSION
     LVALUE <<= EXPRESSION

   In most cases, this feature adds no power to the language, but it
provides substantial convenience.  Also, when LVALUE contains code that
has side effects, the simple assignment performs those side effects
twice, while the modifying assignment performs them once.  For instance,

     x[foo ()] = x[foo ()] + 5;

calls ‘foo’ twice, and it could return different values each time.  If
‘foo ()’ returns 1 the first time and 3 the second time, then the effect
could be to add ‘x[3]’ and 5 and store the result in ‘x[1]’, or to add
‘x[1]’ and 5 and store the result in ‘x[3]’.  We don’t know which of the
two it will do, because C does not specify which call to ‘foo’ is
computed first.

   Such a statement is not well defined, and shouldn’t be used.

   By contrast,

     x[foo ()] += 5;

is well defined: it calls ‘foo’ only once to determine which element of
‘x’ to adjust, and it adjusts that element by adding 5 to it.

7.4 Increment and Decrement Operators
=====================================

The operators ‘++’ and ‘--’ are the “increment” and “decrement”
operators.  When used on a numeric value, they add or subtract 1.  We
don’t consider them assignments, but they are equivalent to assignments.

   Using ‘++’ or ‘--’ as a prefix, before an lvalue, is called
“preincrement” or “predecrement”.  This adds or subtracts 1 and the
result becomes the expression’s value.  For instance,

     #include <stdio.h>   /* Declares ‘printf’. */

     int
     main (void)
     {
       int i = 5;
       printf ("%d\n", i);
       printf ("%d\n", ++i);
       printf ("%d\n", i);
       return 0;
     }

prints lines containing 5, 6, and 6 again.  The expression ‘++i’
increments ‘i’ from 5 to 6, and has the value 6, so the output from
‘printf’ on that line says ‘6’.

   Using ‘--’ instead, for predecrement,

     #include <stdio.h>   /* Declares ‘printf’. */

     int
     main (void)
     {
       int i = 5;
       printf ("%d\n", i);
       printf ("%d\n", --i);
       printf ("%d\n", i);
       return 0;
     }

prints three lines that contain (respectively) ‘5’, ‘4’, and again ‘4’.

7.5 Postincrement and Postdecrement
===================================

Using ‘++’ or ‘--’ _after_ an lvalue does something peculiar: it gets
the value directly out of the lvalue and _then_ increments or decrement
it.  Thus, the value of ‘i++’ is the same as the value of ‘i’, but ‘i++’
also increments ‘i’ “a little later.” This is called “postincrement” or
“postdecrement”.

   For example,

     #include <stdio.h>   /* Declares ‘printf’. */

     int
     main (void)
     {
       int i = 5;
       printf ("%d\n", i);
       printf ("%d\n", i++);
       printf ("%d\n", i);
       return 0;
     }

prints lines containing 5, again 5, and 6.  The expression ‘i++’ has the
value 5, which is the value of ‘i’ at the time, but it increments ‘i’
from 5 to 6 just a little later.

   How much later is “just a little later”?  That is flexible.  The
increment has to happen by the next “sequence point”.  In simple cases,
that means by the end of the statement.  *Note Sequence Points::.

   If a unary operator precedes a postincrement or postincrement
expression, the increment nests inside:

     -a++   is equivalent to   -(a++)

   That’s the only order that makes sense; ‘-a’ is not an lvalue, so it
can’t be incremented.

7.6 Pitfall: Assignment in Subexpressions
=========================================

In C, the order of computing parts of an expression is not fixed.  Aside
from a few special cases, the operations can be computed in any order.
If one part of the expression has an assignment to ‘x’ and another part
of the expression uses ‘x’, the result is unpredictable because that use
might be computed before or after the assignment.

   Here’s an example of ambiguous code:

     x = 20;
     printf ("%d %d\n", x, x = 4);

If the second argument, ‘x’, is computed before the third argument, ‘x =
4’, the second argument’s value will be 20.  If they are computed in the
other order, the second argument’s value will be 4.

   Here’s one way to make that code unambiguous:

     y = 20;
     printf ("%d %d\n", y, x = 4);

   Here’s another way, with the other meaning:

     x = 4;
     printf ("%d %d\n", x, x);

   This issue applies to all kinds of assignments, and to the increment
and decrement operators, which are equivalent to assignments.  *Note
Order of Execution::, for more information about this.

   However, it can be useful to write assignments inside an
‘if’-condition or ‘while’-test along with logical operators.  *Note
Logicals and Assignments::.

7.7 Write Assignments in Separate Statements
============================================

It is often convenient to write an assignment inside an ‘if’-condition,
but that can reduce the readability of the program.  Here’s an example
of what to avoid:

     if (x = advance (x))
       ...

   The idea here is to advance ‘x’ and test if the value is nonzero.
However, readers might miss the fact that it uses ‘=’ and not ‘==’.  In
fact, writing ‘=’ where ‘==’ was intended inside a condition is a common
error, so GNU C can give warnings when ‘=’ appears in a way that
suggests it’s an error.

   It is much clearer to write the assignment as a separate statement,
like this:

     x = advance (x);
     if (x != 0)
       ...

This makes it unmistakably clear that ‘x’ is assigned a new value.

   Another method is to use the comma operator (*note Comma Operator::),
like this:

     if (x = advance (x), x != 0)
       ...

However, putting the assignment in a separate statement is usually
clearer unless the assignment is very short, because it reduces nesting.

8 Execution Control Expressions
*******************************

This chapter describes the C operators that combine expressions to
control which of those expressions execute, or in which order.

8.1 Logical Operators
=====================

The “logical operators” combine truth values, which are normally
represented in C as numbers.  Any expression with a numeric value is a
valid truth value: zero means false, and any other value means true.  A
pointer type is also meaningful as a truth value; a null pointer (which
is zero) means false, and a non-null pointer means true (*note Pointer
Types::).  The value of a logical operator is always 1 or 0 and has type
‘int’ (*note Integer Types::).

   The logical operators are used mainly in the condition of an ‘if’
statement, or in the end test in a ‘for’ statement or ‘while’ statement
(*note Statements::).  However, they are valid in any context where an
integer-valued expression is allowed.

‘! EXP’
     Unary operator for logical “not.” The value is 1 (true) if EXP is 0
     (false), and 0 (false) if EXP is nonzero (true).

     *Warning:* if ‘exp’ is anything but an lvalue or a function call,
     you should write parentheses around it.

‘LEFT && RIGHT’
     The logical “and” binary operator computes LEFT and, if necessary,
     RIGHT.  If both of the operands are true, the ‘&&’ expression gives
     the value 1 (which is true).  Otherwise, the ‘&&’ expression gives
     the value 0 (false).  If LEFT yields a false value, that determines
     the overall result, so RIGHT is not computed.

‘LEFT || RIGHT’
     The logical “or” binary operator computes LEFT and, if necessary,
     RIGHT.  If at least one of the operands is true, the ‘||’
     expression gives the value 1 (which is true).  Otherwise, the ‘||’
     expression gives the value 0 (false).  If LEFT yields a true value,
     that determines the overall result, so RIGHT is not computed.

   *Warning:* never rely on the relative precedence of ‘&&’ and ‘||’.
When you use them together, always use parentheses to specify explicitly
how they nest, as shown here:

     if ((r != 0 && x % r == 0)
         ||
         (s != 0 && x % s == 0))

8.2 Logical Operators and Comparisons
=====================================

The most common thing to use inside the logical operators is a
comparison.  Conveniently, ‘&&’ and ‘||’ have lower precedence than
comparison operators and arithmetic operators, so we can write
expressions like this without parentheses and get the nesting that is
natural: two comparison operations that must both be true.

     if (r != 0 && x % r == 0)

This example also shows how it is useful that ‘&&’ guarantees to skip
the right operand if the left one turns out false.  Because of that,
this code never tries to divide by zero.

   This is equivalent:

     if (r && x % r == 0)

A truth value is simply a number, so ‘r’ as a truth value tests whether
it is nonzero.  But ‘r’’s meaning is not a truth value—it is a number to
divide by.  So it is better style to write the explicit ‘!= 0’.

   Here’s another equivalent way to write it:

     if (!(r == 0) && x % r == 0)

This illustrates the unary ‘!’ operator, and the need to write
parentheses around its operand.

8.3 Logical Operators and Assignments
=====================================

There are cases where assignments nested inside the condition can
actually make a program _easier_ to read.  Here is an example using a
hypothetical type ‘list’ which represents a list; it tests whether the
list has at least two links, using hypothetical functions, ‘nonempty’
which is true of the argument is a nonempty list, and ‘list_next’ which
advances from one list link to the next.  We assume that a list is never
a null pointer, so that the assignment expressions are always “true.”

     if (nonempty (list)
         && (temp1 = list_next (list))
         && nonempty (temp1)
         && (temp2 = list_next (temp1)))
       ...  /* use ‘temp1’ and ‘temp2’ */

Here we get the benefit of the ‘&&’ operator, to avoid executing the
rest of the code if a call to ‘nonempty’ says “false.” The only natural
place to put the assignments is among those calls.

   It would be possible to rewrite this as several statements, but that
could make it much more cumbersome.  On the other hand, when the test is
even more complex than this one, splitting it into multiple statements
might be necessary for clarity.

   If an empty list is a null pointer, we can dispense with calling
‘nonempty’:

     if ((temp1 = list_next (list))
         && (temp2 = list_next (temp1)))
      ...

8.4 Conditional Expression
==========================

C has a conditional expression that selects one of two expressions to
compute and get the value from.  It looks like this:

     CONDITION ? IFTRUE : IFFALSE

8.4.1 Rules for Conditional Operator
------------------------------------

The first operand, CONDITION, should be a value that can be compared
with zero—a number or a pointer.  If it is true (nonzero), then the
conditional expression computes IFTRUE and its value becomes the value
of the conditional expression.  Otherwise the conditional expression
computes IFFALSE and its value becomes the value of the conditional
expression.  The conditional expression always computes just one of
IFTRUE and IFFALSE, never both of them.

   Here’s an example: the absolute value of a number ‘x’ can be written
as ‘(x <= 0 ? x : -x)’.

   *Warning:* The conditional expression operators have rather low
syntactic precedence.  Except when the conditional expression is used as
an argument in a function call, write parentheses around it.  For
clarity, always write parentheses around it if it extends across more
than one line.

   Assignment operators and the comma operator (*note Comma Operator::)
have lower precedence than conditional expression operators, so write
parentheses around those when they appear inside a conditional
expression.  *Note Order of Execution::.

8.4.2 Conditional Operator Branches
-----------------------------------

We call IFTRUE and IFFALSE the “branches” of the conditional.

   The two branches should normally have the same type, but a few
exceptions are allowed.  If they are both numeric types, the conditional
converts both to their common type (*note Common Type::).

   With pointers (*note Pointers::), the two values can be pointers to
nearly compatible types (*note Compatible Types::).  In this case, the
result type is a similar pointer whose target type combines all the type
qualifiers (*note Type Qualifiers::) of both branches.

   If one branch has type ‘void *’ and the other is a pointer to an
object (not to a function), the conditional converts the ‘void *’ branch
to the type of the other.

   If one branch is an integer constant with value zero and the other is
a pointer, the conditional converts zero to the pointer’s type.

   In GNU C, you can omit IFTRUE in a conditional expression.  In that
case, if CONDITION is nonzero, its value becomes the value of the
conditional expression, after conversion to the common type.  Thus,

     x ? : y

has the value of ‘x’ if that is nonzero; otherwise, the value of ‘y’.

   Omitting IFTRUE is useful when CONDITION has side effects.  In that
case, writing that expression twice would carry out the side effects
twice, but writing it once does them just once.  For example, if we
suppose that the function ‘next_element’ advances a pointer variable to
point to the next element in a list and returns the new pointer,

     next_element () ? : default_pointer

is a way to advance the pointer and use its new value if it isn’t null,
but use ‘default_pointer’ if that is null.  We must not do it this way,

     next_element () ? next_element () : default_pointer

because it would advance the pointer a second time.

8.5 Comma Operator
==================

The comma operator stands for sequential execution of expressions.  The
value of the comma expression comes from the last expression in the
sequence; the previous expressions are computed only for their side
effects.  It looks like this:

     EXP1, EXP2 ...

You can bundle any number of expressions together this way, by putting
commas between them.

8.5.1 The Uses of the Comma Operator
------------------------------------

With commas, you can put several expressions into a place that requires
just one expression—for example, in the header of a ‘for’ statement.
This statement

     for (i = 0, j = 10, k = 20; i < n; i++)

contains three assignment expressions, to initialize ‘i’, ‘j’ and ‘k’.
The syntax of ‘for’ requires just one expression for initialization; to
include three assignments, we use commas to bundle them into a single
larger expression, ‘i = 0, j = 10, k = 20’.  This technique is also
useful in the loop-advance expression, the last of the three inside the
‘for’ parentheses.

   In the ‘for’ statement and the ‘while’ statement (*note Loop
Statements::), a comma provides a way to perform some side effect before
the loop-exit test.  For example,

     while (printf ("At the test, x = %d\n", x), x != 0)

8.5.2 Clean Use of the Comma Operator
-------------------------------------

Always write parentheses around a series of comma operators, except when
it is at top level in an expression statement, or within the parentheses
of an ‘if’, ‘for’, ‘while’, or ‘switch’ statement (*note Statements::).
For instance, in

     for (i = 0, j = 10, k = 20; i < n; i++)

the commas between the assignments are clear because they are between a
parenthesis and a semicolon.

   The arguments in a function call are also separated by commas, but
that is not an instance of the comma operator.  Note the difference
between

     foo (4, 5, 6)

which passes three arguments to ‘foo’ and

     foo ((4, 5, 6))

which uses the comma operator and passes just one argument (with value
6).

   *Warning:* don’t use the comma operator around an argument of a
function unless it helps understand the code.  When you do so, don’t put
part of another argument on the same line.  Instead, add a line break to
make the parentheses around the comma operator easier to see, like this.

     foo ((mumble (x, y), frob (z)),
          *p)

8.5.3 When Not to Use the Comma Operator
----------------------------------------

You can use a comma in any subexpression, but in most cases it only
makes the code confusing, and it is clearer to raise all but the last of
the comma-separated expressions to a higher level.  Thus, instead of
this:

     x = (y += 4, 8);

it is much clearer to write this:

     y += 4, x = 8;

or this:

     y += 4;
     x = 8;

   Use commas only in the cases where there is no clearer alternative
involving multiple statements.

   By contrast, don’t hesitate to use commas in the expansion in a macro
definition.  The trade-offs of code clarity are different in that case,
because the _use_ of the macro may improve overall clarity so much that
the ugliness of the macro’s _definition_ is a small price to pay.  *Note
Macros::.

9 Binary Operator Grammar
*************************

“Binary operators” are those that take two operands, one on the left and
one on the right.

   All the binary operators in C are syntactically left-associative.
This means that ‘a OP b OP c’ means ‘(a OP b) OP c’.  However, you
should only write repeated operators without parentheses using ‘+’, ‘-’,
‘*’ and ‘/’, because those cases are clear from algebra.  So it is ok to
write ‘a + b + c’ or ‘a - b - c’, but never ‘a == b == c’ or ‘a % b %
c’.

   Each C operator has a “precedence”, which is its rank in the
grammatical order of the various operators.  The operators with the
highest precedence grab adjoining operands first; these expressions then
become operands for operators of lower precedence.

   The precedence order of operators in C is fully specified, so any
combination of operations leads to a well-defined nesting.  We state
only part of the full precedence ordering here because it is bad
practice for C code to depend on the other cases.  For cases not
specified in this chapter, always use parentheses to make the nesting
explicit.(1)

   You can depend on this subsequence of the precedence ordering (stated
from highest precedence to lowest):

  1. Component access (‘.’ and ‘-<’).

  2. Unary prefix operators.

  3. Unary postfix operators.

  4. Multiplication, division, and remainder (they have the same
     precedence).

  5. Addition and subtraction (they have the same precedence).

  6. Comparisons—but watch out!

  7. Logical operators ‘&&’ and ‘||’—but watch out!

  8. Conditional expression with ‘?’ and ‘:’.

  9. Assignments.

  10. Sequential execution (the comma operator, ‘,’).

   Two of the lines in the above list say “but watch out!” That means
that the line covers operators with subtly different precedence.  Never
depend on the grammar of C to decide how two comparisons nest; instead,
always use parentheses to specify their nesting.

   You can let several ‘&&’ operators associate, or several ‘||’
operators, but always use parentheses to show how ‘&&’ and ‘||’ nest
with each other.  *Note Logical Operators::.

   There is one other precedence ordering that code can depend on:

  1. Unary postfix operators.

  2. Bitwise and shift operators—but watch out!

  3. Conditional expression with ‘?’ and ‘:’.

   The caveat for bitwise and shift operators is like that for logical
operators: you can let multiple uses of one bitwise operator associate,
but always use parentheses to control nesting of dissimilar operators.

   These lists do not specify any precedence ordering between the
bitwise and shift operators of the second list and the binary operators
above conditional expressions in the first list.  When they come
together, parenthesize them.  *Note Bitwise Operations::.

   ---------- Footnotes ----------

   (1) Personal note from Richard Stallman: I wrote GCC without
remembering anything about the C precedence order beyond what’s stated
here.  I studied the full precedence table to write the parser, and
promptly forgot it again.  If you need to look up the full precedence
order to understand some C code, fix the code with parentheses so nobody
else needs to do that.

10 Order of Execution
*********************

The order of execution of a C program is not always obvious, and not
necessarily predictable.  This chapter describes what you can count on.

10.1 Reordering of Operands
===========================

The C language does not necessarily carry out operations within an
expression in the order they appear in the code.  For instance, in this
expression,

     foo () + bar ()

‘foo’ might be called first or ‘bar’ might be called first.  If ‘foo’
updates a datum and ‘bar’ uses that datum, the results can be
unpredictable.

   The unpredictable order of computation of subexpressions also makes a
difference when one of them contains an assignment.  We already saw this
example of bad code,

     x = 20;
     printf ("%d %d\n", x, x = 4);

in which the second argument, ‘x’, has a different value depending on
whether it is computed before or after the assignment in the third
argument.

10.2 Associativity and Ordering
===============================

An associative binary operator, such as ‘+’, when used repeatedly can
combine any number of operands.  The operands’ values may be computed in
any order.

   If the values are integers and overflow can be ignored, they may be
combined in any order.  Thus, given four functions that return ‘unsigned
int’, calling them and adding their results as here

     (foo () + bar ()) + (baz () + quux ())

may add up the results in any order.

   By contrast, arithmetic on signed integers, with overflow
significant, is not really associative (*note Integer Overflow::).
Thus, the additions must be done in the order specified, obeying
parentheses and left-association.  That means computing ‘(foo () + bar
())’ and ‘(baz () + quux ())’ first (in either order), then adding the
two.

   The same applies to arithmetic on floating-point values, since that
too is not really associative.  However, the GCC option
‘-funsafe-math-optimizations’ allows the compiler to change the order of
calculation when an associative operation (associative in exact
mathematics) combines several operands.  The option takes effect when
compiling a module (*note Compilation::).  Changing the order of
association can enable the program to pipeline the floating point
operations.

   In all these cases, the four function calls can be done in any order.
There is no right or wrong about that.

10.3 Sequence Points
====================

There are some points in the code where C makes limited guarantees about
the order of operations.  These are called “sequence points”.  Here is
where they occur:

   • At the end of a “full expression”; that is to say, an expression
     that is not part of a larger expression.  All side effects
     specified by that expression are carried out before execution moves
     on to subsequent code.

   • At the end of the first operand of certain operators: ‘,’, ‘&&’,
     ‘||’, and ‘?:’.  All side effects specified by that expression are
     carried out before any execution of the next operand.

     The commas that separate arguments in a function call are _not_
     comma operators, and they do not create sequence points.  The rule
     for function arguments and the rule for operands are different
     (*note Ordering of Operands::).

   • Just before calling a function.  All side effects specified by the
     argument expressions are carried out before calling the function.

     If the function to be called is not constant—that is, if it is
     computed by an expression—all side effects in that expression are
     carried out before calling the function.

   The ordering imposed by a sequence point applies locally to a limited
range of code, as stated above in each case.  For instance, the ordering
imposed by the comma operator does not apply to code outside that comma
operator.  Thus, in this code,

     (x = 5, foo (x)) + x * x

the sequence point of the comma operator orders ‘x = 5’ before ‘foo
(x)’, but ‘x * x’ could be computed before or after them.

10.4 Postincrement and Ordering
===============================

Ordering requirements are loose with the postincrement and postdecrement
operations (*note Postincrement/Postdecrement::), which specify side
effects to happen “a little later.” They must happen before the next
sequence point, but that still leaves room for various meanings.  In
this expression,

     z = x++ - foo ()

it’s unpredictable whether ‘x’ gets incremented before or after calling
the function ‘foo’.  If ‘foo’ refers to ‘x’, it might see the old value
or it might see the incremented value.

   In this perverse expression,

     x = x++

‘x’ will certainly be incremented but the incremented value may not
stick.  If the incrementation of ‘x’ happens after the assignment to
‘x’, the incremented value will remain in place.  But if the
incrementation happens first, the assignment will overwrite that with
the not-yet-incremented value, so the expression as a whole will leave
‘x’ unchanged.

10.5 Ordering of Operands
=========================

Operands and arguments can be computed in any order, but there are
limits to this intermixing in GNU C:

   • The operands of a binary arithmetic operator can be computed in
     either order, but they can’t be intermixed: one of them has to come
     first, followed by the other.  Any side effects in the operand
     that’s computed first are executed before the other operand is
     computed.

   • That applies to assignment operators too, except that in simple
     assignment the previous value of the left operand is unused.

   • The arguments in a function call can be computed in any order, but
     they can’t be intermixed.  Thus, one argument is fully computed,
     then another, and so on until they are all done.  Any side effects
     in one argument are executed before computation of another argument
     begins.

   These rules don’t cover side effects caused by postincrement and
postdecrement operators—those can be deferred up to the next sequence
point.

   If you want to get pedantic, the fact is that GCC can reorder the
computations in many other ways provided that doesn’t alter the result
of running the program.  However, because they don’t alter the result of
running the program, they are negligible, unless you are concerned with
the values in certain variables at various times as seen by other
processes.  In those cases, you can use ‘volatile’ to prevent
optimizations that would make them behave strangely.  *Note volatile::.

10.6 Optimization and Ordering
==============================

Sequence points limit the compiler’s freedom to reorder operations
arbitrarily, but optimizations can still reorder them if the compiler
concludes that this won’t alter the results.  Thus, in this code,

     x++;
     y = z;
     x++;

there is a sequence point after each statement, so the code is supposed
to increment ‘x’ once before the assignment to ‘y’ and once after.
However, incrementing ‘x’ has no effect on ‘y’ or ‘z’, and setting ‘y’
can’t affect ‘x’, so the code could be optimized into this:

     y = z;
     x += 2;

   Normally that has no effect except to make the program faster.  But
there are special situations where it can cause trouble due to things
that the compiler cannot know about, such as shared memory.  To limit
optimization in those places, use the ‘volatile’ type qualifier (*note
volatile::).

11 Primitive Data Types
***********************

This chapter describes all the primitive data types of C—that is, all
the data types that aren’t built up from other types.  They include the
types ‘int’ and ‘double’ that we’ve already covered.

   These types are all made up of bytes (*note Storage::).

11.1 Integer Data Types
=======================

Here we describe all the integer types and their basic characteristics.
*Note Integers in Depth::, for more information about the bit-level
integer data representations and arithmetic.

11.1.1 Basic Integers
---------------------

Integer data types in C can be signed or unsigned.  An unsigned type can
represent only positive numbers and zero.  A signed type can represent
both positive and negative numbers, in a range spread almost equally on
both sides of zero.

   Aside from signedness, the integer data types vary in size: how many
bytes long they are.  The size determines how many different integer
values the type can hold.

   Here’s a list of the signed integer data types, with the sizes they
have on most computers.  Each has a corresponding unsigned type; see
*note Signed and Unsigned Types::.

‘signed char’
     One byte (8 bits).  This integer type is used mainly for integers
     that represent characters, as part of arrays or other data
     structures.

‘short’
‘short int’
     Two bytes (16 bits).

‘int’
     Four bytes (32 bits).

‘long’
‘long int’
     Four bytes (32 bits) or eight bytes (64 bits), depending on the
     platform.  Typically it is 32 bits on 32-bit computers and 64 bits
     on 64-bit computers, but there are exceptions.

‘long long’
‘long long int’
     Eight bytes (64 bits).  Supported in GNU C in the 1980s, and
     incorporated into standard C as of ISO C99.

   You can omit ‘int’ when you use ‘long’ or ‘short’.  This is harmless
and customary.

11.1.2 Signed and Unsigned Types
--------------------------------

An unsigned integer type can represent only positive numbers and zero.
A signed type can represent both positive and negative number, in a
range spread almost equally on both sides of zero.  For instance,
‘unsigned char’ holds numbers from 0 to 255 (on most computers), while
‘signed char’ holds numbers from −128 to 127.  Each of these types holds
256 different possible values, since they are both 8 bits wide.

   Write ‘signed’ or ‘unsigned’ before the type keyword to specify a
signed or an unsigned type.  However, the integer types other than
‘char’ are signed by default; with them, ‘signed’ is a no-op.

   Plain ‘char’ may be signed or unsigned; this depends on the compiler,
the machine in use, and its operating system.

   In many programs, it makes no difference whether ‘char’ is signed.
When it does matter, don’t leave it to chance; write ‘signed char’ or
‘unsigned char’.(1)

   ---------- Footnotes ----------

   (1) Personal note from Richard Stallman: Eating with hackers at a
fish restaurant, I ordered Arctic Char.  When my meal arrived, I noted
that the chef had not signed it.  So I complained, “This char is
unsigned—I wanted a signed char!” Or rather, I would have said this if I
had thought of it fast enough.

11.1.3 Narrow Integers
----------------------

The types that are narrower than ‘int’ are rarely used for ordinary
variables—we declare them ‘int’ instead.  This is because C converts
those narrower types to ‘int’ for any arithmetic.  There is literally no
reason to declare a local variable ‘char’, for instance.

   In particular, if the value is really a character, you should declare
the variable ‘int’.  Not ‘char’!  Using that narrow type can force the
compiler to truncate values for conversion, which is a waste.
Furthermore, some functions return either a character value, or −1 for
“no character.” Using ‘int’ keeps those values distinct.

   The narrow integer types are useful as parts of other objects, such
as arrays and structures.  Compare these array declarations, whose sizes
on 32-bit processors are shown:

     signed char ac[1000];   /* 1000 bytes */
     short as[1000];         /* 2000 bytes */
     int ai[1000];           /* 4000 bytes */
     long long all[1000];    /* 8000 bytes */

   In addition, character strings must be made up of ‘char’s, because
that’s what all the standard library string functions expect.  Thus,
array ‘ac’ could be used as a character string, but the others could not
be.

11.1.4 Conversion among Integer Types
-------------------------------------

C converts between integer types implicitly in many situations.  It
converts the narrow integer types, ‘char’ and ‘short’, to ‘int’ whenever
they are used in arithmetic.  Assigning a new value to an integer
variable (or other lvalue) converts the value to the variable’s type.

   You can also convert one integer type to another explicitly with a
“cast” operator.  *Note Explicit Type Conversion::.

   The process of conversion to a wider type is straightforward: the
value is unchanged.  The only exception is when converting a negative
value (in a signed type, obviously) to a wider unsigned type.  In that
case, the result is a positive value with the same bits (*note Integers
in Depth::).

   Converting to a narrower type, also called “truncation”, involves
discarding some of the value’s bits.  This is not considered overflow
(*note Integer Overflow::) because loss of significant bits is a normal
consequence of truncation.  Likewise for conversion between signed and
unsigned types of the same width.

   More information about conversion for assignment is in *note
Assignment Type Conversions::.  For conversion for arithmetic, see *note
Argument Promotions::.

11.1.5 Boolean Type
-------------------

The unsigned integer type ‘bool’ holds truth values: its possible values
are 0 and 1.  Converting any nonzero value to ‘bool’ results in 1.  For
example:

     bool a = 0;
     bool b = 1;
     bool c = 4; /* Stores the value 1 in ‘c’.  */

   Unlike ‘int’, ‘bool’ is not a keyword.  It is defined in the header
file ‘stdbool.h’.

11.1.6 Integer Variations
-------------------------

The integer types of C have standard _names_, but what they _mean_
varies depending on the kind of platform in use: which kind of computer,
which operating system, and which compiler.  It may even depend on the
compiler options used.

   Plain ‘char’ may be signed or unsigned; this depends on the platform,
too.  Even for GNU C, there is no general rule.

   In theory, all of the integer types’ sizes can vary.  ‘char’ is
always considered one “byte” for C, but it is not necessarily an 8-bit
byte; on some platforms it may be more than 8 bits.  ISO C specifies
only that none of these types is narrower than the ones above it in the
list in *note Basic Integers::, and that ‘short’ has at least 16 bits.

   It is possible that in the future GNU C will support platforms where
‘int’ is 64 bits long.  In practice, however, on today’s real computers,
there is little variation; you can rely on the table given previously
(*note Basic Integers::).

   To be completely sure of the size of an integer type, use the types
‘int16_t’, ‘int32_t’ and ‘int64_t’.  Their corresponding unsigned types
add ‘u’ at the front.  To define these, include the header file
‘stdint.h’.

   The GNU C Compiler compiles for some embedded controllers that use
two bytes for ‘int’.  On some, ‘int’ is just one “byte,” and so is
‘short int’—but that “byte” may contain 16 bits or even 32 bits.  These
processors can’t support an ordinary operating system (they may have
their own specialized operating systems), and most C programs do not try
to support them.

11.2 Floating-Point Data Types
==============================

“Floating point” is the binary analogue of scientific notation:
internally it represents a number as a fraction and a binary exponent;
the value is that fraction multiplied by the specified power of 2.

   For instance, to represent 6, the fraction would be 0.75 and the
exponent would be 3; together they stand for the value 0.75 * 2^{3},
meaning 0.75 * 8.  The value 1.5 would use 0.75 as the fraction and 1 as
the exponent.  The value 0.75 would use 0.75 as the fraction and 0 as
the exponent.  The value 0.375 would use 0.75 as the fraction and -1 as
the exponent.

   These binary exponents are used by machine instructions.  You can
write a floating-point constant this way if you wish, using hexadecimal;
but normally we write floating-point numbers in decimal.  *Note Floating
Constants::.

   C has three floating-point data types:

‘double’
     “Double-precision” floating point, which uses 64 bits.  This is the
     normal floating-point type, and modern computers normally do their
     floating-point computations in this type, or some wider type.
     Except when there is a special reason to do otherwise, this is the
     type to use for floating-point values.

‘float’
     “Single-precision” floating point, which uses 32 bits.  It is
     useful for floating-point values stored in structures and arrays,
     to save space when the full precision of ‘double’ is not needed.
     In addition, single-precision arithmetic is faster on some
     computers, and occasionally that is useful.  But not often—most
     programs don’t use the type ‘float’.

     C would be cleaner if ‘float’ were the name of the type we use for
     most floating-point values; however, for historical reasons, that’s
     not so.

‘long double’
     “Extended-precision” floating point is either 80-bit or 128-bit
     precision, depending on the machine in use.  On some machines,
     which have no floating-point format wider than ‘double’, this is
     equivalent to ‘double’.

   Floating-point arithmetic raises many subtle issues.  *Note Floating
Point in Depth::, for more information.

11.3 Complex Data Types
=======================

Complex numbers can include both a real part and an imaginary part.  The
numeric constants covered above have real-numbered values.  An
imaginary-valued constant is an ordinary real-valued constant followed
by ‘i’.

   To declare numeric variables as complex, use the ‘_Complex’
keyword.(1)  The standard C complex data types are floating point,

     _Complex float foo;
     _Complex double bar;
     _Complex long double quux;

but GNU C supports integer complex types as well.

   Since ‘_Complex’ is a keyword just like ‘float’ and ‘double’ and
‘long’, the keywords can appear in any order, but the order shown above
seems most logical.

   GNU C supports constants for complex values; for instance, ‘4.0 +
3.0i’ has the value 4 + 3i as type ‘_Complex double’.  *Note Imaginary
Constants::.

   To pull the real and imaginary parts of the number back out, GNU C
provides the keywords ‘__real__’ and ‘__imag__’:

     _Complex double foo = 4.0 + 3.0i;

     double a = __real__ foo; /* ‘a’ is now 4.0. */
     double b = __imag__ foo; /* ‘b’ is now 3.0. */

Standard C does not include these keywords, and instead relies on
functions defined in ‘complex.h’ for accessing the real and imaginary
parts of a complex number: ‘crealf’, ‘creal’, and ‘creall’ extract the
real part of a float, double, or long double complex number,
respectively; ‘cimagf’, ‘cimag’, and ‘cimagl’ extract the imaginary
part.

   GNU C also defines ‘~’ as an operator for complex conjugation, which
means negating the imaginary part of a complex number:

     _Complex double foo = 4.0 + 3.0i;
     _Complex double bar = ~foo; /* ‘bar’ is now 4 − 3i. */

For standard C compatibility, you can use the appropriate library
function: ‘conjf’, ‘conj’, or ‘confl’.

   ---------- Footnotes ----------

   (1) For compatibility with older versions of GNU C, the keyword
‘__complex__’ is also allowed.  Going forward, however, use the new
‘_Complex’ keyword as defined in ISO C11.

11.4 The Void Type
==================

The data type ‘void’ is a dummy—it allows no operations.  It really
means “no value at all.” When a function is meant to return no value, we
write ‘void’ for its return type.  Then ‘return’ statements in that
function should not specify a value (*note return Statement::).  Here’s
an example:

     void
     print_if_positive (double x, double y)
     {
       if (x >=0)
         return;
       if (y >=0)
         return;
       printf ("Next point is (%f,%f)\n", x, y);
     }

   A ‘void’-returning function is comparable to what some other
languages call a “procedure” instead of a “function.”

11.5 Other Data Types
=====================

Beyond the primitive types, C provides several ways to construct new
data types.  For instance, you can define “pointers”, values that
represent the addresses of other data (*note Pointers::).  You can
define “structures”, as in many other languages (*note Structures::),
and “unions”, which specify multiple ways to look at the same memory
space (*note Unions::).  “Enumerations” are collections of named integer
codes (*note Enumeration Types::).

   “Array types” in C are used for allocating space for objects, but C
does not permit operating on an array value as a whole.  *Note Arrays::.

11.6 Type Designators
=====================

Some C constructs require a way to designate a specific data type
independent of any particular variable or expression which has that
type.  The way to do this is with a “type designator”.  The constucts
that need one include casts (*note Explicit Type Conversion::) and
‘sizeof’ (*note Type Size::).

   We also use type designators to talk about the type of a value in C,
so you will see many type designators in this manual.  When we say, “The
value has type ‘int’,” ‘int’ is a type designator.

   To make the designator for any type, imagine a variable declaration
for a variable of that type and delete the variable name and the final
semicolon.

   For example, to designate the type of full-word integers, we start
with the declaration for a variable ‘foo’ with that type, which is this:

     int foo;

Then we delete the variable name ‘foo’ and the semicolon, leaving
‘int’—exactly the keyword used in such a declaration.  Therefore, the
type designator for this type is ‘int’.

   What about long unsigned integers?  From the declaration

     unsigned long int foo;

we determine that the designator is ‘unsigned long int’.

   Following this procedure, the designator for any primitive type is
simply the set of keywords which specifies that type in a declaration.
The same is true for compound types such as structures, unions, and
enumerations.

   Designators for pointer types do follow the rule of deleting the
variable name and semicolon, but the result is not so simple.  *Note
Pointer Type Designators::, as part of the chapter about pointers.
*Note Array Type Designators::), for designators for array types.

   To understand what type a designator stands for, imagine a variable
name inserted into the right place in the designator to make a valid
declaration.  What type would that variable be declared as?  That is the
type the designator designates.

12 Constants
************

A “constant” is an expression that stands for a specific value by
explicitly representing the desired value.  C allows constants for
numbers, characters, and strings.  We have already seen numeric and
string constants in the examples.

12.1 Integer Constants
======================

An integer constant consists of a number to specify the value, followed
optionally by suffix letters to specify the data type.

   The simplest integer constants are numbers written in base 10
(decimal), such as ‘5’, ‘77’, and ‘403’.  A decimal constant cannot
start with the character ‘0’ (zero) because that makes the constant
octal.

   You can get the effect of a negative integer constant by putting a
minus sign at the beginning.  Grammatically speaking, that is an
arithmetic expression rather than a constant, but it behaves just like a
true constant.

   Integer constants can also be written in octal (base 8), hexadecimal
(base 16), or binary (base 2).  An octal constant starts with the
character ‘0’ (zero), followed by any number of octal digits (‘0’ to
‘7’):

     0      // zero
     077    // 63
     0403   // 259

Pedantically speaking, the constant ‘0’ is an octal constant, but we can
think of it as decimal; it has the same value either way.

   A hexadecimal constant starts with ‘0x’ (upper or lower case)
followed by hex digits (‘0’ to ‘9’, as well as ‘a’ through ‘f’ in upper
or lower case):

     0xff   // 255
     0XA0   // 160
     0xffFF // 65535

   A binary constant starts with ‘0b’ (upper or lower case) followed by
bits (each represented by the characters ‘0’ or ‘1’):

     0b101  // 5

   Binary constants are a GNU C extension, not part of the C standard.

   Sometimes a space is needed after an integer constant to avoid
lexical confusion with the following tokens.  *Note Invalid Numbers::.

12.2 Integer Constant Data Types
================================

The type of an integer constant is normally ‘int’, if the value fits in
that type, but here are the complete rules.  The type of an integer
constant is the first one in this sequence that can properly represent
the value,

  1. ‘int’
  2. ‘unsigned int’
  3. ‘long int’
  4. ‘unsigned long int’
  5. ‘long long int’
  6. ‘unsigned long long int’

and that isn’t excluded by the following rules.

   If the constant has ‘l’ or ‘L’ as a suffix, that excludes the first
two types (non-‘long’).

   If the constant has ‘ll’ or ‘LL’ as a suffix, that excludes first
four types (non-‘long long’).

   If the constant has ‘u’ or ‘U’ as a suffix, that excludes the signed
types.

   Otherwise, if the constant is decimal, that excludes the unsigned
types.

   Here are some examples of the suffixes.

     3000000000u      // three billion as ‘unsigned int’.
     0LL              // zero as a ‘long long int’.
     0403l            // 259 as a ‘long int’.

   Suffixes in integer constants are rarely used.  When the precise type
is important, it is cleaner to convert explicitly (*note Explicit Type
Conversion::).

   *Note Integer Types::.

12.3 Floating-Point Constants
=============================

A floating-point constant must have either a decimal point, an
exponent-of-ten, or both; they distinguish it from an integer constant.

   To indicate an exponent, write ‘e’ or ‘E’.  The exponent value
follows.  It is always written as a decimal number; it can optionally
start with a sign.  The exponent N means to multiply the constant’s
value by ten to the Nth power.

   Thus, ‘1500.0’, ‘15e2’, ‘15e+2’, ‘15.0e2’, ‘1.5e+3’, ‘.15e4’, and
‘15000e-1’ are six ways of writing a floating-point number whose value
is 1500.  They are all equivalent.

   Here are more examples with decimal points:

     1.0
     1000.
     3.14159
     .05
     .0005

   For each of them, here are some equivalent constants written with
exponents:

     1e0, 1.0000e0
     100e1, 100e+1, 100E+1, 1e3, 10000e-1
     3.14159e0
     5e-2, .0005e+2, 5E-2, .0005E2
     .05e-2

   A floating-point constant normally has type ‘double’.  You can force
it to type ‘float’ by adding ‘f’ or ‘F’ at the end.  For example,

     3.14159f
     3.14159e0f
     1000.f
     100E1F
     .0005f
     .05e-2f

   Likewise, ‘l’ or ‘L’ at the end forces the constant to type ‘long
double’.

   You can use exponents in hexadecimal floating constants, but since
‘e’ would be interpreted as a hexadecimal digit, the character ‘p’ or
‘P’ (for “power”) indicates an exponent.

   The exponent in a hexadecimal floating constant is a possibly-signed
decimal integer that specifies a power of 2 (_not_ 10 or 16) to multiply
into the number.

   Here are some examples:

     0xAp2        // 40 in decimal
     0xAp-1       // 5 in decimal
     0x2.0Bp4     // 16.75 decimal
     0xE.2p3      // 121 decimal
     0x123.ABCp0  // 291.6708984375 in decimal
     0x123.ABCp4  // 4666.734375 in decimal
     0x100p-8     // 1
     0x10p-4      // 1
     0x1p+4       // 16
     0x1p+8       // 256

   *Note Floating-Point Data Types::.

12.4 Imaginary Constants
========================

A complex number consists of a real part plus an imaginary part.
(Either or both parts may be zero.)  This section explains how to write
numeric constants with imaginary values.  By adding these to ordinary
real-valued numeric constants, we can make constants with complex
values.

   The simple way to write an imaginary-number constant is to attach the
suffix ‘i’ or ‘I’, or ‘j’ or ‘J’, to an integer or floating-point
constant.  For example, ‘2.5fi’ has type ‘_Complex float’ and ‘3i’ has
type ‘_Complex int’.  The four alternative suffix letters are all
equivalent.

   The other way to write an imaginary constant is to multiply a real
constant by ‘_Complex_I’, which represents the imaginary number i.
Standard C doesn’t support suffixing with ‘i’ or ‘j’, so this clunky way
is needed.

   To write a complex constant with a nonzero real part and a nonzero
imaginary part, write the two separately and add them, like this:

     4.0 + 3.0i

That gives the value 4 + 3i, with type ‘_Complex double’.

   Such a sum can include multiple real constants, or none.  Likewise,
it can include multiple imaginary constants, or none.  For example:

     _Complex double foo, bar, quux;

     foo = 2.0i + 4.0 + 3.0i; /* Imaginary part is 5.0. */
     bar = 4.0 + 12.0; /* Imaginary part is 0.0. */
     quux = 3.0i + 15.0i; /* Real part is 0.0. */

   *Note Complex Data Types::.

12.5 Invalid Numbers
====================

Some number-like constructs which are not really valid as numeric
constants are treated as numbers in preprocessing directives.  If these
constructs appear outside of preprocessing, they are erroneous.  *Note
Preprocessing Tokens::.

   Sometimes we need to insert spaces to separate tokens so that they
won’t be combined into a single number-like construct.  For example,
‘0xE+12’ is a preprocessing number that is not a valid numeric constant,
so it is a syntax error.  If what we want is the three tokens
‘0xE + 12’, we have to use those spaces as separators.

12.6 Character Constants
========================

A “character constant” is written with single quotes, as in ‘'C'’.  In
the simplest case, C is a single ASCII character that the constant
should represent.  The constant has type ‘int’, and its value is the
character code of that character.  For instance, ‘'a'’ represents the
character code for the letter ‘a’: 97, that is.

   To put the ‘'’ character (single quote) in the character constant,
“quote” it with a backslash (‘\’).  This character constant looks like
‘'\''’.  This sort of sequence, starting with ‘\’, is called an “escape
sequence”—the backslash character here functions as a kind of “escape
character”.

   To put the ‘\’ character (backslash) in the character constant, quote
it likewise with ‘\’ (another backslash).  This character constant looks
like ‘'\\'’.

   Here are all the escape sequences that represent specific characters
in a character constant.  The numeric values shown are the corresponding
ASCII character codes, as decimal numbers.

     '\a' ⇒ 7       /* alarm, ‘CTRL-g’ */
     '\b' ⇒ 8       /* backspace, >BS<, ‘CTRL-h’ */
     '\t' ⇒ 9       /* tab, >TAB<, ‘CTRL-i’ */
     '\n' ⇒ 10      /* newline, ‘CTRL-j’ */
     '\v' ⇒ 11      /* vertical tab, ‘CTRL-k’ */
     '\f' ⇒ 12      /* formfeed, ‘CTRL-l’ */
     '\r' ⇒ 13      /* carriage return, >RET<, ‘CTRL-m’ */
     '\e' ⇒ 27      /* escape character, >ESC<, ‘CTRL-[’ */
     '\\' ⇒ 92      /* backslash character, ‘\’ */
     '\'' ⇒ 39      /* singlequote character, ‘'’ */
     '\"' ⇒ 34      /* doublequote character, ‘"’ */
     '\?' ⇒ 63      /* question mark, ‘?’ */

   ‘\e’ is a GNU C extension; to stick to standard C, write ‘\33’.

   You can also write octal and hex character codes as ‘\OCTALCODE’ or
‘\xHEXCODE’.  Decimal is not an option here, so octal codes do not need
to start with ‘0’.

   The character constant’s value has type ‘int’.  However, the
character code is treated initially as a ‘char’ value, which is then
converted to ‘int’.  If the character code is greater than 127 (‘0177’
in octal), the resulting ‘int’ may be negative on a platform where the
type ‘char’ is 8 bits long and signed.

12.7 String Constants
=====================

A “string constant” represents a series of characters.  It starts with
‘"’ and ends with ‘"’; in between are the contents of the string.
Quoting special characters such as ‘"’, ‘\’ and newline in the contents
works in string constants as in character constants.  In a string
constant, ‘'’ does not need to be quoted.

   A string constant defines an array of characters which contains the
specified characters followed by the null character (code 0).  Using the
string constant is equivalent to using the name of an array with those
contents.  In simple cases, the length in bytes of the string constant
is one greater than the number of characters written in it.

   As with any array in C, using the string constant in an expression
converts the array to a pointer (*note Pointers::) to the array’s first
element (*note Accessing Array Elements::).  This pointer will have type
‘char *’ because it points to an element of type ‘char’.  ‘char *’ is an
example of a type designator for a pointer type (*note Pointer Type
Designators::).  That type is used for strings generally, not just the
strings expressed as constants in a program.

   Thus, the string constant ‘"Foo!"’ is almost equivalent to declaring
an array like this

     char string_array_1[] = {'F', 'o', 'o', '!', '\0' };

and then using ‘string_array_1’ in the program.  There are two
differences, however:

   • The string constant doesn’t define a name for the array.

   • The string constant is probably stored in a read-only area of
     memory.

   Newlines are not allowed in the text of a string constant.  The
motive for this prohibition is to catch the error of omitting the
closing ‘"’.  To put a newline in a constant string, write it as ‘\n’ in
the string constant.

   A real null character in the source code inside a string constant
causes a warning.  To put a null character in the middle of a string
constant, write ‘\0’ or ‘\000’.

   Consecutive string constants are effectively concatenated.  Thus,

     "Fo" "o!"   is equivalent to   "Foo!"

   This is useful for writing a string containing multiple lines, like
this:

     "This message is so long that it needs more than\n"
     "a single line of text.  C does not allow a newline\n"
     "to represent itself in a string constant, so we have to\n"
     "write \\n to put it in the string.  For readability of\n"
     "the source code, it is advisable to put line breaks in\n"
     "the source where they occur in the contents of the\n"
     "constant.\n"

   The sequence of a backslash and a newline is ignored anywhere in a C
program, and that includes inside a string constant.  Thus, you can
write multi-line string constants this way:

     "This is another way to put newlines in a string constant\n\
     and break the line after them in the source code."

However, concatenation is the recommended way to do this.

   You can also write perverse string constants like this,

     "Fo\
     o!"

but don’t do that—write it like this instead:

     "Foo!"

   Be careful to avoid passing a string constant to a function that
modifies the string it receives.  The memory where the string constant
is stored may be read-only, which would cause a fatal ‘SIGSEGV’ signal
that normally terminates the function (*note Signals::.  Even worse, the
memory may not be read-only.  Then the function might modify the string
constant, thus spoiling the contents of other string constants that are
supposed to contain the same value and are unified by the compiler.

12.8 UTF-8 String Constants
===========================

Writing ‘u8’ immediately before a string constant, with no intervening
space, means to represent that string in UTF-8 encoding as a sequence of
bytes.  UTF-8 represents ASCII characters with a single byte, and
represents non-ASCII Unicode characters (codes 128 and up) as multibyte
sequences.  Here is an example of a UTF-8 constant:

     u8"A cónstàñt"

   This constant occupies 13 bytes plus the terminating null, because
each of the accented letters is a two-byte sequence.

   Concatenating an ordinary string with a UTF-8 string conceptually
produces another UTF-8 string.  However, if the ordinary string contains
character codes 128 and up, the results cannot be relied on.

12.9 Unicode Character Codes
============================

You can specify Unicode characters, for individual character constants
or as part of string constants (*note String Constants::), using escape
sequences.  Use the ‘\u’ escape sequence with a 16-bit hexadecimal
Unicode character code.  If the code value is too big for 16 bits, use
the ‘\U’ escape sequence with a 32-bit hexadecimal Unicode character
code.  (These codes are called “universal character names”.)  For
example,

     \u6C34      /* 16-bit code (UTF-16) */
     \U0010ABCD  /* 32-bit code (UTF-32) */

One way to use these is in UTF-8 string constants (*note UTF-8 String
Constants::).  For instance,

     u8"fóó \u6C34 \U0010ABCD"

   You can also use them in wide character constants (*note Wide
Character Constants::), like this:

     u'\u6C34'      /* 16-bit code */
     U'\U0010ABCD'  /* 32-bit code */

and in wide string constants (*note Wide String Constants::), like this:

     u"\u6C34\u6C33"  /* 16-bit code */
     U"\U0010ABCD"    /* 32-bit code */

   Codes in the range of ‘D800’ through ‘DFFF’ are not valid in Unicode.
Codes less than ‘00A0’ are also forbidden, except for ‘0024’, ‘0040’,
and ‘0060’; these characters are actually ASCII control characters, and
you can specify them with other escape sequences (*note Character
Constants::).

12.10 Wide Character Constants
==============================

A “wide character constant” represents characters with more than 8 bits
of character code.  This is an obscure feature that we need to document
but that you probably won’t ever use.  If you’re just learning C, you
may as well skip this section.

   The original C wide character constant looks like ‘L’ (upper case!)
followed immediately by an ordinary character constant (with no
intervening space).  Its data type is ‘wchar_t’, which is an alias
defined in ‘stddef.h’ for one of the standard integer types.  Depending
on the platform, it could be 16 bits or 32 bits.  If it is 16 bits,
these character constants use the UTF-16 form of Unicode; if 32 bits,
UTF-32.

   There are also Unicode wide character constants which explicitly
specify the width.  These constants start with ‘u’ or ‘U’ instead of
‘L’.  ‘u’ specifies a 16-bit Unicode wide character constant, and ‘U’ a
32-bit Unicode wide character constant.  Their types are, respectively,
‘char16_t’ and ‘char32_t’; they are declared in the header file
‘uchar.h’.  These character constants are valid even if ‘uchar.h’ is not
included, but some uses of them may be inconvenient without including it
to declare those type names.

   The character represented in a wide character constant can be an
ordinary ASCII character.  ‘L'a'’, ‘u'a'’ and ‘U'a'’ are all valid, and
they are all equal to ‘'a'’.

   In all three kinds of wide character constants, you can write a
non-ASCII Unicode character in the constant itself; the constant’s value
is the character’s Unicode character code.  Or you can specify the
Unicode character with an escape sequence (*note Unicode Character
Codes::).

12.11 Wide String Constants
===========================

A “wide string constant” stands for an array of 16-bit or 32-bit
characters.  They are rarely used; if you’re just learning C, you may as
well skip this section.

   There are three kinds of wide string constants, which differ in the
data type used for each character in the string.  Each wide string
constant is equivalent to an array of integers, but the data type of
those integers depends on the kind of wide string.  Using the constant
in an expression will convert the array to a pointer to its first
element, as usual for arrays in C (*note Accessing Array Elements::).
For each kind of wide string constant, we state here what type that
pointer will be.

‘char16_t’
     This is a 16-bit Unicode wide string constant: each element is a
     16-bit Unicode character code with type ‘char16_t’, so the string
     has the pointer type ‘char16_t *’.  (That is a type designator;
     *note Pointer Type Designators::.)  The constant is written as ‘u’
     (which must be lower case) followed (with no intervening space) by
     a string constant with the usual syntax.

‘char32_t’
     This is a 32-bit Unicode wide string constant: each element is a
     32-bit Unicode character code, and the string has type
     ‘char32_t *’.  It’s written as ‘U’ (which must be upper case)
     followed (with no intervening space) by a string constant with the
     usual syntax.

‘wchar_t’
     This is the original kind of wide string constant.  It’s written as
     ‘L’ (which must be upper case) followed (with no intervening space)
     by a string constant with the usual syntax, and the string has type
     ‘wchar_t *’.

     The width of the data type ‘wchar_t’ depends on the target
     platform, which makes this kind of wide string somewhat less useful
     than the newer kinds.

   ‘char16_t’ and ‘char32_t’ are declared in the header file ‘uchar.h’.
‘wchar_t’ is declared in ‘stddef.h’.

   Consecutive wide string constants of the same kind concatenate, just
like ordinary string constants.  A wide string constant concatenated
with an ordinary string constant results in a wide string constant.  You
can’t concatenate two wide string constants of different kinds.  You
also can’t concatenate a wide string constant (of any kind) with a UTF-8
string constant.

13 Type Size
************

Each data type has a “size”, which is the number of bytes (*note
Storage::) that it occupies in memory.  To refer to the size in a C
program, use ‘sizeof’.  There are two ways to use it:

‘sizeof EXPRESSION’
     This gives the size of EXPRESSION, based on its data type.  It does
     not calculate the value of EXPRESSION, only its size, so if
     EXPRESSION includes side effects or function calls, they do not
     happen.  Therefore, ‘sizeof’ is always a compile-time operation
     that has zero run-time cost.

     A value that is a bit field (*note Bit Fields::) is not allowed as
     an operand of ‘sizeof’.

     For example,

          double a;

          i = sizeof a + 10;

     sets ‘i’ to 18 on most computers because ‘a’ occupies 8 bytes.

     Here’s how to determine the number of elements in an array ‘array’:

          (sizeof array / sizeof array[0])

     The expression ‘sizeof array’ gives the size of the array, not the
     size of a pointer to an element.  However, if EXPRESSION is a
     function parameter that was declared as an array, that variable
     really has a pointer type (*note Array Parm Pointer::), so the
     result is the size of that pointer.

‘sizeof (TYPE)’
     This gives the size of TYPE.  For example,

          i = sizeof (double) + 10;

     is equivalent to the previous example.

     You can’t apply ‘sizeof’ to an incomplete type (*note Incomplete
     Types::), nor ‘void’.  Using it on a function type gives 1 in GNU
     C, which makes adding an integer to a function pointer work as
     desired (*note Pointer Arithmetic::).

   *Warning*: When you use ‘sizeof’ with a type instead of an
expression, you must write parentheses around the type.

   *Warning*: When applying ‘sizeof’ to the result of a cast (*note
Explicit Type Conversion::), you must write parentheses around the cast
expression to avoid an ambiguity in the grammar of C.  Specifically,

     sizeof (int) -x

parses as

     (sizeof (int)) - x

If what you want is

     sizeof ((int) -x)

you must write it that way, with parentheses.

   The data type of the value of the ‘sizeof’ operator is always one of
the unsigned integer types; which one of those types depends on the
machine.  The header file ‘stddef.h’ defines the typedef name ‘size_t’
as an alias for this type.  *Note Defining Typedef Names::.

14 Pointers
***********

Among high-level languages, C is rather low level, close to the machine.
This is mainly because it has explicit “pointers”.  A pointer value is
the numeric address of data in memory.  The type of data to be found at
that address is specified by the data type of the pointer itself.  The
unary operator ‘*’ gets the data that a pointer points to—this is called
“dereferencing the pointer”.

   C also allows pointers to functions, but since there are some
differences in how they work, we treat them later.  *Note Function
Pointers::.

14.1 Address of Data
====================

The most basic way to make a pointer is with the “address-of” operator,
‘&’.  Let’s suppose we have these variables available:

     int i;
     double a[5];

   Now, ‘&i’ gives the address of the variable ‘i’—a pointer value that
points to ‘i’’s location—and ‘&a[3]’ gives the address of the element 3
of ‘a’.  (It is actually the fourth element in the array, since the
first element has index 0.)

   The address-of operator is unusual because it operates on a place to
store a value (an lvalue, *note Lvalues::), not on the value currently
stored there.  (The left argument of a simple assignment is unusual in
the same way.)  You can use it on any lvalue except a bit field (*note
Bit Fields::) or a constructor (*note Structure Constructors::).

14.2 Pointer Types
==================

For each data type T, there is a type for pointers to type T.  For these
variables,

     int i;
     double a[5];

   • ‘i’ has type ‘int’; we say ‘&i’ is a “pointer to ‘int’.”

   • ‘a’ has type ‘double[5]’; we say ‘&a’ is a “pointer to arrays of
     five ‘double’s.”

   • ‘a[3]’ has type ‘double’; we say ‘&a[3]’ is a “pointer to
     ‘double’.”

14.3 Pointer-Variable Declarations
==================================

The way to declare that a variable ‘foo’ points to type T is

     T *foo;

   To remember this syntax, think “if you dereference ‘foo’, using the
‘*’ operator, what you get is type T.  Thus, ‘foo’ points to type T.”

   Thus, we can declare variables that hold pointers to these three
types, like this:

     int *ptri;            /* Pointer to ‘int’. */
     double *ptrd;         /* Pointer to ‘double’. */
     double (*ptrda)[5];   /* Pointer to ‘double[5]’. */

   ‘int *ptri;’ means, “if you dereference ‘ptri’, you get an ‘int’.”
‘double (*ptrda)[5];’ means, “if you dereference ‘ptrda’, then subscript
it by an integer less than 5, you get a ‘double’.” The parentheses
express the point that you would dereference it first, then subscript
it.

   Contrast the last one with this:

     double *aptrd[5];     /* Array of five pointers to ‘double’. */

Because ‘*’ has higher syntactic precedence than subscripting, you would
subscript ‘aptrd’ then dereference it.  Therefore, it declares an array
of pointers, not a pointer.

14.4 Pointer-Type Designators
=============================

Every type in C has a designator; you make it by deleting the variable
name and the semicolon from a declaration (*note Type Designators::).
Here are the designators for the pointer types of the example
declarations in the previous section:

     int *           /* Pointer to ‘int’. */
     double *        /* Pointer to ‘double’. */
     double (*)[5]   /* Pointer to ‘double[5]’. */

   Remember, to understand what type a designator stands for, imagine
the variable name that would be in the declaration, and figure out what
type it would declare that variable with.  ‘double (*)[5]’ can only come
from ‘double (*VARIABLE)[5]’, so it’s a pointer which, when
dereferenced, gives an array of 5 ‘double’s.

14.5 Dereferencing Pointers
===========================

The main use of a pointer value is to “dereference it” (access the data
it points at) with the unary ‘*’ operator.  For instance, ‘*&i’ is the
value at ‘i’’s address—which is just ‘i’.  The two expressions are
equivalent, provided ‘&i’ is valid.

   A pointer-dereference expression whose type is data (not a function)
is an lvalue.

   Pointers become really useful when we store them somewhere and use
them later.  Here’s a simple example to illustrate the practice:

     {
       int i;
       int *ptr;

       ptr = &i;

       i = 5;

       ...

       return *ptr;   /* Returns 5, fetched from ‘i’.  */
     }

   This shows how to declare the variable ‘ptr’ as type ‘int *’ (pointer
to ‘int’), store a pointer value into it (pointing at ‘i’), and use it
later to get the value of the object it points at (the value in ‘i’).

   If anyone can provide a useful example which is this basic, I would
be grateful.

14.6 Null Pointers
==================

A pointer value can be “null”, which means it does not point to any
object.  The cleanest way to get a null pointer is by writing ‘NULL’, a
standard macro defined in ‘stddef.h’.  You can also do it by casting 0
to the desired pointer type, as in ‘(char *) 0’.  (The cast operator
performs explicit type conversion; *Note Explicit Type Conversion::.)

   You can store a null pointer in any lvalue whose data type is a
pointer type:

     char *foo;
     foo = NULL;

   These two, if consecutive, can be combined into a declaration with
initializer,

     char *foo = NULL;

   You can also explicitly cast ‘NULL’ to the specific pointer type you
want—it makes no difference.

     char *foo;
     foo = (char *) NULL;

   To test whether a pointer is null, compare it with zero or ‘NULL’, as
shown here:

     if (p != NULL)
       /* ‘p’ is not null.  */
       operate (p);

   Since testing a pointer for not being null is basic and frequent, all
but beginners in C will understand the conditional without need for ‘!=
NULL’:

     if (p)
       /* ‘p’ is not null.  */
       operate (p);

14.7 Dereferencing Null or Invalid Pointers
===========================================

Trying to dereference a null pointer is an error.  On most platforms, it
generally causes a signal, usually ‘SIGSEGV’ (*note Signals::).

     char *foo = NULL;
     c = *foo;    /* This causes a signal and terminates.  */

Likewise a pointer that has the wrong alignment for the target data type
(on most types of computer), or points to a part of memory that has not
been allocated in the process’s address space.

   The signal terminates the program, unless the program has arranged to
handle the signal (*note The GNU C Library: (libc)Signal Handling.).

   However, the signal might not happen if the dereference is optimized
away.  In the example above, if you don’t subsequently use the value of
‘c’, GCC might optimize away the code for ‘*foo’.  You can prevent such
optimization using the ‘volatile’ qualifier, as shown here:

     volatile char *p;
     volatile char c;
     c = *p;

   You can use this to test whether ‘p’ points to unallocated memory.
Set up a signal handler first, so the signal won’t terminate the
program.

14.8 Void Pointers
==================

The peculiar type ‘void *’, a pointer whose target type is ‘void’, is
used often in C.  It represents a pointer to we-don’t-say-what.  Thus,

     void *numbered_slot_pointer (int);

declares a function ‘numbered_slot_pointer’ that takes an integer
parameter and returns a pointer, but we don’t say what type of data it
points to.

   With type ‘void *’, you can pass the pointer around and test whether
it is null.  However, dereferencing it gives a ‘void’ value that can’t
be used (*note The Void Type::).  To dereference the pointer, first
convert it to some other pointer type.

   Assignments convert ‘void *’ automatically to any other pointer type,
if the left operand has a pointer type; for instance,

     {
       int *p;
       /* Converts return value to ‘int *’.  */
       p = numbered_slot_pointer (5);
       ...
     }

   Passing an argument of type ‘void *’ for a parameter that has a
pointer type also converts.  For example, supposing the function ‘hack’
is declared to require type ‘float *’ for its argument, this will
convert the null pointer to that type.

     /* Declare ‘hack’ that way.
        We assume it is defined somewhere else.  */
     void hack (float *);
     ...
     /* Now call ‘hack’.  */
     {
       /* Converts return value of ‘numbered_slot_pointer’
          to ‘float *’ to pass it to ‘hack’.  */
       hack (numbered_slot_pointer (5));
       ...
     }

   You can also convert to another pointer type with an explicit cast
(*note Explicit Type Conversion::), like this:
     (int *) numbered_slot_pointer (5)

   Here is an example which decides at run time which pointer type to
convert to:

     void
     extract_int_or_double (void *ptr, bool its_an_int)
     {
       if (its_an_int)
         handle_an_int (*(int *)ptr);
       else
         handle_a_double (*(double *)ptr);
     }

   The expression ‘*(int *)ptr’ means to convert ‘ptr’ to type ‘int *’,
then dereference it.

14.9 Pointer Comparison
=======================

Two pointer values are equal if they point to the same location, or if
they are both null.  You can test for this with ‘==’ and ‘!=’.  Here’s a
trivial example:

     {
       int i;
       int *p, *q;

       p = &i;
       q = &i;
       if (p == q)
         printf ("This will be printed.\n");
       if (p != q)
         printf ("This won't be printed.\n");
     }

   Ordering comparisons such as ‘<’ and ‘<=’ operate on pointers by
converting them to unsigned integers.  The C standard says the two
pointers must point within the same object in memory, but on GNU/Linux
systems these operations simply compare the numeric values of the
pointers.

   The pointer values to be compared should in principle have the same
type, but they are allowed to differ in limited cases.  First of all, if
the two pointers’ target types are nearly compatible (*note Compatible
Types::), the comparison is allowed.

   If one of the operands is ‘void *’ (*note Void Pointers::) and the
other is another pointer type, the comparison operator converts the
‘void *’ pointer to the other type so as to compare them.  (In standard
C, this is not allowed if the other type is a function pointer type, but
that works in GNU C.)

   Comparison operators also allow comparing the integer 0 with a
pointer value.  Thus works by converting 0 to a null pointer of the same
type as the other operand.

14.10 Pointer Arithmetic
========================

Adding an integer (positive or negative) to a pointer is valid in C.  It
assumes that the pointer points to an element in an array, and advances
or retracts the pointer across as many array elements as the integer
specifies.  Here is an example, in which adding a positive integer
advances the pointer to a later element in the same array.

     void
     incrementing_pointers ()
     {
       int array[5] = { 45, 29, 104, -3, 123456 };
       int elt0, elt1, elt4;

       int *p = &array[0];
       /* Now ‘p’ points at element 0.  Fetch it.  */
       elt0 = *p;

       ++p;
       /* Now ‘p’ points at element 1.  Fetch it.  */
       elt1 = *p;

       p += 3;
       /* Now ‘p’ points at element 4 (the last).  Fetch it.  */
       elt4 = *p;

       printf ("elt0 %d  elt1 %d  elt4 %d.\n",
               elt0, elt1, elt4);
       /* Prints elt0 45  elt1 29  elt4 123456.  */
     }

   Here’s an example where adding a negative integer retracts the
pointer to an earlier element in the same array.

     void
     decrementing_pointers ()
     {
       int array[5] = { 45, 29, 104, -3, 123456 };
       int elt0, elt3, elt4;

       int *p = &array[4];
       /* Now ‘p’ points at element 4 (the last).  Fetch it.  */
       elt4 = *p;

       --p;
       /* Now ‘p’ points at element 3.  Fetch it.  */
       elt3 = *p;

       p -= 3;
       /* Now ‘p’ points at element 0.  Fetch it.  */
       elt0 = *p;

       printf ("elt0 %d  elt3 %d  elt4 %d.\n",
               elt0, elt3, elt4);
       /* Prints elt0 45  elt3 -3  elt4 123456.  */
     }

   If one pointer value was made by adding an integer to another pointer
value, it should be possible to subtract the pointer values and recover
that integer.  That works too in C.

     void
     subtract_pointers ()
     {
       int array[5] = { 45, 29, 104, -3, 123456 };
       int *p0, *p3, *p4;

       int *p = &array[4];
       /* Now ‘p’ points at element 4 (the last).  Save the value.  */
       p4 = p;

       --p;
       /* Now ‘p’ points at element 3.  Save the value.  */
       p3 = p;

       p -= 3;
       /* Now ‘p’ points at element 0.  Save the value.  */
       p0 = p;

       printf ("%d, %d, %d, %d\n",
               p4 - p0, p0 - p0, p3 - p0, p0 - p3);
       /* Prints 4, 0, 3, -3.  */
     }

   The addition operation does not know where arrays are.  All it does
is add the integer (multiplied by object size) to the value of the
pointer.  When the initial pointer and the result point into a single
array, the result is well-defined.

   *Warning:* Only experts should do pointer arithmetic involving
pointers into different memory objects.

   The difference between two pointers has type ‘int’, or ‘long’ if
necessary (*note Integer Types::).  The clean way to declare it is to
use the typedef name ‘ptrdiff_t’ defined in the file ‘stddef.h’.

   This definition of pointer subtraction is consistent with
pointer-integer addition, in that ‘(p3 - p1) + p1’ equals ‘p3’, as in
ordinary algebra.

   In standard C, addition and subtraction are not allowed on ‘void *’,
since the target type’s size is not defined in that case.  Likewise,
they are not allowed on pointers to function types.  However, these
operations work in GNU C, and the “size of the target type” is taken as
1.

14.11 Pointers and Arrays
=========================

The clean way to refer to an array element is ‘ARRAY[INDEX]’.  Another,
complicated way to do the same job is to get the address of that element
as a pointer, then dereference it: ‘* (&ARRAY[0] + INDEX)’ (or
equivalently ‘* (ARRAY + INDEX)’).  This first gets a pointer to element
zero, then increments it with ‘+’ to point to the desired element, then
gets the value from there.

   That pointer-arithmetic construct is the _definition_ of square
brackets in C.  ‘A[B]’ means, by definition, ‘*(A + B)’.  This
definition uses A and B symmetrically, so one must be a pointer and the
other an integer; it does not matter which comes first.

   Since indexing with square brackets is defined in terms of addition
and dereference, that too is symmetrical.  Thus, you can write
‘3[array]’ and it is equivalent to ‘array[3]’.  However, it would be
foolish to write ‘3[array]’, since it has no advantage and could confuse
people who read the code.

   It may seem like a discrepancy that the definition ‘*(A + B)’
requires a pointer, but ‘array[3]’ uses an array value instead.  Why is
this valid?  The name of the array, when used by itself as an expression
(other than in ‘sizeof’), stands for a pointer to the arrays’s zeroth
element.  Thus, ‘array + 3’ converts ‘array’ implicitly to ‘&array[0]’,
and the result is a pointer to element 3, equivalent to ‘&array[3]’.

   Since square brackets are defined in terms of such addition,
‘array[3]’ first converts ‘array’ to a pointer.  That’s why it works to
use an array directly in that construct.

14.12 Pointer Arithmetic at Low Level
=====================================

The behavior of pointer arithmetic is theoretically defined only when
the pointer values all point within one object allocated in memory.  But
the addition and subtraction operators can’t tell whether the pointer
values are all within one object.  They don’t know where objects start
and end.  So what do they really do?

   Adding pointer P to integer I treats P as a memory address, which is
in fact an integer—call it PINT.  It treats I as a number of elements of
the type that P points to.  These elements’ sizes add up to ‘I * sizeof
(*P)’.  So the sum, as an integer, is ‘PINT + I * sizeof (*P)’.  This
value is reinterpreted as a pointer like P.

   If the starting pointer value P and the result do not point at parts
of the same object, the operation is not officially legitimate, and C
code is not “supposed” to do it.  But you can do it anyway, and it gives
precisely the results described by the procedure above.  In some special
situations it can do something useful, but non-wizards should avoid it.

   Here’s a function to offset a pointer value _as if_ it pointed to an
object of any given size, by explicitly performing that calculation:

     #include <stdint.h>

     void *
     ptr_add (void *p, int i, int objsize)
     {
       intptr_t p_address = (long) p;
       intptr_t totalsize = i * objsize;
       intptr_t new_address = p_address + totalsize;
       return (void *) new_address;
     }

This does the same job as ‘P + I’ with the proper pointer type for P.
It uses the type ‘intptr_t’, which is defined in the header file
‘stdint.h’.  (In practice, ‘long long’ would always work, but it is
cleaner to use ‘intptr_t’.)

14.13 Pointer Increment and Decrement
=====================================

The ‘++’ operator adds 1 to a variable.  We have seen it for integers
(*note Increment/Decrement::), but it works for pointers too.  For
instance, suppose we have a series of positive integers, terminated by a
zero, and we want to add them all up.

     int
     sum_array_till_0 (int *p)
     {
       int sum = 0;

       for (;;)
         {
           /* Fetch the next integer.  */
           int next = *p++;
           /* Exit the loop if it’s 0.  */
           if (next == 0)
             break;
           /* Add it into running total.  */
           sum += next;
         }

       return sum;
     }

The statement ‘break;’ will be explained further on (*note break
Statement::).  Used in this way, it immediately exits the surrounding
‘for’ statement.

   ‘*p++’ parses as ‘*(p++)’, because a postfix operator always takes
precedence over a prefix operator.  Therefore, it dereferences ‘p’, and
increments ‘p’ afterwards.  Incrementing a variable means adding 1 to
it, as in ‘p = p + 1’.  Since ‘p’ is a pointer, adding 1 to it advances
it by the width of the datum it points to—in this case, one ‘int’.
Therefore, each iteration of the loop picks up the next integer from the
series and puts it into ‘next’.

   This ‘for’-loop has no initialization expression since ‘p’ and ‘sum’
are already initialized, it has no end-test since the ‘break;’ statement
will exit it, and needs no expression to advance it since that’s done
within the loop by incrementing ‘p’ and ‘sum’.  Thus, those three
expressions after ‘for’ are left empty.

   Another way to write this function is by keeping the parameter value
unchanged and using indexing to access the integers in the table.

     int
     sum_array_till_0_indexing (int *p)
     {
       int i;
       int sum = 0;

       for (i = 0; ; i++)
         {
           /* Fetch the next integer.  */
           int next = p[i];
           /* Exit the loop if it’s 0.  */
           if (next == 0)
             break;
           /* Add it into running total.  */
           sum += next;
         }

       return sum;
     }

   In this program, instead of advancing ‘p’, we advance ‘i’ and add it
to ‘p’.  (Recall that ‘p[i]’ means ‘*(p + i)’.)  Either way, it uses the
same address to get the next integer.

   It makes no difference in this program whether we write ‘i++’ or
‘++i’, because the value is not used.  All that matters is the effect,
to increment ‘i’.

   The ‘--’ operator also works on pointers; it can be used to scan
backwards through an array, like this:

     int
     after_last_nonzero (int *p, int len)
     {
       /* Set up ‘q’ to point just after the last array element.  */
       int *q = p + len;

       while (q != p)
         /* Step ‘q’ back until it reaches a nonzero element.  */
         if (*--q != 0)
           /* Return the index of the element after that nonzero.  */
           return q - p + 1;

       return 0;
     }

   That function returns the length of the nonzero part of the array
specified by its arguments; that is, the index of the first zero of the
run of zeros at the end.

14.14 Drawbacks of Pointer Arithmetic
=====================================

Pointer arithmetic is clean and elegant, but it is also the cause of a
major security flaw in the C language.  Theoretically, it is only valid
to adjust a pointer within one object allocated as a unit in memory.
However, if you unintentionally adjust a pointer across the bounds of
the object and into some other object, the system has no way to detect
this error.

   A bug which does that can easily result in clobbering part of another
object.  For example, with ‘array[-1]’ you can read or write the
nonexistent element before the beginning of an array—probably part of
some other data.

   Combining pointer arithmetic with casts between pointer types, you
can create a pointer that fails to be properly aligned for its type.
For example,

     int a[2];
     char *pa = (char *)a;
     int *p = (int *)(pa + 1);

gives ‘p’ a value pointing to an “integer” that includes part of ‘a[0]’
and part of ‘a[1]’.  Dereferencing that with ‘*p’ can cause a fatal
‘SIGSEGV’ signal or it can return the contents of that badly aligned
‘int’ (*note Signals::.  If it “works,” it may be quite slow.  It can
also cause aliasing confusions (*note Aliasing::).

   *Warning:* Using improperly aligned pointers is risky—don’t do it
unless it is really necessary.

14.15 Pointer-Integer Conversion
================================

On modern computers, an address is simply a number.  It occupies the
same space as some size of integer.  In C, you can convert a pointer to
the appropriate integer types and vice versa, without losing
information.  The appropriate integer types are ‘uintptr_t’ (an unsigned
type) and ‘intptr_t’ (a signed type).  Both are defined in ‘stdint.h’.

   For instance,

     #include <stdint.h>
     #include <stdio.h>

     void
     print_pointer (void *ptr)
     {
       uintptr_t converted = (uintptr_t) ptr;

       printf ("Pointer value is 0x%x\n",
               (unsigned int) converted);
     }

The specification ‘%x’ in the template (the first argument) for ‘printf’
means to represent this argument using hexadecimal notation.  It’s
cleaner to use ‘uintptr_t’, since hexadecimal printing treats the number
as unsigned, but it won’t actually matter: all ‘printf’ gets to see is
the series of bits in the number.

   *Warning:* Converting pointers to integers is risky—don’t do it
unless it is really necessary.

14.16 Printing Pointers
=======================

To print the numeric value of a pointer, use the ‘%p’ specifier.  For
example:

     void
     print_pointer (void *ptr)
     {
       printf ("Pointer value is %p\n", ptr);
     }

   The specification ‘%p’ works with any pointer type.  It prints ‘0x’
followed by the address in hexadecimal, printed as the appropriate
unsigned integer type.

15 Structures
*************

A “structure” is a user-defined data type that holds various “fields” of
data.  Each field has a name and a data type specified in the
structure’s definition.

   Here we define a structure suitable for storing a linked list of
integers.  Each list item will hold one integer, plus a pointer to the
next item.

     struct intlistlink
       {
         int datum;
         struct intlistlink *next;
       };

   The structure definition has a “type tag” so that the code can refer
to this structure.  The type tag here is ‘intlistlink’.  The definition
refers recursively to the same structure through that tag.

   You can define a structure without a type tag, but then you can’t
refer to it again.  That is useful only in some special contexts, such
as inside a ‘typedef’ or a ‘union’.

   The contents of the structure are specified by the “field
declarations” inside the braces.  Each field in the structure needs a
declaration there.  The fields in one structure definition must have
distinct names, but these names do not conflict with any other names in
the program.

   A field declaration looks just like a variable declaration.  You can
combine field declarations with the same beginning, just as you can
combine variable declarations.

   This structure has two fields.  One, named ‘datum’, has type ‘int’
and will hold one integer in the list.  The other, named ‘next’, is a
pointer to another ‘struct intlistlink’ which would be the rest of the
list.  In the last list item, it would be ‘NULL’.

   This structure definition is recursive, since the type of the ‘next’
field refers to the structure type.  Such recursion is not a problem; in
fact, you can use the type ‘struct intlistlink *’ before the definition
of the type ‘struct intlistlink’ itself.  That works because pointers to
all kinds of structures really look the same at the machine level.

   After defining the structure, you can declare a variable of type
‘struct intlistlink’ like this:

     struct intlistlink foo;

   The structure definition itself can serve as the beginning of a
variable declaration, so you can declare variables immediately after,
like this:

     struct intlistlink
       {
         int datum;
         struct intlistlink *next;
       } foo;

But that is ugly.  It is almost always clearer to separate the
definition of the structure from its uses.

   Declaring a structure type inside a block (*note Blocks::) limits the
scope of the structure type name to that block.  That means the
structure type is recognized only within that block.  Declaring it in a
function parameter list, as here,

     int f (struct foo {int a, b} parm);

(assuming that ‘struct foo’ is not already defined) limits the scope of
the structure type ‘struct foo’ to that parameter list; that is
basically useless, so it triggers a warning.

   Standard C requires at least one field in a structure.  GNU C does
not require this.

15.1 Referencing Structure Fields
=================================

To make a structure useful, there has to be a way to examine and store
its fields.  The ‘.’ (period) operator does that; its use looks like
‘OBJECT.FIELD’.

   Given this structure and variable,

     struct intlistlink
       {
         int datum;
         struct intlistlink *next;
       };

     struct intlistlink foo;

you can write ‘foo.datum’ and ‘foo.next’ to refer to the two fields in
the value of ‘foo’.  These fields are lvalues, so you can store values
into them, and read the values out again.

   Most often, structures are dynamically allocated (see the next
section), and we refer to the objects via pointers.  ‘(*p).FIELD’ is
somewhat cumbersome, so there is an abbreviation: ‘p-<FIELD’.  For
instance, assume the program contains this declaration:

     struct intlistlink *ptr;

You can write ‘ptr-<datum’ and ‘ptr-<next’ to refer to the two fields in
the object that ‘ptr’ points to.

   If a unary operator precedes an expression using ‘-<’, the ‘-<’ nests
inside:

       -ptr-<datum   is equivalent to   -(ptr-<datum)

   You can intermix ‘-<’ and ‘.’ without parentheses, as shown here:

     struct { double d; struct intlistlink l; } foo;

     ...foo.l.next-<next-<datum...

15.2 Dynamic Memory Allocation
==============================

To allocate an object dynamically, call the library function ‘malloc’
(*note The GNU C Library: (libc)Basic Allocation.).  Here is how to
allocate an object of type ‘struct intlistlink’.  To make this code
work, include the file ‘stdlib.h’, like this:

     #include <stddef.h>  /* Defines ‘NULL’. */
     #include <stdlib.h>  /* Declares ‘malloc’.  */

     ...

     struct intlistlink *
     alloc_intlistlink ()
     {
       struct intlistlink *p;

       p = malloc (sizeof (struct intlistlink));

       if (p == NULL)
         fatal ("Ran out of storage");

       /* Initialize the contents. */
       p-<datum = 0;
       p-<next = NULL;

       return p;
     }

‘malloc’ returns ‘void *’, so the assignment to ‘p’ will automatically
convert it to type ‘struct intlistlink *’.  The return value of ‘malloc’
is always sufficiently aligned (*note Type Alignment::) that it is valid
for any data type.

   The test for ‘p == NULL’ is necessary because ‘malloc’ returns a null
pointer if it cannot get any storage.  We assume that the program
defines the function ‘fatal’ to report a fatal error to the user.

   Here’s how to add one more integer to the front of such a list:

     struct intlistlink *my_list = NULL;

     void
     add_to_mylist (int my_int)
     {
       struct intlistlink *p = alloc_intlistlink ();

       p-<datum = my_int;
       p-<next = mylist;
       mylist = p;
     }

   The way to free the objects is by calling ‘free’.  Here’s a function
to free all the links in one of these lists:

     void
     free_intlist (struct intlistlink *p)
     {
       while (p)
         {
           struct intlistlink *q = p;
           p = p-<next;
           free (q);
         }
     }

   We must extract the ‘next’ pointer from the object before freeing it,
because ‘free’ can clobber the data that was in the object.  For the
same reason, the program must not use the list any more after freeing
its elements.  To make sure it won’t, it is best to clear out the
variable where the list was stored, like this:

     free_intlist (mylist);

     mylist = NULL;

15.3 Field Offset
=================

To determine the offset of a given field FIELD in a structure type TYPE,
use the macro ‘offsetof’, which is defined in the file ‘stddef.h’.  It
is used like this:

     offsetof (TYPE, FIELD)

   Here is an example:

     struct foo
     {
       int element;
       struct foo *next;
     };

     offsetof (struct foo, next)
     /* On most machines that is 4.  It may be 8.  */

15.4 Structure Layout
=====================

The rest of this chapter covers advanced topics about structures.  If
you are just learning C, you can skip it.

   The precise layout of a ‘struct’ type is crucial when using it to
overlay hardware registers, to access data structures in shared memory,
or to assemble and disassemble packets for network communication.  It is
also important for avoiding memory waste when the program makes many
objects of that type.  However, the layout depends on the target
platform.  Each platform has conventions for structure layout, which
compilers need to follow.

   Here are the conventions used on most platforms.

   The structure’s fields appear in the structure layout in the order
they are declared.  When possible, consecutive fields occupy consecutive
bytes within the structure.  However, if a field’s type demands more
alignment than it would get that way, C gives it the alignment it
requires by leaving a gap after the previous field.

   Once all the fields have been laid out, it is possible to determine
the structure’s alignment and size.  The structure’s alignment is the
maximum alignment of any of the fields in it.  Then the structure’s size
is rounded up to a multiple of its alignment.  That may require leaving
a gap at the end of the structure.

   Here are some examples, where we assume that ‘char’ has size and
alignment 1 (always true), and ‘int’ has size and alignment 4 (true on
most kinds of computers):

     struct foo
     {
       char a, b;
       int c;
     };

This structure occupies 8 bytes, with an alignment of 4.  ‘a’ is at
offset 0, ‘b’ is at offset 1, and ‘c’ is at offset 4.  There is a gap of
2 bytes before ‘c’.

   Contrast that with this structure:

     struct foo
     {
       char a;
       int c;
       char b;
     };

   This structure has size 12 and alignment 4.  ‘a’ is at offset 0, ‘c’
is at offset 4, and ‘b’ is at offset 8.  There are two gaps: three bytes
before ‘c’, and three bytes at the end.

   These two structures have the same contents at the C level, but one
takes 8 bytes and the other takes 12 bytes due to the ordering of the
fields.  A reliable way to avoid this sort of wastage is to order the
fields by size, biggest fields first.

15.5 Packed Structures
======================

In GNU C you can force a structure to be laid out with no gaps by adding
‘__attribute__((packed))’ after ‘struct’ (or at the end of the structure
type declaration).  Here’s an example:

     struct __attribute__((packed)) foo
     {
       char a;
       int c;
       char b;
     };

   Without ‘__attribute__((packed))’, this structure occupies 12 bytes
(as described in the previous section), assuming 4-byte alignment for
‘int’.  With ‘__attribute__((packed))’, it is only 6 bytes long—the sum
of the lengths of its fields.

   Use of ‘__attribute__((packed))’ often results in fields that don’t
have the normal alignment for their types.  Taking the address of such a
field can result in an invalid pointer because of its improper
alignment.  Dereferencing such a pointer can cause a ‘SIGSEGV’ signal on
a machine that doesn’t, in general, allow unaligned pointers.

   *Note Attributes::.

15.6 Bit Fields
===============

A structure field declaration with an integer type can specify the
number of bits the field should occupy.  We call that a “bit field”.
These are useful because consecutive bit fields are packed into a larger
storage unit.  For instance,

     unsigned char opcode: 4;

specifies that this field takes just 4 bits.  Since it is unsigned, its
possible values range from 0 to 15.  A signed field with 4 bits, such as
this,

     signed char small: 4;

can hold values from -8 to 7.

   You can subdivide a single byte into those two parts by writing

     unsigned char opcode: 4;
     signed char small: 4;

in the structure.  With bit fields, these two numbers fit into a single
‘char’.

   Here’s how to declare a one-bit field that can hold either 0 or 1:

     unsigned char special_flag: 1;

   You can also use the ‘bool’ type for bit fields:

     bool special_flag: 1;

   Except when using ‘bool’ (which is always unsigned, *note Boolean
Type::), always specify ‘signed’ or ‘unsigned’ for a bit field.  There
is a default, if that’s not specified: the bit field is signed if plain
‘char’ is signed, except that the option ‘-funsigned-bitfields’ forces
unsigned as the default.  But it is cleaner not to depend on this
default.

   Bit fields are special in that you cannot take their address with
‘&’.  They are not stored with the size and alignment appropriate for
the specified type, so they cannot be addressed through pointers to that
type.

15.7 Bit Field Packing
======================

Programs to communicate with low-level hardware interfaces need to
define bit fields laid out to match the hardware data.  This section
explains how to do that.

   Consecutive bit fields are packed together, but each bit field must
fit within a single object of its specified type.  In this example,

     unsigned short a : 3, b : 3, c : 3, d : 3, e : 3;

all five fields fit consecutively into one two-byte ‘short’.  They need
15 bits, and one ‘short’ provides 16.  By contrast,

     unsigned char a : 3, b : 3, c : 3, d : 3, e : 3;

needs three bytes.  It fits ‘a’ and ‘b’ into one ‘char’, but ‘c’ won’t
fit in that ‘char’ (they would add up to 9 bits).  So ‘c’ and ‘d’ go
into a second ‘char’, leaving a gap of two bits between ‘b’ and ‘c’.
Then ‘e’ needs a third ‘char’.  By contrast,

     unsigned char a : 3, b : 3;
     unsigned int c : 3;
     unsigned char d : 3, e : 3;

needs only two bytes: the type ‘unsigned int’ allows ‘c’ to straddle
bytes that are in the same word.

   You can leave a gap of a specified number of bits by defining a
nameless bit field.  This looks like ‘TYPE : NBITS;’.  It is allocated
space in the structure just as a named bit field would be allocated.

   You can force the following bit field to advance to the following
aligned memory object with ‘TYPE : 0;’.

   Both of these constructs can syntactically share TYPE with ordinary
bit fields.  This example illustrates both:

     unsigned int a : 5, : 3, b : 5, : 0, c : 5, : 3, d : 5;

It puts ‘a’ and ‘b’ into one ‘int’, with a 3-bit gap between them.  Then
‘: 0’ advances to the next ‘int’, so ‘c’ and ‘d’ fit into that one.

   These rules for packing bit fields apply to most target platforms,
including all the usual real computers.  A few embedded controllers have
special layout rules.

15.8 ‘const’ Fields
===================

A structure field declared ‘const’ cannot be assigned to (*note
const::).  For instance, let’s define this modified version of ‘struct
intlistlink’:

     struct intlistlink_ro  /* “ro” for read-only.  */
       {
         const int datum;
         struct intlistlink *next;
       };

   This structure can be used to prevent part of the code from modifying
the ‘datum’ field:

     /* ‘p’ has type ‘struct intlistlink *’.
        Convert it to ‘struct intlistlink_ro *’.  */
     struct intlistlink_ro *q
       = (struct intlistlink_ro *) p;

     q-<datum = 5;     /* Error! */
     p-<datum = 5;     /* Valid since ‘*p’ is
                          not a ‘struct intlistlink_ro’.  */

   A ‘const’ field can get a value in two ways: by initialization of the
whole structure, and by making a pointer-to-structure point to an object
in which that field already has a value.

   Any ‘const’ field in a structure type makes assignment impossible for
structures of that type (*note Structure Assignment::).  That is because
structure assignment works by assigning the structure’s fields, one by
one.

15.9 Arrays of Length Zero
==========================

GNU C allows zero-length arrays.  They are useful as the last element of
a structure that is really a header for a variable-length object.
Here’s an example, where we construct a variable-size structure to hold
a line which is ‘this_length’ characters long:

     struct line {
       int length;
       char contents[0];
     };

     struct line *thisline
       = ((struct line *)
          malloc (sizeof (struct line)
                  + this_length));
     thisline-<length = this_length;

   In ISO C90, we would have to give ‘contents’ a length of 1, which
means either wasting space or complicating the argument to ‘malloc’.

15.10 Flexible Array Fields
===========================

The C99 standard adopted a more complex equivalent of zero-length array
fields.  It’s called a “flexible array”, and it’s indicated by omitting
the length, like this:

     struct line
     {
       int length;
       char contents[];
     };

   The flexible array has to be the last field in the structure, and
there must be other fields before it.

   Under the C standard, a structure with a flexible array can’t be part
of another structure, and can’t be an element of an array.

   GNU C allows static initialization of flexible array fields.  The
effect is to “make the array long enough” for the initializer.

     struct f1 { int x; int y[]; } f1
       = { 1, { 2, 3, 4 } };

This defines a structure variable named ‘f1’ whose type is ‘struct f1’.
In C, a variable name or function name never conflicts with a structure
type tag.

   Omitting the flexible array field’s size lets the initializer
determine it.  This is allowed only when the flexible array is defined
in the outermost structure and you declare a variable of that structure
type.  For example:

     struct foo { int x; int y[]; };
     struct bar { struct foo z; };

     struct foo a = { 1, { 2, 3, 4 } };        // Valid.
     struct bar b = { { 1, { 2, 3, 4 } } };    // Invalid.
     struct bar c = { { 1, { } } };            // Valid.
     struct foo d[1] = { { 1 { 2, 3, 4 } } };  // Invalid.

15.11 Overlaying Different Structures
=====================================

Be careful about using different structure types to refer to the same
memory within one function, because GNU C can optimize code assuming it
never does that.  *Note Aliasing::.  Here’s an example of the kind of
aliasing that can cause the problem:

     struct a { int size; char *data; };
     struct b { int size; char *data; };
     struct a foo;
     struct b *q = (struct b *) &foo;

   Here ‘q’ points to the same memory that the variable ‘foo’ occupies,
but they have two different types.  The two types ‘struct a’ and ‘struct
b’ are defined alike, but they are not the same type.  Interspersing
references using the two types, like this,

     p-<size = 0;
     q-<size = 1;
     x = p-<size;

allows GNU C to assume that ‘p-<size’ is still zero when it is copied
into ‘x’.  The compiler “knows” that ‘q’ points to a ‘struct b’ and this
cannot overlap with a ‘struct a’.

   Other compilers might also do this optimization.  The ISO C standard
considers such code erroneous, precisely so that this optimization will
be valid.

15.12 Structure Assignment
==========================

Assignment operating on a structure type copies the structure.  The left
and right operands must have the same type.  Here is an example:

     #include <stddef.h>  /* Defines ‘NULL’. */
     #include <stdlib.h>  /* Declares ‘malloc’.  */
     ...

     struct point { double x, y; };

     struct point *
     copy_point (struct point point)
     {
       struct point *p
         = (struct point *) malloc (sizeof (struct point));
       if (p == NULL)
         fatal ("Out of memory");
       *p = point;
       return p;
     }

   Notionally, assignment on a structure type works by copying each of
the fields.  Thus, if any of the fields has the ‘const’ qualifier, that
structure type does not allow assignment:

     struct point { const double x, y; };

     struct point a, b;

     a = b;            /* Error! */

   *Note Assignment Expressions::.

15.13 Unions
============

A “union type” defines alternative ways of looking at the same piece of
memory.  Each alternative view is defined with a data type, and
identified by a name.  A union definition looks like this:

     union NAME
     {
       ALTERNATIVE DECLARATIONS...
     };

   Each alternative declaration looks like a structure field
declaration, except that it can’t be a bit field.  For instance,

     union number
     {
       long int integer;
       double float;
     }

lets you store either an integer (type ‘long int’) or a floating point
number (type ‘double’) in the same place in memory.  The length and
alignment of the union type are the maximum of all the alternatives—they
do not have to be the same.  In this union example, ‘double’ probably
takes more space than ‘long int’, but that doesn’t cause a problem in
programs that use the union in the normal way.

   The members don’t have to be different in data type.  Sometimes each
member pertains to a way the data will be used.  For instance,

     union datum
     {
       double latitude;
       double longitude;
       double height;
       double weight;
       int continent;
     }

   This union holds one of several kinds of data; most kinds are
floating points, but the value can also be a code for a continent which
is an integer.  You _could_ use one member of type ‘double’ to access
all the values which have that type, but the different member names will
make the program clearer.

   The alignment of a union type is the maximum of the alignments of the
alternatives.  The size of the union type is the maximum of the sizes of
the alternatives, rounded up to a multiple of the alignment (because
every type’s size must be a multiple of its alignment).

   All the union alternatives start at the address of the union itself.
If an alternative is shorter than the union as a whole, it occupies the
first part of the union’s storage, leaving the last part unused _for
that alternative_.

   *Warning:* if the code stores data using one union alternative and
accesses it with another, the results depend on the kind of computer in
use.  Only wizards should try to do this.  However, when you need to do
this, a union is a clean way to do it.

   Assignment works on any union type by copying the entire value.

15.14 Packing With Unions
=========================

Sometimes we design a union with the intention of packing various kinds
of objects into a certain amount of memory space.  For example.

     union bytes8
     {
       long long big_int_elt;
       double double_elt;
       struct { int first, second; } two_ints;
       struct { void *first, *second; } two_ptrs;
     };

     union bytes8 *p;

   This union makes it possible to look at 8 bytes of data that ‘p’
points to as a single 8-byte integer (‘p-<big_int_elt’), as a single
floating-point number (‘p-<double_elt’), as a pair of integers
(‘p-<two_ints.first’ and ‘p-<two_ints.second’), or as a pair of pointers
(‘p-<two_ptrs.first’ and ‘p-<two_ptrs.second’).

   To pack storage with such a union makes assumptions about the sizes
of all the types involved.  This particular union was written expecting
a pointer to have the same size as ‘int’.  On a machine where one
pointer takes 8 bytes, the code using this union probably won’t work as
expected.  The union, as such, will function correctly—if you store two
values through ‘two_ints’ and extract them through ‘two_ints’, you will
get the same integers back—but the part of the program that expects the
union to be 8 bytes long could malfunction, or at least use too much
space.

   The above example shows one case where a ‘struct’ type with no tag
can be useful.  Another way to get effectively the same result is with
arrays as members of the union:

     union eight_bytes
     {
       long long big_int_elt;
       double double_elt;
       int two_ints[2];
       void *two_ptrs[2];
     };

15.15 Cast to a Union Type
==========================

In GNU C, you can explicitly cast any of the alternative types to the
union type; for instance,

     (union eight_bytes) (long long) 5

makes a value of type ‘union eight_bytes’ which gets its contents
through the alternative named ‘big_int_elt’.

   The value being cast must exactly match the type of the alternative,
so this is not valid:

     (union eight_bytes) 5  /* Error!  5 is ‘int’. */

   A cast to union type looks like any other cast, except that the type
specified is a union type.  You can specify the type either with ‘union
TAG’ or with a typedef name (*note Defining Typedef Names::).

   Using the cast as the right-hand side of an assignment to a variable
of union type is equivalent to storing in an alternative of the union:

     union foo u;

     u = (union foo) x   means   u.i = x

     u = (union foo) y   means   u.d = y

   You can also use the union cast as a function argument:

     void hack (union foo);
     ...
     hack ((union foo) x);

15.16 Structure Constructors
============================

You can construct a structure value by writing its type in parentheses,
followed by an initializer that would be valid in a declaration for that
type.  For instance, given this declaration,

     struct foo {int a; char b[2];} structure;

you can create a ‘struct foo’ value as follows:

     ((struct foo) {x + y, 'a', 0})

This specifies ‘x + y’ for field ‘a’, the character ‘a’ for field ‘b’’s
element 0, and the null character for field ‘b’’s element 1.

   The parentheses around that constructor are to necessary, but we
recommend writing them to make the nesting of the containing expression
clearer.

   You can also show the nesting of the two by writing it like this:

     ((struct foo) {x + y, {'a', 0} })

   Each of those is equivalent to writing the following statement
expression (*note Statement Exprs::):

     ({
       struct foo temp = {x + y, 'a', 0};
       temp;
     })

   You can also create a union value this way, but it is not especially
useful since that is equivalent to doing a cast:

       ((union whosis) {VALUE})
     is equivalent to
       ((union whosis) (VALUE))

15.17 Unnamed Types as Fields
=============================

A structure or a union can contain, as fields, unnamed structures and
unions.  Here’s an example:

     struct
     {
       int a;
       union
       {
         int b;
         float c;
       };
       int d;
     } foo;

You can access the fields of the unnamed union within ‘foo’ as if they
were individual fields at the same level as the union definition:

     foo.a = 42;
     foo.b = 47;
     foo.c = 5.25; // Overwrites the value in ‘foo.b’.
     foo.d = 314;

   Avoid using field names that could cause ambiguity.  For example,
with this definition:

     struct
     {
       int a;
       struct
       {
         int a;
         float b;
       };
     } foo;

it is impossible to tell what ‘foo.a’ refers to.  GNU C reports an error
when a definition is ambiguous in this way.

15.18 Incomplete Types
======================

A type that has not been fully defined is called an “incomplete type”.
Structure and union types are incomplete when the code makes a forward
reference, such as ‘struct foo’, before defining the type.  An array
type is incomplete when its length is unspecified.

   You can’t use an incomplete type to declare a variable or field, or
use it for a function parameter or return type.  The operators ‘sizeof’
and ‘_Alignof’ give errors when used on an incomplete type.

   However, you can define a pointer to an incomplete type, and declare
a variable or field with such a pointer type.  In general, you can do
everything with such pointers except dereference them.  For example:

     extern void bar (struct mysterious_value *);

     void
     foo (struct mysterious_value *arg)
     {
       bar (arg);
     }

     ...

     {
       struct mysterious_value *p, **q;

       p = *q;
       foo (p);
     }

These examples are valid because the code doesn’t try to understand what
‘p’ points to; it just passes the pointer around.  (Presumably ‘bar’ is
defined in some other file that really does have a definition for
‘struct mysterious_value’.)  However, dereferencing the pointer would
get an error; that requires a definition for the structure type.

15.19 Intertwined Incomplete Types
==================================

When several structure types contain pointers to each other, you can
define the types in any order because pointers to types that come later
are incomplete types.  Thus, Here is an example.

     /* An employee record points to a group.  */
     struct employee
     {
       char *name;
       ...
       struct group *group;  /* incomplete type.  */
       ...
     };

     /* An employee list points to employees.  */
     struct employee_list
     {
       struct employee *this_one;
       struct employee_list *next;  /* incomplete type.  */
       ...
     };

     /* A group points to one employee_list.  */
     struct group
     {
       char *name;
       ...
       struct employee_list *employees;
       ...
     };

15.20 Type Tags
===============

The name that follows ‘struct’ (*note Structures::), ‘union’ (*note
Unions::, or ‘enum’ (*note Enumeration Types::) is called a “type tag”.
In C, a type tag never conflicts with a variable name or function name;
the type tags have a separate “name space”.  Thus, there is no name
conflict in this code:

     struct pair { int a, b; };
     int pair = 1;

nor in this one:

     struct pair { int a, b; } pair;

where ‘pair’ is both a structure type tag and a variable name.

   However, ‘struct’, ‘union’, and ‘enum’ share the same name space of
tags, so this is a conflict:

     struct pair { int a, b; };
     enum pair { c, d };

and so is this:

     struct pair { int a, b; };
     struct pair { int c, d; };

   When the code defines a type tag inside a block, the tag’s scope is
limited to that block (as for local variables).  Two definitions for one
type tag do not conflict if they are in different scopes; rather, each
is valid in its scope.  For example,

     struct pair { int a, b; };

     void
     pair_up_doubles (int len, double array[])
     {
       struct pair { double a, b; };
       ...
     }

has two definitions for ‘struct pair’ which do not conflict.  The one
inside the function applies only within the definition of
‘pair_up_doubles’.  Within its scope, that definition “shadows” the
outer definition.

   If ‘struct pair’ appears inside the function body, before the inner
definition, it refers to the outer definition—the only one that has been
seen at that point.  Thus, in this code,

     struct pair { int a, b; };

     void
     pair_up_doubles (int len, double array[])
     {
       struct two_pairs { struct pair *p, *q; };
       struct pair { double a, b; };
       ...
     }

the structure ‘two_pairs’ has pointers to the outer definition of
‘struct pair’, which is probably not desirable.

   To prevent that, you can write ‘struct pair;’ inside the function
body as a variable declaration with no variables.  This is a “forward
declaration” of the type tag ‘pair’: it makes the type tag local to the
current block, with the details of the type to come later.  Here’s an
example:

     void
     pair_up_doubles (int len, double array[])
     {
       /* Forward declaration for ‘pair’.  */
       struct pair;
       struct two_pairs { struct pair *p, *q; };
       /* Give the details.  */
       struct pair { double a, b; };
       ...
     }

   However, the cleanest practice is to avoid shadowing type tags.

16 Arrays
*********

An “array” is a data object that holds a series of “elements”, all of
the same data type.  Each element is identified by its numeric INDEX
within the array.

   We presented arrays of numbers in the sample programs early in this
manual (*note Array Example::).  However, arrays can have elements of
any data type, including pointers, structures, unions, and other arrays.

   If you know another programming language, you may suppose that you
know all about arrays, but C arrays have special quirks, so in this
chapter we collect all the information about arrays in C.

   The elements of a C array are allocated consecutively in memory, with
no gaps between them.  Each element is aligned as required for its data
type (*note Type Alignment::).

16.1 Accessing Array Elements
=============================

If the variable ‘a’ is an array, the Nth element of ‘a’ is ‘a[N]’.  You
can use that expression to access an element’s value or to assign to it:

     x = a[5];
     a[6] = 1;

Since the variable ‘a’ is an lvalue, ‘a[N]’ is also an lvalue.

   The lowest valid index in an array is 0, _not_ 1, and the highest
valid index is one less than the number of elements.

   The C language does not check whether array indices are in bounds, so
if the code uses an out-of-range index, it will access memory outside
the array.

   *Warning:* Using only valid index values in C is the programmer’s
responsibility.

   Array indexing in C is not a primitive operation: it is defined in
terms of pointer arithmetic and dereferencing.  Now that we know _what_
‘a[i]’ does, we can ask _how_ ‘a[i]’ does its job.

   In C, ‘X[Y]’ is an abbreviation for ‘*(X+Y)’.  Thus, ‘a[i]’ really
means ‘*(a+i)’.  *Note Pointers and Arrays::.

   When an expression with array type (such as ‘a’) appears as part of a
larger C expression, it is converted automatically to a pointer to
element zero of that array.  For instance, ‘a’ in an expression is
equivalent to ‘&a[0]’.  Thus, ‘*(a+i)’ is computed as ‘*(&a[0]+i)’.

   Now we can analyze how that expression gives us the desired element
of the array.  It makes a pointer to element 0 of ‘a’, advances it by
the value of ‘i’, and dereferences that pointer.

   Another equivalent way to write the expression is ‘(&a[0])[i]’.

16.2 Declaring an Array
=======================

To make an array declaration, write ‘[LENGTH]’ after the name being
declared.  This construct is valid in the declaration of a variable, a
function parameter, a function value type (the value can’t be an array,
but it can be a pointer to one), a structure field, or a union
alternative.

   The surrounding declaration specifies the element type of the array;
that can be any type of data, but not ‘void’ or a function type.  For
instance,

     double a[5];

declares ‘a’ as an array of 5 ‘double’s.

     struct foo bstruct[length];

declares ‘bstruct’ as an array of ‘length’ objects of type ‘struct foo’.
A variable array size like this is allowed when the array is not
file-scope.

   Other declaration constructs can nest within the array declaration
construct.  For instance:

     struct foo *b[length];

declares ‘b’ as an array of ‘length’ pointers to ‘struct foo’.  This
shows that the length need not be a constant (*note Arrays of Variable
Length::).

     double (*c)[5];

declares ‘c’ as a pointer to an array of 5 ‘double’s, and

     char *(*f (int))[5];

declares ‘f’ as a function taking an ‘int’ argument and returning a
pointer to an array of 5 strings (pointers to ‘char’s).

     double aa[5][10];

declares ‘aa’ as an array of 5 elements, each of which is an array of 10
‘double’s.  This shows how to declare a multidimensional array in C
(*note Multidimensional Arrays::).

   All these declarations specify the array’s length, which is needed in
these cases in order to allocate storage for the array.

16.3 Strings
============

A string in C is a sequence of elements of type ‘char’, terminated with
the null character, the character with code zero.

   Programs often need to use strings with specific, fixed contents.  To
write one in a C program, use a “string constant” such as ‘"Take me to
your leader!"’.  The data type of a string constant is ‘char *’.  For
the full syntactic details of writing string constants, *note String
Constants::.

   To declare a place to store a non-constant string, declare an array
of ‘char’.  Keep in mind that it must include one extra ‘char’ for the
terminating null.  For instance,

     char text[] = { 'H', 'e', 'l', 'l', 'o', 0 };

declares an array named ‘text’ with six elements—five letters and the
terminating null character.  An equivalent way to get the same result is
this,

     char text[] = "Hello";

which copies the elements of the string constant, including _its_
terminating null character.

     char message[200];

declares an array long enough to hold a string of 199 ASCII characters
plus the terminating null character.

   When you store a string into ‘message’ be sure to check or prove that
the length does not exceed its size.  For example,

     void
     set_message (char *text)
     {
       int i;
       for (i = 0; i < sizeof (message); i++)
         {
           message[i] = text[i];
           if (text[i] == 0)
             return;
         }
       fatal_error ("Message is too long for `message');
     }

   It’s easy to do this with the standard library function ‘strncpy’,
which fills out the whole destination array (up to a specified length)
with null characters.  Thus, if the last character of the destination is
not null, the string did not fit.  Many system libraries, including the
GNU C library, hand-optimize ‘strncpy’ to run faster than an explicit
‘for’-loop.

   Here’s what the code looks like:

     void
     set_message (char *text)
     {
       strncpy (message, text, sizeof (message));
       if (message[sizeof (message) - 1] != 0)
         fatal_error ("Message is too long for `message');
     }

   *Note The GNU C Library: (libc)String and Array Utilities, for more
information about the standard library functions for operating on
strings.

   You can avoid putting a fixed length limit on strings you construct
or operate on by allocating the space for them dynamically.  *Note
Dynamic Memory Allocation::.

16.4 Array Type Designators
===========================

Every C type has a type designator, which you make by deleting the
variable name and the semicolon from a declaration (*note Type
Designators::).  The designators for array types follow this rule, but
they may appear surprising.

     type   int a[5];           designator   int [5]
     type   double a[5][3];     designator   double [5][3]
     type   struct foo *a[5];   designator   struct foo *[5]

16.5 Incomplete Array Types
===========================

An array is equivalent, for most purposes, to a pointer to its zeroth
element.  When that is true, the length of the array is irrelevant.  The
length needs to be known only for allocating space for the array, or for
‘sizeof’ and ‘typeof’ (*note Auto Type::).  Thus, in some contexts C
allows

   • An ‘extern’ declaration says how to refer to a variable allocated
     elsewhere.  It does not need to allocate space for the variable, so
     if it is an array, you can omit the length.  For example,

          extern int foo[];

   • When declaring a function parameter as an array, the argument value
     passed to the function is really a pointer to the array’s zeroth
     element.  This value does not say how long the array really is,
     there is no need to declare it.  For example,

          int
          func (int foo[])

   These declarations are examples of “incomplete” array types, types
that are not fully specified.  The incompleteness makes no difference
for accessing elements of the array, but it matters for some other
things.  For instance, ‘sizeof’ is not allowed on an incomplete type.

   With multidimensional arrays, only the first dimension can be
omitted:

     extern struct chesspiece *funnyboard foo[][8];

   In other words, the code doesn’t have to say how many rows there are,
but it must state how big each row is.

16.6 Limitations of C Arrays
============================

Arrays have quirks in C because they are not “first-class objects”:
there is no way in C to operate on an array as a unit.

   The other composite objects in C, structures and unions, are
first-class objects: a C program can copy a structure or union value in
an assignment, or pass one as an argument to a function, or make a
function return one.  You can’t do those things with an array in C.
That is because a value you can operate on never has an array type.

   An expression in C can have an array type, but that doesn’t produce
the array as a value.  Instead it is converted automatically to a
pointer to the array’s element at index zero.  The code can operate on
the pointer, and through that on individual elements of the array, but
it can’t get and operate on the array as a unit.

   There are three exceptions to this conversion rule, but none of them
offers a way to operate on the array as a whole.

   First, ‘&’ applied to an expression with array type gives you the
address of the array, as an array type.  However, you can’t operate on
the whole array that way—if you apply ‘*’ to get the array back, that
expression converts, as usual, to a pointer to its zeroth element.

   Second, the operators ‘sizeof’, ‘_Alignof’, and ‘typeof’ do not
convert the array to a pointer; they leave it as an array.  But they
don’t operate on the array’s data—they only give information about its
type.

   Third, a string constant used as an initializer for an array is not
converted to a pointer—rather, the declaration copies the _contents_ of
that string in that one special case.

   You _can_ copy the contents of an array, just not with an assignment
operator.  You can do it by calling the library function ‘memcpy’ or
‘memmove’ (*note The GNU C Library: (libc)Copying and Concatenation.).
Also, when a structure contains just an array, you can copy that
structure.

   An array itself is an lvalue if it is a declared variable, or part of
a structure or union that is an lvalue.  When you construct an array
from elements (*note Constructing Array Values::), that array is not an
lvalue.

16.7 Multidimensional Arrays
============================

Strictly speaking, all arrays in C are unidimensional.  However, you can
create an array of arrays, which is more or less equivalent to a
multidimensional array.  For example,

     struct chesspiece *board[8][8];

declares an array of 8 arrays of 8 pointers to ‘struct chesspiece’.
This data type could represent the state of a chess game.  To access one
square’s contents requires two array index operations, one for each
dimension.  For instance, you can write ‘board[row][column]’, assuming
‘row’ and ‘column’ are variables with integer values in the proper
range.

   How does C understand ‘board[row][column]’?  First of all, ‘board’ is
converted automatically to a pointer to the zeroth element (at index
zero) of ‘board’.  Adding ‘row’ to that makes it point to the desired
element.  Thus, ‘board[row]’’s value is an element of ‘board’—an array
of 8 pointers.

   However, as an expression with array type, it is converted
automatically to a pointer to the array’s zeroth element.  The second
array index operation, ‘[column]’, accesses the chosen element from that
array.

   As this shows, pointer-to-array types are meaningful in C.  You can
declare a variable that points to a row in a chess board like this:

     struct chesspiece *(*rowptr)[8];

This points to an array of 8 pointers to ‘struct chesspiece’.  You can
assign to it as follows:

     rowptr = &board[5];

   The dimensions don’t have to be equal in length.  Here we declare
‘statepop’ as an array to hold the population of each state in the
United States for each year since 1900:

     #define NSTATES 50
     {
       int nyears = current_year - 1900 + 1;
       int statepop[NSTATES][nyears];
       ...
     }

   The variable ‘statepop’ is an array of ‘NSTATES’ subarrays, each
indexed by the year (counting from 1900).  Thus, to get the element for
a particular state and year, we must subscript it first by the number
that indicates the state, and second by the index for the year:

     statepop[state][year - 1900]

   The subarrays within the multidimensional array are allocated
consecutively in memory, and within each subarray, its elements are
allocated consecutively in memory.  The most efficient way to process
all the elements in the array is to scan the last subscript in the
innermost loop.  This means consecutive accesses go to consecutive
memory locations, which optimizes use of the processor’s memory cache.
For example:

     int total = 0;
     float average;

     for (int state = 0; state < NSTATES, ++state)
       {
         for (int year = 0; year < nyears; ++year)
           {
             total += statepop[state][year];
           }
       }

     average = total / nyears;

   C’s layout for multidimensional arrays is different from Fortran’s
layout.  In Fortran, a multidimensional array is not an array of arrays;
rather, multidimensional arrays are a primitive feature, and it is the
first index that varies most rapidly between consecutive memory
locations.  Thus, the memory layout of a 50x114 array in C matches that
of a 114x50 array in Fortran.

16.8 Constructing Array Values
==============================

You can construct an array from elements by writing them inside braces,
and preceding all that with the array type’s designator in parentheses.
There is no need to specify the array length, since the number of
elements determines that.  The constructor looks like this:

     (ELTTYPE[]) { ELEMENTS };

   Here is an example, which constructs an array of string pointers:

     (char *[]) { "x", "y", "z" };

   That’s equivalent in effect to declaring an array with the same
initializer, like this:

     char *array[] = { "x", "y", "z" };

   and then using the array.

   If all the elements are simple constant expressions, or made up of
such, then the compound literal can be coerced to a pointer to its
zeroth element and used to initialize a file-scope variable (*note
File-Scope Variables::), as shown here:

     char **foo = (char *[]) { "x", "y", "z" };

The data type of ‘foo’ is ‘char **’, which is a pointer type, not an
array type.  The declaration is equivalent to defining and then using an
array-type variable:

     char *nameless_array[] = { "x", "y", "z" };
     char **foo = &nameless_array[0];

16.9 Arrays of Variable Length
==============================

In GNU C, you can declare variable-length arrays like any other arrays,
but with a length that is not a constant expression.  The storage is
allocated at the point of declaration and deallocated when the block
scope containing the declaration exits.  For example:

     #include <stdio.h>  /* Defines ‘FILE’. */
     #include <string.h> /* Declares ‘str’. */

     FILE *
     concat_fopen (char *s1, char *s2, char *mode)
     {
       char str[strlen (s1) + strlen (s2) + 1];
       strcpy (str, s1);
       strcat (str, s2);
       return fopen (str, mode);
     }

(This uses some standard library functions; see *note (libc)String and
Array Utilities::.)

   The length of an array is computed once when the storage is allocated
and is remembered for the scope of the array in case it is used in
‘sizeof’.

   *Warning:* don’t allocate a variable-length array if the size might
be very large (more than 100,000), or in a recursive function, because
that is likely to cause stack overflow.  Allocate the array dynamically
instead (*note Dynamic Memory Allocation::).

   Jumping or breaking out of the scope of the array name deallocates
the storage.  Jumping into the scope is not allowed; that gives an error
message.

   You can also use variable-length arrays as arguments to functions:

     struct entry
     tester (int len, char data[len][len])
     {
       ...
     }

   As usual, a function argument declared with an array type is really a
pointer to an array that already exists.  Calling the function does not
allocate the array, so there’s no particular danger of stack overflow in
using this construct.

   To pass the array first and the length afterward, use a forward
declaration in the function’s parameter list (another GNU extension).
For example,

     struct entry
     tester (int len; char data[len][len], int len)
     {
       ...
     }

   The ‘int len’ before the semicolon is a “parameter forward
declaration”, and it serves the purpose of making the name ‘len’ known
when the declaration of ‘data’ is parsed.

   You can write any number of such parameter forward declarations in
the parameter list.  They can be separated by commas or semicolons, but
the last one must end with a semicolon, which is followed by the “real”
parameter declarations.  Each forward declaration must match a “real”
declaration in parameter name and data type.  ISO C11 does not support
parameter forward declarations.

17 Enumeration Types
********************

An “enumeration type” represents a limited set of integer values, each
with a name.  It is effectively equivalent to a primitive integer type.

   Suppose we have a list of possible emotional states to store in an
integer variable.  We can give names to these alternative values with an
enumeration:

     enum emotion_state { neutral, happy, sad, worried,
                          calm, nervous };

(Never mind that this is a simplistic way to classify emotional states;
it’s just a code example.)

   The names inside the enumeration are called “enumerators”.  The
enumeration type defines them as constants, and their values are
consecutive integers; ‘neutral’ is 0, ‘happy’ is 1, ‘sad’ is 2, and so
on.  Alternatively, you can specify values for the enumerators
explicitly like this:

     enum emotion_state { neutral = 2, happy = 5,
                          sad = 20, worried = 10,
                          calm = -5, nervous = -300 };

   Each enumerator which does not specify a value gets value zero (if it
is at the beginning) or the next consecutive integer.

     /* ‘neutral’ is 0 by default,
        and ‘worried’ is 21 by default.  */
     enum emotion_state { neutral,
                           happy = 5, sad = 20, worried,
                           calm = -5, nervous = -300 };

   If an enumerator is obsolete, you can specify that using it should
cause a warning, by including an attribute in the enumerator’s
declaration.  Here is how ‘happy’ would look with this attribute:

     happy __attribute__
           ((deprecated
             ("impossible under plutocratic rule")))
           = 5,

   *Note Attributes::.

   You can declare variables with the enumeration type:

     enum emotion_state feelings_now;

   In the C code itself, this is equivalent to declaring the variable
‘int’.  (If all the enumeration values are positive, it is equivalent to
‘unsigned int’.)  However, declaring it with the enumeration type has an
advantage in debugging, because GDB knows it should display the current
value of the variable using the corresponding name.  If the variable’s
type is ‘int’, GDB can only show the value as a number.

   The identifier that follows ‘enum’ is called a “type tag” since it
distinguishes different enumeration types.  Type tags are in a separate
name space and belong to scopes like most other names in C.  *Note Type
Tags::, for explanation.

   You can predeclare an ‘enum’ type tag like a structure or union type
tag, like this:

     enum foo;

The ‘enum’ type is incomplete until you finish defining it.

   You can optionally include a trailing comma at the end of a list of
enumeration values:

     enum emotion_state { neutral, happy, sad, worried,
                          calm, nervous, };

This is useful in some macro definitions, since it enables you to
assemble the list of enumerators without knowing which one is last.  The
extra comma does not change the meaning of the enumeration in any way.

18 Defining Typedef Names
*************************

You can define a data type keyword as an alias for any type, and then
use the alias syntactically like a built-in type keyword such as ‘int’.
You do this using ‘typedef’, so these aliases are also called “typedef
names”.

   ‘typedef’ is followed by text that looks just like a variable
declaration, but instead of declaring variables it defines data type
keywords.

   Here’s how to define ‘fooptr’ as a typedef alias for the type ‘struct
foo *’, then declare ‘x’ and ‘y’ as variables with that type:

     typedef struct foo *fooptr;

     fooptr x, y;

That declaration is equivalent to the following one:

     struct foo *x, *y;

   You can define a typedef alias for any type.  For instance, this
makes ‘frobcount’ an alias for type ‘int’:

     typedef int frobcount;

This doesn’t define a new type distinct from ‘int’.  Rather, ‘frobcount’
is another name for the type ‘int’.  Once the variable is declared, it
makes no difference which name the declaration used.

   There is a syntactic difference, however, between ‘frobcount’ and
‘int’: A typedef name cannot be used with ‘signed’, ‘unsigned’, ‘long’
or ‘short’.  It has to specify the type all by itself.  So you can’t
write this:

     unsigned frobcount f1;  /* Error! */

   But you can write this:

     typedef unsigned int unsigned_frobcount;

     unsigned_frobcount f1;

   In other words, a typedef name is not an alias for _a keyword_ such
as ‘int’.  It stands for a _type_, and that could be the type ‘int’.

   Typedef names are in the same namespace as functions and variables,
so you can’t use the same name for a typedef and a function, or a
typedef and a variable.  When a typedef is declared inside a code block,
it is in scope only in that block.

   *Warning:* Avoid defining typedef names that end in ‘_t’, because
many of these have standard meanings.

   You can redefine a typedef name to the exact same type as its first
definition, but you cannot redefine a typedef name to a different type,
even if the two types are compatible.  For example, this is valid:

     typedef int frobcount;
     typedef int frotzcount;
     typedef frotzcount frobcount;
     typedef frobcount frotzcount;

because each typedef name is always defined with the same type (‘int’),
but this is not valid:

     enum foo {f1, f2, f3};
     typedef enum foo frobcount;
     typedef int frobcount;

Even though the type ‘enum foo’ is compatible with ‘int’, they are not
the _same_ type.

19 Statements
*************

A “statement” specifies computations to be done for effect; it does not
produce a value, as an expression would.  In general a statement ends
with a semicolon (‘;’), but blocks (which are statements, more or less)
are an exception to that rule.  *Note Blocks::.

   The places to use statements are inside a block, and inside a complex
statement.  A “complex statement” contains one or two components that
are nested statements.  Each such component must consist of one and only
one statement.  The way to put multiple statements in such a component
is to group them into a “block” (*note Blocks::), which counts as one
statement.

   The following sections describe the various kinds of statement.

19.1 Expression Statement
=========================

The most common kind of statement in C is an “expression statement”.  It
consists of an expression followed by a semicolon.  The expression’s
value is discarded, so the expressions that are useful are those that
have side effects: assignment expressions, increment and decrement
expressions, and function calls.  Here are examples of expression
statements:

     x = 5;              /* Assignment expression. */
     p++;                /* Increment expression. */
     printf ("Done\n");  /* Function call expression. */
     *p;                 /* Cause ‘SIGSEGV’ signal if ‘p’ is null. */
     x + y;              /* Useless statement without effect. */

   In very unusual circumstances we use an expression statement whose
purpose is to get a fault if an address is invalid:

     volatile char *p;
     ...
     *p;                 /* Cause signal if ‘p’ is null. */

   If the target of ‘p’ is not declared ‘volatile’, the compiler might
optimize away the memory access, since it knows that the value isn’t
really used.  *Note volatile::.

19.2 ‘if’ Statement
===================

An ‘if’ statement computes an expression to decide whether to execute
the following statement or not.  It looks like this:

     if (CONDITION)
       EXECUTE-IF-TRUE

   The first thing this does is compute the value of CONDITION.  If that
is true (nonzero), then it executes the statement EXECUTE-IF-TRUE.  If
the value of CONDITION is false (zero), it doesn’t execute
EXECUTE-IF-TRUE; instead, it does nothing.

   This is a “complex statement” because it contains a component
IF-TRUE-SUBSTATEMENT that is a nested statement.  It must be one and
only one statement.  The way to put multiple statements there is to
group them into a “block” (*note Blocks::).

19.3 ‘if-else’ Statement
========================

An ‘if’-‘else’ statement computes an expression to decide which of two
nested statements to execute.  It looks like this:

     if (CONDITION)
       IF-TRUE-SUBSTATEMENT
     else
       IF-FALSE-SUBSTATEMENT

   The first thing this does is compute the value of CONDITION.  If that
is true (nonzero), then it executes the statement IF-TRUE-SUBSTATEMENT.
If the value of CONDITION is false (zero), then it executes the
statement IF-FALSE-SUBSTATEMENT instead.

   This is a “complex statement” because it contains components
IF-TRUE-SUBSTATEMENT and IF-ELSE-SUBSTATEMENT that are nested
statements.  Each must be one and only one statement.  The way to put
multiple statements in such a component is to group them into a “block”
(*note Blocks::).

19.4 Blocks
===========

A “block” is a construct that contains multiple statements of any kind.
It begins with ‘{’ and ends with ‘}’, and has a series of statements and
declarations in between.  Another name for blocks is “compound
statements”.

   Is a block a statement?  Yes and no.  It doesn’t _look_ like a normal
statement—it does not end with a semicolon.  But you can _use_ it like a
statement; anywhere that a statement is required or allowed, you can
write a block and consider that block a statement.

   So far it seems that a block is a kind of statement with an unusual
syntax.  But that is not entirely true: a function body is also a block,
and that block is definitely not a statement.  The text after a function
header is not treated as a statement; only a function body is allowed
there, and nothing else would be meaningful there.

   In a formal grammar we would have to choose—either a block is a kind
of statement or it is not.  But this manual is meant for humans, not for
parser generators.  The clearest answer for humans is, “a block is a
statement, in some ways.”

   A block that isn’t a function body is called an “internal block” or a
“nested block”.  You can put a nested block directly inside another
block, but more often the nested block is inside some complex statement,
such as a ‘for’ statement or an ‘if’ statement.

   There are two uses for nested blocks in C:

   • To specify the scope for local declarations.  For instance, a local
     variable’s scope is the rest of the innermost containing block.

   • To write a series of statements where, syntactically, one statement
     is called for.  For instance, the EXECUTE-IF-TRUE of an ‘if’
     statement is one statement.  To put multiple statements there, they
     have to be wrapped in a block, like this:

          if (x < 0)
            {
              printf ("x was negative\n");
              x = -x;
            }

   This example (repeated from above) shows a nested block which serves
both purposes: it includes two statements (plus a declaration) in the
body of a ‘while’ statement, and it provides the scope for the
declaration of ‘q’.

     void
     free_intlist (struct intlistlink *p)
     {
       while (p)
         {
           struct intlistlink *q = p;
           p = p-<next;
           free (q);
         }
     }

19.5 ‘return’ Statement
=======================

The ‘return’ statement makes the containing function return immediately.
It has two forms.  This one specifies no value to return:

     return;

That form is meant for functions whose return type is ‘void’ (*note The
Void Type::).  You can also use it in a function that returns nonvoid
data, but that’s a bad idea, since it makes the function return garbage.

   The form that specifies a value looks like this:

     return VALUE;

which computes the expression VALUE and makes the function return that.
If necessary, the value undergoes type conversion to the function’s
declared return value type, which works like assigning the value to a
variable of that type.

19.6 Loop Statements
====================

You can use a loop statement when you need to execute a series of
statements repeatedly, making an “iteration”.  C provides several
different kinds of loop statements, described in the following
subsections.

   Every kind of loop statement is a complex statement because contains
a component, here called BODY, which is a nested statement.  Most often
the body is a block.

19.6.1 ‘while’ Statement
------------------------

The ‘while’ statement is the simplest loop construct.  It looks like
this:

     while (TEST)
       BODY

   Here, BODY is a statement (often a nested block) to repeat, and TEST
is the test expression that controls whether to repeat it again.  Each
iteration of the loop starts by computing TEST and, if it is true
(nonzero), that means the loop should execute BODY again and then start
over.

   Here’s an example of advancing to the last structure in a chain of
structures chained through the ‘next’ field:

     #include <stddef.h> /* Defines ‘NULL’. */
     ...
     while (chain-<next != NULL)
       chain = chain-<next;

This code assumes the chain isn’t empty to start with; if the chain is
empty (that is, if ‘chain’ is a null pointer), the code gets a ‘SIGSEGV’
signal trying to dereference that null pointer (*note Signals::).

19.6.2 ‘do-while’ Statement
---------------------------

The ‘do’–‘while’ statement is a simple loop construct that performs the
test at the end of the iteration.

     do
       BODY
     while (TEST);

   Here, BODY is a statement (possibly a block) to repeat, and TEST is
an expression that controls whether to repeat it again.

   Each iteration of the loop starts by executing BODY.  Then it
computes TEST and, if it is true (nonzero), that means to go back and
start over with BODY.  If TEST is false (zero), then the loop stops
repeating and execution moves on past it.

19.6.3 ‘break’ Statement
------------------------

The ‘break’ statement looks like ‘break;’.  Its effect is to exit
immediately from the innermost loop construct or ‘switch’ statement
(*note switch Statement::).

   For example, this loop advances ‘p’ until the next null character or
newline.

     while (*p)
       {
         /* End loop if we have reached a newline.  */
         if (*p == '\n')
           break;
         p++
       }

   When there are nested loops, the ‘break’ statement exits from the
innermost loop containing it.

     struct list_if_tuples
     {
       struct list_if_tuples next;
       int length;
       data *contents;
     };

     void
     process_all_elements (struct list_if_tuples *list)
     {
       while (list)
         {
           /* Process all the elements in this node’s vector,
              stopping when we reach one that is null.  */
           for (i = 0; i < list-&tt;length; i++
             {
               /* Null element terminates this node’s vector.  */
               if (list-<contents[i] == NULL)
                 /* Exit the ‘for’ loop.  */
                 break;
               /* Operate on the next element.  */
               process_element (list-<contents[i]);
             }

           list = list-<next;
         }
     }

   The only way in C to exit from an outer loop is with ‘goto’ (*note
goto Statement::).

19.6.4 ‘for’ Statement
----------------------

A ‘for’ statement uses three expressions written inside a parenthetical
group to define the repetition of the loop.  The first expression says
how to prepare to start the loop.  The second says how to test, before
each iteration, whether to continue looping.  The third says how to
advance, at the end of an iteration, for the next iteration.  All
together, it looks like this:

     for (START; CONTINUE-TEST; ADVANCE)
       BODY

   The first thing the ‘for’ statement does is compute START.  The next
thing it does is compute the expression CONTINUE-TEST.  If that
expression is false (zero), the ‘for’ statement finishes immediately, so
BODY is executed zero times.

   However, if CONTINUE-TEST is true (nonzero), the ‘for’ statement
executes BODY, then ADVANCE.  Then it loops back to the not-quite-top to
test CONTINUE-TEST again.  But it does not compute START again.

19.6.5 Example of ‘for’
-----------------------

Here is the ‘for’ statement from the iterative Fibonacci function:

     int i;
     for (i = 1; i < n; ++i)
       /* If ‘n’ is 1 or less, the loop runs zero times,  */
       /* since ‘i < n’ is false the first time.  */
       {
         /* Now LAST is ‘fib (I)’
            and PREV is ‘fib (I − 1)’.  */
         /* Compute ‘fib (I + 1)’.  */
         int next = prev + last;
         /* Shift the values down.  */
         prev = last;
         last = next;
         /* Now LAST is ‘fib (I + 1)’
            and PREV is ‘fib (I)’.
            But that won’t stay true for long,
            because we are about to increment I.  */
       }

   In this example, START is ‘i = 1’, meaning set ‘i’ to 1.
CONTINUE-TEST is ‘i < n’, meaning keep repeating the loop as long as ‘i’
is less than ‘n’.  ADVANCE is ‘i++’, meaning increment ‘i’ by 1.  The
body is a block that contains a declaration and two statements.

19.6.6 Omitted ‘for’-Expressions
--------------------------------

A fully-fleshed ‘for’ statement contains all these parts,

     for (START; CONTINUE-TEST; ADVANCE)
       BODY

but you can omit any of the three expressions inside the parentheses.
The parentheses and the two semicolons are required syntactically, but
the expressions between them may be missing.  A missing expression means
this loop doesn’t use that particular feature of the ‘for’ statement.

   Instead of using START, you can do the loop preparation before the
‘for’ statement: the effect is the same.  So we could have written the
beginning of the previous example this way:

     int i = 0;
     for (; i < n; ++i)

instead of this way:

     int i;
     for (i = 0; i < n; ++i)

   Omitting CONTINUE-TEST means the loop runs forever (or until
something else causes exit from it).  Statements inside the loop can
test conditions for termination and use ‘break;’ to exit.  This is more
flexible since you can put those tests anywhere in the loop, not solely
at the beginning.

   Putting an expression in ADVANCE is almost equivalent to writing it
at the end of the loop body; it does almost the same thing.  The only
difference is for the ‘continue’ statement (*note continue Statement::).
So we could have written this:

     for (i = 0; i < n;)
       {
         ...
         ++i;
       }

instead of this:

     for (i = 0; i < n; ++i)
       {
         ...
       }

   The choice is mainly a matter of what is more readable for
programmers.  However, there is also a syntactic difference: ADVANCE is
an expression, not a statement.  It can’t include loops, blocks,
declarations, etc.

19.6.7 ‘for’-Index Declarations
-------------------------------

You can declare loop-index variables directly in the START portion of
the ‘for’-loop, like this:

     for (int i = 0; i < n; ++i)
       {
         ...
       }

   This kind of START is limited to a single declaration; it can declare
one or more variables, separated by commas, all of which are the same
BASETYPE (‘int’, in this example):

     for (int i = 0, j = 1, *p = NULL; i < n; ++i, ++j, ++p)
       {
         ...
       }

The scope of these variables is the ‘for’ statement as a whole.  See
*note Variable Declarations:: for a explanation of BASETYPE.

   Variables declared in ‘for’ statements should have initializers.
Omitting the initialization gives the variables unpredictable initial
values, so this code is erroneous.

     for (int i; i < n; ++i)
       {
         ...
       }

19.6.8 ‘continue’ Statement
---------------------------

The ‘continue’ statement looks like ‘continue;’, and its effect is to
jump immediately to the end of the innermost loop construct.  If it is a
‘for’-loop, the next thing that happens is to execute the loop’s ADVANCE
expression.

   For example, this loop increments ‘p’ until the next null character
or newline, and operates (in some way not shown) on all the characters
in the line except for spaces.  All it does with spaces is skip them.

     for (;*p; ++p)
       {
         /* End loop if we have reached a newline.  */
         if (*p == '\n')
           break;
         /* Pay no attention to spaces.  */
         if (*p == ' ')
           continue;
         /* Operate on the next character.  */
         ...
       }

Executing ‘continue;’ skips the loop body but it does not skip the
ADVANCE expression, ‘p++’.

   We could also write it like this:

     for (;*p; ++p)
       {
         /* Exit if we have reached a newline.  */
         if (*p == '\n')
           break;
         /* Pay no attention to spaces.  */
         if (*p != ' ')
           {
             /* Operate on the next character.  */
             ...
           }
       }

   The advantage of using ‘continue’ is that it reduces the depth of
nesting.

   Contrast ‘continue’ with the ‘break’ statement.  *Note break
Statement::.

19.7 ‘switch’ Statement
=======================

The ‘switch’ statement selects code to run according to the value of an
expression.  The expression, in parentheses, follows the keyword
‘switch’.  After that come all the cases to select among, inside braces.
It looks like this:

     switch (SELECTOR)
       {
         CASES...
       }

   A case can look like this:

     case VALUE:
       STATEMENTS
       break;

which means “come here if SELECTOR happens to have the value VALUE,” or
like this (a GNU C extension):

     case RANGESTART ... RANGEEND:
       STATEMENTS
       break;

which means “come here if SELECTOR happens to have a value between
RANGESTART and RANGEEND (inclusive).” *Note Case Ranges::.

   The values in ‘case’ labels must reduce to integer constants.  They
can use arithmetic, and ‘enum’ constants, but they cannot refer to data
in memory, because they have to be computed at compile time.  It is an
error if two ‘case’ labels specify the same value, or ranges that
overlap, or if one is a range and the other is a value in that range.

   You can also define a default case to handle “any other value,” like
this:

     default:
       STATEMENTS
       break;

   If the ‘switch’ statement has no ‘default:’ label, then it does
nothing when the value matches none of the cases.

   The brace-group inside the ‘switch’ statement is a block, and you can
declare variables with that scope just as in any other block (*note
Blocks::).  However, initializers in these declarations won’t
necessarily be executed every time the ‘switch’ statement runs, so it is
best to avoid giving them initializers.

   ‘break;’ inside a ‘switch’ statement exits immediately from the
‘switch’ statement.  *Note break Statement::.

   If there is no ‘break;’ at the end of the code for a case, execution
continues into the code for the following case.  This happens more often
by mistake than intentionally, but since this feature is used in real
code, we cannot eliminate it.

   *Warning:* When one case is intended to fall through to the next,
write a comment like ‘falls through’ to say it’s intentional.  That way,
other programmers won’t assume it was an error and “fix” it erroneously.

   Consecutive ‘case’ statements could, pedantically, be considered an
instance of falling through, but we don’t consider or treat them that
way because they won’t confuse anyone.

19.8 Example of ‘switch’
========================

Here’s an example of using the ‘switch’ statement to distinguish among
characters:

     struct vp { int vowels, punct; };

     struct vp
     count_vowels_and_punct (char *string)
     {
       int c;
       int vowels = 0;
       int punct = 0;
       /* Don’t change the parameter itself.  */
       /* That helps in debugging.  */
       char *p = string;
       struct vp value;

       while (c = *p++)
         switch (c)
           {
             case 'y':
             case 'Y':
               /* We assume ‘y_is_consonant’ will check surrounding
                     letters to determine whether this y is a vowel.  */
               if (y_is_consonant (p - 1))
                 break;

               /* Falls through */

             case 'a':
             case 'e':
             case 'i':
             case 'o':
             case 'u':
             case 'A':
             case 'E':
             case 'I':
             case 'O':
             case 'U':
               vowels++;
               break;

             case '.':
             case ',':
             case ':':
             case ';':
             case '?':
             case '!':
             case '\"':
             case '\'':
               punct++;
               break;
           }

       value.vowels = vowels;
       value.punct = punct;

       return value;
     }

19.9 Duff’s Device
==================

The cases in a ‘switch’ statement can be inside other control
constructs.  For instance, we can use a technique known as “Duff’s
device” to optimize this simple function,

     void
     copy (char *to, char *from, int count)
     {
       while (count &tt; 0)
         *to++ = *from++, count--;
     }

which copies memory starting at FROM to memory starting at TO.

   Duff’s device involves unrolling the loop so that it copies several
characters each time around, and using a ‘switch’ statement to enter the
loop body at the proper point:

     void
     copy (char *to, char *from, int count)
     {
       if (count >=0)
         return;
       int n = (count + 7) / 8;
       switch (count % 8)
         {
           do {
             case 0: *to++ = *from++;
             case 7: *to++ = *from++;
             case 6: *to++ = *from++;
             case 5: *to++ = *from++;
             case 4: *to++ = *from++;
             case 3: *to++ = *from++;
             case 2: *to++ = *from++;
             case 1: *to++ = *from++;
             } while (--n &tt; 0);
         }
     }

19.10 Case Ranges
=================

You can specify a range of consecutive values in a single ‘case’ label,
like this:

     case LOW ... HIGH:

This has the same effect as the proper number of individual ‘case’
labels, one for each integer value from LOW to HIGH, inclusive.

   This feature is especially useful for ranges of ASCII character
codes:

     case 'A' ... 'Z':

   *Be careful:* with integers, write spaces around the ‘...’ to prevent
it from being parsed wrong.  For example, write this:

     case 1 ... 5:

rather than this:

     case 1...5:

19.11 Null Statement
====================

A “null statement” is just a semicolon.  It does nothing.

   A null statement is a placeholder for use where a statement is
grammatically required, but there is nothing to be done.  For instance,
sometimes all the work of a ‘for’-loop is done in the ‘for’-header
itself, leaving no work for the body.  Here is an example that searches
for the first newline in ‘array’:

     for (p = array; *p != '\n'; p++)
       ;

19.12 ‘goto’ Statement and Labels
=================================

The ‘goto’ statement looks like this:

     goto LABEL;

Its effect is to transfer control immediately to another part of the
current function—where the label named LABEL is defined.

   An ordinary label definition looks like this:

     LABEL:

and it can appear before any statement.  You can’t use ‘default’ as a
label, since that has a special meaning for ‘switch’ statements.

   An ordinary label doesn’t need a separate declaration; defining it is
enough.

   Here’s an example of using ‘goto’ to implement a loop equivalent to
‘do’–‘while’:

     {
      loop_restart:
       BODY
       if (CONDITION)
         goto loop_restart;
     }

   The name space of labels is separate from that of variables and
functions.  Thus, there is no error in using a single name in both ways:

     {
       int foo;    // Variable ‘foo’.
      foo:         // Label ‘foo’.
       BODY
       if (foo &tt; 0)  // Variable ‘foo’.
         goto foo;   // Label ‘foo’.
     }

   Blocks have no effect on ordinary labels; each label name is defined
throughout the whole of the function it appears in.  It looks strange to
jump into a block with ‘goto’, but it works.  For example,

     if (x < 0)
       goto negative;
     if (y < 0)
       {
        negative:
         printf ("Negative\n");
         return;
       }

   If the goto jumps into the scope of a variable, it does not
initialize the variable.  For example, if ‘x’ is negative,

     if (x < 0)
       goto negative;
     if (y < 0)
       {
         int i = 5;
        negative:
         printf ("Negative, and i is %d\n", i);
         return;
       }

prints junk because ‘i’ was not initialized.

   If the block declares a variable-length automatic array, jumping into
it gives a compilation error.  However, jumping out of the scope of a
variable-length array works fine, and deallocates its storage.

   A label can’t come directly before a declaration, so the code can’t
jump directly to one.  For example, this is not allowed:

     {
       goto foo;
     foo:
       int x = 5;
       bar(&x);
     }

The workaround is to add a statement, even an empty statement, directly
after the label.  For example:

     {
       goto foo;
     foo:
       ;
       int x = 5;
       bar(&x);
     }

   Likewise, a label can’t be the last thing in a block.  The workaround
solution is the same: add a semicolon after the label.

   These unnecessary restrictions on labels make no sense, and ought in
principle to be removed; but they do only a little harm since labels and
‘goto’ are rarely the best way to write a program.

   These examples are all artificial; it would be more natural to write
them in other ways, without ‘goto’.  For instance, the clean way to
write the example that prints ‘Negative’ is this:

     if (x < 0 || y < 0)
       {
         printf ("Negative\n");
         return;
       }

It is hard to construct simple examples where ‘goto’ is actually the
best way to write a program.  Its rare good uses tend to be in complex
code, thus not apt for the purpose of explaining the meaning of ‘goto’.

   The only good time to use ‘goto’ is when it makes the code simpler
than any alternative.  Jumping backward is rarely desirable, because
usually the other looping and control constructs give simpler code.
Using ‘goto’ to jump forward is more often desirable, for instance when
a function needs to do some processing in an error case and errors can
occur at various different places within the function.

19.13 Locally Declared Labels
=============================

In GNU C you can declare “local labels” in any nested block scope.  A
local label is used in a ‘goto’ statement just like an ordinary label,
but you can only reference it within the block in which it was declared.

   A local label declaration looks like this:

     __label__ LABEL;

or

     __label__ LABE1, LABE2, ...;

   Local label declarations must come at the beginning of the block,
before any ordinary declarations or statements.

   The label declaration declares the label _name_, but does not define
the label itself.  That’s done in the usual way, with ‘LABEL:’, before
one of the statements in the block.

   The local label feature is useful for complex macros.  If a macro
contains nested loops, a ‘goto’ can be useful for breaking out of them.
However, an ordinary label whose scope is the whole function cannot be
used: if the macro can be expanded several times in one function, the
label will be multiply defined in that function.  A local label avoids
this problem.  For example:

     #define SEARCH(value, array, target)              \
     do {                                              \
       __label__ found;                                \
       __auto_type _SEARCH_target = (target);          \
       __auto_type _SEARCH_array = (array);            \
       int i, j;                                       \
       int value;                                      \
       for (i = 0; i < max; i++)                       \
         for (j = 0; j < max; j++)                     \
           if (_SEARCH_array[i][j] == _SEARCH_target)  \
             { (value) = i; goto found; }              \
       (value) = -1;                                   \
      found:;                                          \
     } while (0)

   This could also be written using a statement expression (*note
Statement Exprs::):

     #define SEARCH(array, target)                     \
     ({                                                \
       __label__ found;                                \
       __auto_type _SEARCH_target = (target);      \
       __auto_type _SEARCH_array = (array);     \
       int i, j;                                       \
       int value;                                      \
       for (i = 0; i < max; i++)                       \
         for (j = 0; j < max; j++)                     \
           if (_SEARCH_array[i][j] == _SEARCH_target)  \
             { value = i; goto found; }                \
       value = -1;                                     \
      found:                                           \
       value;                                          \
     })

   Ordinary labels are visible throughout the function where they are
defined, and only in that function.  However, explicitly declared local
labels of a block are visible in nested functions declared within that
block.  *Note Nested Functions::, for details.

   *Note goto Statement::.

19.14 Labels as Values
======================

In GNU C, you can get the address of a label defined in the current
function (or a local label defined in the containing function) with the
unary operator ‘&&’.  The value has type ‘void *’.  This value is a
constant and can be used wherever a constant of that type is valid.  For
example:

     void *ptr;
     ...
     ptr = &&foo;

   To use these values requires a way to jump to one.  This is done with
the computed goto statement(1), ‘goto *EXP;’.  For example,

     goto *ptr;

Any expression of type ‘void *’ is allowed.

   *Note goto Statement::.

   ---------- Footnotes ----------

   (1) The analogous feature in Fortran is called an assigned goto, but
that name seems inappropriate in C, since you can do more with label
addresses than store them in special label variables.

19.14.1 Label Value Uses
------------------------

One use for label-valued constants is to initialize a static array to
serve as a jump table:

     static void *array[] = { &&foo, &&bar, &&hack };

   Then you can select a label with indexing, like this:

     goto *array[i];

Note that this does not check whether the subscript is in bounds—array
indexing in C never checks that.

   You can make the table entries offsets instead of addresses by
subtracting one label from the others.  Here is an example:

     static const int array[] = { &&foo - &&foo, &&bar - &&foo,
                                  &&hack - &&foo };
     goto *(&&foo + array[i]);

Using offsets is preferable in shared libraries, as it avoids the need
for dynamic relocation of the array elements; therefore, the array can
be read-only.

   An array of label values or offsets serves a purpose much like that
of the ‘switch’ statement.  The ‘switch’ statement is cleaner, so use
‘switch’ by preference when feasible.

   Another use of label values is in an interpreter for threaded code.
The labels within the interpreter function can be stored in the threaded
code for super-fast dispatching.

19.14.2 Label Value Caveats
---------------------------

Jumping to a label defined in another function does not work.  It can
cause unpredictable results.

   The best way to avoid this is to store label values only in automatic
variables, or static variables whose names are declared within the
function.  Never pass them as arguments.

   An optimization known as “cloning” generates multiple simplified
variants of a function’s code, for use with specific fixed arguments.
Using label values in certain ways, such as saving the address in one
call to the function and using it again in another call, would make
cloning give incorrect results.  These functions must disable cloning.

   Inlining calls to the function would also result in multiple copies
of the code, each with its own value of the same label.  Using the label
in a computed goto is no problem, because the computed goto inhibits
inlining.  However, using the label value in some other way, such as an
indication of where an error occurred, would be optimized wrong.  These
functions must disable inlining.

   To prevent inlining or cloning of a function, specify
‘__attribute__((__noinline__,__noclone__))’ in its definition.  *Note
Attributes::.

   When a function uses a label value in a static variable initializer,
that automatically prevents inlining or cloning the function.

19.15 Statements and Declarations in Expressions
================================================

A block enclosed in parentheses can be used as an expression in GNU C.
This provides a way to use local variables, loops and switches within an
expression.  We call it a “statement expression”.

   Recall that a block is a sequence of statements surrounded by braces.
In this construct, parentheses go around the braces.  For example:

     ({ int y = foo (); int z;
        if (y &tt; 0) z = y;
        else z = - y;
        z; })

is a valid (though slightly more complex than necessary) expression for
the absolute value of ‘foo ()’.

   The last statement in the block should be an expression statement; an
expression followed by a semicolon, that is.  The value of this
expression serves as the value of statement expression.  If the last
statement is anything else, the statement expression’s value is ‘void’.

   This feature is mainly useful in making macro definitions compute
each operand exactly once.  *Note Macros and Auto Type::.

   Statement expressions are not allowed in expressions that must be
constant, such as the value for an enumerator, the width of a bit-field,
or the initial value of a static variable.

   Jumping into a statement expression—with ‘goto’, or using a ‘switch’
statement outside the statement expression—is an error.  With a computed
‘goto’ (*note Labels as Values::), the compiler can’t detect the error,
but it still won’t work.

   Jumping out of a statement expression is permitted, but since
subexpressions in C are not computed in a strict order, it is
unpredictable which other subexpressions will have been computed by
then.  For example,

       foo (), (({ bar1 (); goto a; 0; }) + bar2 ()), baz();

calls ‘foo’ and ‘bar1’ before it jumps, and never calls ‘baz’, but may
or may not call ‘bar2’.  If ‘bar2’ does get called, that occurs after
‘foo’ and before ‘bar1’.

20 Variables
************

Every variable used in a C program needs to be made known by a
“declaration”.  It can be used only after it has been declared.  It is
an error to declare a variable name more than once in the same scope; an
exception is that ‘extern’ declarations and tentative definitions can
coexist with another declaration of the same variable.

   Variables can be declared anywhere within a block or file.  (Older
versions of C required that all variable declarations within a block
occur before any statements.)

   Variables declared within a function or block are “local” to it.
This means that the variable name is visible only until the end of that
function or block, and the memory space is allocated only while control
is within it.

   Variables declared at the top level in a file are called
“file-scope”.  They are assigned fixed, distinct memory locations, so
they retain their values for the whole execution of the program.

20.1 Variable Declarations
==========================

Here’s what a variable declaration looks like:

     KEYWORDS BASETYPE DECORATED-VARIABLE [= INIT];

   The KEYWORDS specify how to handle the scope of the variable name and
the allocation of its storage.  Most declarations have no keywords
because the defaults are right for them.

   C allows these keywords to come before or after BASETYPE, or even in
the middle of it as in ‘unsigned static int’, but don’t do that—it would
surprise other programmers.  Always write the keywords first.

   The BASETYPE can be any of the predefined types of C, or a type
keyword defined with ‘typedef’.  It can also be ‘struct TAG’, ‘union
TAG’, or ‘enum TAG’.  In addition, it can include type qualifiers such
as ‘const’ and ‘volatile’ (*note Type Qualifiers::).

   In the simplest case, DECORATED-VARIABLE is just the variable name.
That declares the variable with the type specified by BASETYPE.  For
instance,

     int foo;

uses ‘int’ as the BASETYPE and ‘foo’ as the DECORATED-VARIABLE.  It
declares ‘foo’ with type ‘int’.

     struct tree_node foo;

declares ‘foo’ with type ‘struct tree_node’.

20.1.1 Declaring Arrays and Pointers
------------------------------------

To declare a variable that is an array, write ‘VARIABLE[LENGTH]’ for
DECORATED-VARIABLE:

     int foo[5];

   To declare a variable that has a pointer type, write ‘*VARIABLE’ for
DECORATED-VARIABLE:

     struct list_elt *foo;

   These constructs nest.  For instance,

     int foo[3][5];

declares ‘foo’ as an array of 3 arrays of 5 integers each,

     struct list_elt *foo[5];

declares ‘foo’ as an array of 5 pointers to structures, and

     struct list_elt **foo;

declares ‘foo’ as a pointer to a pointer to a structure.

     int **(*foo[30])(int, double);

declares ‘foo’ as an array of 30 pointers to functions (*note Function
Pointers::), each of which must accept two arguments (one ‘int’ and one
‘double’) and return type ‘int **’.

     void
     bar (int size)
     {
       int foo[size];
       ...
     }

declares ‘foo’ as an array of integers with a size specified at run time
when the function ‘bar’ is called.

20.1.2 Combining Variable Declarations
--------------------------------------

When multiple declarations have the same KEYWORDS and BASETYPE, you can
combine them using commas.  Thus,

     KEYWORDS BASETYPE
        DECORATED-VARIABLE-1 [= INIT1],
        DECORATED-VARIABLE-2 [= INIT2];

is equivalent to

     KEYWORDS BASETYPE
        DECORATED-VARIABLE-1 [= INIT1];
     KEYWORDS BASETYPE
        DECORATED-VARIABLE-2 [= INIT2];

   Here are some simple examples:

     int a, b;
     int a = 1, b = 2;
     int a, *p, array[5];
     int a = 0, *p = &a, array[5] = {1, 2};

In the last two examples, ‘a’ is an ‘int’, ‘p’ is a pointer to ‘int’,
and ‘array’ is an array of 5 ‘int’s.  Since the initializer for ‘array’
specifies only two elements, the other three elements are initialized to
zero.

20.2 Initializers
=================

A variable’s declaration, unless it is ‘extern’, should also specify its
initial value.  For numeric and pointer-type variables, the initializer
is an expression for the value.  If necessary, it is converted to the
variable’s type, just as in an assignment.

   You can also initialize a local structure-type (*note Structures::)
or local union-type (*note Unions::) variable this way, from an
expression whose value has the same type.  But you can’t initialize an
array this way (*note Arrays::), since arrays are not first-class
objects in C (*note Limitations of C Arrays::) and there is no array
assignment.

   You can initialize arrays and structures componentwise, with a list
of the elements or components.  You can initialize a union with any one
of its alternatives.

   • A component-wise initializer for an array consists of element
     values surrounded by ‘{...}’.  If the values in the initializer
     don’t cover all the elements in the array, the remaining elements
     are initialized to zero.

     You can omit the size of the array when you declare it, and let the
     initializer specify the size:

          int array[] = { 3, 9, 12 };

   • A component-wise initializer for a structure consists of field
     values surrounded by ‘{...}’.  Write the field values in the same
     order as the fields are declared in the structure.  If the values
     in the initializer don’t cover all the fields in the structure, the
     remaining fields are initialized to zero.

   • The initializer for a union-type variable has the form ‘{ VALUE }’,
     where VALUE initializes the _first alternative_ in the union
     definition.

   For an array of arrays, a structure containing arrays, an array of
structures, etc., you can nest these constructs.  For example,

     struct point { double x, y; };

     struct point series[]
       = { {0, 0}, {1.5, 2.8}, {99, 100.0004} };

   You can omit a pair of inner braces if they contain the right number
of elements for the sub-value they initialize, so that no elements or
fields need to be filled in with zeros.  But don’t do that very much, as
it gets confusing.

   An array of ‘char’ can be initialized using a string constant.
Recall that the string constant includes an implicit null character at
the end (*note String Constants::).  Using a string constant as
initializer means to use its contents as the initial values of the array
elements.  Here are examples:

     char text[6] = "text!";     /* Includes the null. */
     char text[5] = "text!";     /* Excludes the null. */
     char text[] = "text!";      /* Gets length 6. */
     char text[]
       = { 't', 'e', 'x', 't', '!', 0 };  /* same as above. */
     char text[] = { "text!" };  /* Braces are optional. */

and this kind of initializer can be nested inside braces to initialize
structures or arrays that contain a ‘char’-array.

   In like manner, you can use a wide string constant to initialize an
array of ‘wchar_t’.

20.3 Designated Initializers
============================

In a complex structure or long array, it’s useful to indicate which
field or element we are initializing.

   To designate specific array elements during initialization, include
the array index in brackets, and an assignment operator, for each
element:

     int foo[10] = { [3] = 42, [7] = 58 };

This does the same thing as:

     int foo[10] = { 0, 0, 0, 42, 0, 0, 0, 58, 0, 0 };

   The array initialization can include non-designated element values
alongside designated indices; these follow the expected ordering of the
array initialization, so that

     int foo[10] = { [3] = 42, 43, 44, [7] = 58 };

does the same thing as:

     int foo[10] = { 0, 0, 0, 42, 43, 44, 0, 58, 0, 0 };

   Note that you can only use constant expressions as array index
values, not variables.

   If you need to initialize a subsequence of sequential array elements
to the same value, you can specify a range:

     int foo[100] = { [0 ... 19] = 42, [20 ... 99] = 43 };

Using a range this way is a GNU C extension.

   When subsequence ranges overlap, each element is initialized by the
last specification that applies to it.  Thus, this initialization is
equivalent to the previous one.

     int foo[100] = { [0 ... 99] = 43, [0 ... 19] = 42 };

as the second overrides the first for elements 0 through 19.

   The value used to initialize a range of elements is evaluated only
once, for the first element in the range.  So for example, this code

     int random_values[100]
       = { [0 ... 99] = get_random_number() };

would initialize all 100 elements of the array ‘random_values’ to the
same value—probably not what is intended.

   Similarly, you can initialize specific fields of a structure variable
by specifying the field name prefixed with a dot:

     struct point { int x; int y; };

     struct point foo = { .y = 42; };

The same syntax works for union variables as well:

     union int_double { int i; double d; };

     union int_double foo = { .d = 34 };

This casts the integer value 34 to a double and stores it in the union
variable ‘foo’.

   You can designate both array elements and structure elements in the
same initialization; for example, here’s an array of point structures:

     struct point point_array[10] = { [4].y = 32, [6].y = 39 };

   Along with the capability to specify particular array and structure
elements to initialize comes the possibility of initializing the same
element more than once:

     int foo[10] = { [4] = 42, [4] = 98 };

In such a case, the last initialization value is retained.

20.4 Referring to a Type with ‘__auto_type’
===========================================

You can declare a variable copying the type from the initializer by
using ‘__auto_type’ instead of a particular type.  Here’s an example:

     #define max(a,b) \
       ({ __auto_type _a = (a); \
           __auto_type _b = (b); \
         _a &tt; _b ? _a : _b })

   This defines ‘_a’ to be of the same type as ‘a’, and ‘_b’ to be of
the same type as ‘b’.  This is a useful thing to do in a macro that
ought to be able to handle any type of data (*note Macros and Auto
Type::).

   The original GNU C method for obtaining the type of a value is to use
‘typeof’, which takes as an argument either a value or the name of a
type.  The previous example could also be written as:

     #define max(a,b) \
       ({ typeof(a) _a = (a); \
           typeof(b) _b = (b); \
         _a &tt; _b ? _a : _b })

   ‘typeof’ is more flexible than ‘__auto_type’; however, the principal
use case for ‘typeof’ is in variable declarations with initialization,
which is exactly what ‘__auto_type’ handles.

20.5 Local Variables
====================

Declaring a variable inside a function definition (*note Function
Definitions::) makes the variable name “local” to the containing
block—that is, the containing pair of braces.  More precisely, the
variable’s name is visible starting just after where it appears in the
declaration, and its visibility continues until the end of the block.

   Local variables in C are generally “automatic” variables: each
variable’s storage exists only from the declaration to the end of the
block.  Execution of the declaration allocates the storage, computes the
initial value, and stores it in the variable.  The end of the block
deallocates the storage.(1)

   *Warning:* Two declarations for the same local variable in the same
scope are an error.

   *Warning:* Automatic variables are stored in the run-time stack.  The
total space for the program’s stack may be limited; therefore, in using
very large arrays, it may be necessary to allocate them in some other
way to stop the program from crashing.

   *Warning:* If the declaration of an automatic variable does not
specify an initial value, the variable starts out containing garbage.
In this example, the value printed could be anything at all:

     {
       int i;

       printf ("Print junk %d\n", i);
     }

   In a simple test program, that statement is likely to print 0, simply
because every process starts with memory zeroed.  But don’t rely on it
to be zero—that is erroneous.

   *Note:* Make sure to store a value into each local variable (by
assignment, or by initialization) before referring to its value.

   ---------- Footnotes ----------

   (1) Due to compiler optimizations, allocation and deallocation don’t
necessarily really happen at those times.

20.6 File-Scope Variables
=========================

A variable declaration at the top level in a file (not inside a function
definition) declares a “file-scope variable”.  Loading a program
allocates the storage for all the file-scope variables in it, and
initializes them too.

   Each file-scope variable is either “static” (limited to one
compilation module) or “global” (shared with all compilation modules in
the program).  To make the variable static, write the keyword ‘static’
at the start of the declaration.  Omitting ‘static’ makes the variable
global.

   The initial value for a file-scope variable can’t depend on the
contents of storage, and can’t call any functions.

     int foo = 5;         /* Valid. */
     int bar = foo;       /* Invalid! */
     int bar = sin (1.0); /* Invalid! */

   But it can use the address of another file-scope variable:

     int foo;
     int *bar = &foo;     /* Valid. */
     int arr[5];
     int *bar3 = &arr[3]; /* Valid. */
     int *bar4 = arr + 4; /* Valid. */

   It is valid for a module to have multiple declarations for a
file-scope variable, as long as they are all global or all static, but
at most one declaration can specify an initial value for it.

20.7 Static Local Variables
===========================

The keyword ‘static’ in a local variable declaration says to allocate
the storage for the variable permanently, just like a file-scope
variable, even if the declaration is within a function.

   Here’s an example:

     int
     increment_counter ()
     {
       static int counter = 0;
       return ++counter;
     }

   The scope of the name ‘counter’ runs from the declaration to the end
of the containing block, just like an automatic local variable, but its
storage is permanent, so the value persists from one call to the next.
As a result, each call to ‘increment_counter’ returns a different,
unique value.

   The initial value of a static local variable has the same limitations
as for file-scope variables: it can’t depend on the contents of storage
or call any functions.  It can use the address of a file-scope variable
or a static local variable, because those addresses are determined
before the program runs.

20.8 ‘extern’ Declarations
==========================

An ‘extern’ declaration is used to refer to a global variable whose
principal declaration comes elsewhere—in the same module, or in another
compilation module.  It looks like this:

     extern BASETYPE DECORATED-VARIABLE;

   Its meaning is that, in the current scope, the variable name refers
to the file-scope variable of that name—which needs to be declared in a
non-‘extern’, non-‘static’ way somewhere else.

   For instance, if one compilation module has this global variable
declaration

     int error_count = 0;

then other compilation modules can specify this

     extern int error_count;

to allow reference to the same variable.

   The usual place to write an ‘extern’ declaration is at top level in a
source file, but you can write an ‘extern’ declaration inside a block to
make a global or static file-scope variable accessible in that block.

   Since an ‘extern’ declaration does not allocate space for the
variable, it can omit the size of an array:

     extern int array[];

   You can use ‘array’ normally in all contexts where it is converted
automatically to a pointer.  However, to use it as the operand of
‘sizeof’ is an error, since the size is unknown.

   It is valid to have multiple ‘extern’ declarations for the same
variable, even in the same scope, if they give the same type.  They do
not conflict—they agree.  For an array, it is legitimate for some
‘extern’ declarations can specify the size while others omit it.
However, if two declarations give different sizes, that is an error.

   Likewise, you can use ‘extern’ declarations at file scope (*note
File-Scope Variables::) followed by an ordinary global (non-static)
declaration of the same variable.  They do not conflict, because they
say compatible things about the same meaning of the variable.

20.9 Allocating File-Scope Variables
====================================

Some file-scope declarations allocate space for the variable, and some
don’t.

   A file-scope declaration with an initial value _must_ allocate space
for the variable; if there are two of such declarations for the same
variable, even in different compilation modules, they conflict.

   An ‘extern’ declaration _never_ allocates space for the variable.  If
all the top-level declarations of a certain variable are ‘extern’, the
variable never gets memory space.  If that variable is used anywhere in
the program, the use will be reported as an error, saying that the
variable is not defined.

   A file-scope declaration without an initial value is called a
“tentative definition”.  This is a strange hybrid: it _can_ allocate
space for the variable, but does not insist.  So it causes no conflict,
no error, if the variable has another declaration that allocates space
for it, perhaps in another compilation module.  But if nothing else
allocates space for the variable, the tentative definition will do it.
Any number of compilation modules can declare the same variable in this
way, and that is sufficient for all of them to use the variable.

   In programs that are very large or have many contributors, it may be
wise to adopt the convention of never using tentative definitions.  You
can use the compilation option ‘-fno-common’ to make them an error, or
‘--warn-common’ to warn about them.

   If a file-scope variable gets its space through a tentative
definition, it starts out containing all zeros.

20.10 ‘auto’ and ‘register’
===========================

For historical reasons, you can write ‘auto’ or ‘register’ before a
local variable declaration.  ‘auto’ merely emphasizes that the variable
isn’t static; it changes nothing.

   ‘register’ suggests to the compiler storing this variable in a
register.  However, GNU C ignores this suggestion, since it can choose
the best variables to store in registers without any hints.

   It is an error to take the address of a variable declared ‘register’,
so you cannot use the unary ‘&’ operator on it.  If the variable is an
array, you can’t use it at all (other than as the operand of ‘sizeof’),
which makes it rather useless.

20.11 Omitting Types in Declarations
====================================

The syntax of C traditionally allows omitting the data type in a
declaration if it specifies a storage class, a type qualifier (see the
next chapter), or ‘auto’ or ‘register’.  Then the type defaults to
‘int’.  For example:

     auto foo = 42;

   This is bad practice; if you see it, fix it.

21 Type Qualifiers
******************

A declaration can include type qualifiers to advise the compiler about
how the variable will be used.  There are three different qualifiers,
‘const’, ‘volatile’ and ‘restrict’.  They pertain to different issues,
so you can use more than one together.  For instance, ‘const volatile’
describes a value that the program is not allowed to change, but might
have a different value each time the program examines it.  (This might
perhaps be a special hardware register, or part of shared memory.)

   If you are just learning C, you can skip this chapter.

21.1 ‘const’ Variables and Fields
=================================

You can mark a variable as “constant” by writing ‘const’ in front of the
declaration.  This says to treat any assignment to that variable as an
error.  It may also permit some compiler optimizations—for instance, to
fetch the value only once to satisfy multiple references to it.  The
construct looks like this:

     const double pi = 3.14159;

   After this definition, the code can use the variable ‘pi’ but cannot
assign a different value to it.

     pi = 3.0; /* Error! */

   Simple variables that are constant can be used for the same purposes
as enumeration constants, and they are not limited to integers.  The
constantness of the variable propagates into pointers, too.

   A pointer type can specify that the _target_ is constant.  For
example, the pointer type ‘const double *’ stands for a pointer to a
constant ‘double’.  That’s the typethat results from taking the address
of ‘pi’.  Such a pointer can’t be dereferenced in the left side of an
assignment.

     *(&pi) = 3.0; /* Error! */

   Nonconstant pointers can be converted automatically to constant
pointers, but not vice versa.  For instance,

     const double *cptr;
     double *ptr;

     cptr = π    /* Valid. */
     cptr = ptr;    /* Valid. */
     ptr = cptr;    /* Error! */
     ptr = π     /* Error! */

   This is not an ironclad protection against modifying the value.  You
can always cast the constant pointer to a nonconstant pointer type:

     ptr = (double *)cptr;    /* Valid. */
     ptr = (double *)π     /* Valid. */

   However, ‘const’ provides a way to show that a certain function won’t
modify the data structure whose address is passed to it.  Here’s an
example:

     int
     string_length (const char *string)
     {
       int count = 0;
       while (*string++)
         count++;
       return count;
     }

Using ‘const char *’ for the parameter is a way of saying this function
never modifies the memory of the string itself.

   In calling ‘string_length’, you can specify an ordinary ‘char *’
since that can be converted automatically to ‘const char *’.

21.2 ‘volatile’ Variables and Fields
====================================

The GNU C compiler often performs optimizations that eliminate the need
to write or read a variable.  For instance,

     int foo;
     foo = 1;
     foo++;

might simply store the value 2 into ‘foo’, without ever storing 1.
These optimizations can also apply to structure fields in some cases.

   If the memory containing ‘foo’ is shared with another program, or if
it is examined asynchronously by hardware, such optimizations could
confuse the communication.  Using ‘volatile’ is one way to prevent them.

   Writing ‘volatile’ with the type in a variable or field declaration
says that the value may be examined or changed for reasons outside the
control of the program at any moment.  Therefore, the program must
execute in a careful way to assure correct interaction with those
accesses, whenever they may occur.

   The simplest use looks like this:

     volatile int lock;

   This directs the compiler not to do certain common optimizations on
use of the variable ‘lock’.  All the reads and writes for a volatile
variable or field are really done, and done in the order specified by
the source code.  Thus, this code:

     lock = 1;
     list = list-<next;
     if (lock)
       lock_broken (&lock);
     lock = 0;

really stores the value 1 in ‘lock’, even though there is no sign it is
really used, and the ‘if’ statement reads and checks the value of
‘lock’, rather than assuming it is still 1.

   A limited amount of optimization can be done, in principle, on
‘volatile’ variables and fields: multiple references between two
sequence points (*note Sequence Points::) can be simplified together.

   Use of ‘volatile’ does not eliminate the flexibility in ordering the
computation of the operands of most operators.  For instance, in ‘lock +
foo ()’, the order of accessing ‘lock’ and calling ‘foo’ is not
specified, so they may be done in either order; the fact that ‘lock’ is
‘volatile’ has no effect on that.

21.3 ‘restrict’-Qualified Pointers
==================================

You can declare a pointer as “restricted” using the ‘restrict’ type
qualifier, like this:

     int *restrict p = x;

This enables better optimization of code that uses the pointer.

   If ‘p’ is declared with ‘restrict’, and then the code references the
object that ‘p’ points to (using ‘*p’ or ‘p[I]’), the ‘restrict’
declaration promises that the code will not access that object in any
other way—only through ‘p’.

   For instance, it means the code must not use another pointer to
access the same space, as shown here:

     int *restrict p = WHATEVER;
     int *q = p;
     foo (*p, *q);

That contradicts the ‘restrict’ promise by accessing the object that ‘p’
points to using ‘q’, which bypasses ‘p’.  Likewise, it must not do this:

     int *restrict p = WHATEVER;
     struct { int *a, *b; } s;
     s.a = p;
     foo (*p, *s.a);

This example uses a structure field instead of the variable ‘q’ to hold
the other pointer, and that contradicts the promise just the same.

   The keyword ‘restrict’ also promises that ‘p’ won’t point to the
allocated space of any automatic or static variable.  So the code must
not do this:

     int a;
     int *restrict p = &a;
     foo (*p, a);

because that does direct access to the object (‘a’) that ‘p’ points to,
which bypasses ‘p’.

   If the code makes such promises with ‘restrict’ then breaks them,
execution is unpredictable.

21.4 ‘restrict’ Pointer Example
===============================

Here are examples where ‘restrict’ enables real optimization.

   In this example, ‘restrict’ assures GCC that the array ‘out’ points
to does not overlap with the array ‘in’ points to.

     void
     process_data (const char *in,
                   char * restrict out,
                   size_t size)
     {
       for (i = 0; i < size; i++)
         out[i] = in[i] + in[i + 1];
     }

   Here’s a simple tree structure, where each tree node holds data of
type ‘PAYLOAD’ plus two subtrees.

     struct foo
       {
         PAYLOAD payload;
         struct foo *left;
         struct foo *right;
       };

   Now here’s a function to null out both pointers in the ‘left’
subtree.

     void
     null_left (struct foo *a)
     {
       a-<left-<left = NULL;
       a-<left-<right = NULL;
     }

   Since ‘*a’ and ‘*a-<left’ have the same data type, they could
legitimately alias (*note Aliasing::).  Therefore, the compiled code for
‘null_left’ must read ‘a-<left’ again from memory when executing the
second assignment statement.

   We can enable optimization, so that it does not need to read
‘a-<left’ again, by writing ‘null_left’ this in a less obvious way.

     void
     null_left (struct foo *a)
     {
       struct foo *b = a-<left;
       b-<left = NULL;
       b-<right = NULL;
     }

   A more elegant way to fix this is with ‘restrict’.

     void
     null_left (struct foo *restrict a)
     {
       a-<left-<left = NULL;
       a-<left-<right = NULL;
     }

   Declaring ‘a’ as ‘restrict’ asserts that other pointers such as
‘a-<left’ will not point to the same memory space as ‘a’.  Therefore,
the memory location ‘a-<left-<left’ cannot be the same memory as
‘a-<left’.  Knowing this, the compiled code may avoid reloading
‘a-<left’ for the second statement.

22 Functions
************

We have already presented many examples of functions, so if you’ve read
this far, you basically understand the concept of a function.  It is
vital, nonetheless, to have a chapter in the manual that collects all
the information about functions.

22.1 Function Definitions
=========================

We have already presented many examples of function definitions.  To
summarize the rules, a function definition looks like this:

     RETURNTYPE
     FUNCTIONNAME (PARM_DECLARATIONS...)
     {
       BODY
     }

   The part before the open-brace is called the “function header”.

   Write ‘void’ as the RETURNTYPE if the function does not return a
value.

22.1.1 Function Parameter Variables
-----------------------------------

A function parameter variable is a local variable (*note Local
Variables::) used within the function to store the value passed as an
argument in a call to the function.  Usually we say “function parameter”
or “parameter” for short, not mentioning the fact that it’s a variable.

   We declare these variables in the beginning of the function
definition, in the “parameter list”.  For example,

     fib (int n)

has a parameter list with one function parameter ‘n’, which has type
‘int’.

   Function parameter declarations differ from ordinary variable
declarations in several ways:

   • Inside the function definition header, commas separate parameter
     declarations, and each parameter needs a complete declaration
     including the type.  For instance, if a function ‘foo’ has two
     ‘int’ parameters, write this:

          foo (int a, int b)

     You can’t share the common ‘int’ between the two declarations:

          foo (int a, b)      /* Invalid! */

   • A function parameter variable is initialized to whatever value is
     passed in the function call, so its declaration cannot specify an
     initial value.

   • Writing an array type in a function parameter declaration has the
     effect of declaring it as a pointer.  The size specified for the
     array has no effect at all, and we normally omit the size.  Thus,

          foo (int a[5])
          foo (int a[])
          foo (int *a)

     are equivalent.

   • The scope of the parameter variables is the entire function body,
     notwithstanding the fact that they are written in the function
     header, which is just outside the function body.

   If a function has no parameters, it would be most natural for the
list of parameters in its definition to be empty.  But that, in C, has a
special meaning for historical reasons: “Do not check that calls to this
function have the right number of arguments.” Thus,

     int
     foo ()
     {
       return 5;
     }

     int
     bar (int x)
     {
       return foo (x);
     }

would not report a compilation error in passing ‘x’ as an argument to
‘foo’.  By contrast,

     int
     foo (void)
     {
       return 5;
     }

     int
     bar (int x)
     {
       return foo (x);
     }

would report an error because ‘foo’ is supposed to receive no arguments.

22.1.2 Forward Function Declarations
------------------------------------

The order of the function definitions in the source code makes no
difference, except that each function needs to be defined or declared
before code uses it.

   The definition of a function also declares its name for the rest of
the containing scope.  But what if you want to call the function before
its definition?  To permit that, write a compatible declaration of the
same function, before the first call.  A declaration that prefigures a
subsequent definition in this way is called a “forward declaration”.
The function declaration can be at top level or within a block, and it
applies until the end of the containing scope.

   *Note Function Declarations::, for more information about these
declarations.

22.1.3 Static Functions
-----------------------

The keyword ‘static’ in a function definition limits the visibility of
the name to the current compilation module.  (That’s the same thing
‘static’ does in variable declarations; *note File-Scope Variables::.)
For instance, if one compilation module contains this code:

     static int
     foo (void)
     {
       ...
     }

then the code of that compilation module can call ‘foo’ anywhere after
the definition, but other compilation modules cannot refer to it at all.

   To call ‘foo’ before its definition, it needs a forward declaration,
which should use ‘static’ since the function definition does.  For this
function, it looks like this:

     static int foo (void);

   It is generally wise to use ‘static’ on the definitions of functions
that won’t be called from outside the same compilation module.  This
makes sure that calls are not added in other modules.  If programmers
decide to change the function’s calling convention, or understand all
the consequences of its use, they will only have to check for calls in
the same compilation module.

22.1.4 Arrays as Parameters
---------------------------

Arrays in C are not first-class objects: it is impossible to copy them.
So they cannot be passed as arguments like other values.  *Note
Limitations of C Arrays::.  Rather, array parameters work in a special
way.

22.1.4.1 Array parameters are pointers
......................................

Declaring a function parameter variable as an array really gives it a
pointer type.  C does this because an expression with array type, if
used as an argument in a function call, is converted automatically to a
pointer (to the zeroth element of the array).  If you declare the
corresponding parameter as an “array”, it will work correctly with the
pointer value that really gets passed.

   This relates to the fact that C does not check array bounds in access
to elements of the array (*note Accessing Array Elements::).

   For example, in this function,

     void
     clobber4 (int array[20])
     {
       array[4] = 0;
     }

the parameter ‘array’’s real type is ‘int *’; the specified length, 20,
has no effect on the program.  You can leave out the length and write
this:

     void
     clobber4 (int array[])
     {
       array[4] = 0;
     }

or write the parameter declaration explicitly as a pointer:

     void
     clobber4 (int *array)
     {
       array[4] = 0;
     }

   They are all equivalent.

22.1.4.2 Passing array arguments
................................

The function call passes this pointer by value, like all argument values
in C.  However, the result is paradoxical in that the array itself is
passed by reference: its contents are treated as shared memory—shared
between the caller and the called function, that is.  When ‘clobber4’
assigns to element 4 of ‘array’, the effect is to alter element 4 of the
array specified in the call.

     #include <stddef.h>  /* Defines ‘NULL’. */
     #include <stdlib.h>  /* Declares ‘malloc’, */
                          /* Defines ‘EXIT_SUCCESS’. */

     int
     main (void)
     {
       int data[] = {1, 2, 3, 4, 5, 6};
       int i;

       /* Show the initial value of element 4. */
       for (i = 0; i < 6; i++)
         printf ("data[%d] = %d\n", i, data[i]);

       printf ("\n");

       clobber4 (data);

       /* Show that element 4 has been changed. */
       for (i = 0; i < 6; i++)
         printf ("data[%d] = %d\n", i, data[i]);

       printf ("\n");

       return EXIT_SUCCESS;
     }

shows that ‘data[4]’ has become zero after the call to ‘clobber4’.

   The array ‘data’ has 6 elements, but passing it to a function whose
argument type is written as ‘int [20]’ is not an error, because that
really stands for ‘int *’.  The pointer that is the real argument
carries no indication of the length of the array it points into.  It is
not required to point to the beginning of the array, either.  For
instance,

     clobber4 (data+1);

passes an “array” that starts at element 1 of ‘data’, and the effect is
to zero ‘data[5]’ instead of ‘data[4]’.

   If all calls to the function will provide an array of a particular
size, you can specify the size of the array to be ‘static’:

     void
     clobber4 (int array[static 20])
     ...

This is a promise to the compiler that the function will always be
called with an array of 20 elements, so that the compiler can optimize
code accordingly.  If the code breaks this promise and calls the
function with, for example, a shorter array, unpredictable things may
happen.

22.1.4.3 Type qualifiers on array parameters
............................................

You can use the type qualifiers ‘const’, ‘restrict’, and ‘volatile’ with
array parameters; for example:

     void
     clobber4 (volatile int array[20])
     ...

denotes that ‘array’ is equivalent to a pointer to a volatile ‘int’.
Alternatively:

     void
     clobber4 (int array[const 20])
     ...

makes the array parameter equivalent to a constant pointer to an ‘int’.
If we want the ‘clobber4’ function to succeed, it would not make sense
to write

     void
     clobber4 (const int array[20])
     ...

as this would tell the compiler that the parameter should point to an
array of constant ‘int’ values, and then we would not be able to store
zeros in them.

   In a function with multiple array parameters, you can use ‘restrict’
to tell the compiler that each array parameter passed in will be
distinct:

     void
     foo (int array1[restrict 10], int array2[restrict 10])
     ...

Using ‘restrict’ promises the compiler that callers will not pass in the
same array for more than one ‘restrict’ array parameter.  Knowing this
enables the compiler to perform better code optimization.  This is the
same effect as using ‘restrict’ pointers (*note restrict Pointers::),
but makes it clear when reading the code that an array of a specific
size is expected.

22.1.5 Functions That Accept Structure Arguments
------------------------------------------------

Structures in GNU C are first-class objects, so using them as function
parameters and arguments works in the natural way.  This function
‘swapfoo’ takes a ‘struct foo’ with two fields as argument, and returns
a structure of the same type but with the fields exchanged.

     struct foo { int a, b; };

     struct foo x;

     struct foo
     swapfoo (struct foo inval)
     {
       struct foo outval;
       outval.a = inval.b;
       outval.b = inval.a;
       return outval;
     }

   This simpler definition of ‘swapfoo’ avoids using a local variable to
hold the result about to be return, by using a structure constructor
(*note Structure Constructors::), like this:

     struct foo
     swapfoo (struct foo inval)
     {
       return (struct foo) { inval.b, inval.a };
     }

   It is valid to define a structure type in a function’s parameter
list, as in

     int
     frob_bar (struct bar { int a, b; } inval)
     {
       BODY
     }

and BODY can access the fields of INVAL since the structure type ‘struct
bar’ is defined for the whole function body.  However, there is no way
to create a ‘struct bar’ argument to pass to ‘frob_bar’, except with
kludges.  As a result, defining a structure type in a parameter list is
useless in practice.

22.2 Function Declarations
==========================

To call a function, or use its name as a pointer, a “function
declaration” for the function name must be in effect at that point in
the code.  The function’s definition serves as a declaration of that
function for the rest of the containing scope, but to use the function
in code before the definition, or from another compilation module, a
separate function declaration must precede the use.

   A function declaration looks like the start of a function definition.
It begins with the return value type (‘void’ if none) and the function
name, followed by argument declarations in parentheses (though these can
sometimes be omitted).  But that’s as far as the similarity goes:
instead of the function body, the declaration uses a semicolon.

   A declaration that specifies argument types is called a “function
prototype”.  You can include the argument names or omit them.  The
names, if included in the declaration, have no effect, but they may
serve as documentation.

   This form of prototype specifies fixed argument types:

     RETTYPE FUNCTION (ARGTYPES...);

This form says the function takes no arguments:

     RETTYPE FUNCTION (void);

This form declares types for some arguments, and allows additional
arguments whose types are not specified:

     RETTYPE FUNCTION (ARGTYPES..., ...);

   For a parameter that’s an array of variable length, you can write its
declaration with ‘*’ where the “length” of the array would normally go;
for example, these are all equivalent.

     double maximum (int n, int m, double a[n][m]);
     double maximum (int n, int m, double a[*][*]);
     double maximum (int n, int m, double a[ ][*]);
     double maximum (int n, int m, double a[ ][m]);

The old-fashioned form of declaration, which is not a prototype, says
nothing about the types of arguments or how many they should be:

     RETTYPE FUNCTION ();

   *Warning:* Arguments passed to a function declared without a
prototype are converted with the default argument promotions (*note
Argument Promotions::.  Likewise for additional arguments whose types
are unspecified.

   Function declarations are usually written at the top level in a
source file, but you can also put them inside code blocks.  Then the
function name is visible for the rest of the containing scope.  For
example:

     void
     foo (char *file_name)
     {
       void save_file (char *);
       save_file (file_name);
     }

   If another part of the code tries to call the function ‘save_file’,
this declaration won’t be in effect there.  So the function will get an
implicit declaration of the form ‘extern int save_file ();’.  That
conflicts with the explicit declaration here, and the discrepancy
generates a warning.

   The syntax of C traditionally allows omitting the data type in a
function declaration if it specifies a storage class or a qualifier.
Then the type defaults to ‘int’.  For example:

     static foo (double x);

defaults the return type to ‘int’.  This is bad practice; if you see it,
fix it.

   Calling a function that is undeclared has the effect of an creating
“implicit” declaration in the innermost containing scope, equivalent to
this:

     extern int “function” ();

This declaration says that the function returns ‘int’ but leaves its
argument types unspecified.  If that does not accurately fit the
function, then the program *needs* an explicit declaration of the
function with argument types in order to call it correctly.

   Implicit declarations are deprecated, and a function call that
creates one causes a warning.

22.3 Function Calls
===================

Starting a program automatically calls the function named ‘main’ (*note
The main Function::).  Aside from that, a function does nothing except
when it is “called”.  That occurs during the execution of a
function-call expression specifying that function.

   A function-call expression looks like this:

     FUNCTION (ARGUMENTS...)

   Most of the time, FUNCTION is a function name.  However, it can also
be an expression with a function pointer value; that way, the program
can determine at run time which function to call.

   The ARGUMENTS are a series of expressions separated by commas.  Each
expression specifies one argument to pass to the function.

   The list of arguments in a function call looks just like use of the
comma operator (*note Comma Operator::), but the fact that it fills the
parentheses of a function call gives it a different meaning.

   Here’s an example of a function call, taken from an example near the
beginning (*note Complete Program::).

     printf ("Fibonacci series item %d is %d\n",
             19, fib (19));

   The three arguments given to ‘printf’ are a constant string, the
integer 19, and the integer returned by ‘fib (19)’.

22.4 Function Call Semantics
============================

The meaning of a function call is to compute the specified argument
expressions, convert their values according to the function’s
declaration, then run the function giving it copies of the converted
values.  (This method of argument passing is known as “call-by-value”.)
When the function finishes, the value it returns becomes the value of
the function-call expression.

   Call-by-value implies that an assignment to the function argument
variable has no direct effect on the caller.  For instance,

     #include <stdlib.h>  /* Defines ‘EXIT_SUCCESS’. */
     #include <stdio.h>   /* Declares ‘printf’. */

     void
     subroutine (int x)
     {
       x = 5;
     }

     void
     main (void)
     {
       int y = 20;
       subroutine (y);
       printf ("y is %d\n", y);
       return EXIT_SUCCESS;
     }

prints ‘y is 20’.  Calling ‘subroutine’ initializes ‘x’ from the value
of ‘y’, but this does not establish any other relationship between the
two variables.  Thus, the assignment to ‘x’, inside ‘subroutine’,
changes only _that_ ‘x’.

   If an argument’s type is specified by the function’s declaration, the
function call converts the argument expression to that type if possible.
If the conversion is impossible, that is an error.

   If the function’s declaration doesn’t specify the type of that
argument, then the _default argument promotions_ apply.  *Note Argument
Promotions::.

22.5 Function Pointers
======================

A function name refers to a fixed function.  Sometimes it is useful to
call a function to be determined at run time; to do this, you can use a
“function pointer value” that points to the chosen function (*note
Pointers::).

   Pointer-to-function types can be used to declare variables and other
data, including array elements, structure fields, and union
alternatives.  They can also be used for function arguments and return
values.  These types have the peculiarity that they are never converted
automatically to ‘void *’ or vice versa.  However, you can do that
conversion with a cast.

22.5.1 Declaring Function Pointers
----------------------------------

The declaration of a function pointer variable (or structure field)
looks almost like a function declaration, except it has an additional
‘*’ just before the variable name.  Proper nesting requires a pair of
parentheses around the two of them.  For instance, ‘int (*a) ();’ says,
“Declare ‘a’ as a pointer such that ‘*a’ is an ‘int’-returning
function.”

   Contrast these three declarations:

     /* Declare a function returning ‘char *’.  */
     char *a (char *);
     /* Declare a pointer to a function returning ‘char’.  */
     char (*a) (char *);
     /* Declare a pointer to a function returning ‘char *’.  */
     char *(*a) (char *);

   The possible argument types of the function pointed to are the same
as in a function declaration.  You can write a prototype that specifies
all the argument types:

     RETTYPE (*FUNCTION) (ARGUMENTS...);

or one that specifies some and leaves the rest unspecified:

     RETTYPE (*FUNCTION) (ARGUMENTS..., ...);

or one that says there are no arguments:

     RETTYPE (*FUNCTION) (void);

   You can also write a non-prototype declaration that says nothing
about the argument types:

     RETTYPE (*FUNCTION) ();

   For example, here’s a declaration for a variable that should point to
some arithmetic function that operates on two ‘double’s:

     double (*binary_op) (double, double);

   Structure fields, union alternatives, and array elements can be
function pointers; so can parameter variables.  The function pointer
declaration construct can also be combined with other operators allowed
in declarations.  For instance,

     int **(*foo)();

declares ‘foo’ as a pointer to a function that returns type ‘int **’,
and

     int **(*foo[30])();

declares ‘foo’ as an array of 30 pointers to functions that return type
‘int **’.

     int **(**foo)();

declares ‘foo’ as a pointer to a pointer to a function that returns type
‘int **’.

22.5.2 Assigning Function Pointers
----------------------------------

Assuming we have declared the variable ‘binary_op’ as in the previous
section, giving it a value requires a suitable function to use.  So
let’s define a function suitable for the variable to point to.  Here’s
one:

     double
     double_add (double a, double b)
     {
       return a+b;
     }

   Now we can give it a value:

     binary_op = double_add;

   The target type of the function pointer must be upward compatible
with the type of the function (*note Compatible Types::).

   There is no need for ‘&’ in front of ‘double_add’.  Using a function
name such as ‘double_add’ as an expression automatically converts it to
the function’s address, with the appropriate function pointer type.
However, it is ok to use ‘&’ if you feel that is clearer:

     binary_op = &double_add;

22.5.3 Calling Function Pointers
--------------------------------

To call the function specified by a function pointer, just write the
function pointer value in a function call.  For instance, here’s a call
to the function ‘binary_op’ points to:

     binary_op (x, 5)

   Since the data type of ‘binary_op’ explicitly specifies type ‘double’
for the arguments, the call converts ‘x’ and 5 to ‘double’.

   The call conceptually dereferences the pointer ‘binary_op’ to “get”
the function it points to, and calls that function.  If you wish, you
can explicitly represent the derefence by writing the ‘*’ operator:

     (*binary_op) (x, 5)

   The ‘*’ reminds people reading the code that ‘binary_op’ is a
function pointer rather than the name of a specific function.

22.6 The ‘main’ Function
========================

Every complete executable program requires at least one function, called
‘main’, which is where execution begins.  You do not have to explicitly
declare ‘main’, though GNU C permits you to do so.  Conventionally,
‘main’ should be defined to follow one of these calling conventions:

     int main (void) {...}
     int main (int argc, char *argv[]) {...}
     int main (int argc, char *argv[], char *envp[]) {...}

Using ‘void’ as the parameter list means that ‘main’ does not use the
arguments.  You can write ‘char **argv’ instead of ‘char *argv[]’, and
likewise for ‘envp’, as the two constructs are equivalent.

   You can call ‘main’ from C code, as you can call any other function,
though that is an unusual thing to do.  When you do that, you must write
the call to pass arguments that match the parameters in the definition
of ‘main’.

   The ‘main’ function is not actually the first code that runs when a
program starts.  In fact, the first code that runs is system code from
the file ‘crt0.o’.  In Unix, this was hand-written assembler code, but
in GNU we replaced it with C code.  Its job is to find the arguments for
‘main’ and call that.

22.6.1 Returning Values from ‘main’
-----------------------------------

When ‘main’ returns, the process terminates.  Whatever value ‘main’
returns becomes the exit status which is reported to the parent process.
While nominally the return value is of type ‘int’, in fact the exit
status gets truncated to eight bits; if ‘main’ returns the value 256,
the exit status is 0.

   Normally, programs return only one of two values: 0 for success, and
1 for failure.  For maximum portability, use the macro values
‘EXIT_SUCCESS’ and ‘EXIT_FAILURE’ defined in ‘stdlib.h’.  Here’s an
example:

     #include <stdlib.h>  /* Defines ‘EXIT_SUCCESS’ */
                          /* and ‘EXIT_FAILURE’. */

     int
     main (void)
     {
       ...
       if (foo)
         return EXIT_SUCCESS;
       else
         return EXIT_FAILURE;
     }

   Some types of programs maintain special conventions for various
return values; for example, comparison programs including ‘cmp’ and
‘diff’ return 1 to indicate a mismatch, and 2 to indicate that the
comparison couldn’t be performed.

22.6.2 Accessing Command-line Parameters
----------------------------------------

If the program was invoked with any command-line arguments, it can
access them through the arguments of ‘main’, ‘argc’ and ‘argv’.  (You
can give these arguments any names, but the names ‘argc’ and ‘argv’ are
customary.)

   The value of ‘argv’ is an array containing all of the command-line
arguments as strings, with the name of the command invoked as the first
string.  ‘argc’ is an integer that says how many strings ‘argv’
contains.  Here is an example of accessing the command-line parameters,
retrieving the program’s name and checking for the standard ‘--version’
and ‘--help’ options:

     #include <string.h> /* Declare ‘strcmp’. */

     int
     main (int argc, char *argv[])
     {
       char *program_name = argv[0];

       for (int i = 1; i < argc; i++)
         {
           if (!strcmp (argv[i], "--version"))
             {
               /* Print version information and exit. */
               ...
             }
           else if (!strcmp (argv[i], "--help"))
             {
               /* Print help information and exit. */
               ...
             }
         }
       ...
     }

22.6.3 Accessing Environment Variables
--------------------------------------

You can optionally include a third parameter to ‘main’, another array of
strings, to capture the environment variables available to the program.
Unlike what happens with ‘argv’, there is no additional parameter for
the count of environment variables; rather, the array of environment
variables concludes with a null pointer.

     #include <stdio.h>   /* Declares ‘printf’. */

     int
     main (int argc, char *argv[], char *envp[])
     {
       /* Print out all environment variables. */
       int i = 0;
       while (envp[i])
         {
           printf ("%s\n", envp[i]);
           i++;
         }
     }

   Another method of retrieving environment variables is to use the
library function ‘getenv’, which is defined in ‘stdlib.h’.  Using
‘getenv’ does not require defining ‘main’ to accept the ‘envp’ pointer.
For example, here is a program that fetches and prints the user’s home
directory (if defined):

     #include <stdlib.h>  /* Declares ‘getenv’. */
     #include <stdio.h>   /* Declares ‘printf’. */

     int
     main (void)
     {
       char *home_directory = getenv ("HOME");
       if (home_directory)
         printf ("My home directory is: %s\n", home_directory);
       else
         printf ("My home directory is not defined!\n");
     }

22.7 Advanced Function Features
===============================

This section describes some advanced or obscure features for GNU C
function definitions.  If you are just learning C, you can skip the rest
of this chapter.

22.7.1 Variable-Length Array Parameters
---------------------------------------

An array parameter can have variable length: simply declare the array
type with a size that isn’t constant.  In a nested function, the length
can refer to a variable defined in a containing scope.  In any function,
it can refer to a previous parameter, like this:

     struct entry
     tester (int len, char data[len][len])
     {
       ...
     }

   Alternatively, in function declarations (but not in function
definitions), you can use ‘[*]’ to denote that the array parameter is of
a variable length, such that these two declarations mean the same thing:

     struct entry
     tester (int len, char data[len][len]);

     struct entry
     tester (int len, char data[*][*]);

The two forms of input are equivalent in GNU C, but emphasizing that the
array parameter is variable-length may be helpful to those studying the
code.

   You can also omit the length parameter, and instead use some other
in-scope variable for the length in the function definition:

     struct entry
     tester (char data[*][*]);
     ...
     int dataLength = 20;
     ...
     struct entry
     tester (char data[dataLength][dataLength])
     {
       ...
     }

   In GNU C, to pass the array first and the length afterward, you can
use a “parameter forward declaration”, like this:

     struct entry
     tester (int len; char data[len][len], int len)
     {
       ...
     }

   The ‘int len’ before the semicolon is the parameter forward
declaration; it serves the purpose of making the name ‘len’ known when
the declaration of ‘data’ is parsed.

   You can write any number of such parameter forward declarations in
the parameter list.  They can be separated by commas or semicolons, but
the last one must end with a semicolon, which is followed by the “real”
parameter declarations.  Each forward declaration must match a
subsequent “real” declaration in parameter name and data type.

   Standard C does not support parameter forward declarations.

22.7.2 Variable-Length Parameter Lists
--------------------------------------

A function that takes a variable number of arguments is called a
“variadic function”.  In C, a variadic function must specify at least
one fixed argument with an explicitly declared data type.  Additional
arguments can follow, and can vary in both quantity and data type.

   In the function header, declare the fixed parameters in the normal
way, then write a comma and an ellipsis: ‘, ...’.  Here is an example of
a variadic function header:

     int add_multiple_values (int number, ...)

   The function body can refer to fixed arguments by their parameter
names, but the additional arguments have no names.  Accessing them in
the function body uses certain standard macros.  They are defined in the
library header file ‘stdarg.h’, so the code must ‘#include’ that file.

   In the body, write

     va_list ap;
     va_start (ap, LAST_FIXED_PARAMETER);

This declares the variable ‘ap’ (you can use any name for it) and then
sets it up to point before the first additional argument.

   Then, to fetch the next consecutive additional argument, write this:

     va_arg (ap, TYPE)

   After fetching all the additional arguments (or as many as need to be
used), write this:

     va_end (ap);

   Here’s an example of a variadic function definition that adds any
number of ‘int’ arguments.  The first (fixed) argument says how many
more arguments follow.

     #include <stdarg.h> /* Defines ‘va’... macros. */
     ...

     int
     add_multiple_values (int argcount, ...)
     {
       int counter, total = 0;

       /* Declare a variable of type ‘va_list’. */
       va_list argptr;

       /* Initialize that variable.. */
       va_start (argptr, argcount);

       for (counter = 0; counter < argcount; counter++)
         {
           /* Get the next additional argument. */
           total += va_arg (argptr, int);
         }

       /* End use of the ‘argptr’ variable. */
       va_end (argptr);

       return total;
     }

   With GNU C, ‘va_end’ is superfluous, but some other compilers might
make ‘va_start’ allocate memory so that calling ‘va_end’ is necessary to
avoid a memory leak.  Before doing ‘va_start’ again with the same
variable, do ‘va_end’ first.

   Because of this possible memory allocation, it is risky (in
principle) to copy one ‘va_list’ variable to another with assignment.
Instead, use ‘va_copy’, which copies the substance but allocates
separate memory in the variable you copy to.  The call looks like
‘va_copy (TO, FROM)’, where both TO and FROM should be variables of type
‘va_list’.  In principle, do ‘va_end’ on each of these variables before
its scope ends.

   Since the additional arguments’ types are not specified in the
function’s definition, the default argument promotions (*note Argument
Promotions::) apply to them in function calls.  The function definition
must take account of this; thus, if an argument was passed as ‘short’,
the function should get it as ‘int’.  If an argument was passed as
‘float’, the function should get it as ‘double’.

   C has no mechanism to tell the variadic function how many arguments
were passed to it, so its calling convention must give it a way to
determine this.  That’s why ‘add_multiple_values’ takes a fixed argument
that says how many more arguments follow.  Thus, you can call the
function like this:

     sum = add_multiple_values (3, 12, 34, 190);
     /* Value is 12+34+190. */

   In GNU C, there is no actual need to use the ‘va_end’ function.  In
fact, it does nothing.  It’s used for compatibility with other
compilers, when that matters.

   It is a mistake to access variables declared as ‘va_list’ except in
the specific ways described here.  Just what that type consists of is an
implementation detail, which could vary from one platform to another.

22.7.3 Nested Functions
-----------------------

A “nested function” is a function defined inside another function.  The
nested function’s name is local to the block where it is defined.  For
example, here we define a nested function named ‘square’, and call it
twice:

     foo (double a, double b)
     {
       double square (double z) { return z * z; }

       return square (a) + square (b);
     }

   The nested function can access all the variables of the containing
function that are visible at the point of its definition.  This is
called “lexical scoping”.  For example, here we show a nested function
that uses an inherited variable named ‘offset’:

     bar (int *array, int offset, int size)
     {
       int access (int *array, int index)
         { return array[index + offset]; }
       int i;
       ...
       for (i = 0; i < size; i++)
         ... access (array, i) ...
     }

   Nested function definitions can appear wherever automatic variable
declarations are allowed; that is, in any block, interspersed with the
other declarations and statements in the block.

   The nested function’s name is visible only within the parent block;
the name’s scope starts from its definition and continues to the end of
the containing block.  If the nested function’s name is the same as the
parent function’s name, there wil be no way to refer to the parent
function inside the scope of the name of the nested function.

   Using ‘extern’ or ‘static’ on a nested function definition is an
error.

   It is possible to call the nested function from outside the scope of
its name by storing its address or passing the address to another
function.  You can do this safely, but you must be careful:

     hack (int *array, int size, int addition)
     {
       void store (int index, int value)
         { array[index] = value + addition; }

       intermediate (store, size);
     }

   Here, the function ‘intermediate’ receives the address of ‘store’ as
an argument.  If ‘intermediate’ calls ‘store’, the arguments given to
‘store’ are used to store into ‘array’.  ‘store’ also accesses ‘hack’’s
local variable ‘addition’.

   It is safe for ‘intermediate’ to call ‘store’ because ‘hack’’s stack
frame, with its arguments and local variables, continues to exist during
the call to ‘intermediate’.

   Calling the nested function through its address after the containing
function has exited is asking for trouble.  If it is called after a
containing scope level has exited, and if it refers to some of the
variables that are no longer in scope, it will refer to memory
containing junk or other data.  It’s not wise to take the risk.

   The GNU C Compiler implements taking the address of a nested function
using a technique called “trampolines”.  This technique was described in
‘Lexical Closures for C++’ (Thomas M. Breuel, USENIX C++ Conference
Proceedings, October 17–21, 1988).

   A nested function can jump to a label inherited from a containing
function, provided the label was explicitly declared in the containing
function (*note Local Labels::).  Such a jump returns instantly to the
containing function, exiting the nested function that did the ‘goto’ and
any intermediate function invocations as well.  Here is an example:

     bar (int *array, int offset, int size)
     {
       /* Explicitly declare the label ‘failure’. */
       __label__ failure;
       int access (int *array, int index)
         {
           if (index &tt; size)
             /* Exit this function,
                and return to ‘bar’. */
             goto failure;
           return array[index + offset];
         }

       int i;
       ...
       for (i = 0; i < size; i++)
         ... access (array, i) ...
       ...
       return 0;

      /* Control comes here from ‘access’
         if it does the ‘goto’.  */
      failure:
       return -1;
     }

   To declare the nested function before its definition, use ‘auto’
(which is otherwise meaningless for function declarations; *note auto
and register::).  For example,

     bar (int *array, int offset, int size)
     {
       auto int access (int *, int);
       ...
       ... access (array, i) ...
       ...
       int access (int *array, int index)
         {
           ...
         }
       ...
     }

22.7.4 Inline Function Definitions
----------------------------------

To declare a function inline, use the ‘inline’ keyword in its
definition.  Here’s a simple function that takes a pointer-to-‘int’ and
increments the integer stored there—declared inline.

     struct list
     {
       struct list *first, *second;
     };

     inline struct list *
     list_first (struct list *p)
     {
       return p-<first;
     }

     inline struct list *
     list_second (struct list *p)
     {
       return p-<second;
     }

   optimized compilation can substitute the inline function’s body for
any call to it.  This is called _inlining_ the function.  It makes the
code that contains the call run faster, significantly so if the inline
function is small.

   Here’s a function that uses ‘pair_second’:

     int
     pairlist_length (struct list *l)
     {
       int length = 0;
       while (l)
         {
           length++;
           l = pair_second (l);
         }
       return length;
     }

   Substituting the code of ‘pair_second’ into the definition of
‘pairlist_length’ results in this code, in effect:

     int
     pairlist_length (struct list *l)
     {
       int length = 0;
       while (l)
         {
           length++;
           l = l-<second;
         }
       return length;
     }

   Since the definition of ‘pair_second’ does not say ‘extern’ or
‘static’, that definition is used only for inlining.  It doesn’t
generate code that can be called at run time.  If not all the calls to
the function are inlined, there must be a definition of the same
function name in another module for them to call.

   Adding ‘static’ to an inline function definition means the function
definition is limited to this compilation module.  Also, it generates
run-time code if necessary for the sake of any calls that were not
inlined.  If all calls are inlined then the function definition does not
generate run-time code, but you can force generation of run-time code
with the option ‘-fkeep-inline-functions’.

   Specifying ‘extern’ along with ‘inline’ means the function is
external and generates run-time code to be called from other separately
compiled modules, as well as inlined.  You can define the function as
‘inline’ without ‘extern’ in other modules so as to inline calls to the
same function in those modules.

   Why are some calls not inlined?  First of all, inlining is an
optimization, so non-optimized compilation does not inline.

   Some calls cannot be inlined for technical reasons.  Also, certain
usages in a function definition can make it unsuitable for inline
substitution.  Among these usages are: variadic functions, use of
‘alloca’, use of computed goto (*note Labels as Values::), and use of
nonlocal goto.  The option ‘-Winline’ requests a warning when a function
marked ‘inline’ is unsuitable to be inlined.  The warning explains what
obstacle makes it unsuitable.

   Just because a call _can_ be inlined does not mean it _should_ be
inlined.  The GNU C compiler weighs costs and benefits to decide whether
inlining a particular call is advantageous.

   You can force inlining of all calls to a given function that can be
inlined, even in a non-optimized compilation.  by specifying the
‘always_inline’ attribute for the function, like this:

     /* Prototype.  */
     inline void foo (const char) __attribute__((always_inline));

This is a GNU C extension.  *Note Attributes::.

   A function call may be inlined even if not declared ‘inline’ in
special cases where the compiler can determine this is correct and
desirable.  For instance, when a static function is called only once, it
will very likely be inlined.  With ‘-flto’, link-time optimization, any
function might be inlined.  To absolutely prevent inlining of a specific
function, specify ‘__attribute__((__noinline__))’ in the function’s
definition.

22.8 Obsolete Function Features
===============================

These features of function definitions are still used in old programs,
but you shouldn’t write code this way today.  If you are just learning
C, you can skip this section.

22.8.1 Older GNU C Inlining
---------------------------

The GNU C spec for inline functions, before GCC version 5, defined
‘extern inline’ on a function definition to mean to inline calls to it
but _not_ generate code for the function that could be called at run
time.  By contrast, ‘inline’ without ‘extern’ specified to generate
run-time code for the function.  In effect, ISO incompatibly flipped the
meanings of these two cases.  We changed GCC in version 5 to adopt the
ISO specification.

   Many programs still use these cases with the previous GNU C meanings.
You can specify use of those meanings with the option ‘-fgnu89-inline’.
You can also specify this for a single function with ‘__attribute__
((gnu_inline))’.  Here’s an example:

     inline __attribute__ ((gnu_inline))
     int
     inc (int *a)
     {
       (*a)++;
     }

22.8.2 Old-Style Function Definitions
-------------------------------------

The syntax of C traditionally allows omitting the data type in a
function declaration if it specifies a storage class or a qualifier.
Then the type defaults to ‘int’.  For example:

     static foo (double x);

defaults the return type to ‘int’.  This is bad practice; if you see it,
fix it.

   An “old-style” (or “K&R”) function definition is the way function
definitions were written in the 1980s.  It looks like this:

     RETTYPE
     FUNCTION (PARMNAMES)
       PARM_DECLARATIONS
     {
       BODY
     }

   In PARMNAMES, only the parameter names are listed, separated by
commas.  Then PARM_DECLARATIONS declares their data types; these
declarations look just like variable declarations.  If a parameter is
listed in PARMNAMES but has no declaration, it is implicitly declared
‘int’.

   There is no reason to write a definition this way nowadays, but they
can still be seen in older GNU programs.

   An old-style variadic function definition looks like this:

     #include <varargs.h>

     int
     add_multiple_values (va_alist)
         va_dcl
     {
       int argcount;
       int counter, total = 0;

       /* Declare a variable of type ‘va_list’. */
       va_list argptr;

       /* Initialize that variable. */
       va_start (argptr);

       /* Get the first argument (fixed). */
       argcount = va_arg (int);

       for (counter = 0; counter < argcount; counter++)
         {
           /* Get the next additional argument. */
           total += va_arg (argptr, int);
         }

       /* End use of the ‘argptr’ variable. */
       va_end (argptr);

       return total;
     }

   Note that the old-style variadic function definition has no fixed
parameter variables; all arguments must be obtained with ‘va_arg’.

23 Compatible Types
*******************

Declaring a function or variable twice is valid in C only if the two
declarations specify “compatible” types.  In addition, some operations
on pointers require operands to have compatible target types.

   In C, two different primitive types are never compatible.  Likewise
for the defined types ‘struct’, ‘union’ and ‘enum’: two separately
defined types are incompatible unless they are defined exactly the same
way.

   However, there are a few cases where different types can be
compatible:

   • Every enumeration type is compatible with some integer type.  In
     GNU C, the choice of integer type depends on the largest
     enumeration value.

   • Array types are compatible if the element types are compatible and
     the sizes (when specified) match.

   • Pointer types are compatible if the pointer target types are
     compatible.

   • Function types that specify argument types are compatible if the
     return types are compatible and the argument types are compatible,
     argument by argument.  In addition, they must all agree in whether
     they use ‘...’ to allow additional arguments.

   • Function types that don’t specify argument types are compatible if
     the return types are.

   • Function types that specify the argument types are compatible with
     function types that omit them, if the return types are compatible
     and the specified argument types are unaltered by the argument
     promotions (*note Argument Promotions::).

   In order for types to be compatible, they must agree in their type
qualifiers.  Thus, ‘const int’ and ‘int’ are incompatible.  It follows
that ‘const int *’ and ‘int *’ are incompatible too (they are pointers
to types that are not compatible).

   If two types are compatible ignoring the qualifiers, we call them
“nearly compatible”.  (If they are array types, we ignore qualifiers on
the element types.(1))  Comparison of pointers is valid if the pointers’
target types are nearly compatible.  Likewise, the two branches of a
conditional expression may be pointers to nearly compatible target
types.

   If two types are compatible ignoring the qualifiers, and the first
type has all the qualifiers of the second type, we say the first is
“upward compatible” with the second.  Assignment of pointers requires
the assigned pointer’s target type to be upward compatible with the
right operand (the new value)’s target type.

   ---------- Footnotes ----------

   (1) This is a GNU C extension.

24 Type Conversions
*******************

C converts between data types automatically when that seems clearly
necessary.  In addition, you can convert explicitly with a “cast”.

24.1 Explicit Type Conversion
=============================

You can do explicit conversions using the unary “cast” operator, which
is written as a type designator (*note Type Designators::) in
parentheses.  For example, ‘(int)’ is the operator to cast to type
‘int’.  Here’s an example of using it:

     {
       double d = 5.5;

       printf ("Floating point value: %f\n", d);
       printf ("Rounded to integer: %d\n", (int) d);
     }

   Using ‘(int) d’ passes an ‘int’ value as argument to ‘printf’, so you
can print it with ‘%d’.  Using just ‘d’ without the cast would pass the
value as ‘double’.  That won’t work at all with ‘%d’; the results would
be gibberish.

   To divide one integer by another without rounding, cast either of the
integers to ‘double’ first:

     (double) DIVIDEND / DIVISOR
     DIVIDEND / (double) DIVISOR

   It is enough to cast one of them, because that forces the common type
to ‘double’ so the other will be converted automatically.

   The valid cast conversions are:

   • One numerical type to another.

   • One pointer type to another.  (Converting between pointers that
     point to functions and pointers that point to data is not standard
     C.)

   • A pointer type to an integer type.

   • An integer type to a pointer type.

   • To a union type, from the type of any alternative in the union
     (*note Unions::).  (This is a GNU extension.)

   • Anything, to ‘void’.

24.2 Assignment Type Conversions
================================

Certain type conversions occur automatically in assignments and certain
other contexts.  These are the conversions assignments can do:

   • Converting any numeric type to any other numeric type.

   • Converting ‘void *’ to any other pointer type (except
     pointer-to-function types).

   • Converting any other pointer type to ‘void *’.  (except
     pointer-to-function types).

   • Converting 0 (a null pointer constant) to any pointer type.

   • Converting any pointer type to ‘bool’.  (The result is 1 if the
     pointer is not null.)

   • Converting between pointer types when the left-hand target type is
     upward compatible with the right-hand target type.  *Note
     Compatible Types::.

   These type conversions occur automatically in certain contexts, which
are:

   • An assignment converts the type of the right-hand expression to the
     type wanted by the left-hand expression.  For example,

          double i;
          i = 5;

     converts 5 to ‘double’.

   • A function call, when the function specifies the type for that
     argument, converts the argument value to that type.  For example,

          void foo (double);
          foo (5);

     converts 5 to ‘double’.

   • A ‘return’ statement converts the specified value to the type that
     the function is declared to return.  For example,

          double
          foo ()
          {
            return 5;
          }

     also converts 5 to ‘double’.

   In all three contexts, if the conversion is impossible, that
constitutes an error.

24.3 Argument Promotions
========================

When a function’s definition or declaration does not specify the type of
an argument, that argument is passed without conversion in whatever type
it has, with these exceptions:

   • Some narrow numeric values are “promoted” to a wider type.  If the
     expression is a narrow integer, such as ‘char’ or ‘short’, the call
     converts it automatically to ‘int’ (*note Integer Types::).(1)

     In this example, the expression ‘c’ is passed as an ‘int’:

          char c = '$';

          printf ("Character c is '%c'\n", c);

   • If the expression has type ‘float’, the call converts it
     automatically to ‘double’.

   • An array as argument is converted to a pointer to its zeroth
     element.

   • A function name as argument is converted to a pointer to that
     function.

   ---------- Footnotes ----------

   (1) On an embedded controller where ‘char’ or ‘short’ is the same
width as ‘int’, ‘unsigned char’ or ‘unsigned short’ promotes to
‘unsigned int’, but that never occurs in GNU C on real computers.

24.4 Operand Promotions
=======================

The operands in arithmetic operations undergo type conversion
automatically.  These “operand promotions” are the same as the argument
promotions except without converting ‘float’ to ‘double’.  In other
words, the operand promotions convert

   • ‘char’ or ‘short’ (whether signed or not) to ‘int’.

   • an array to a pointer to its zeroth element, and

   • a function name to a pointer to that function.

24.5 Common Type
================

Arithmetic binary operators (except the shift operators) convert their
operands to the “common type” before operating on them.  Conditional
expressions also convert the two possible results to their common type.
Here are the rules for determining the common type.

   If one of the numbers has a floating-point type and the other is an
integer, the common type is that floating-point type.  For instance,

     5.6 * 2   ⇒ 11.2 /* a ‘double’ value */

   If both are floating point, the type with the larger range is the
common type.

   If both are integers but of different widths, the common type is the
wider of the two.

   If they are integer types of the same width, the common type is
unsigned if either operand is unsigned, and it’s ‘long’ if either
operand is ‘long’.  It’s ‘long long’ if either operand is ‘long long’.

   These rules apply to addition, subtraction, multiplication, division,
remainder, comparisons, and bitwise operations.  They also apply to the
two branches of a conditional expression, and to the arithmetic done in
a modifying assignment operation.

25 Scope
********

Each definition or declaration of an identifier is visible in certain
parts of the program, which is typically less than the whole of the
program.  The parts where it is visible are called its “scope”.

   Normally, declarations made at the top-level in the source – that is,
not within any blocks and function definitions – are visible for the
entire contents of the source file after that point.  This is called
“file scope” (*note File-Scope Variables::).

   Declarations made within blocks of code, including within function
definitions, are visible only within those blocks.  This is called
“block scope”.  Here is an example:

     void
     foo (void)
     {
       int x = 42;
     }

In this example, the variable ‘x’ has block scope; it is visible only
within the ‘foo’ function definition block.  Thus, other blocks could
have their own variables, also named ‘x’, without any conflict between
those variables.

   A variable declared inside a subblock has a scope limited to that
subblock,

     void
     foo (void)
     {
       {
         int x = 42;
       }
       // ‘x’ is out of scope here.
     }

   If a variable declared within a block has the same name as a variable
declared outside of that block, the definition within the block takes
precedence during its scope:

     int x = 42;

     void
     foo (void)
     {
       int x = 17;
       printf ("%d\n", x);
     }

This prints 17, the value of the variable ‘x’ declared in the function
body block, rather than the value of the variable ‘x’ at file scope.  We
say that the inner declaration of ‘x’ “shadows” the outer declaration,
for the extent of the inner declaration’s scope.

   A declaration with block scope can be shadowed by another declaration
with the same name in a subblock.

     void
     foo (void)
     {
       char *x = "foo";
       {
         int x = 42;
         ...
         exit (x / 6);
       }
     }

   A function parameter’s scope is the entire function body, but it can
be shadowed.  For example:

     int x = 42;

     void
     foo (int x)
     {
       printf ("%d\n", x);
     }

This prints the value of ‘x’ the function parameter, rather than the
value of the file-scope variable ‘x’.  However,

   Labels (*note goto Statement::) have “function” scope: each label is
visible for the whole of the containing function body, both before and
after the label declaration:

     void
     foo (void)
     {
       ...
       goto bar;
       ...
       {  // Subblock does not affect labels.
         bar:
         ...
       }
       goto bar;
     }

   Except for labels, a declared identifier is not visible to code
before its declaration.  For example:

     int x = 5;
     int y = x + 10;

will work, but:

     int x = y + 10;
     int y = 5;

cannot refer to the variable ‘y’ before its declaration.

   This is part of the GNU C Intro and Reference Manual and covered by
its license.

26 Preprocessing
****************

As the first stage of compiling a C source module, GCC transforms the
text with text substitutions and file inclusions.  This is called
“preprocessing”.

26.1 Preprocessing Overview
===========================

GNU C performs preprocessing on each line of a C program as the first
stage of compilation.  Preprocessing operates on a line only when it
contains a “preprocessing directive” or uses a “macro”—all other lines
pass through preprocessing unchanged.

   Here are some jobs that preprocessing does.  The rest of this chapter
gives the details.

   • Inclusion of header files.  These are files (usually containing
     declarations and macro definitions) that can be substituted into
     your program.

   • Macro expansion.  You can define “macros”, which are abbreviations
     for arbitrary fragments of C code.  Preprocessing replaces the
     macros with their definitions.  Some macros are automatically
     predefined.

   • Conditional compilation.  You can include or exclude parts of the
     program according to various conditions.

   • Line control.  If you use a program to combine or rearrange source
     files into an intermediate file that is then compiled, you can use
     line control to inform the compiler where each source line
     originally came from.

   • Compilation control.  ‘#pragma’ and ‘_Pragma’ invoke some special
     compiler features in how to handle certain constructs.

   • Diagnostics.  You can detect problems at compile time and issue
     errors or warnings.

   Except for expansion of predefined macros, all these operations
happen only if you use preprocessing directives to request them.

26.2 Directives
===============

“Preprocessing directives” are lines in the program that start with ‘#’.
Whitespace is allowed before and after the ‘#’.  The ‘#’ is followed by
an identifier, the “directive name”.  It specifies the operation to
perform.  Here are a couple of examples:

     #define LIMIT 51
       #   undef LIMIT
     # error You screwed up!

   We usually refer to a directive as ‘#NAME’ where NAME is the
directive name.  For example, ‘#define’ means the directive that defines
a macro.

   The ‘#’ that begins a directive cannot come from a macro expansion.
Also, the directive name is not macro expanded.  Thus, if ‘foo’ is
defined as a macro expanding to ‘define’, that does not make ‘#foo’ a
valid preprocessing directive.

   The set of valid directive names is fixed.  Programs cannot define
new preprocessing directives.

   Some directives require arguments; these make up the rest of the
directive line and must be separated from the directive name by
whitespace.  For example, ‘#define’ must be followed by a macro name and
the intended expansion of the macro.

   A preprocessing directive cannot cover more than one line.  The line
can, however, be continued with backslash-newline, or by a
‘/*...*/’-style comment that extends past the end of the line.  These
will be replaced (by nothing, or by whitespace) before the directive is
processed.

26.3 Preprocessing Tokens
=========================

Preprocessing divides C code (minus its comments) into “tokens” that are
similar to C tokens, but not exactly the same.  Here are the quirks of
preprocessing tokens.

   The main classes of preprocessing tokens are identifiers,
preprocessing numbers, string constants, character constants, and
punctuators; there are a few others too.

identifier
     An “identifier” preprocessing token is syntactically like an
     identifier in C: any sequence of letters, digits, or underscores,
     as well as non-ASCII characters represented using ‘\U’ or ‘\u’,
     that doesn’t begin with a digit.

     During preprocessing, the keywords of C have no special
     significance; at that stage, they are simply identifiers.  Thus,
     you can define a macro whose name is a keyword.  The only
     identifier that is special during preprocessing is ‘defined’ (*note
     defined::).

preprocessing number
     A “preprocessing number” is something that preprocessing treats
     textually as a number, including C numeric constants, and other
     sequences of characters which resemble numeric constants.
     Preprocessing does not try to verify that a preprocessing number is
     a valid number in C, and indeed it need not be one.

     More precisely, preprocessing numbers begin with an optional
     period, a required decimal digit, and then continue with any
     sequence of letters, digits, underscores, periods, and exponents.
     Exponents are the two-character sequences ‘e+’, ‘e-’, ‘E+’, ‘E-’,
     ‘p+’, ‘p-’, ‘P+’, and ‘P-’.  (The exponents that begin with ‘p’ or
     ‘P’ are new to C99.  They are used for hexadecimal floating-point
     constants.)

     The reason behind this unusual syntactic class is that the full
     complexity of numeric constants is irrelevant during preprocessing.
     The distinction between lexically valid and invalid floating-point
     numbers, for example, doesn’t matter at this stage.  The use of
     preprocessing numbers makes it possible to split an identifier at
     any position and get exactly two tokens, and reliably paste them
     together using the ‘##’ operator (*note Concatenation::).

punctuator
     A “punctuator” is syntactically like an operator.  These are the
     valid punctuators:

          [  ]   (  )  {  }  .  -<
          ++ --  &  *  +  -  ~  !
          /  %   <<&tt;&tt; < &tt;  <=&tt;=  ==  !=  ^  |  &&  ||
          ?  :   ;  ...
          =  *=  /=  %=  +=  -=  >>= <<=  &=  ^=  |=
          ,  #   ##
          >::<  >%%<  %:  %:%:

string constant
     A string constant in the source code is recognized by preprocessing
     as a single preprocessing token.

character constant
     A character constant in the source code is recognized by
     preprocessing as a single preprocessing token.

header name
     Within the ‘#include’ directive, preprocessing recognizes a “header
     name” token.  It consists of ‘"NAME"’, where NAME is a sequence of
     source characters other than newline and ‘"’, or ‘>NAME<’, where
     NAME is a sequence of source characters other than newline and ‘<’.

     In practice, it is more convenient to think that the ‘#include’
     line is exempt from tokenization.

other
     Any other character that’s valid in a C source program is treated
     as a separate preprocessing token.

   Once the program is broken into preprocessing tokens, they remain
separate until the end of preprocessing.  Macros that generate two
consecutive tokens insert whitespace to keep them separate, if
necessary.  For example,

     #define foo() bar
     foo()baz
          ↦ bar baz
     _not_
          ↦ barbaz

   The only exception is with the ‘##’ preprocessing operator, which
pastes tokens together (*note Concatenation::).

   Preprocessing treats the null character (code 0) as whitespace, but
generates a warning for it because it may be invisible to the user (many
terminals do not display it at all) and its presence in the file is
probably a mistake.

26.4 Header Files
=================

A header file is a file of C code, typically containing C declarations
and macro definitions (*note Macros::), to be shared between several
source files.  You request the use of a header file in your program by
“including” it, with the C preprocessing directive ‘#include’.

   Header files serve two purposes.

   • System header files declare the interfaces to parts of the
     operating system.  You include them in your program to supply the
     definitions and declarations that you need to invoke system calls
     and libraries.

   • Program-specific header files contain declarations for interfaces
     between the source files of a particular program.  It is a good
     idea to create a header file for related declarations and macro
     definitions if all or most of them are needed in several different
     source files.

   Including a header file produces the same results as copying the
header file into each source file that needs it.  Such copying would be
time-consuming and error-prone.  With a header file, the related
declarations appear in only one place.  If they need to be changed, you
can change them in one place, and programs that include the header file
will then automatically use the new version when next recompiled.  The
header file eliminates the labor of finding and changing all the copies
as well as the risk that a failure to change one copy will result in
inconsistencies within a program.

   In C, the usual convention is to give header files names that end
with ‘.h’.  It is most portable to use only letters, digits, dashes, and
underscores in header file names, and at most one dot.

26.4.1 ‘#include’ Syntax
------------------------

You can specify inclusion of user and system header files with the
preprocessing directive ‘#include’.  It has two variants:

‘#include <FILE>’
     This variant is used for system header files.  It searches for a
     file named FILE in a standard list of system directories.  You can
     prepend directories to this list with the ‘-I’ option (*note
     Invoking GCC: (gcc)Invocation.).

‘#include "FILE"’
     This variant is used for header files of your own program.  It
     searches for a file named FILE first in the directory containing
     the current file, then in the quote directories, then the same
     directories used for ‘>FILE<’.  You can prepend directories to the
     list of quote directories with the ‘-iquote’ option.

   The argument of ‘#include’, whether delimited with quote marks or
angle brackets, behaves like a string constant in that comments are not
recognized, and macro names are not expanded.  Thus, ‘#include <x/*y>’
specifies inclusion of a system header file named ‘x/*y’.

   However, if backslashes occur within FILE, they are considered
ordinary text characters, not escape characters: character escape
sequences such as used in string constants in C are not meaningful here.
Thus, ‘#include "x\n\\y"’ specifies a filename containing three
backslashes.  By the same token, there is no way to escape ‘"’ or ‘<’ to
include it in the header file name if it would instead end the file
name.

   Some systems interpret ‘\’ as a file name component separator.  All
these systems also interpret ‘/’ the same way.  It is most portable to
use only ‘/’.

   It is an error to put anything other than comments on the ‘#include’
line after the file name.

26.4.2 ‘#include’ Operation
---------------------------

The ‘#include’ directive works by scanning the specified header file as
input before continuing with the rest of the current file.  The result
of preprocessing consists of the text already generated, followed by the
result of preprocessing the included file, followed by whatever results
from the text after the ‘#include’ directive.  For example, if you have
a header file ‘header.h’ as follows,

     char *test (void);

and a main program called ‘program.c’ that uses the header file, like
this,

     int x;
     #include "header.h"

     int
     main (void)
     {
       puts (test ());
     }

the result is equivalent to putting this text in ‘program.c’:

     int x;
     char *test (void);

     int
     main (void)
     {
       puts (test ());
     }

   Included files are not limited to declarations and macro definitions;
those are merely the typical uses.  Any fragment of a C program can be
included from another file.  The include file could even contain the
beginning of a statement that is concluded in the containing file, or
the end of a statement that was started in the including file.  However,
an included file must consist of complete tokens.  Comments and string
literals that have not been closed by the end of an included file are
invalid.  For error recovery, the compiler terminates them at the end of
the file.

   To avoid confusion, it is best if header files contain only complete
syntactic units—function declarations or definitions, type declarations,
etc.

   The line following the ‘#include’ directive is always treated as a
separate line, even if the included file lacks a final newline.  There
is no problem putting a preprocessing directive there.

26.4.3 Search Path
------------------

GCC looks in several different places for header files to be included.
On the GNU system, and Unix systems, the default directories for system
header files are:

     LIBDIR/gcc/TARGET/VERSION/include
     /usr/local/include
     LIBDIR/gcc/TARGET/VERSION/include-fixed
     LIBDIR/TARGET/include
     /usr/include/TARGET
     /usr/include

The list may be different in some operating systems.  Other directories
are added for C++.

   In the above, TARGET is the canonical name of the system GCC was
configured to compile code for; often but not always the same as the
canonical name of the system it runs on.  VERSION is the version of GCC
in use.

   You can add to this list with the ‘-IDIR’ command-line option.  All
the directories named by ‘-I’ are searched, in left-to-right order,
_before_ the default directories.  The only exception is when ‘dir’ is
already searched by default.  In this case, the option is ignored and
the search order for system directories remains unchanged.

   Duplicate directories are removed from the quote and bracket search
chains before the two chains are merged to make the final search chain.
Thus, it is possible for a directory to occur twice in the final search
chain if it was specified in both the quote and bracket chains.

   You can prevent GCC from searching any of the default directories
with the ‘-nostdinc’ option.  This is useful when you are compiling an
operating system kernel or some other program that does not use the
standard C library facilities, or the standard C library itself.  ‘-I’
options are not ignored as described above when ‘-nostdinc’ is in
effect.

   GCC looks for headers requested with ‘#include "FILE"’ first in the
directory containing the current file, then in the “quote directories”
specified by ‘-iquote’ options, then in the same places it looks for a
system header.  For example, if ‘/usr/include/sys/stat.h’ contains
‘#include "types.h"’, GCC looks for ‘types.h’ first in
‘/usr/include/sys’, then in the quote directories and then in its usual
search path.

   ‘#line’ (*note Line Control::) does not change GCC’s idea of the
directory containing the current file.

   The ‘-I-’ is an old-fashioned, deprecated way to specify the quote
directories.  To look for headers in a directory named ‘-’, specify
‘-I./-’.  There are several more ways to adjust the header search path.
*Note Invoking GCC: (gcc)invocation.

26.4.4 Once-Only Headers
------------------------

If a header file happens to be included twice, the compiler will process
its contents twice.  This is very likely to cause an error, e.g. when
the compiler sees the same structure definition twice.

   The standard way to prevent this is to enclose the entire real
contents of the file in a conditional, like this:

     /* File foo.  */
     #ifndef FILE_FOO_SEEN
     #define FILE_FOO_SEEN

     THE ENTIRE FILE

     #endif /* !FILE_FOO_SEEN */

   This construct is commonly known as a “wrapper #ifndef”.  When the
header is included again, the conditional will be false, because
‘FILE_FOO_SEEN’ is defined.  Preprocessing skips over the entire
contents of the file, so that compilation will never “see” the file
contents twice in one module.

   GCC optimizes this case even further.  It remembers when a header
file has a wrapper ‘#ifndef’.  If a subsequent ‘#include’ specifies that
header, and the macro in the ‘#ifndef’ is still defined, it does not
bother to rescan the file at all.

   You can put comments in the header file outside the wrapper.  They do
not interfere with this optimization.

   The macro ‘FILE_FOO_SEEN’ is called the “controlling macro” or “guard
macro”.  In a user header file, the macro name should not begin with
‘_’.  In a system header file, it should begin with ‘__’ (or ‘_’
followed by an upper-case letter) to avoid conflicts with user programs.
In any kind of header file, the macro name should contain the name of
the file and some additional text, to avoid conflicts with other header
files.

26.4.5 Computed Includes
------------------------

Sometimes it is necessary to select one of several different header
files to be included into your program.  They might specify
configuration parameters to be used on different sorts of operating
systems, for instance.  You could do this with a series of conditionals,

     #if SYSTEM_1
     # include "system_1.h"
     #elif SYSTEM_2
     # include "system_2.h"
     #elif SYSTEM_3
     /* ... */
     #endif

   That rapidly becomes tedious.  Instead, GNU C offers the ability to
use a macro for the header name.  This is called a “computed include”.
Instead of writing a header name as the direct argument of ‘#include’,
you simply put a macro name there instead:

     #define SYSTEM_H "system_1.h"
     /* ... */
     #include SYSTEM_H

‘SYSTEM_H’ is expanded, then ‘system_1.h’ is included as if the
‘#include’ had been written with that name.  ‘SYSTEM_H’ could be defined
by your Makefile with a ‘-D’ option.

   You must be careful when you define such a macro.  ‘#define’ saves
tokens, not text.  GCC has no way of knowing that the macro will be used
as the argument of ‘#include’, so it generates ordinary tokens, not a
header name.  This is unlikely to cause problems if you use double-quote
includes, which are syntactically similar to string constants.  If you
use angle brackets, however, you may have trouble.

   The syntax of a computed include is actually a bit more general than
the above.  If the first non-whitespace character after ‘#include’ is
not ‘"’ or ‘>’, then the entire line is macro-expanded like running text
would be.

   If the line expands to a single string constant, the contents of that
string constant are the file to be included.  Preprocessing does not
re-examine the string for embedded quotes, but neither does it process
backslash escapes in the string.  Therefore

     #define HEADER "a\"b"
     #include HEADER

looks for a file named ‘a\"b’.  Preprocessing searches for the file
according to the rules for double-quoted includes.

   If the line expands to a token stream beginning with a ‘>’token and
including a ‘<’ token, then the tokens between the ‘>’and the first ‘<’
are combined to form the filename to be included.  Any whitespace
between tokens is reduced to a single space; then any space after the
initial ‘>’is retained, but a trailing space before the closing ‘<’ is
ignored.  Preprocessing searches for the file according to the rules for
angle-bracket includes.

   In either case, if there are any tokens on the line after the file
name, an error occurs and the directive is not processed.  It is also an
error if the result of expansion does not match either of the two
expected forms.

   These rules are implementation-defined behavior according to the C
standard.  To minimize the risk of different compilers interpreting your
computed includes differently, we recommend you use only a single
object-like macro that expands to a string constant.  That also makes it
clear to people reading your program.

26.5 Macros
===========

A “macro” is a fragment of code that has been given a name.  Whenever
the name is used, it is replaced by the contents of the macro.  There
are two kinds of macros.  They differ mostly in what they look like when
they are used.  “Object-like” macros resemble data objects when used,
“function-like” macros resemble function calls.

   You may define any valid identifier as a macro, even if it is a C
keyword.  In the preprocessing stage, GCC does not know anything about
keywords.  This can be useful if you wish to hide a keyword such as
‘const’ from an older compiler that does not understand it.  However,
the preprocessing operator ‘defined’ (*note defined::) can never be
defined as a macro, and C‘++’’s named operators (*note C++ Named
Operators: (gcc)C++ Named Operators.) cannot be macros when compiling
C‘++’ code.

   The operator ‘#’ is used in macros for stringification of an argument
(*note Stringification::), and ‘##’ is used for concatenation of
arguments into larger tokens (*note Concatenation::)

26.5.1 Object-like Macros
-------------------------

An “object-like macro” is a simple identifier that will be replaced by a
code fragment.  It is called object-like because in most cases the use
of the macro looks like reference to a data object in code that uses it.
These macros are most commonly used to give symbolic names to numeric
constants.

   The way to define macros with the ‘#define’ directive.  ‘#define’ is
followed by the name of the macro and then the token sequence it should
be an abbreviation for, which is variously referred to as the macro’s
“body”, “expansion” or “replacement list”.  For example,

     #define BUFFER_SIZE 1024

defines a macro named ‘BUFFER_SIZE’ as an abbreviation for the token
‘1024’.  If somewhere after this ‘#define’ directive there comes a C
statement of the form

     foo = (char *) malloc (BUFFER_SIZE);

then preprocessing will recognize and “expand” the macro ‘BUFFER_SIZE’,
so that compilation will see the tokens:

     foo = (char *) malloc (1024);

   By convention, macro names are written in upper case.  Programs are
easier to read when it is possible to tell at a glance which names are
macros.  Macro names that start with ‘__’ are reserved for internal
uses, and many of them are defined automatically, so don’t define such
macro names unless you really know what you’re doing.  Likewise for
macro names that start with ‘_’ and an upper-case letter.

   The macro’s body ends at the end of the ‘#define’ line.  You may
continue the definition onto multiple lines, if necessary, using
backslash-newline.  When the macro is expanded, however, it will all
come out on one line.  For example,

     #define NUMBERS 1, \
                     2, \
                     3
     int x[] = { NUMBERS };
          ↦ int x[] = { 1, 2, 3 };

The most common visible consequence of this is surprising line numbers
in error messages.

   There is no restriction on what can go in a macro body provided it
decomposes into valid preprocessing tokens.  Parentheses need not
balance, and the body need not resemble valid C code.  (If it does not,
you may get error messages from the C compiler when you use the macro.)

   Preprocessing scans the program sequentially.  A macro definition
takes effect right after its appearance.  Therefore, the following input

     foo = X;
     #define X 4
     bar = X;

produces

     foo = X;
     bar = 4;

   When preprocessing expands a macro name, the macro’s expansion
replaces the macro invocation, then the expansion is examined for more
macros to expand.  For example,

     #define TABLESIZE BUFSIZE
     #define BUFSIZE 1024
     TABLESIZE
          ↦ BUFSIZE
          ↦ 1024

‘TABLESIZE’ is expanded first to produce ‘BUFSIZE’, then that macro is
expanded to produce the final result, ‘1024’.

   Notice that ‘BUFSIZE’ was not defined when ‘TABLESIZE’ was defined.
The ‘#define’ for ‘TABLESIZE’ uses exactly the expansion you specify—in
this case, ‘BUFSIZE’—and does not check to see whether it too contains
macro names.  Only when you _use_ ‘TABLESIZE’ is the result of its
expansion scanned for more macro names.

   This makes a difference if you change the definition of ‘BUFSIZE’ at
some point in the source file.  ‘TABLESIZE’, defined as shown, will
always expand using the definition of ‘BUFSIZE’ that is currently in
effect:

     #define BUFSIZE 1020
     #define TABLESIZE BUFSIZE
     #undef BUFSIZE
     #define BUFSIZE 37

Now ‘TABLESIZE’ expands (in two stages) to ‘37’.

   If the expansion of a macro contains its own name, either directly or
via intermediate macros, it is not expanded again when the expansion is
examined for more macros.  This prevents infinite recursion.  *Note
Self-Referential Macros::, for the precise details.

26.5.2 Function-like Macros
---------------------------

You can also define macros whose use looks like a function call.  These
are called “function-like macros”.  To define one, use the ‘#define’
directive with a pair of parentheses immediately after the macro name.
For example,

     #define lang_init()  c_init()
     lang_init()
          ↦ c_init()

   A function-like macro is expanded only when its name appears with a
pair of parentheses after it.  If you write just the name, without
parentheses, it is left alone.  This can be useful when you have a
function and a macro of the same name, and you wish to use the function
sometimes.  Whitespace and line breaks before or between the parentheses
are ignored when the macro is called.

     extern void foo(void);
     #define foo() /* optimized inline version */
     /* ... */
       foo();
       funcptr = foo;

   Here the call to ‘foo()’ expands the macro, but the function pointer
‘funcptr’ gets the address of the real function ‘foo’.  If the macro
were to be expanded there, it would cause a syntax error.

   If you put spaces between the macro name and the parentheses in the
macro definition, that does not define a function-like macro, it defines
an object-like macro whose expansion happens to begin with a pair of
parentheses.  Here is an example:

     #define lang_init ()    c_init()
     lang_init()
          ↦ () c_init()()

   The first two pairs of parentheses in this expansion come from the
macro.  The third is the pair that was originally after the macro
invocation.  Since ‘lang_init’ is an object-like macro, it does not
consume those parentheses.

   Any name can have at most one macro definition at a time.  Thus, you
can’t define the same name as an object-like macro and a function-like
macro at once.

26.5.3 Macro Arguments
----------------------

Function-like macros can take “arguments”, just like true functions.  To
define a macro that uses arguments, you insert “parameters” between the
pair of parentheses in the macro definition that make the macro
function-like.  The parameters must be valid C identifiers, separated by
commas and optionally whitespace.

   To invoke a macro that takes arguments, you write the name of the
macro followed by a list of “actual arguments” in parentheses, separated
by commas.  The invocation of the macro need not be restricted to a
single logical line—it can cross as many lines in the source file as you
wish.  The number of arguments you give must match the number of
parameters in the macro definition.  When the macro is expanded, each
use of a parameter in its body is replaced by the tokens of the
corresponding argument.  (The macro body is not required to use all of
the parameters.)

   As an example, here is a macro that computes the minimum of two
numeric values, as it is defined in many C programs, and some uses.

     #define min(X, Y)  ((X) < (Y) ? (X) : (Y))
       x = min(a, b);      ↦ x = ((a) < (b) ? (a) : (b));
       y = min(1, 2);      ↦ y = ((1) < (2) ? (1) : (2));
       z = min(a+28, *p);  ↦ z = ((a+28) < (*p) ? (a+28) : (*p));

In this small example you can already see several of the dangers of
macro arguments.  *Note Macro Pitfalls::, for detailed explanations.

   Leading and trailing whitespace in each argument is dropped, and all
whitespace between the tokens of an argument is reduced to a single
space.  Parentheses within each argument must balance; a comma within
such parentheses does not end the argument.  However, there is no
requirement for square brackets or braces to balance, and they do not
prevent a comma from separating arguments.  Thus,

     macro (array[x = y, x + 1])

passes two arguments to ‘macro’: ‘array[x = y’ and ‘x + 1]’.  If you
want to supply ‘array[x = y, x + 1]’ as an argument, you can write it as
‘array[(x = y, x + 1)]’, which is equivalent C code.  However, putting
an assignment inside an array subscript is to be avoided anyway.

   All arguments to a macro are completely macro-expanded before they
are substituted into the macro body.  After substitution, the complete
text is scanned again for macros to expand, including the arguments.
This rule may seem strange, but it is carefully designed so you need not
worry about whether any function call is actually a macro invocation.
You can run into trouble if you try to be too clever, though.  *Note
Argument Prescan::, for detailed discussion.

   For example, ‘min (min (a, b), c)’ is first expanded to

       min (((a) < (b) ? (a) : (b)), (c))

and then to

     ((((a) < (b) ? (a) : (b))) < (c)
      ? (((a) < (b) ? (a) : (b)))
      : (c))

(The line breaks shown here for clarity are not actually generated.)

   You can leave macro arguments empty without error, but many macros
will then expand to invalid code.  You cannot leave out arguments
entirely; if a macro takes two arguments, there must be exactly one
comma at the top level of its argument list.  Here are some silly
examples using ‘min’:

     min(, b)        ↦ ((   ) < (b) ? (   ) : (b))
     min(a, )        ↦ ((a  ) < ( ) ? (a  ) : ( ))
     min(,)          ↦ ((   ) < ( ) ? (   ) : ( ))
     min((,),)       ↦ (((,)) < ( ) ? ((,)) : ( ))

     min()      error→ macro "min" requires 2 arguments, but only 1 given
     min(,,)    error→ macro "min" passed 3 arguments, but takes just 2

   Whitespace is not a preprocessing token, so if a macro ‘foo’ takes
one argument, ‘foo ()’ and ‘foo ( )’ both supply it an empty argument.

   Macro parameters appearing inside string literals are not replaced by
their corresponding actual arguments.

     #define foo(x) x, "x"
     foo(bar)        ↦ bar, "x"

See the next subsection for how to insert macro arguments into a string
literal.

   The token following the macro call and the last token of the macro
expansion do not become one token even if it looks like they could:

     #define foo()  abc
     foo()def        ↦ abc def

26.5.4 Stringification
----------------------

Sometimes you may want to convert a macro argument into a string
constant.  Parameters are not replaced inside string constants, but you
can use the ‘#’ preprocessing operator instead.  When a macro parameter
is used with a leading ‘#’, preprocessing replaces it with the literal
text of the actual argument, converted to a string constant.  Unlike
normal parameter replacement, the argument is not macro-expanded first.
This is called “stringification”.

   There is no way to combine an argument with surrounding text and
stringify it all together.  But you can write a series of string
constants and stringified arguments.  After preprocessing replaces the
stringified arguments with string constants, the consecutive string
constants will be concatenated into one long string constant (*note
String Constants::).

   Here is an example that uses stringification and concatenation of
string constants:

     #define WARN_IF(EXP) \
       do { if (EXP) \
               fprintf (stderr, "Warning: " #EXP "\n"); } \
       while (0)

     WARN_IF (x == 0);
          ↦
       do { if (x == 0)
               fprintf (stderr, "Warning: " "x == 0" "\n"); }
       while (0);

The argument for ‘EXP’ is substituted once, as is, into the ‘if’
statement, and once, stringified, into the argument to ‘fprintf’.  If
‘x’ were a macro, it would be expanded in the ‘if’ statement but not in
the string.

   The ‘do’ and ‘while (0)’ are a kludge to make it possible to write
‘WARN_IF (ARG);’.  The resemblance of ‘WARN_IF’ to a function makes that
a natural way to write it.  *Note Swallowing the Semicolon::.

   Stringification in C involves more than putting double-quote
characters around the fragment.  It also backslash-escapes the quotes
surrounding embedded string constants, and all backslashes within string
and character constants, in order to get a valid C string constant with
the proper contents.  Thus, stringifying ‘p = "foo\n";’ results in
"p = \"foo\\n\";".  However, backslashes that are not inside string or
character constants are not duplicated: ‘\n’ by itself stringifies to
"\n".

   All leading and trailing whitespace in text being stringified is
ignored.  Any sequence of whitespace in the middle of the text is
converted to a single space in the stringified result.  Comments are
replaced by whitespace long before stringification happens, so they
never appear in stringified text.

   There is no way to convert a macro argument into a character
constant.

   To stringify the result of expansion of a macro argument, you have to
use two levels of macros, like this:

     #define xstr(S) str(S)
     #define str(s) #s
     #define foo 4
     str (foo)
          ↦ "foo"
     xstr (foo)
          ↦ xstr (4)
          ↦ str (4)
          ↦ "4"

   ‘s’ is stringified when it is used in ‘str’, so it is not
macro-expanded first.  But ‘S’ is an ordinary argument to ‘xstr’, so it
is completely macro-expanded before ‘xstr’ itself is expanded (*note
Argument Prescan::).  Therefore, by the time ‘str’ gets to its argument
text, that text already been macro-expanded.

26.5.5 Concatenation
--------------------

It is often useful to merge two tokens into one while expanding macros.
This is called “token pasting” or “token concatenation”.  The ‘##’
preprocessing operator performs token pasting.  When a macro is
expanded, the two tokens on either side of each ‘##’ operator are
combined into a single token, which then replaces the ‘##’ and the two
original tokens in the macro expansion.  Usually both will be
identifiers, or one will be an identifier and the other a preprocessing
number.  When pasted, they make a longer identifier.

   Concatenation into an identifier isn’t the only valid case.  It is
also possible to concatenate two numbers (or a number and a name, such
as ‘1.5’ and ‘e3’) into a number.  Also, multi-character operators such
as ‘+=’ can be formed by token pasting.

   However, two tokens that don’t together form a valid token cannot be
pasted together.  For example, you cannot concatenate ‘x’ with ‘+’, not
in either order.  Trying this issues a warning and keeps the two tokens
separate.  Whether it puts white space between the tokens is undefined.
It is common to find unnecessary uses of ‘##’ in complex macros.  If you
get this warning, it is likely that you can simply remove the ‘##’.

   The tokens combined by ‘##’ could both come from the macro body, but
then you could just as well write them as one token in the first place.
Token pasting is useful when one or both of the tokens comes from a
macro argument.  If either of the tokens next to an ‘##’ is a parameter
name, it is replaced by its actual argument before ‘##’ executes.  As
with stringification, the actual argument is not macro-expanded first.
If the argument is empty, that ‘##’ has no effect.

   Keep in mind that preprocessing converts comments to whitespace
before it looks for uses of macros.  Therefore, you cannot create a
comment by concatenating ‘/’ and ‘*’.  You can put as much whitespace
between ‘##’ and its operands as you like, including comments, and you
can put comments in arguments that will be concatenated.

   It is an error to use ‘##’ at the beginning or end of a macro body.

   Multiple ‘##’ operators are handled left-to-right, so that ‘1 ## e ##
-2’ pastes into ‘1e-2’.  (Right-to-left processing would first generate
‘e-2’, which is an invalid token.)  When ‘#’ and ‘##’ are used together,
they are all handled left-to-right.

   Consider a C program that interprets named commands.  There probably
needs to be a table of commands, perhaps an array of structures declared
as follows:

     struct command
     {
       char *name;
       void (*function) (void);
     };

     struct command commands[] =
     {
       { "quit", quit_command },
       { "help", help_command },
       /* ... */
     };

   It would be cleaner not to have to write each command name twice,
once in the string constant and once in the function name.  A macro that
takes the name of a command as an argument can make this unnecessary.
It can create the string constant with stringification, and the function
name by concatenating the argument with ‘_command’.  Here is how it is
done:

     #define COMMAND(NAME)  { #NAME, NAME ## _command }

     struct command commands[] =
     {
       COMMAND (quit),
       COMMAND (help),
       /* ... */
     };

26.5.6 Variadic Macros
----------------------

A macro can be declared to accept a variable number of arguments much as
a function can.  The syntax for defining the macro is similar to that of
a function.  Here is an example:

     #define eprintf(...) fprintf (stderr, __VA_ARGS__)

   This kind of macro is called “variadic”.  When the macro is invoked,
all the tokens in its argument list after the last named argument (this
macro has none), including any commas, become the “variable argument”.
This sequence of tokens replaces the identifier ‘__VA_ARGS__’ in the
macro body wherever it appears.  Thus, we have this expansion:

     eprintf ("%s:%d: ", input_file, lineno)
          ↦  fprintf (stderr, "%s:%d: ", input_file, lineno)

   The variable argument is completely macro-expanded before it is
inserted into the macro expansion, just like an ordinary argument.  You
may use the ‘#’ and ‘##’ operators to stringify the variable argument or
to paste its leading or trailing token with another token.  (But see
below for an important special case for ‘##’.)

   *Warning:* don’t use the identifier ‘__VA_ARGS__’ for anything other
than this.

   If your macro is complicated, you may want a more descriptive name
for the variable argument than ‘__VA_ARGS__’.  You can write an argument
name immediately before the ‘...’; that name is used for the variable
argument.(1)  The ‘eprintf’ macro above could be written thus:

     #define eprintf(args...) fprintf (stderr, args)

   A variadic macro can have named arguments as well as variable
arguments, so ‘eprintf’ can be defined like this, instead:

     #define eprintf(format, ...) \
       fprintf (stderr, format, __VA_ARGS__)

This formulation is more descriptive, but what if you want to specify a
format string that takes no arguments?  In GNU C, you can omit the comma
before the variable arguments if they are empty, but that puts an extra
comma in the expansion:

     eprintf ("success!\n")
          ↦ fprintf(stderr, "success!\n", );

That’s an error in the call to ‘fprintf’.

   To get rid of that comma, the ‘##’ token paste operator has a special
meaning when placed between a comma and a variable argument.(2)  If you
write

     #define eprintf(format, ...) \
       fprintf (stderr, format, ##__VA_ARGS__)

then use the macro ‘eprintf’ with empty variable arguments, ‘##’ deletes
the preceding comma.

     eprintf ("success!\n")
          ↦ fprintf(stderr, "success!\n");

This does _not_ happen if you pass an empty argument, nor does it happen
if the token preceding ‘##’ is anything other than a comma.

When the only macro parameter is a variable arguments parameter, and the
macro call has no argument at all, it is not obvious whether that means
an empty argument or a missing argument.  Should the comma be kept, or
deleted?  The C standard says to keep the comma, but the preexisting GNU
C extension deleted the comma.  Nowadays, GNU C retains the comma when
implementing a specific C standard, and deletes it otherwise.

   C99 mandates that the only place the identifier ‘__VA_ARGS__’ can
appear is in the replacement list of a variadic macro.  It may not be
used as a macro name, macro parameter name, or within a different type
of macro.  It may also be forbidden in open text; the standard is
ambiguous.  We recommend you avoid using that name except for its
special purpose.

   Variadic macros where you specify the parameter name is a GNU C
feature that has been supported for a long time.  Standard C, as of C99,
supports only the form where the parameter is called ‘__VA_ARGS__’.  For
portability to previous versions of GNU C you should use only named
variable argument parameters.  On the other hand, for portability to
other C99 compilers, you should use only ‘__VA_ARGS__’.

   ---------- Footnotes ----------

   (1) GNU C extension.

   (2) GNU C extension.

26.5.7 Predefined Macros
------------------------

Several object-like macros are predefined; you use them without
supplying their definitions.  Here we explain the ones user programs
often need to use.  Many other macro names starting with ‘__’ are
predefined; in general, you should not define such macro names yourself.

‘__FILE__’
     This macro expands to the name of the current input file, in the
     form of a C string constant.  This is the full name by which the
     GCC opened the file, not the short name specified in ‘#include’ or
     as the input file name argument.  For example,
     ‘"/usr/local/include/myheader.h"’ is a possible expansion of this
     macro.

‘__LINE__’
     This macro expands to the current input line number, in the form of
     a decimal integer constant.  While we call it a predefined macro,
     it’s a pretty strange macro, since its “definition” changes with
     each new line of source code.

‘__func__’
‘__FUNCTION__’
     These names are like variables that have as value a string
     containing the name of the current function definition.  They are
     not really macros, but this is the best place to mention them.

     ‘__FUNCTION__’ is the name that has been defined in GNU C since
     time immemorial; ‘__func__’ is defined by the C standard.  With the
     following conditionals, you can use whichever one is defined.

          #if __STDC_VERSION__ < 199901L
          # if __GNUC__ <= 2
          #  define __func__ __FUNCTION__
          # else
          #  define __func__ ">unknown<"
          # endif
          #endif

‘__PRETTY_FUNCTION__’
     This is equivalent to ‘__FUNCTION__’ in C, but in C‘++’ the string
     includes argument type information as well.  It is a GNU C
     extension.

   Those features are useful in generating an error message to report an
inconsistency detected by the program; the message can state the source
line where the inconsistency was detected.  For example,

     fprintf (stderr, "Internal error: "
                      "negative string length "
                      "in function %s "
                      "%d at %s, line %d.",
              __func__, length, __FILE__, __LINE__);

   A ‘#line’ directive changes ‘__LINE__’, and may change ‘__FILE__’ as
well.  *Note Line Control::.

‘__DATE__’
     This macro expands to a string constant that describes the date of
     compilation.  The string constant contains eleven characters and
     looks like ‘"Feb 12 1996"’.  If the day of the month is just one
     digit, an extra space precedes it so that the date is always eleven
     characters.

     If the compiler cannot determine the current date, it emits a
     warning messages (once per compilation) and ‘__DATE__’ expands to
     ‘"??? ?? ????"’.

     We deprecate the use of ‘__DATE__’ for the sake of reproducible
     compilation.

‘__TIME__’
     This macro expands to a string constant that describes the time of
     compilation.  The string constant contains eight characters and
     looks like ‘"23:59:01"’.

     If the compiler cannot determine the current time, it emits a
     warning message (once per compilation) and ‘__TIME__’ expands to
     ‘"??:??:??"’.

     We deprecate the use of ‘__TIME__’ for the sake of reproducible
     compilation.

‘__STDC__’
     In normal operation, this macro expands to the constant 1, to
     signify that this compiler implements ISO Standard C.

‘__STDC_VERSION__’
     This macro expands to the C Standard’s version number, a long
     integer constant of the form ‘YYYYMML’ where YYYY and MM are the
     year and month of the Standard version.  This states which version
     of the C Standard the compiler implements.

     The current default value is ‘201112L’, which signifies the C 2011
     standard.

‘__STDC_HOSTED__’
     This macro is defined, with value 1, if the compiler’s target is a
     “hosted environment”.  A hosted environment provides the full
     facilities of the standard C library.

   The rest of the predefined macros are GNU C extensions.

‘__COUNTER__’
     This macro expands to sequential integral values starting from 0.
     In other words, each time the program uses this acro, it generates
     the next successive integer.  This, with the ‘##’ operator,
     provides a convenient means for macros to generate unique
     identifiers.

‘__GNUC__’
‘__GNUC_MINOR__’
‘__GNUC_PATCHLEVEL__’
     These macros expand to the major version, minor version, and patch
     level of the compiler, as integer constants.  For example, GCC
     3.2.1 expands ‘__GNUC__’ to 3, ‘__GNUC_MINOR__’ to 2, and
     ‘__GNUC_PATCHLEVEL__’ to 1.

     If all you need to know is whether or not your program is being
     compiled by GCC, or a non-GCC compiler that claims to accept the
     GNU C extensions, you can simply test ‘__GNUC__’.  If you need to
     write code that depends on a specific version, you must check more
     carefully.  Each change in the minor version resets the patch level
     to zero; each change in the major version (which happens rarely)
     resets the minor version and the patch level to zero.  To use the
     predefined macros directly in the conditional, write it like this:

          /* Test for version 3.2.0 or later. */
          #if __GNUC__ &tt; 3 || \
              (__GNUC__ == 3 && (__GNUC_MINOR__ &tt; 2 || \
                                 (__GNUC_MINOR__ == 2 && \
                                  __GNUC_PATCHLEVEL__ &tt; 0))

     Another approach is to use the predefined macros to calculate a
     single number, then compare that against a threshold:

          #define GCC_VERSION (__GNUC__ * 10000 \
                               + __GNUC_MINOR__ * 100 \
                               + __GNUC_PATCHLEVEL__)
          /* ... */
          /* Test for GCC &tt; 3.2.0 */
          #if GCC_VERSION &tt; 30200

     Many people find this form easier to understand.

‘__VERSION__’
     This macro expands to a string constant that describes the version
     of the compiler in use.  You should not rely on its contents’
     having any particular form, but you can count on it to contain at
     least the release number.

‘__TIMESTAMP__’
     This macro expands to a string constant that describes the date and
     time of the last modification of the current source file.  The
     string constant contains abbreviated day of the week, month, day of
     the month, time in hh:mm:ss form, and the year, in the format
     ‘"Sun Sep 16 01:03:52 1973"’.  If the day of the month is less than
     10, it is padded with a space on the left.

     If GCC cannot determine that information date, it emits a warning
     message (once per compilation) and ‘__TIMESTAMP__’ expands to
     ‘"??? ??? ?? ??:??:?? ????"’.

     We deprecate the use of this macro for the sake of reproducible
     compilation.

26.5.8 Undefining and Redefining Macros
---------------------------------------

You can “undefine” a macro with the ‘#undef’ directive.  ‘#undef’ takes
a single argument, the name of the macro to undefine.  You use the bare
macro name, even if the macro is function-like.  It is an error if
anything appears on the line after the macro name.  ‘#undef’ has no
effect if the name is not a macro.

     #define FOO 4
     x = FOO;        ↦ x = 4;
     #undef FOO
     x = FOO;        ↦ x = FOO;

   Once a macro has been undefined, that identifier may be “redefined”
as a macro by a subsequent ‘#define’ directive.  The new definition need
not have any resemblance to the old definition.

   You can define a macro again without first undefining it only if the
new definition is “effectively the same” as the old one.  Two macro
definitions are effectively the same if:

   • Both are the same type of macro (object- or function-like).
   • All the tokens of the replacement list are the same.
   • If there are any parameters, they are the same.
   • Whitespace appears in the same places in both.  It need not be
     exactly the same amount of whitespace, though.  Remember that
     comments count as whitespace.

These definitions are effectively the same:
     #define FOUR (2 + 2)
     #define FOUR         (2    +    2)
     #define FOUR (2 /* two */ + 2)
but these are not:
     #define FOUR (2 + 2)
     #define FOUR ( 2+2 )
     #define FOUR (2 * 2)
     #define FOUR(score,and,seven,years,ago) (2 + 2)

   This allows two different header files to define a common macro.

   You can redefine an existing macro with #define, but redefining an
existing macro name with a different definition results in a warning.

26.5.9 Directives Within Macro Arguments
----------------------------------------

GNU C permits and handles preprocessing directives in the text provided
as arguments for a macro.  That case is undefined in the C standard.
but in GNU C conditional directives in macro arguments are clear and
valid.

   A paradoxical case is to redefine a macro within the call to that
same macro.  What happens is, the new definition takes effect in time
for pre-expansion of _all_ the arguments, then the original definition
is expanded to replace the call.  Here is a pathological example:

     #define f(x) x x
     f (first f second
     #undef f
     #define f 2
     f)

which expands to

     first 2 second 2 first 2 second 2

with the semantics described above.  We suggest you avoid writing code
which does this sort of thing.

26.5.10 Macro Pitfalls
----------------------

In this section we describe some special rules that apply to macros and
macro expansion, and point out certain cases in which the rules have
counter-intuitive consequences that you must watch out for.

26.5.10.1 Misnesting
....................

When a macro is called with arguments, the arguments are substituted
into the macro body and the result is checked, together with the rest of
the input file, for more macro calls.  It is possible to piece together
a macro call coming partially from the macro body and partially from the
arguments.  For example,

     #define twice(x) (2*(x))
     #define call_with_1(x) x(1)
     call_with_1 (twice)
          ↦ twice(1)
          ↦ (2*(1))

   Macro definitions do not have to have balanced parentheses.  By
writing an unbalanced open parenthesis in a macro body, it is possible
to create a macro call that begins inside the macro body but ends
outside of it.  For example,

     #define strange(file) fprintf (file, "%s %d",
     /* ... */
     strange(stderr) p, 35)
          ↦ fprintf (stderr, "%s %d", p, 35)

   The ability to piece together a macro call can be useful, but the use
of unbalanced open parentheses in a macro body is just confusing, and
should be avoided.

26.5.10.2 Operator Precedence Problems
......................................

You may have noticed that in most of the macro definition examples shown
above, each occurrence of a macro parameter name had parentheses around
it.  In addition, another pair of parentheses usually surrounds the
entire macro definition.  Here is why it is best to write macros that
way.

   Suppose you define a macro as follows,

     #define ceil_div(x, y) (x + y - 1) / y

whose purpose is to divide, rounding up.  (One use for this operation is
to compute how many ‘int’ objects are needed to hold a certain number of
‘char’ objects.)  Then suppose it is used as follows:

     a = ceil_div (b & c, sizeof (int));
          ↦ a = (b & c + sizeof (int) - 1) / sizeof (int);

This does not do what is intended.  The operator-precedence rules of C
make it equivalent to this:

     a = (b & (c + sizeof (int) - 1)) / sizeof (int);

What we want is this:

     a = ((b & c) + sizeof (int) - 1)) / sizeof (int);

Defining the macro as

     #define ceil_div(x, y) ((x) + (y) - 1) / (y)

provides the desired result.

   Unintended grouping can result in another way.  Consider ‘sizeof
ceil_div(1, 2)’.  That has the appearance of a C expression that would
compute the size of the type of ‘ceil_div (1, 2)’, but in fact it means
something very different.  Here is what it expands to:

     sizeof ((1) + (2) - 1) / (2)

This would take the size of an integer and divide it by two.  The
precedence rules have put the division outside the ‘sizeof’ when it was
intended to be inside.

   Parentheses around the entire macro definition prevent such problems.
Here, then, is the recommended way to define ‘ceil_div’:

     #define ceil_div(x, y) (((x) + (y) - 1) / (y))

26.5.10.3 Swallowing the Semicolon
..................................

Often it is desirable to define a macro that expands into a compound
statement.  Consider, for example, the following macro, that advances a
pointer (the parameter ‘p’ says where to find it) across whitespace
characters:

     #define SKIP_SPACES(p, limit)  \
     { char *lim = (limit);         \
       while (p < lim) {            \
         if (*p++ != ' ') {         \
           p--; break; }}}

Here backslash-newline is used to split the macro definition, which must
be a single logical line, so that it resembles the way such code would
be laid out if not part of a macro definition.

   A call to this macro might be ‘SKIP_SPACES (p, lim)’.  Strictly
speaking, the call expands to a compound statement, which is a complete
statement with no need for a semicolon to end it.  However, since it
looks like a function call, it minimizes confusion if you can use it
like a function call, writing a semicolon afterward, as in ‘SKIP_SPACES
(p, lim);’

   This can cause trouble before ‘else’ statements, because the
semicolon is actually a null statement.  Suppose you write

     if (*p != 0)
       SKIP_SPACES (p, lim);
     else /* ... */

The presence of two statements—the compound statement and a null
statement—in between the ‘if’ condition and the ‘else’ makes invalid C
code.

   The definition of the macro ‘SKIP_SPACES’ can be altered to solve
this problem, using a ‘do ... while’ statement.  Here is how:

     #define SKIP_SPACES(p, limit)     \
     do { char *lim = (limit);         \
          while (p < lim) {            \
            if (*p++ != ' ') {         \
              p--; break; }}}          \
     while (0)

   Now ‘SKIP_SPACES (p, lim);’ expands into

     do { /* ... */ } while (0);

which is one statement.  The loop executes exactly once; most compilers
generate no extra code for it.

26.5.10.4 Duplication of Side Effects
.....................................

Many C programs define a macro ‘min’, for “minimum”, like this:

     #define min(X, Y)  ((X) < (Y) ? (X) : (Y))

   When you use this macro with an argument containing a side effect, as
shown here,

     next = min (x + y, foo (z));

it expands as follows:

     next = ((x + y) < (foo (z)) ? (x + y) : (foo (z)));

where ‘x + y’ has been substituted for ‘X’ and ‘foo (z)’ for ‘Y’.

   The function ‘foo’ is used only once in the statement as it appears
in the program, but the expression ‘foo (z)’ has been substituted twice
into the macro expansion.  As a result, ‘foo’ might be called twice when
the statement is executed.  If it has side effects or if it takes a long
time to compute, that may be undesirable.  We say that ‘min’ is an
“unsafe” macro.

   The best solution to this problem is to define ‘min’ in a way that
computes the value of ‘foo (z)’ only once.  In general, that requires
using ‘__auto_type’ (*note Auto Type::).  How to use it for this is
described in the following section.  *Note Macros and Auto Type::.

   Otherwise, you will need to be careful when _using_ the macro ‘min’.
For example, you can calculate the value of ‘foo (z)’, save it in a
variable, and use that variable in ‘min’:

     #define min(X, Y)  ((X) < (Y) ? (X) : (Y))
     /* ... */
     {
       int tem = foo (z);
       next = min (x + y, tem);
     }

(where we assume that ‘foo’ returns type ‘int’).

   When the repeated value appears as the condition of the ‘?:’ operator
and again as its IFTRUE expression, you can avoid repeated execution by
omitting the IFTRUE expression, like this:

     #define x_or_y(X, Y)  ((X) ? : (Y))

In GNU C, this expands to use the first macro argument’s value if that
isn’t zero.  If that’s zero, it compiles the second argument and uses
that value.  *Note Conditional Expression::.

26.5.10.5 Using ‘__auto_type’ for Local Variables
.................................................

The operator ‘__auto_type’ makes it possible to define macros that can
work on any data type even though they need to generate local variable
declarations.  *Note Auto Type::.

   For instance, here’s how to define a safe “maximum” macro that
operates on any arithmetic type and computes each of its arguments
exactly once:

     #define max(a,b) \
       ({ __auto_type _a = (a); \
           __auto_type _b = (b); \
         _a &tt; _b ? _a : _b; })

   The ‘({ ... })’ notation produces “statement expression”—a statement
that can be used as an expression (*note Statement Exprs::).  Its value
is the value of its last statement.  This permits us to define local
variables and store each argument value into one.

   The reason for using names that start with underscores for the local
variables is to avoid conflicts with variable names that occur within
the expressions that are substituted for ‘a’ and ‘b’.  Underscore
followed by a lower case letter won’t be predefined by the system in any
way.

26.5.10.6 Self-Referential Macros
.................................

A “self-referential” macro is one whose name appears in its definition.
Recall that all macro definitions are rescanned for more macros to
replace.  If the self-reference were considered a use of the macro, it
would produce an infinitely large expansion.  To prevent this, the
self-reference is not considered a macro call: preprocessing leaves it
unchanged.  Consider an example:

     #define foo (4 + foo)

where ‘foo’ is also a variable in your program.

   Following the ordinary rules, each reference to ‘foo’ will expand
into ‘(4 + foo)’; then this will be rescanned and will expand into ‘(4 +
(4 + foo))’; and so on until the computer runs out of memory.

   The self-reference rule cuts this process short after one step, at
‘(4 + foo)’.  Therefore, this macro definition has the possibly useful
effect of causing the program to add 4 to the value of ‘foo’ wherever
‘foo’ is referred to.

   In most cases, it is a bad idea to take advantage of this feature.  A
person reading the program who sees that ‘foo’ is a variable will not
expect that it is a macro as well.  The reader will come across the
identifier ‘foo’ in the program and think its value should be that of
the variable ‘foo’, whereas in fact the value is four greater.

   It is useful to make a macro definition that expands to the macro
name itself.  If you write

     #define EPERM EPERM

then the macro ‘EPERM’ expands to ‘EPERM’.  Effectively, preprocessing
leaves it unchanged in the source code.  You can tell that it’s a macro
with ‘#ifdef’.  You might do this if you want to define numeric
constants with an ‘enum’, but have ‘#ifdef’ be true for each constant.

   If a macro ‘x’ expands to use a macro ‘y’, and the expansion of ‘y’
refers to the macro ‘x’, that is an “indirect self-reference” of ‘x’.
‘x’ is not expanded in this case either.  Thus, if we have

     #define x (4 + y)
     #define y (2 * x)

then ‘x’ and ‘y’ expand as follows:

     x    ↦ (4 + y)
          ↦ (4 + (2 * x))

     y    ↦ (2 * x)
          ↦ (2 * (4 + y))

Each macro is expanded when it appears in the definition of the other
macro, but not when it indirectly appears in its own definition.

26.5.10.7 Argument Prescan
..........................

Macro arguments are completely macro-expanded before they are
substituted into a macro body, unless they are stringified or pasted
with other tokens.  After substitution, the entire macro body, including
the substituted arguments, is scanned again for macros to be expanded.
The result is that the arguments are scanned _twice_ to expand macro
calls in them.

   Most of the time, this has no effect.  If the argument contained any
macro calls, they were expanded during the first scan.  The result
therefore contains no macro calls, so the second scan does not change
it.  If the argument were substituted as given, with no prescan, the
single remaining scan would find the same macro calls and produce the
same results.

   You might expect the double scan to change the results when a
self-referential macro is used in an argument of another macro (*note
Self-Referential Macros::): the self-referential macro would be expanded
once in the first scan, and a second time in the second scan.  However,
this is not what happens.  The self-references that do not expand in the
first scan are marked so that they will not expand in the second scan
either.

   You might wonder, “Why mention the prescan, if it makes no
difference?  And why not skip it and make preprocessing go faster?” The
answer is that the prescan does make a difference in three special
cases:

   • Nested calls to a macro.

     We say that “nested” calls to a macro occur when a macro’s argument
     contains a call to that very macro.  For example, if ‘f’ is a macro
     that expects one argument, ‘f (f (1))’ is a nested pair of calls to
     ‘f’.  The desired expansion is made by expanding ‘f (1)’ and
     substituting that into the definition of ‘f’.  The prescan causes
     the expected result to happen.  Without the prescan, ‘f (1)’ itself
     would be substituted as an argument, and the inner use of ‘f’ would
     appear during the main scan as an indirect self-reference and would
     not be expanded.

   • Macros that call other macros that stringify or concatenate.

     If an argument is stringified or concatenated, the prescan does not
     occur.  If you _want_ to expand a macro, then stringify or
     concatenate its expansion, you can do that by causing one macro to
     call another macro that does the stringification or concatenation.
     For instance, if you have

          #define AFTERX(x) X_ ## x
          #define XAFTERX(x) AFTERX(x)
          #define TABLESIZE 1024
          #define BUFSIZE TABLESIZE

     then ‘AFTERX(BUFSIZE)’ expands to ‘X_BUFSIZE’, and
     ‘XAFTERX(BUFSIZE)’ expands to ‘X_1024’.  (Not to ‘X_TABLESIZE’.
     Prescan always does a complete expansion.)

   • Macros used in arguments, whose expansions contain unshielded
     commas.

     This can cause a macro expanded on the second scan to be called
     with the wrong number of arguments.  Here is an example:

          #define foo  a,b
          #define bar(x) lose(x)
          #define lose(x) (1 + (x))

     We would like ‘bar(foo)’ to turn into ‘(1 + (foo))’, which would
     then turn into ‘(1 + (a,b))’.  Instead, ‘bar(foo)’ expands into
     ‘lose(a,b)’, which gives an error because ‘lose’ requires a single
     argument.  In this case, the problem is easily solved by the same
     parentheses that ought to be used to prevent misnesting of
     arithmetic operations:

          #define foo (a,b)
     or
          #define bar(x) lose((x))

     The extra pair of parentheses prevents the comma in ‘foo’’s
     definition from being interpreted as an argument separator.

26.6 Conditionals
=================

A “conditional” is a preprocessing directive that controls whether or
not to include a chunk of code in the final token stream that is
compiled.  Preprocessing conditionals can test arithmetic expressions,
or whether a name is defined as a macro, or both together using the
special ‘defined’ operator.

   A preprocessing conditional in C resembles in some ways an ‘if’
statement in C, but it is important to understand the difference between
them.  The condition in an ‘if’ statement is tested during the execution
of your program.  Its purpose is to allow your program to behave
differently from run to run, depending on the data it is operating on.
The condition in a preprocessing conditional directive is tested when
your program is compiled.  Its purpose is to allow different code to be
included in the program depending on the situation at the time of
compilation.

   Sometimes this distinction makes no practical difference.  GCC and
other modern compilers often do test ‘if’ statements when a program is
compiled, if their conditions are known not to vary at run time, and
eliminate code that can never be executed.  If you can count on your
compiler to do this, you may find that your program is more readable if
you use ‘if’ statements with constant conditions (perhaps determined by
macros).  Of course, you can only use this to exclude code, not type
definitions or other preprocessing directives, and you can only do it if
the file remains syntactically valid when that code is not used.

26.6.1 Uses of Conditional Directives
-------------------------------------

There are three usual reasons to use a preprocessing conditional.

   • A program may need to use different code depending on the machine
     or operating system it is to run on.  In some cases the code for
     one operating system may be erroneous on another operating system;
     for example, it might refer to data types or constants that do not
     exist on the other system.  When this happens, it is not enough to
     avoid executing the invalid code.  Its mere presence will cause the
     compiler to reject the program.  With a preprocessing conditional,
     the offending code can be effectively excised from the program when
     it is not valid.

   • You may want to be able to compile the same source file into two
     different programs.  One version might make frequent time-consuming
     consistency checks on its intermediate data, or print the values of
     those data for debugging, and the other not.

   • A conditional whose condition is always false is one way to exclude
     code from the program but keep it as a sort of comment for future
     reference.

   Simple programs that do not need system-specific logic or complex
debugging hooks generally will not need to use preprocessing
conditionals.

26.6.2 Syntax of Preprocessing Conditionals
-------------------------------------------

A preprocessing conditional begins with a “conditional directive”:
‘#if’, ‘#ifdef’ or ‘#ifndef’.

26.6.2.1 The ‘#ifdef’ directive
...............................

The simplest sort of conditional is

     #ifdef MACRO

     CONTROLLED TEXT

     #endif /* MACRO */

   This block is called a “conditional group”.  The body, CONTROLLED
TEXT, will be included in compilation if and only if MACRO is defined.
We say that the conditional “succeeds” if MACRO is defined, “fails” if
it is not.

   The CONTROLLED TEXT inside a conditional can include preprocessing
directives.  They are executed only if the conditional succeeds.  You
can nest conditional groups inside other conditional groups, but they
must be completely nested.  In other words, ‘#endif’ always matches the
nearest ‘#ifdef’ (or ‘#ifndef’, or ‘#if’).  Also, you cannot start a
conditional group in one file and end it in another.

   Even if a conditional fails, the CONTROLLED TEXT inside it is still
run through initial transformations and tokenization.  Therefore, it
must all be lexically valid C.  Normally the only way this matters is
that all comments and string literals inside a failing conditional group
must still be properly ended.

   The comment following the ‘#endif’ is not required, but it is a good
practice if there is a lot of CONTROLLED TEXT, because it helps people
match the ‘#endif’ to the corresponding ‘#ifdef’.

   Older programs sometimes put MACRO directly after the ‘#endif’
without enclosing it in a comment.  This is invalid code according to
the C standard, but it only causes a warning in GNU C.  It never affects
which ‘#ifndef’ the ‘#endif’ matches.

   Sometimes you wish to use some code if a macro is _not_ defined.  You
can do this by writing ‘#ifndef’ instead of ‘#ifdef’.  One common use of
‘#ifndef’ is to include code only the first time a header file is
included.  *Note Once-Only Headers::.

   Macro definitions can vary between compilations for several reasons.
Here are some samples.

   • Some macros are predefined on each kind of machine (*note
     System-specific Predefined Macros: (gcc)System-specific Predefined
     Macros.).  This allows you to provide code specially tuned for a
     particular machine.

   • System header files define more macros, associated with the
     features they implement.  You can test these macros with
     conditionals to avoid using a system feature on a machine where it
     is not implemented.

   • Macros can be defined or undefined with the ‘-D’ and ‘-U’
     command-line options when you compile the program.  You can arrange
     to compile the same source file into two different programs by
     choosing a macro name to specify which program you want, writing
     conditionals to test whether or how this macro is defined, and then
     controlling the state of the macro with command-line options,
     perhaps set in the file ‘Makefile’.  *Note Invoking GCC:
     (gcc)Invocation.

   • Your program might have a special header file (often called
     ‘config.h’) that is adjusted when the program is compiled.  It can
     define or not define macros depending on the features of the system
     and the desired capabilities of the program.  The adjustment can be
     automated by a tool such as ‘autoconf’, or done by hand.

26.6.2.2 The ‘#if’ directive
............................

The ‘#if’ directive allows you to test the value of an integer
arithmetic expression, rather than the mere existence of one macro.  Its
syntax is

     #if EXPRESSION

     CONTROLLED TEXT

     #endif /* EXPRESSION */

   EXPRESSION is a C expression of integer type, subject to stringent
restrictions so its value can be computed at compile time.  It may
contain

   • Integer constants.

   • Character constants, which are interpreted as they would be in
     normal code.

   • Arithmetic operators for addition, subtraction, multiplication,
     division, bitwise operations, shifts, comparisons, and logical
     operations (‘&&’ and ‘||’).  The latter two obey the usual
     short-circuiting rules of standard C.

   • Macros.  All macros in the expression are expanded before actual
     computation of the expression’s value begins.

   • Uses of the ‘defined’ operator, which lets you check whether macros
     are defined in the middle of an ‘#if’.

   • Identifiers that are not macros, which are all considered to be the
     number zero.  This allows you to write ‘#if MACRO’ instead of
     ‘#ifdef MACRO’, if you know that MACRO, when defined, will always
     have a nonzero value.  Function-like macros used without their
     function call parentheses are also treated as zero.

     In some contexts this shortcut is undesirable.  The ‘-Wundef’
     requests warnings for any identifier in an ‘#if’ that is not
     defined as a macro.

   Preprocessing does not know anything about the data types of C.
Therefore, ‘sizeof’ operators are not recognized in ‘#if’; ‘sizeof’ is
simply an identifier, and if it is not a macro, it stands for zero.
This is likely to make the expression invalid.  Preprocessing does not
recognize ‘enum’ constants; they too are simply identifiers, so if they
are not macros, they stand for zero.

   Preprocessing calculates the value of EXPRESSION, and carries out all
calculations in the widest integer type known to the compiler; on most
machines supported by GNU C this is 64 bits.  This is not the same rule
as the compiler uses to calculate the value of a constant expression,
and may give different results in some cases.  If the value comes out to
be nonzero, the ‘#if’ succeeds and the CONTROLLED TEXT is compiled;
otherwise it is skipped.

26.6.2.3 The ‘defined’ test
...........................

The special operator ‘defined’ is used in ‘#if’ and ‘#elif’ expressions
to test whether a certain name is defined as a macro.  ‘defined NAME’
and ‘defined (NAME)’ are both expressions whose value is 1 if NAME is
defined as a macro at the current point in the program, and 0 otherwise.
Thus, ‘#if defined MACRO’ is precisely equivalent to ‘#ifdef MACRO’.

   ‘defined’ is useful when you wish to test more than one macro for
existence at once.  For example,

     #if defined (__arm__) || defined (__PPC__)

would succeed if either of the names ‘__arm__’ or ‘__PPC__’ is defined
as a macro—in other words, when compiling for ARM processors or PowerPC
processors.

   Conditionals written like this:

     #if defined BUFSIZE && BUFSIZE <= 1024

can generally be simplified to just ‘#if BUFSIZE <= 1024’, since if
‘BUFSIZE’ is not defined, it will be interpreted as having the value
zero.

   In GCC, you can include ‘defined’ as part of another macro
definition, like this:

     #define MACRO_DEFINED(X) defined X

     #if MACRO_DEFINED(BUFSIZE)

which would expand the ‘#if’ expression to:

     #if defined BUFSIZE

Generating ‘defined’ in this way is a GNU C extension.

26.6.2.4 The ‘#else’ directive
..............................

The ‘#else’ directive can be added to a conditional to provide
alternative text to be used if the condition fails.  This is what it
looks like:

     #if EXPRESSION
     TEXT-IF-TRUE
     #else /* Not EXPRESSION */
     TEXT-IF-FALSE
     #endif /* Not EXPRESSION */

If EXPRESSION is nonzero, the TEXT-IF-TRUE is included and the
TEXT-IF-FALSE is skipped.  If EXPRESSION is zero, the opposite happens.

   You can use ‘#else’ with ‘#ifdef’ and ‘#ifndef’, too.

26.6.2.5 The ‘#elif’ directive
..............................

One common case of nested conditionals is used to check for more than
two possible alternatives.  For example, you might have

     #if X == 1
     /* ... */
     #else /* X != 1 */
     #if X == 2
     /* ... */
     #else /* X != 2 */
     /* ... */
     #endif /* X != 2 */
     #endif /* X != 1 */

   Another conditional directive, ‘#elif’, allows this to be abbreviated
as follows:

     #if X == 1
     /* ... */
     #elif X == 2
     /* ... */
     #else /* X != 2 and X != 1*/
     /* ... */
     #endif /* X != 2 and X != 1*/

   ‘#elif’ stands for “else if”.  Like ‘#else’, it goes in the middle of
a conditional group and subdivides it; it does not require a matching
‘#endif’ of its own.  Like ‘#if’, the ‘#elif’ directive includes an
expression to be tested.  The text following the ‘#elif’ is processed
only if the original ‘#if’-condition failed and the ‘#elif’ condition
succeeds.

   More than one ‘#elif’ can go in the same conditional group.  Then the
text after each ‘#elif’ is processed only if the ‘#elif’ condition
succeeds after the original ‘#if’ and all previous ‘#elif’ directives
within it have failed.

   ‘#else’ is allowed after any number of ‘#elif’ directives, but
‘#elif’ may not follow ‘#else’.

26.6.3 Deleted Code
-------------------

If you replace or delete a part of the program but want to keep the old
code in the file for future reference, commenting it out is not so
straightforward in C. Block comments do not nest, so the first comment
inside the old code will end the commenting-out.  The probable result is
a flood of syntax errors.

   One way to avoid this problem is to use an always-false conditional
instead.  For instance, put ‘#if 0’ before the deleted code and ‘#endif’
after it.  This works even if the code being turned off contains
conditionals, but they must be entire conditionals (balanced ‘#if’ and
‘#endif’).

   Some people use ‘#ifdef notdef’ instead.  This is risky, because
‘notdef’ might be accidentally defined as a macro, and then the
conditional would succeed.  ‘#if 0’ can be counted on to fail.

   Do not use ‘#if 0’ around text that is not C code.  Use a real
comment, instead.  The interior of ‘#if 0’ must consist of complete
tokens; in particular, single-quote characters must balance.  Comments
often contain unbalanced single-quote characters (known in English as
apostrophes).  These confuse ‘#if 0’.  They don’t confuse ‘/*’.

26.7 Diagnostics
================

The directive ‘#error’ reports a fatal error.  The tokens forming the
rest of the line following ‘#error’ are used as the error message.

   The usual place to use ‘#error’ is inside a conditional that detects
a combination of parameters that you know the program does not properly
support.  For example,

     #if !defined(UNALIGNED_INT_ASM_OP) && defined(DWARF2_DEBUGGING_INFO)
     #error "DWARF2_DEBUGGING_INFO requires UNALIGNED_INT_ASM_OP."
     #endif

   The directive ‘#warning’ is like ‘#error’, but it reports a warning
instead of an error.  The tokens following ‘#warning’ are used as the
warning message.

   You might use ‘#warning’ in obsolete header files, with a message
saying which header file to use instead.

   Neither ‘#error’ nor ‘#warning’ macro-expands its argument.  Internal
whitespace sequences are each replaced with a single space.  The line
must consist of complete tokens.  It is wisest to make the argument of
these directives be a single string constant; this avoids problems with
apostrophes and the like.

26.8 Line Control
=================

Due to C’s widespread availability and low-level nature, it is often
used as the target language for translation of other languages, or for
the output of lexical analyzers and parsers (e.g., lex/flex and
yacc/bison).  Line control enables the user to track diagnostics back to
the location in the original language.

   The C compiler knows the location in the source file where each token
came from: file name, starting line and column, and final line and
column.  (Column numbers are used only for error messages.)

   When a program generates C source code, as the Bison parser generator
does, often it copies some of that C code from another file.  For
instance parts of the output from Bison are generated from scratch or
come from a standard parser file, but Bison copies the rest from Bison’s
input file.  Errors in that code, at compile time or run time, should
refer to that file, which is the real source code.  To make that happen,
Bison generates line-control directives that the C compiler understands.

   ‘#line’ is a directive that specifies the original line number and
source file name for subsequent code.  ‘#line’ has three variants:

‘#line LINENUM’
     LINENUM is a non-negative decimal integer constant.  It specifies
     the line number that should be reported for the following line of
     input.  Subsequent lines are counted from LINENUM.

‘#line LINENUM FILENAME’
     LINENUM is the same as for the first form, and has the same effect.
     In addition, FILENAME is a string constant that specifies the
     source file name.  Subsequent source lines are recorded as coming
     from that file, until something else happens to change that.
     FILENAME is interpreted according to the normal rules for a string
     constant.  Backslash escapes are interpreted, in contrast to
     ‘#include’.

‘#line ANYTHING ELSE’
     ANYTHING ELSE is checked for macro calls, which are expanded.  The
     result should match one of the above two forms.

   ‘#line’ directives alter the results of the ‘__FILE__’ and ‘__LINE__’
symbols from that point on.  *Note Predefined Macros::.

26.9 Null Directive
===================

The “null directive” consists of a ‘#’ followed by a newline, with only
whitespace and comments in between.  It has no effect on the output of
the compiler.

27 Integers in Depth
********************

This chapter explains the machine-level details of integer types: how
they are represented as bits in memory, and the range of possible values
for each integer type.

27.1 Integer Representations
============================

Modern computers store integer values as binary (base-2) numbers that
occupy a single unit of storage, typically either as an 8-bit ‘char’, a
16-bit ‘short int’, a 32-bit ‘int’, or possibly, a 64-bit ‘long long
int’.  Whether a ‘long int’ is a 32-bit or a 64-bit value is system
dependent.(1)

   The macro ‘CHAR_BIT’, defined in ‘limits.h’, gives the number of bits
in type ‘char’.  On any real operating system, the value is 8.

   The fixed sizes of numeric types necessarily limits their “range of
values”, and the particular encoding of integers decides what that range
is.

   For unsigned integers, the entire space is used to represent a
nonnegative value.  Signed integers are stored using “two’s-complement
representation”: a signed integer with N bits has a range from -2^{(N -
1)} to −1 to 0 to 1 to +2^{(N - 1)} - 1, inclusive.  The leftmost, or
high-order, bit is called the “sign bit”.

   There is only one value that means zero, and the most negative number
lacks a positive counterpart.  As a result, negating that number causes
overflow; in practice, its result is that number back again.  For
example, a two’s-complement signed 8-bit integer can represent all
decimal numbers from −128 to +127.  We will revisit that peculiarity
shortly.

   Decades ago, there were computers that didn’t use two’s-complement
representation for integers (*note Integers in Depth::), but they are
long gone and not worth any effort to support.

   When an arithmetic operation produces a value that is too big to
represent, the operation is said to “overflow”.  In C, integer overflow
does not interrupt the control flow or signal an error.  What it does
depends on signedness.

   For unsigned arithmetic, the result of an operation that overflows is
the N low-order bits of the correct value.  If the correct value is
representable in N bits, that is always the result; thus we often say
that “integer arithmetic is exact,” omitting the crucial qualifying
phrase “as long as the exact result is representable.”

   In principle, a C program should be written so that overflow never
occurs for signed integers, but in GNU C you can specify various ways of
handling such overflow (*note Integer Overflow::).

   Integer representations are best understood by looking at a table for
a tiny integer size; here are the possible values for an integer with
three bits:

Unsigned           Signed             Bits               2s Complement
----------------------------------------------------------------------------
0                  0                  000                000 (0)
1                  1                  001                111 (-1)
2                  2                  010                110 (-2)
3                  3                  011                101 (-3)
4                  -4                 100                100 (-4)
5                  -3                 101                011 (3)
6                  -2                 110                010 (2)
7                  -1                 111                001 (1)

   The parenthesized decimal numbers in the last column represent the
signed meanings of the two’s-complement of the line’s value.  Recall
that, in two’s-complement encoding, the high-order bit is 0 when the
number is nonnegative.

   We can now understand the peculiar behavior of negation of the most
negative two’s-complement integer: start with 0b100, invert the bits to
get 0b011, and add 1: we get 0b100, the value we started with.

   We can also see overflow behavior in two’s-complement:

     3 + 1 = 0b011 + 0b001 = 0b100 = (-4)
     3 + 2 = 0b011 + 0b010 = 0b101 = (-3)
     3 + 3 = 0b011 + 0b011 = 0b110 = (-2)

A sum of two nonnegative signed values that overflows has a 1 in the
sign bit, so the exact positive result is truncated to a negative value.

   ---------- Footnotes ----------

   (1) In theory, any of these types could have some other size, bit
it’s not worth even a minute to cater to that possibility.  It never
happens on GNU/Linux.

27.2 Maximum and Minimum Values
===============================

For each primitive integer type, there is a standard macro defined in
‘limits.h’ that gives the largest value that type can hold.  For
instance, for type ‘int’, the maximum value is ‘INT_MAX’.  On a 32-bit
computer, that is equal to 2,147,483,647.  The maximum value for
‘unsigned int’ is ‘UINT_MAX’, which on a 32-bit computer is equal to
4,294,967,295.  Likewise, there are ‘SHRT_MAX’, ‘LONG_MAX’, and
‘LLONG_MAX’, and corresponding unsigned limits ‘USHRT_MAX’, ‘ULONG_MAX’,
and ‘ULLONG_MAX’.

   Since there are three ways to specify a ‘char’ type, there are also
three limits: ‘CHAR_MAX’, ‘SCHAR_MAX’, and ‘UCHAR_MAX’.

   For each type that is or might be signed, there is another symbol
that gives the minimum value it can hold.  (Just replace ‘MAX’ with
‘MIN’ in the names listed above.)  There is no minimum limit symbol for
types specified with ‘unsigned’ because the minimum for them is
universally zero.

   ‘INT_MIN’ is not the negative of ‘INT_MAX’.  In two’s-complement
representation, the most negative number is 1 less than the negative of
the most positive number.  Thus, ‘INT_MIN’ on a 32-bit computer has the
value −2,147,483,648.  You can’t actually write the value that way in C,
since it would overflow.  That’s a good reason to use ‘INT_MIN’ to
specify that value.  Its definition is written to avoid overflow.

   This is part of the GNU C Intro and Reference Manual and covered by
its license.

28 Floating Point in Depth
**************************

28.1 Floating-Point Representations
===================================

Storing numbers as “floating point” allows representation of numbers
with fractional values, in a range larger than that of hardware
integers.  A floating-point number consists of a sign bit, a
“significand” (also called the “mantissa”), and a power of a fixed base.
GNU C uses the floating-point representations specified by the ‘IEEE
754-2008 Standard for Floating-Point Arithmetic’.

   The IEEE 754-2008 specification defines basic binary floating-point
formats of five different sizes: 16-bit, 32-bit, 64-bit, 128-bit, and
256-bit.  The formats of 32, 64, and 128 bits are used for the standard
C types ‘float’, ‘double’, and ‘long double’.  GNU C supports the 16-bit
floating point type ‘_Float16’ on some platforms, but does not support
the 256-bit floating point type.

   Each of the formats encodes the floating-point number as a sign bit.
After this comes an exponent that specifies a power of 2 (with a fixed
offset).  Then comes the significand.

   The first bit of the significand, before the binary point, is always
1, so there is no need to store it in memory.  It is called the “hidden
bit” because it doesn’t appear in the floating-point number as used in
the computer itself.

   All of those floating-point formats are sign-magnitude
representations, so +0 and −0 are different values.

   Besides the IEEE 754 format 128-bit float, GNU C also offers a format
consisting of a pair of 64-bit floating point numbers.  This lacks the
full exponent range of the IEEE 128-bit format, but is useful when the
underlying hardware platform does not support that.

28.2 Floating-Point Type Specifications
=======================================

The standard library header file ‘float.h’ defines a number of constants
that describe the platform’s implementation of floating-point types
‘float’, ‘double’ and ‘long double’.  They include:

‘FLT_MIN’
‘DBL_MIN’
‘LDBL_MIN’
     Defines the minimum normalized positive floating-point values that
     can be represented with the type.

‘FLT_HAS_SUBNORM’
‘DBL_HAS_SUBNORM’
‘LDBL_HAS_SUBNORM’
     Defines if the floating-point type supports subnormal (or
     “denormalized”) numbers or not (*note subnormal numbers::).

‘FLT_TRUE_MIN’
‘DBL_TRUE_MIN’
‘LDBL_TRUE_MIN’
     Defines the minimum positive values (including subnormal values)
     that can be represented with the type.

‘FLT_MAX’
‘DBL_MAX’
‘LDBL_MAX’
     Defines the largest values that can be represented with the type.

‘FLT_DECIMAL_DIG’
‘DBL_DECIMAL_DIG’
‘LDBL_DECIMAL_DIG’
     Defines the number of decimal digits ‘n’ such that any
     floating-point number that can be represented in the type can be
     rounded to a floating-point number with ‘n’ decimal digits, and
     back again, without losing any precision of the value.

28.3 Special Floating-Point Values
==================================

IEEE floating point provides for special values that are not ordinary
numbers.

infinities
     ‘+Infinity’ and ‘-Infinity’ are two different infinite values, one
     positive and one negative.  These result from operations such as ‘1
     / 0’, ‘Infinity + Infinity’, ‘Infinity * Infinity’, and ‘Infinity +
     FINITE’, and also from a result that is finite, but larger than the
     most positive possible value or smaller than the most negative
     possible value.

     *Note Handling Infinity::, for more about working with infinities.

NaNs (not a number)
     There are two special values, called Not-a-Number (NaN): a quiet
     NaN (QNaN), and a signaling NaN (SNaN).

     A QNaN is produced by operations for which the value is undefined
     in real arithmetic, such as ‘0 / 0’, ‘sqrt (-1)’, ‘Infinity -
     Infinity’, and any basic operation in which an operand is a QNaN.

     The signaling NaN is intended for initializing otherwise-unassigned
     storage, and the goal is that unlike a QNaN, an SNaN _does_ cause
     an interrupt that can be caught by a software handler, diagnosed,
     and reported.  In practice, little use has been made of signaling
     NaNs, because the most common CPUs in desktop and portable
     computers fail to implement the full IEEE 754 Standard, and supply
     only one kind of NaN, the quiet one.  Also, programming-language
     standards have taken decades to catch up to the IEEE 754 standard,
     and implementations of those language standards make an additional
     delay before programmers become willing to use these features.

     To enable support for signaling NaNs, use the GCC command-line
     option ‘-fsignaling-nans’, but this is an experimental feature and
     may not work as expected in every situation.

     A NaN has a sign bit, but its value means nothing.

     *Note Handling NaN::, for more about working with NaNs.

subnormal numbers
     It can happen that a computed floating-point value is too small to
     represent, such as when two tiny numbers are multiplied.  The
     result is then said to “underflow”.  The traditional behavior
     before the IEEE 754 Standard was to use zero as the result, and
     possibly to report the underflow in some sort of program output.

     The IEEE 754 Standard is vague about whether rounding happens
     before detection of floating underflow and overflow, or after, and
     CPU designers may choose either.

     However, the Standard does something unusual compared to earlier
     designs, and that is that when the result is smaller than the
     smallest “normalized” representable value (i.e., one in which the
     leading significand bit is ‘1’), the normalization requirement is
     relaxed, leading zero bits are permitted, and precision is
     gradually lost until there are no more bits in the significand.
     That phenomenon is called “gradual underflow”, and it serves
     important numerical purposes, although it does reduce the precision
     of the final result.  Some floating-point designs allow you to
     choose at compile time, or even at run time, whether underflows are
     gradual, or are flushed abruptly to zero.  Numbers that have
     entered the region of gradual underflow are called “subnormal”.

     You can use the library functions ‘fesetround’ and ‘fegetround’ to
     set and get the rounding mode.  Rounding modes are defined (if
     supported by the platform) in ‘fenv.h’ as: ‘FE_UPWARD’ to round
     toward positive infinity; ‘FE_DOWNWARD’ to round toward negative
     infinity; ‘FE_TOWARDZERO’ to round toward zero; and ‘FE_TONEAREST’
     to round to the nearest representable value, the default mode.  It
     is best to use ‘FE_TONEAREST’ except when there is a special need
     for some other mode.

28.4 Invalid Optimizations
==========================

Signed zeros, Infinity, and NaN invalidate some optimizations by
programmers and compilers that might otherwise have seemed obvious:

   • ‘x + 0’ and ‘x - 0’ are not the same as ‘x’ when ‘x’ is zero,
     because the result depends on the rounding rule.  *Note Rounding::,
     for more about rounding rules.

   • ‘x * 0.0’ is not the same as ‘0.0’ when ‘x’ is Infinity, a NaN, or
     negative zero.

   • ‘x / x’ is not the same as ‘1.0’ when ‘x’ is Infinity, a NaN, or
     zero.

   • ‘(x - y)’ is not the same as ‘-(y - x)’ because when the operands
     are finite and equal, one evaluates to ‘+0’ and the other to ‘-0’.

   • ‘x - x’ is not the same as ‘0.0’ when X is Infinity or a NaN.

   • ‘x == x’ and ‘x != x’ are not equivalent to ‘1’ and ‘0’ when X is a
     NaN.

   • ‘x < y’ and ‘isless (x, y)’ are not equivalent, because the first
     sets a sticky exception flag (*note Exception Flags::) when an
     operand is a NaN, whereas the second does not affect that flag.
     The same holds for the other ‘isxxx’ functions that are companions
     to relational operators.  *Note (libc)FP Comparison Functions::.

   The ‘-funsafe-math-optimizations’ option enables these optimizations.

28.5 Floating Arithmetic Exception Flags
========================================

“Sticky exception flags” record the occurrence of particular conditions:
once set, they remain set until the program explicitly clears them.

   The conditions include _invalid operand_, _division-by_zero_,
_inexact result_ (i.e., one that required rounding), _underflow_, and
_overflow_.  Some extended floating-point designs offer several
additional exception flags.  The functions ‘feclearexcept’,
‘feraiseexcept’, ‘fetestexcept’, ‘fegetexceptflags’, and
‘fesetexceptflags’ provide a standardized interface to those flags.
*Note (libc)Status bit operations::.

   One important use of those flags is to do a computation that is
normally expected to be exact in floating-point arithmetic, but
occasionally might not be, in which case, corrective action is needed.
You can clear the _inexact result_ flag with a call to ‘feclearexcept
(FE_INEXACT)’, do the computation, and then test the flag with
‘fetestexcept (FE_INEXACT)’; the result of that call is 0 if the flag is
not set (there was no rounding), and 1 when there was rounding (which,
we presume, implies the program has to correct for that).

28.6 Exact Floating-Point Arithmetic
====================================

As long as the numbers are exactly representable (fractions whose
denominator is a power of 2), and intermediate results do not require
rounding, then floating-point arithmetic is _exact_.  It is easy to
predict how many digits are needed for the results of arithmetic
operations:

   • addition and subtraction of two N-digit values with the _same_
     exponent require at most ‘N + 1’ digits, but when the exponents
     differ, many more digits may be needed;

   • multiplication of two N-digit values requires exactly 2 N digits;

   • although integer division produces a quotient and a remainder of no
     more than N-digits, floating-point remainder and square root may
     require an unbounded number of digits, and the quotient can need
     many more digits than can be stored.

   Whenever a result requires more than N digits, rounding is needed.

28.7 Rounding
=============

When floating-point arithmetic produces a result that can’t fit exactly
in the significand of the type that’s in use, it has to “round” the
value.  The basic arithmetic operations—addition, subtraction,
multiplication, division, and square root—always produce a result that
is equivalent to the exact, possibly infinite-precision result rounded
to storage precision according to the current rounding rule.

   Rounding sets the ‘FE_INEXACT’ exception flag (*note Exception
Flags::).  This enables programs to determine that rounding has
occurred.

   Rounding consists of adjusting the exponent to bring the significand
back to the required base-point alignment, then applying the current
“rounding rule” to squeeze the significand into the fixed available
size.

   The current rule is selected at run time from four options.  Here
they are:

   * _round-to-nearest_, with ties rounded to an even integer;

   * _round-up_, towards ‘+Infinity’;

   * _round-down_, towards ‘-Infinity’;

   * _round-towards-zero_.

   Under those four rounding rules, a decimal value ‘-1.2345’ that is to
be rounded to a four-digit result would become ‘-1.234’, ‘-1.234’,
‘-1.235’, and ‘-1.234’, respectively.

   The default rounding rule is _round-to-nearest_, because that has the
least bias, and produces the lowest average error.  When the true result
lies exactly halfway between two representable machine numbers, the
result is rounded to the one that ends with an even digit.

   The _round-towards-zero_ rule was common on many early computer
designs, because it is the easiest to implement: it just requires silent
truncation of all extra bits.

   The two other rules, _round-up_ and _round-down_, are essential for
implementing “interval arithmetic”, whereby each arithmetic operation
produces lower and upper bounds that are guaranteed to enclose the exact
result.

   *Note Rounding Control::, for details on getting and setting the
current rounding mode.

28.8 Rounding Issues
====================

The default IEEE 754 rounding mode minimizes errors, and most normal
computations should not suffer any serious accumulation of errors from
rounding.

   Of course, you can contrive examples where that is not so.  Here is
one: iterate a square root, then attempt to recover the original value
by repeated squaring.

     #include <stdio.h>
     #include <math.h>

     int main (void)
     {
       double x = 100.0;
       double y;
       for (n = 10; n >=100; n += 10)
         {
           y = x;
           for (k = 0; k < n; ++k) y = sqrt (y);
           for (k = 0; k < n; ++k) y *= y;
           printf ("n = %3d; x = %.0f\ty = %.6f\n", n, x, y);
         }
       return 0;
     }

Here is the output:

     n =  10; x = 100        y = 100.000000
     n =  20; x = 100        y = 100.000000
     n =  30; x = 100        y = 99.999977
     n =  40; x = 100        y = 99.981025
     n =  50; x = 100        y = 90.017127
     n =  60; x = 100        y = 1.000000
     n =  70; x = 100        y = 1.000000
     n =  80; x = 100        y = 1.000000
     n =  90; x = 100        y = 1.000000
     n = 100; x = 100        y = 1.000000

   After 50 iterations, ‘y’ has barely one correct digit, and soon
after, there are no correct digits.

28.9 Significance Loss
======================

A much more serious source of error in floating-point computation is
“significance loss” from subtraction of nearly equal values.  This means
that the number of bits in the significand of the result is fewer than
the size of the value would permit.  If the values being subtracted are
close enough, but still not equal, a _single subtraction_ can wipe out
all correct digits, possibly contaminating all future computations.

   Floating-point calculations can sometimes be carefully designed so
that significance loss is not possible, such as summing a series where
all terms have the same sign.  For example, the Taylor series expansions
of the trigonometric and hyperbolic sines have terms of identical
magnitude, of the general form ‘X**(2*N + 1) / (2*N + 1)!’.  However,
those in the trigonometric sine series alternate in sign, while those in
the hyperbolic sine series are all positive.  Here is the output of two
small programs that sum K terms of the series for ‘sin (X)’, and compare
the computed sums with known-to-be-accurate library functions:

     x = 10      k = 51
     s (x)   = -0.544_021_110_889_270
     sin (x) = -0.544_021_110_889_370

     x = 20      k = 81
     s (x)   = 0.912_945_250_749_573
     sin (x) = 0.912_945_250_727_628

     x = 30      k = 109
     s (x)   = -0.987_813_746_058_855
     sin (x) = -0.988_031_624_092_862

     x = 40      k = 137
     s (x)   = 0.617_400_430_980_474
     sin (x) = 0.745_113_160_479_349

     x = 50      k = 159
     s (x)   = 57_105.187_673_745_720_532
     sin (x) = -0.262_374_853_703_929

     // sinh(x) series summation with positive signs
     // with k terms needed to converge to machine precision

     x = 10      k = 47
     t (x)    = 1.101_323_287_470_340e+04
     sinh (x) = 1.101_323_287_470_339e+04

     x = 20      k = 69
     t (x)    = 2.425_825_977_048_951e+08
     sinh (x) = 2.425_825_977_048_951e+08

     x = 30      k = 87
     t (x)    = 5.343_237_290_762_229e+12
     sinh (x) = 5.343_237_290_762_231e+12

     x = 40      k = 105
     t (x)    = 1.176_926_334_185_100e+17
     sinh (x) = 1.176_926_334_185_100e+17

     x = 50      k = 121
     t (x)    = 2.592_352_764_293_534e+21
     sinh (x) = 2.592_352_764_293_536e+21

We have added underscores to the numbers to enhance readability.

   The ‘sinh (X)’ series with positive terms can be summed to high
accuracy.  By contrast, the series for ‘sin (X)’ suffers increasing
significance loss, so that when X = 30 only two correct digits remain.
Soon after, all digits are wrong, and the answers are complete nonsense.

   An important skill in numerical programming is to recognize when
significance loss is likely to contaminate a computation, and revise the
algorithm to reduce this problem.  Sometimes, the only practical way to
do so is to compute in higher intermediate precision, which is why the
extended types like ‘long double’ are important.

28.10 Fused Multiply-Add
========================

In 1990, when IBM introduced the POWER architecture, the CPU provided a
previously unknown instruction, the “fused multiply-add” (FMA). It
computes the value ‘x * y + z’ with an *exact* double-length product,
followed by an addition with a _single_ rounding.  Numerical computation
often needs pairs of multiply and add operations, for which the FMA is
well-suited.

   On the POWER architecture, there are two dedicated registers that
hold permanent values of ‘0.0’ and ‘1.0’, and the normal _multiply_ and
_add_ instructions are just wrappers around the FMA that compute ‘x * y
+ 0.0’ and ‘x * 1.0 + z’, respectively.

   In the early days, it appeared that the main benefit of the FMA was
getting two floating-point operations for the price of one, almost
doubling the performance of some algorithms.  However, numerical
analysts have since shown numerous uses of the FMA for significantly
enhancing accuracy.  We discuss one of the most important ones in the
next section.

   A few other architectures have since included the FMA, and most
provide variants for the related operations ‘x * y - z’ (FMS), ‘-x * y +
z’ (FNMA), and ‘-x * y - z’ (FNMS).

   The functions ‘fmaf’, ‘fma’, and ‘fmal’ implement fused multiply-add
for the ‘float’, ‘double’, and ‘long double’ data types.  Correct
implementation of the FMA in software is difficult, and some systems
that appear to provide those functions do not satisfy the
single-rounding requirement.  That situation should change as more
programmers use the FMA operation, and more CPUs provide FMA in
hardware.

   Use the ‘-ffp-contract=fast’ option to allow generation of FMA
instructions, or ‘-ffp-contract=off’ to disallow it.

28.11 Error Recovery
====================

When two numbers are combined by one of the four basic operations, the
result often requires rounding to storage precision.  For accurate
computation, one would like to be able to recover that rounding error.
With historical floating-point designs, it was difficult to do so
portably, but now that IEEE 754 arithmetic is almost universal, the job
is much easier.

   For addition with the default _round-to-nearest_ rounding mode, we
can determine the error in a sum like this:

     volatile double err, sum, tmp, x, y;

     if (fabs (x) <= fabs (y))
       {
         sum = x + y;
         tmp = sum - x;
         err = y - tmp;
       }
     else /* fabs (x) < fabs (y) */
       {
         sum = x + y;
         tmp = sum - y;
         err = x - tmp;
       }

Now, ‘x + y’ is _exactly_ represented by ‘sum + err’.  This basic
operation, which has come to be called “twosum” in the
numerical-analysis literature, is the first key to tracking, and
accounting for, rounding error.

   To determine the error in subtraction, just swap the ‘+’ and ‘-’
operators.

   We used the ‘volatile’ qualifier (*note volatile::) in the
declaration of the variables, which forces the compiler to store and
retrieve them from memory, and prevents the compiler from optimizing
‘err = y - ((x + y) - x)’ into ‘err = 0’.

   For multiplication, we can compute the rounding error without
magnitude tests with the FMA operation (*note Fused Multiply-Add::),
like this:

     volatile double err, prod, x, y;
     prod = x * y;                /* rounded product */
     err  = fma (x, y, -prod);    /* exact product ‘= PROD + ERR’ */

   For addition, subtraction, and multiplication, we can represent the
exact result with the notional sum of two values.  However, the exact
result of division, remainder, or square root potentially requires an
infinite number of digits, so we can at best approximate it.
Nevertheless, we can compute an error term that is close to the true
error: it is just that error value, rounded to machine precision.

   For division, you can approximate ‘x / y’ with ‘quo + err’ like this:

     volatile double err, quo, x, y;
     quo = x / y;
     err = fma (-quo, y, x) / y;

   For square root, we can approximate ‘sqrt (x)’ with ‘root + err’ like
this:

     volatile double err, root, x;
     root = sqrt (x);
     err = fma (-root, root, x) / (root + root);

   With the reliable and predictable floating-point design provided by
IEEE 754 arithmetic, we now have the tools we need to track errors in
the five basic floating-point operations, and we can effectively
simulate computing in twice working precision, which is sometimes
sufficient to remove almost all traces of arithmetic errors.

28.12 Exact Floating-Point Constants
====================================

One of the frustrations that numerical programmers have suffered with
since the dawn of digital computers is the inability to precisely
specify numbers in their programs.  On the early decimal machines, that
was not an issue: you could write a constant ‘1e-30’ and be confident of
that exact value being used in floating-point operations.  However, when
the hardware works in a base other than 10, then human-specified numbers
have to be converted to that base, and then converted back again at
output time.  The two base conversions are rarely exact, and unwanted
rounding errors are introduced.

   As computers usually represent numbers in a base other than 10,
numbers often must be converted to and from different bases, and
rounding errors can occur during conversion.  This problem is solved in
C using hexademical floating-point constants.  For example,
‘+0x1.fffffcp-1’ is the number that is the IEEE 754 32-bit value closest
to, but below, ‘1.0’.  The significand is represented as a hexadecimal
fraction, and the _power of two_ is written in decimal following the
exponent letter ‘p’ (the traditional exponent letter ‘e’ is not
possible, because it is a hexadecimal digit).

   In ‘printf’ and ‘scanf’ and related functions, you can use the ‘%a’
and ‘%A’ format specifiers for writing and reading hexadecimal
floating-point values.  ‘%a’ writes them with lower case letters and
‘%A’ writes them with upper case letters.  For instance, this code
reproduces our sample number:

     printf ("%a\n", 1.0 - pow (2.0, -23));
         ⊣ 0x1.fffffcp-1

The ‘strtod’ family was similarly extended to recognize numbers in that
new format.

   If you want to ensure exact data representation for transfer of
floating-point numbers between C programs on different computers, then
hexadecimal constants are an optimum choice.

28.13 Handling Infinity
=======================

As we noted earlier, the IEEE 754 model of computing is not to stop the
program when exceptional conditions occur.  It takes note of exceptional
values or conditions by setting sticky “exception flags”, or by
producing results with the special values Infinity and QNaN. In this
section, we discuss Infinity; *note Handling NaN:: for the other.

   In GNU C, you can create a value of negative Infinity in software
like this:

double x;

x = -1.0 / 0.0;

   GNU C supplies the ‘__builtin_inf’, ‘__builtin_inff’, and
‘__builtin_infl’ macros, and the GNU C Library provides the ‘INFINITY’
macro, all of which are compile-time constants for positive infinity.

   GNU C also provides a standard function to test for an Infinity:
‘isinf (x)’ returns ‘1’ if the argument is a signed infinity, and ‘0’ if
not.

   Infinities can be compared, and all Infinities of the same sign are
equal: there is no notion in IEEE 754 arithmetic of different kinds of
Infinities, as there are in some areas of mathematics.  Positive
Infinity is larger than any finite value, and negative Infinity is
smaller than finite value.

   Infinities propagate in addition, subtraction, multiplication, and
square root, but in division, they disappear, because of the rule that
‘finite / Infinity’ is ‘0.0’.  Thus, an overflow in an intermediate
computation that produces an Infinity is likely to be noticed later in
the final results.  The programmer can then decide whether the overflow
is expected, and acceptable, or whether the code possibly has a bug, or
needs to be run in higher precision, or redesigned to avoid the
production of the Infinity.

28.14 Handling NaN
==================

NaNs are not numbers: they represent values from computations that
produce undefined results.  They have a distinctive property that makes
them unlike any other floating-point value: they are _unequal to
everything, including themselves_!  Thus, you can write a test for a NaN
like this:

     if (x != x)
       printf ("x is a NaN\n");

This test works in GNU C, but some compilers might evaluate that test
expression as false without properly checking for the NaN value.  A more
portable way to test for NaN is to use the ‘isnan’ function declared in
‘math.h’:

     if (isnan (x))
       printf ("x is a NaN\n");

*Note (libc)Floating Point Classes::.

   One important use of NaNs is marking of missing data.  For example,
in statistics, such data must be omitted from computations.  Use of any
particular finite value for missing data would eventually collide with
real data, whereas such data could never be a NaN, so it is an ideal
marker.  Functions that deal with collections of data that may have
holes can be written to test for, and ignore, NaN values.

   It is easy to generate a NaN in computations: evaluating ‘0.0 / 0.0’
is the commonest way, but ‘Infinity - Infinity’, ‘Infinity / Infinity’,
and ‘sqrt (-1.0)’ also work.  Functions that receive out-of-bounds
arguments can choose to return a stored NaN value, such as with the
‘NAN’ macro defined in ‘math.h’, but that does not set the _invalid
operand_ exception flag, and that can fool some programs.

   Like Infinity, NaNs propagate in computations, but they are even
stickier, because they never disappear in division.  Thus, once a NaN
appears in a chain of numerical operations, it is almost certain to pop
out into the final results.  The programmer has to decide whether that
is expected, or whether there is a coding or algorithmic error that
needs repair.

   In general, when function gets a NaN argument, it usually returns a
NaN. However, there are some exceptions in the math-library functions
that you need to be aware of, because they violate the
_NaNs-always-propagate_ rule:

   • ‘pow (x, 0.0)’ always returns ‘1.0’, even if ‘x’ is 0.0, Infinity,
     or a NaN.

   • ‘pow (1, y)’ always returns ‘1’, even if ‘y’ is a NaN.

   • ‘hypot (INFINITY, y)’ and ‘hypot (-INFINITY, y)’ both always return
     ‘INFINITY’, even if ‘y’ is a Nan.

   • If just one of the arguments to ‘fmax (x, y)’ or ‘fmin (x, y)’ is a
     NaN, it returns the other argument.  If both arguments are NaNs, it
     returns a NaN, but there is no requirement about where it comes
     from: it could be ‘x’, or ‘y’, or some other quiet NaN.

   NaNs are also used for the return values of math-library functions
where the result is not representable in real arithmetic, or is
mathematically undefined or uncertain, such as ‘sqrt (-1.0)’ and ‘sin
(Infinity)’.  However, note that a result that is merely too big to
represent should always produce an Infinity, such as with ‘exp (1000.0)’
(too big) and ‘exp (Infinity)’ (truly infinite).

28.15 Signed Zeros
==================

The sign of zero is significant, and important, because it records the
creation of a value that is too small to represent, but came from either
the negative axis, or from the positive axis.  Such fine distinctions
are essential for proper handling of “branch cuts” in complex arithmetic
(*note Complex Arithmetic::).

   The key point about signed zeros is that in comparisons, their sign
does not matter: ‘0.0 == -0.0’ must _always_ evaluate to ‘1’ (true).
However, they are not _the same number_, and ‘-0.0’ in C code stands for
a negative zero.

28.16 Scaling by Powers of the Base
===================================

We have discussed rounding errors several times in this chapter, but it
is important to remember that when results require no more bits than the
exponent and significand bits can represent, those results are _exact_.

   One particularly useful exact operation is scaling by a power of the
base.  While one, in principle, could do that with code like this:

     y = x * pow (2.0, (double)k);   /* Undesirable scaling: avoid! */

that is not advisable, because it relies on the quality of the
math-library power function, and that happens to be one of the most
difficult functions in the C math library to make accurate.  What is
likely to happen on many systems is that the returned value from ‘pow’
will be close to a power of two, but slightly different, so the
subsequent multiplication introduces rounding error.

   The correct, and fastest, way to do the scaling is either via the
traditional C library function, or with its C99 equivalent:

     y = ldexp (x, k);            /* Traditional pre-C99 style. */
     y = scalbn (x, k);           /* C99 style. */

Both functions return ‘x * 2**k’.  *Note (libc)Normalization
Functions::.

28.17 Rounding Control
======================

Here we describe how to specify the rounding mode at run time.  System
header file ‘fenv.h’ provides the prototypes for these functions.  *Note
(libc)Rounding::.

That header file also provides constant names for the four rounding
modes: ‘FE_DOWNWARD’, ‘FE_TONEAREST’, ‘FE_TOWARDZERO’, and ‘FE_UPWARD’.

   The function ‘fegetround’ examines and returns the current rounding
mode.  On a platform with IEEE 754 floating point, the value will always
equal one of those four constants.  On other platforms, it may return a
negative value.  The function ‘fesetround’ sets the current rounding
mode.

   Changing the rounding mode can be slow, so it is useful to minimize
the number of changes.  For interval arithmetic, we seem to need three
changes for each operation, but we really only need two, because we can
write code like this example for interval addition of two reals:

     {
       struct interval_double
         {
           double hi, lo;
         } v;
       volatile double x, y;
       int rule;

       rule = fegetround ();

       if (fesetround (FE_UPWARD) == 0)
         {
           v.hi = x + y;
           v.lo = -(-x - y);
         }
       else
         fatal ("ERROR: failed to change rounding rule");

       if (fesetround (rule) != 0)
         fatal ("ERROR: failed to restore rounding rule");
     }

The ‘volatile’ qualifier (*note volatile::) is essential on x86
platforms to prevent an optimizing compiler from producing the same
value for both bounds.

28.18 Machine Epsilon
=====================

In any floating-point system, three attributes are particularly
important to know: “base” (the number that the exponent specifies a
power of), “precision” (number of digits in the significand), and
“range” (difference between most positive and most negative values).
The allocation of bits between exponent and significand decides the
answers to those questions.

   A measure of the precision is the answer to the question: what is the
smallest number that can be added to ‘1.0’ such that the sum differs
from ‘1.0’?  That number is called the “machine epsilon”.

   We could define the needed machine-epsilon constants for ‘float’,
‘double’, and ‘long double’ like this:

     static const float  epsf = 0x1p-23;  /* about 1.192e-07 */
     static const double eps  = 0x1p-52;  /* about 2.220e-16 */
     static const long double epsl = 0x1p-63;  /* about 1.084e-19 */

Instead of the hexadecimal constants, we could also have used the
Standard C macros, ‘FLT_EPSILON’, ‘DBL_EPSILON’, and ‘LDBL_EPSILON’.

   It is useful to be able to compute the machine epsilons at run time,
and we can easily generalize the operation by replacing the constant
‘1.0’ with a user-supplied value:

     double
     macheps (double x)
     { /* Return machine epsilon for X,  */
           such that X + macheps (X) &tt; X.  */
       static const double base = 2.0;
       double eps;

       if (isnan (x))
           eps = x;
       else
         {
           eps = (x == 0.0) ? 1.0 : x;

           while ((x + eps / base) != x)
               eps /= base;          /* Always exact!  */
         }

       return (eps);
     }

If we call that function with arguments from ‘0’ to ‘10’, as well as
Infinity and NaN, and print the returned values in hexadecimal, we get
output like this:

     macheps (  0) = 0x1.0000000000000p-1074
     macheps (  1) = 0x1.0000000000000p-52
     macheps (  2) = 0x1.0000000000000p-51
     macheps (  3) = 0x1.8000000000000p-52
     macheps (  4) = 0x1.0000000000000p-50
     macheps (  5) = 0x1.4000000000000p-51
     macheps (  6) = 0x1.8000000000000p-51
     macheps (  7) = 0x1.c000000000000p-51
     macheps (  8) = 0x1.0000000000000p-49
     macheps (  9) = 0x1.2000000000000p-50
     macheps ( 10) = 0x1.4000000000000p-50
     macheps (Inf) = infinity
     macheps (NaN) = nan

Notice that ‘macheps’ has a special test for a NaN to prevent an
infinite loop.

   Our code made another test for a zero argument to avoid getting a
zero return.  The returned value in that case is the smallest
representable floating-point number, here the subnormal value
‘2**(-1074)’, which is about ‘4.941e-324’.

   No special test is needed for an Infinity, because the
‘eps’-reduction loop then terminates at the first iteration.

   Our ‘macheps’ function here assumes binary floating point; some
architectures may differ.

   The C library includes some related functions that can also be used
to determine machine epsilons at run time:

     #include <math.h>           /* Include for these prototypes. */

     double      nextafter  (double x, double y);
     float       nextafterf (float x, float y);
     long double nextafterl (long double x, long double y);

These return the machine number nearest X in the direction of Y.  For
example, ‘nextafter (1.0, 2.0)’ produces the same result as ‘1.0 +
macheps (1.0)’ and ‘1.0 + DBL_EPSILON’.  *Note (libc)FP Bit Twiddling::.

   It is important to know that the machine epsilon is not symmetric
about all numbers.  At the boundaries where normalization changes the
exponent, the epsilon below X is smaller than that just above X by a
factor ‘1 / base’.  For example, ‘macheps (1.0)’ returns ‘+0x1p-52’,
whereas ‘macheps (-1.0)’ returns ‘+0x1p-53’.  Some authors distinguish
those cases by calling them the _positive_ and _negative_, or _big_ and
_small_, machine epsilons.  You can produce their values like this:

     eps_neg = 1.0 - nextafter (1.0, -1.0);
     eps_pos = nextafter (1.0, +2.0) - 1.0;

   If X is a variable, such that you do not know its value at compile
time, then you can substitute literal Y values with either ‘-inf()’ or
‘+inf()’, like this:

     eps_neg = x - nextafter (x, -inf ());
     eps_pos = nextafter (x, +inf() - x);

In such cases, if X is Infinity, then _the ‘nextafter’ functions return
Y if X equals Y_.  Our two assignments then produce
‘+0x1.fffffffffffffp+1023’ (about 1.798e+308) for EPS_NEG and Infinity
for EPS_POS.  Thus, the call ‘nextafter (INFINITY, -INFINITY)’ can be
used to find the largest representable finite number, and with the call
‘nextafter (0.0, 1.0)’, the smallest representable number (here,
‘0x1p-1074’ (about 4.491e-324), a number that we saw before as the
output from ‘macheps (0.0)’).

28.19 Complex Arithmetic
========================

We’ve already looked at defining and referring to complex numbers (*note
Complex Data Types::).  What is important to discuss here are some
issues that are unlikely to be obvious to programmers without extensive
experience in both numerical computing, and in complex arithmetic in
mathematics.

   The first important point is that, unlike real arithmetic, in complex
arithmetic, the danger of significance loss is _pervasive_, and affects
_every one_ of the basic operations, and _almost all_ of the
math-library functions.  To understand why, recall the rules for complex
multiplication and division:

     a = u + I*v              /* First operand. */
     b = x + I*y              /* Second operand. */

     prod = a * b
          = (u + I*v) * (x + I*y)
          = (u * x - v * y) + I*(v * x + u * y)

     quo  = a / b
          = (u + I*v) / (x + I*y)
          = [(u + I*v) * (x - I*y)] / [(x + I*y) * (x - I*y)]
          = [(u * x + v * y) + I*(v * x - u * y)] / (x**2 + y**2)

There are four critical observations about those formulas:

   • the multiplications on the right-hand side introduce the
     possibility of premature underflow or overflow;

   • the products must be accurate to twice working precision;

   • there is _always_ one subtraction on the right-hand sides that is
     subject to catastrophic significance loss; and

   • complex multiplication has up to _six_ rounding errors, and complex
     division has _ten_ rounding errors.

   Another point that needs careful study is the fact that many
functions in complex arithmetic have “branch cuts”.  You can view a
function with a complex argument, ‘f (z)’, as ‘f (x + I*y)’, and thus,
it defines a relation between a point ‘(x, y)’ on the complex plane with
an elevation value on a surface.  A branch cut looks like a tear in that
surface, so approaching the cut from one side produces a particular
value, and from the other side, a quite different value.  Great care is
needed to handle branch cuts properly, and even small numerical errors
can push a result from one side to the other, radically changing the
returned value.  As we reported earlier, correct handling of the sign of
zero is critically important for computing near branch cuts.

   The best advice that we can give to programmers who need complex
arithmetic is to always use the _highest precision available_, and then
to carefully check the results of test calculations to gauge the likely
accuracy of the computed results.  It is easy to supply test values of
real and imaginary parts where all five basic operations in complex
arithmetic, and almost all of the complex math functions, lose _all_
significance, and fail to produce even a single correct digit.

   Even though complex arithmetic makes some programming tasks easier,
it may be numerically preferable to rework the algorithm so that it can
be carried out in real arithmetic.  That is commonly possible in matrix
algebra.

   GNU C can perform code optimization on complex number multiplication
and division if certain boundary checks will not be needed.  The
command-line option ‘-fcx-limited-range’ tells the compiler that a range
reduction step is not needed when performing complex division, and that
there is no need to check if a complex multiplication or division
results in the value ‘Nan + I*NaN’.  By default these checks are
enabled.  You can explicitly enable them with the
‘-fno-cx-limited-range’ option.

28.20 Round-Trip Base Conversion
================================

Most numeric programs involve converting between base-2 floating-point
numbers, as represented by the computer, and base-10 floating-point
numbers, as entered and handled by the programmer.  What might not be
obvious is the number of base-2 bits vs.  base-10 digits required for
each representation.  Consider the following tables showing the number
of decimal digits representable in a given number of bits, and vice
versa:

binary in                            24      53      64      113     237
decimal out                          9       17      21      36      73

decimal in                           7       16      34      70
binary out                           25      55      114     234

   We can compute the table numbers with these two functions:

     int
     matula(int nbits)
     {   /* Return output decimal digits needed for nbits-bits input. */
         return ((int)ceil((double)nbits / log2(10.0) + 1.0));
     }

     int
     goldberg(int ndec)
     {   /* Return output bits needed for ndec-digits input. */
         return ((int)ceil((double)ndec / log10(2.0) + 1.0));
     }

   One significant observation from those numbers is that we cannot
achieve correct round-trip conversion between the decimal and binary
formats in the same storage size!  For example, we need 25 bits to
represent a 7-digit value from the 32-bit decimal format, but the binary
format only has 24 available.  Similar observations hold for each of the
other conversion pairs.

   The general input/output base-conversion problem is astonishingly
complicated, and solutions were not generally known until the
publication of two papers in 1990 that are listed later near the end of
this chapter.  For the 128-bit formats, the worst case needs more than
11,500 decimal digits of precision to guarantee correct rounding in a
binary-to-decimal conversion!

   For further details see the references for Bennett Goldberg and David
Matula.

28.21 Further Reading
=====================

The subject of floating-point arithmetic is much more complex than many
programmers seem to think, and few books on programming languages spend
much time in that area.  In this chapter, we have tried to expose the
reader to some of the key ideas, and to warn of easily overlooked
pitfalls that can soon lead to nonsensical results.  There are a few
good references that we recommend for further reading, and for finding
other important material about computer arithmetic:

   • Paul H. Abbott and 15 others, ‘Architecture and software support in
     IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point
     arithmetic’, IBM Journal of Research and Development 43(5/6)
     723–760 (1999), >https://doi.org/10.1147/rd.435.0723<.  This
     article gives a good description of IBM’s algorithm for exact
     decimal-to-binary conversion, complementing earlier ones by Clinger
     and others.

   • Nelson H. F. Beebe, ‘The Mathematical-Function Computation
     Handbook: Programming Using the MathCW Portable Software Library’,
     Springer (2017), ISBN 3-319-64109-3 (hardcover), 3-319-64110-7
     (e-book) (xxxvi + 1114 pages),
     >https://doi.org/10.1007/978-3-319-64110-2<.  This book describes
     portable implementations of a large superset of the mathematical
     functions available in many programming languages, extended to a
     future 256-bit format (70 decimal digits), for both binary and
     decimal floating point.  It includes a substantial portion of the
     functions described in the famous ‘NIST Handbook of Mathematical
     Functions’, Cambridge (2018), ISBN 0-521-19225-0.  See
     >http://www.math.utah.edu/pub/mathcw< for compilers and libraries.

   • William D. Clinger, ‘How to Read Floating Point Numbers
     Accurately’, ACM SIGPLAN Notices 25(6) 92–101 (June 1990),
     >https://doi.org/10.1145/93548.93557<.  See also the papers by
     Steele & White.

   • William D. Clinger, ‘Retrospective: How to read floating point
     numbers accurately’, ACM SIGPLAN Notices 39(4) 360–371 (April
     2004), >http://doi.acm.org/10.1145/989393.989430<.  Reprint of 1990
     paper, with additional commentary.

   • I. Bennett Goldberg, ‘27 Bits Are Not Enough For 8-Digit Accuracy’,
     Communications of the ACM 10(2) 105–106 (February 1967),
     >http://doi.acm.org/10.1145/363067.363112<.  This paper, and its
     companions by David Matula, address the base-conversion problem,
     and show that the naive formulas are wrong by one or two digits.

   • David Goldberg, ‘What Every Computer Scientist Should Know About
     Floating-Point Arithmetic’, ACM Computing Surveys 23(1) 5–58 (March
     1991), corrigendum 23(3) 413 (September 1991),
     >https://doi.org/10.1145/103162.103163<.  This paper has been
     widely distributed, and reissued in vendor programming-language
     documentation.  It is well worth reading, and then rereading from
     time to time.

   • Norbert Juffa and Nelson H. F. Beebe, ‘A Bibliography of
     Publications on Floating-Point Arithmetic’,
     >http://www.math.utah.edu/pub/tex/bib/fparith.bib<.  This is the
     largest known bibliography of publications about floating-point,
     and also integer, arithmetic.  It is actively maintained, and in
     mid 2019, contains more than 6400 references to original research
     papers, reports, theses, books, and Web sites on the subject
     matter.  It can be used to locate the latest research in the field,
     and the historical coverage dates back to a 1726 paper on
     signed-digit arithmetic, and an 1837 paper by Charles Babbage, the
     intellectual father of mechanical computers.  The entries for the
     Abbott, Clinger, and Steele & White papers cited earlier contain
     pointers to several other important related papers on the
     base-conversion problem.

   • William Kahan, ‘Branch Cuts for Complex Elementary Functions, or
     Much Ado About Nothing’s Sign Bit’, (1987),
     >http://people.freebsd.org/~das/kahan86branch.pdf<.  This Web
     document about the fine points of complex arithmetic also appears
     in the volume edited by A. Iserles and M. J. D. Powell, ‘The State
     of the Art in Numerical Analysis: Proceedings of the Joint IMA/SIAM
     Conference on the State of the Art in Numerical Analysis held at
     the University of Birmingham, 14–18 April 1986’, Oxford University
     Press (1987), ISBN 0-19-853614-3 (xiv + 719 pages).  Its author is
     the famous chief architect of the IEEE 754 arithmetic system, and
     one of the world’s greatest experts in the field of floating-point
     arithmetic.  An entire generation of his students at the University
     of California, Berkeley, have gone on to careers in academic and
     industry, spreading the knowledge of how to do floating-point
     arithmetic right.

   • Donald E. Knuth, ‘A Simple Program Whose Proof Isn’t’, in ‘Beauty
     is our business: a birthday salute to Edsger W. Dijkstra’, W. H. J.
     Feijen, A. J. M. van Gasteren, D. Gries, and J. Misra (eds.),
     Springer (1990), ISBN 1-4612-8792-8,
     >https://doi.org/10.1007/978-1-4612-4476-9<.  This book chapter
     supplies a correctness proof of the decimal to binary, and binary
     to decimal, conversions in fixed-point arithmetic in the TeX
     typesetting system.  The proof evaded its author for a dozen years.

   • David W. Matula, ‘In-and-out conversions’, Communications of the
     ACM 11(1) 57–50 (January 1968),
     >https://doi.org/10.1145/362851.362887<.

   • David W. Matula, ‘The Base Conversion Theorem’, Proceedings of the
     American Mathematical Society 19(3) 716–723 (June 1968).  See also
     other papers here by this author, and by I. Bennett Goldberg.

   • David W. Matula, ‘A Formalization of Floating-Point Numeric Base
     Conversion’, IEEE Transactions on Computers C-19(8) 681–692 (August
     1970), >https://doi.org/10.1109/T-C.1970.223017<.

   • Jean-Michel Muller and eight others, ‘Handbook of Floating-Point
     Arithmetic’, Birkhäuser-Boston (2010), ISBN 0-8176-4704-X (xxiii +
     572 pages), >https://doi.org/10.1007/978-0-8176-4704-9<.  This is a
     comprehensive treatise from a French team who are among the world’s
     greatest experts in floating-point arithmetic, and among the most
     prolific writers of research papers in that field.  They have much
     to teach, and their book deserves a place on the shelves of every
     serious numerical programmer.

   • Jean-Michel Muller and eight others, ‘Handbook of Floating-Point
     Arithmetic’, Second edition, Birkhäuser-Boston (2018), ISBN
     3-319-76525-6 (xxv + 627 pages),
     >https://doi.org/10.1007/978-3-319-76526-6<.  This is a new edition
     of the preceding entry.

   • Michael Overton, ‘Numerical Computing with IEEE Floating Point
     Arithmetic, Including One Theorem, One Rule of Thumb, and One
     Hundred and One Exercises’, SIAM (2001), ISBN 0-89871-482-6 (xiv +
     104 pages), >http://www.ec-securehost.com/SIAM/ot76.html<.  This is
     a small volume that can be covered in a few hours.

   • Guy L. Steele Jr.  and Jon L. White, ‘How to Print Floating-Point
     Numbers Accurately’, ACM SIGPLAN Notices 25(6) 112–126 (June 1990),
     >https://doi.org/10.1145/93548.93559<.  See also the papers by
     Clinger.

   • Guy L. Steele Jr.  and Jon L. White, ‘Retrospective: How to Print
     Floating-Point Numbers Accurately’, ACM SIGPLAN Notices 39(4)
     372–389 (April 2004), >http://doi.acm.org/10.1145/989393.989431<.
     Reprint of 1990 paper, with additional commentary.

   • Pat H. Sterbenz, ‘Floating Point Computation’, Prentice-Hall
     (1974), ISBN 0-13-322495-3 (xiv + 316 pages).  This often-cited
     book provides solid coverage of what floating-point arithmetic was
     like _before_ the introduction of IEEE 754 arithmetic.

29 Compilation
**************

Early in the manual we explained how to compile a simple C program that
consists of a single source file (*note Compile Example::).  However, we
handle only short programs that way.  A typical C program consists of
many source files, each of which is a separate “compilation
module”—meaning that it has to be compiled separately.

   The full details of how to compile with GCC are documented in xxxx.
Here we give only a simple introduction.

   These are the commands to compile two compilation modules, ‘foo.c’
and ‘bar.c’, with a command for each module:

     gcc -c -O -g foo.c
     gcc -c -O -g bar.c

In these commands, ‘-g’ says to generate debugging information, ‘-O’
says to do some optimization, and ‘-c’ says to put the compiled code for
that module into a corresponding “object file” and go no further.  The
object file for ‘foo.c’ is called ‘foo.o’, and so on.

   If you wish, you can specify the additional options ‘-Wformat
-Wparenthesis -Wstrict-prototypes’, which request additional warnings.

   One reason to divide a large program into multiple compilation
modules is to control how each module can access the internals of the
others.  When a module declares a function or variable ‘extern’, other
modules can access it.  The other functions and variables in a module
can’t be accessed from outside that module.

   The other reason for using multiple modules is so that changing one
source file does not require recompiling all of them in order to try the
modified program.  Dividing a large program into many substantial
modules in this way typically makes recompilation much faster.

   After you compile all the program’s modules, in order to run the
program you must “link” the object files into a combined executable,
like this:

     gcc -o foo foo.o bar.o

In this command, ‘-o foo’ species the file name for the executable file,
and the other arguments are the object files to link.  Always specify
the executable file name in a command that generates one.

   Normally we don’t run any of these commands directly.  Instead we
write a set of “make rules” for the program, then use the ‘make’ program
to recompile only the source files that need to be recompiled.

30 Directing Compilation
************************

This chapter describes C constructs that don’t alter the program’s
meaning _as such_, but rather direct the compiler how to treat some
aspects of the program.

30.1 Pragmas
============

A “pragma” is an annotation in a program that gives direction to the
compiler.

30.1.1 Pragma Basics
--------------------

C defines two syntactical forms for pragmas, the line form and the token
form.  You can write any pragma in either form, with the same meaning.

   The line form is a line in the source code, like this:

     #pragma LINE

The line pragma has no effect on the parsing of the lines around it.
This form has the drawback that it can’t be generated by a macro
expansion.

   The token form is a series of tokens; it can appear anywhere in the
program between the other tokens.

     _Pragma (STRINGCONSTANT)

The pragma has no effect on the syntax of the tokens that surround it;
thus, here’s a pragma in the middle of an ‘if’ statement:

     if _Pragma ("hello") (x &tt; 1)

However, that’s an unclear thing to do; for the sake of
understandability, it is better to put a pragma on a line by itself and
not embedded in the middle of another construct.

   Both forms of pragma have a textual argument.  In a line pragma, the
text is the rest of the line.  The textual argument to ‘_Pragma’ uses
the same syntax as a C string constant: surround the text with two ‘"’
characters, and add a backslash before each ‘"’ or ‘\’ character in it.

   With either syntax, the textual argument specifies what to do.  It
begins with one or several words that specify the operation.  If the
compiler does not recognize them, it ignores the pragma.

   Here are the pragma operations supported in GNU C.

‘#pragma GCC dependency "FILE" [MESSAGE]’
‘_Pragma ("GCC dependency \"FILE\" [MESSAGE]")’
     Declares that the current source file depends on FILE, so GNU C
     compares the file times and gives a warning if FILE is newer than
     the current source file.

     This directive searches for FILE the way ‘#include’ searches for a
     non-system header file.

     If MESSAGE is given, the warning message includes that text.

     Examples:

          #pragma GCC dependency "parse.y"
          _pragma ("GCC dependency \"/usr/include/time.h\" \
          rerun fixincludes")

‘#pragma GCC poison IDENTIFIERS’
‘_Pragma ("GCC poison IDENTIFIERS")’
     Poisons the identifiers listed in IDENTIFIERS.

     This is useful to make sure all mention of IDENTIFIERS has been
     deleted from the program and that no reference to them creeps back
     in.  If any of those identifiers appears anywhere in the source
     after the directive, it causes a compilation error.  For example,

          #pragma GCC poison printf sprintf fprintf
          sprintf(some_string, "hello");

     generates an error.

     If a poisoned identifier appears as part of the expansion of a
     macro that was defined before the identifier was poisoned, it will
     _not_ cause an error.  Thus, system headers that define macros that
     use the identifier will not cause errors.

     For example,

          #define strrchr rindex
          _Pragma ("GCC poison rindex")
          strrchr(some_string, 'h');

     does not cause a compilation error.

‘#pragma GCC system_header’
‘_Pragma ("GCC system_header")’
     Specify treating the rest of the current source file as if it came
     from a system header file.  *Note System Headers: (gcc)System
     Headers.

‘#pragma GCC warning MESSAGE’
‘_Pragma ("GCC warning MESSAGE")’
     Equivalent to ‘#warning’.  Its advantage is that the ‘_Pragma’ form
     can be included in a macro definition.

‘#pragma GCC error MESSAGE’
‘_Pragma ("GCC error MESSAGE")’
     Equivalent to ‘#error’.  Its advantage is that the ‘_Pragma’ form
     can be included in a macro definition.

‘#pragma GCC message MESSAGE’
‘_Pragma ("GCC message MESSAGE")’
     Similar to ‘GCC warning’ and ‘GCC error’, this simply prints an
     informational message, and could be used to include additional
     warning or error text without triggering more warnings or errors.
     (Note that unlike ‘warning’ and ‘error’, ‘message’ does not include
     ‘GCC’ as part of the pragma.)

30.1.2 Severity Pragmas
-----------------------

These pragmas control the severity of classes of diagnostics.  You can
specify the class of diagnostic with the GCC option that causes those
diagnostics to be generated.

‘#pragma GCC diagnostic error OPTION’
‘_Pragma ("GCC diagnostic error OPTION")’
     For code following this pragma, treat diagnostics of the variety
     specified by OPTION as errors.  For example:

          _Pragma ("GCC diagnostic error -Wformat")

     specifies to treat diagnostics enabled by the -WFORMAT option as
     errors rather than warnings.

‘#pragma GCC diagnostic warning OPTION’
‘_Pragma ("GCC diagnostic warning OPTION")’
     For code following this pragma, treat diagnostics of the variety
     specified by OPTION as warnings.  This overrides the -WERROR option
     which says to treat warnings as errors.

‘#pragma GCC diagnostic ignore OPTION’
‘_Pragma ("GCC diagnostic ignore OPTION")’
     For code following this pragma, refrain from reporting any
     diagnostics of the variety specified by OPTION.

‘#pragma GCC diagnostic push’
‘_Pragma ("GCC diagnostic push")’
‘#pragma GCC diagnostic pop’
‘_Pragma ("GCC diagnostic pop")’
     These pragmas maintain a stack of states for severity settings.
     ‘GCC diagnostic push’ saves the current settings on the stack, and
     ‘GCC diagnostic pop’ pops the last stack item and restores the
     current settings from that.

     ‘GCC diagnostic pop’ when the severity setting stack is empty
     restores the settings to what they were at the start of
     compilation.

     Here is an example:

          _Pragma ("GCC diagnostic error -Wformat")

          /* ‘-Wformat’ messages treated as errors.  */

          _Pragma ("GCC diagnostic push")
          _Pragma ("GCC diagnostic warning -Wformat")

          /* ‘-Wformat’ messages treated as warnings.  */

          _Pragma ("GCC diagnostic push")
          _Pragma ("GCC diagnostic ignored -Wformat")

          /* ‘-Wformat’ messages suppressed.  */

          _Pragma ("GCC diagnostic pop")

          /* ‘-Wformat’ messages treated as warnings again.  */

          _Pragma ("GCC diagnostic pop")

          /* ‘-Wformat’ messages treated as errors again.  */

          /* This is an excess ‘pop’ that matches no ‘push’.  */
          _Pragma ("GCC diagnostic pop")

          /* ‘-Wformat’ messages treated once again
             as specified by the GCC command-line options.  */

30.1.3 Optimization Pragmas
---------------------------

These pragmas enable a particular optimization for specific function
definitions.  The settings take effect at the end of a function
definition, so the clean place to use these pragmas is between function
definitions.

‘#pragma GCC optimize OPTIMIZATION’
‘_Pragma ("GCC optimize OPTIMIZATION")’
     These pragmas enable the optimization OPTIMIZATION for the
     following functions.  For example,

          _Pragma ("GCC optimize -fforward-propagate")

     says to apply the ‘forward-propagate’ optimization to all following
     function definitions.  Specifying optimizations for individual
     functions, rather than for the entire program, is rare but can be
     useful for getting around a bug in the compiler.

     If OPTIMIZATION does not correspond to a defined optimization
     option, the pragma is erroneous.  To turn off an optimization, use
     the corresponding ‘-fno-’ option, such as ‘-fno-forward-propagate’.

‘#pragma GCC target OPTIMIZATIONS’
‘_Pragma ("GCC target OPTIMIZATIONS")’
     The pragma ‘GCC target’ is similar to ‘GCC optimize’ but is used
     for platform-specific optimizations.  Thus,

          _Pragma ("GCC target popcnt")

     activates the optimization ‘popcnt’ for all following function
     definitions.  This optimization is supported on a few common
     targets but not on others.

‘#pragma GCC push_options’
‘_Pragma ("GCC push_options")’
     The ‘push_options’ pragma saves on a stack the current settings
     specified with the ‘target’ and ‘optimize’ pragmas.

‘#pragma GCC pop_options’
‘_Pragma ("GCC pop_options")’
     The ‘pop_options’ pragma pops saved settings from that stack.

     Here’s an example of using this stack.

          _Pragma ("GCC push_options")
          _Pragma ("GCC optimize forward-propagate")

          /* Functions to compile
             with the ‘forward-propagate’ optimization. */

          _Pragma ("GCC pop_options")
          /* Ends enablement of ‘forward-propagate’. */

‘#pragma GCC reset_options’
‘_Pragma ("GCC reset_options")’
     Clears all pragma-defined ‘target’ and ‘optimize’ optimization
     settings.

30.2 Static Assertions
======================

You can add compiler-time tests for necessary conditions into your code
using ‘_Static_assert’.  This can be useful, for example, to check that
the compilation target platform supports the type sizes that the code
expects.  For example,

     _Static_assert ((sizeof (long int) <= 8),
         "long int needs to be at least 8 bytes");

reports a compile-time error if compiled on a system with long integers
smaller than 8 bytes, with ‘long int needs to be at least 8 bytes’ as
the error message.

   Since calls ‘_Static_assert’ are processed at compile time, the
expression must be computable at compile time and the error message must
be a literal string.  The expression can refer to the sizes of
variables, but can’t refer to their values.  For example, the following
static assertion is invalid for two reasons:

     char *error_message
       = "long int needs to be at least 8 bytes";
     int size_of_long_int = sizeof (long int);

     _Static_assert (size_of_long_int == 8, error_message);

The expression ‘size_of_long_int == 8’ isn’t computable at compile time,
and the error message isn’t a literal string.

   You can, though, use preprocessor definition values with
‘_Static_assert’:

     #define LONG_INT_ERROR_MESSAGE "long int needs to be \
     at least 8 bytes"

     _Static_assert ((sizeof (long int) == 8),
       LONG_INT_ERROR_MESSAGE);

   Static assertions are permitted wherever a statement or declaration
is permitted, including at top level in the file, and also inside the
definition of a type.

     union y
     {
       int i;
       int *ptr;
       _Static_assert (sizeof (int *) == sizeof (int),
     		  "Pointer and int not same size");
     };

Appendix A Type Alignment
*************************

Code for device drivers and other communication with low-level hardware
sometimes needs to be concerned with the alignment of data objects in
memory.

   Each data type has a required “alignment”, always a power of 2, that
says at which memory addresses an object of that type can validly start.
A valid address for the type must be a multiple of its alignment.  If a
type’s alignment is 1, that means it can validly start at any address.
If a type’s alignment is 2, that means it can only start at an even
address.  If a type’s alignment is 4, that means it can only start at an
address that is a multiple of 4.

   The alignment of a type (except ‘char’) can vary depending on the
kind of computer in use.  To refer to the alignment of a type in a C
program, use ‘_Alignof’, whose syntax parallels that of ‘sizeof’.  Like
‘sizeof’, ‘_Alignof’ is a compile-time operation, and it doesn’t compute
the value of the expression used as its argument.

   Nominally, each integer and floating-point type has an alignment
equal to the largest power of 2 that divides its size.  Thus, ‘int’ with
size 4 has a nominal alignment of 4, and ‘long long int’ with size 8 has
a nominal alignment of 8.

   However, each kind of computer generally has a maximum alignment, and
no type needs more alignment than that.  If the computer’s maximum
alignment is 4 (which is common), then no type’s alignment is more than
4.

   The size of any type is always a multiple of its alignment; that way,
in an array whose elements have that type, all the elements are properly
aligned if the first one is.

   These rules apply to all real computers today, but some embedded
controllers have odd exceptions.  We don’t have references to cite for
them.

   Ordinary C code guarantees that every object of a given type is in
fact aligned as that type requires.

   If the operand of ‘_Alignof’ is a structure field, the value is the
alignment it requires.  It may have a greater alignment by coincidence,
due to the other fields, but ‘_Alignof’ is not concerned about that.
*Note Structures::.

   Older versions of GNU C used the keyword ‘__alignof__’ for this, but
now that the feature has been standardized, it is better to use the
standard keyword ‘_Alignof’.

   You can explicitly specify an alignment requirement for a particular
variable or structure field by adding ‘_Alignas (ALIGNMENT)’ to the
declaration, where ALIGNMENT is a power of 2 or a type name.  For
instance:

     char _Alignas (8) x;

or

     char _Alignas (double) x;

specifies that ‘x’ must start on an address that is a multiple of 8.
However, if ALIGNMENT exceeds the maximum alignment for the machine,
that maximum is how much alignment ‘x’ will get.

   The older GNU C syntax for this feature looked like ‘__attribute__
((__aligned__ (ALIGNMENT)))’ to the declaration, and was added after the
variable.  For instance:

     char x __attribute__ ((__aligned__ 8));

   *Note Attributes::.

Appendix B Aliasing
*******************

We have already presented examples of casting a ‘void *’ pointer to
another pointer type, and casting another pointer type to ‘void *’.

   One common kind of pointer cast is guaranteed safe: casting the value
returned by ‘malloc’ and related functions (*note Dynamic Memory
Allocation::).  It is safe because these functions do not save the
pointer anywhere else; the only way the program will access the newly
allocated memory is via the pointer just returned.

   In fact, C allows casting any pointer type to any other pointer type.
Using this to access the same place in memory using two different data
types is called “aliasing”.

   Aliasing is necessary in some programs that do sophisticated memory
management, such as GNU Emacs, but most C programs don’t need to do
aliasing.  When it isn’t needed, *stay away from it!*  To do aliasing
correctly requires following the rules stated below.  Otherwise, the
aliasing may result in malfunctions when the program runs.

   The rest of this appendix explains the pitfalls and rules of
aliasing.

B.1 Aliasing and Alignment
==========================

In order for a type-converted pointer to be valid, it must have the
alignment that the new pointer type requires.  For instance, on most
computers, ‘int’ has alignment 4; the address of an ‘int’ must be a
multiple of 4.  However, ‘char’ has alignment 1, so the address of a
‘char’ is usually not a multiple of 4.  Taking the address of such a
‘char’ and casting it to ‘int *’ probably results in an invalid pointer.
Trying to dereference it may cause a ‘SIGBUS’ signal, depending on the
platform in use (*note Signals::).

     foo ()
     {
       char i[4];
       int *p = (int *) &i[1]; /* Misaligned pointer! */
       return *p;              /* Crash! */
     }

   This requirement is never a problem when casting the return value of
‘malloc’ because that function always returns a pointer with as much
alignment as any type can require.

B.2 Aliasing and Length
=======================

When converting a pointer to a different pointer type, make sure the
object it really points to is at least as long as the target of the
converted pointer.  For instance, suppose ‘p’ has type ‘int *’ and it’s
cast as follows:

     int *p;

     struct
       {
         double d, e, f;
       } foo;

     struct foo *q = (struct foo *)p;

     q-<f = 5.14159;

the value ‘q-<f’ will run past the end of the ‘int’ that ‘p’ points to.
If ‘p’ was initialized to the start of an array of type ‘int[6]’, the
object is long enough for three ‘double’s.  But if ‘p’ points to
something shorter, ‘q-<f’ will run on beyond the end of that, overlaying
some other data.  Storing that will garble that other data.  Or it could
extend past the end of memory space and cause a ‘SIGSEGV’ signal (*note
Signals::).

B.3 Type Rules for Aliasing
===========================

C code that converts a pointer to a different pointer type can use the
pointers to access the same memory locations with two different data
types.  If the same address is accessed with different types in a single
control thread, optimization can make the code do surprising things (in
effect, make it malfunction).

   Here’s a concrete example where aliasing that can change the code’s
behavior when it is optimized.  We assume that ‘float’ is 4 bytes long,
like ‘int’, and so is every pointer.  Thus, the structures ‘struct a’
and ‘struct b’ are both 8 bytes.

     #include <stdio.h>
     struct a { int size; char *data; };
     struct b { float size; char *data; };

     void sub (struct a *p, struct b *q)
     {
       int x;
       p-<size = 0;
       q-<size = 1;
       x = p-<size;
       printf("x       =%d\n", x);
       printf("p-<size =%d\n", (int)p-<size);
       printf("q-<size =%d\n", (int)q-<size);
     }

     int main(void)
     {
       struct a foo;
       struct a *p = &foo;
       struct b *q = (struct b *) &foo;

       sub (p, q);
     }

   This code works as intended when compiled without optimization.  All
the operations are carried out sequentially as written.  The code sets
‘x’ to ‘p-<size’, but what it actually gets is the bits of the floating
point number 1, as type ‘int’.

   However, when optimizing, the compiler is allowed to assume
(mistakenly, here) that ‘q’ does not point to the same storage as ‘p’,
because their data types are not allowed to alias.

   From this assumption, the compiler can deduce (falsely, here) that
the assignment into ‘q-<size’ has no effect on the value of ‘p-<size’,
which must therefore still be 0.  Thus, ‘x’ will be set to 0.

   GNU C, following the C standard, _defines_ this optimization as
legitimate.  Code that misbehaves when optimized following these rules
is, by definition, incorrect C code.

   The rules for storage aliasing in C are based on the two data types:
the type of the object, and the type it is accessed through.  The rules
permit accessing part of a storage object of type T using only these
types:

   • T.

   • A type compatible with T.  *Note Compatible Types::.

   • A signed or unsigned version of one of the above.

   • A qualifed version of one of the above.  *Note Type Qualifiers::.

   • An array, structure (*note Structures::), or union type (‘Unions’)
     that contains one of the above, either directly as a field or
     through multiple levels of fields.  If T is ‘double’, this would
     include ‘struct s { union { double d[2]; int i[4]; } u; int i; };’
     because there’s a ‘double’ inside it somewhere.

   • A character type.

   What do these rules say about the example in this subsection?

   For ‘foo.size’ (equivalently, ‘a-<size’), T is ‘int’.  The type
‘float’ is not allowed as an aliasing type by those rules, so ‘b-<size’
is not supposed to alias with elements of ‘j’.  Based on that
assumption, GNU C makes a permitted optimization that was not, in this
case, consistent with what the programmer intended the program to do.

   Whether GCC actually performs type-based aliasing analysis depends on
the details of the code.  GCC has other ways to determine (in some
cases) whether objects alias, and if it gets a reliable answer that way,
it won’t fall back on type-based heuristics.

   The importance of knowing the type-based aliasing rules is not so as
to ensure that the optimization is done where it would be safe, but so
as to ensure it is _not_ done in a way that would break the program.
You can turn off type-based aliasing analysis by giving GCC the option
‘-fno-strict-aliasing’.

Appendix C Digraphs
*******************

C accepts aliases for certain characters.  Apparently in the 1990s some
computer systems had trouble inputting these characters, or trouble
displaying them.  These digraphs almost never appear in C programs
nowadays, but we mention them for completeness.

‘>:’
     An alias for ‘[’.
‘:<’
     An alias for ‘]’.
‘>%’
     An alias for ‘{’.
‘%<’
     An alias for ‘}’.
‘%:’
     An alias for ‘#’, used for preprocessing directives (*note
     Directives::) and macros (*note Macros::).

Appendix D Attributes in Declarations
*************************************

You can specify certain additional requirements in a declaration, to get
fine-grained control over code generation, and helpful informational
messages during compilation.  We use a few attributes in code examples
throughout this manual, including

‘aligned’
     The ‘aligned’ attribute specifies a minimum alignment for a
     variable or structure field, measured in bytes:

          int foo __attribute__ ((aligned (8))) = 0;

     This directs GNU C to allocate ‘foo’ at an address that is a
     multiple of 8 bytes.  However, you can’t force an alignment bigger
     than the computer’s maximum meaningful alignment.

‘packed’
     The ‘packed’ attribute specifies to compact the fields of a
     structure by not leaving gaps between fields.  For example,

          struct __attribute__ ((packed)) bar
          {
            char a;
            int b;
          };

     allocates the integer field ‘b’ at byte 1 in the structure,
     immediately after the character field ‘a’.  The packed structure is
     just 5 bytes long (assuming ‘int’ is 4 bytes) and its alignment is
     1, that of ‘char’.

‘deprecated’
     Applicable to both variables and functions, the ‘deprecated’
     attribute tells the compiler to issue a warning if the variable or
     function is ever used in the source file.

          int old_foo __attribute__ ((deprecated));

          int old_quux () __attribute__ ((deprecated));

‘__noinline__’
     The ‘__noinline__’ attribute, in a function’s declaration or
     definition, specifies never to inline calls to that function.  All
     calls to that function, in a compilation unit where it has this
     attribute, will be compiled to invoke the separately compiled
     function.  *Note Inline Function Definitions::.

‘__noclone__’
     The ‘__noclone__’ attribute, in a function’s declaration or
     definition, specifies never to clone that function.  Thus, there
     will be only one compiled version of the function.  *Note Label
     Value Caveats::, for more information about cloning.

‘always_inline’
     The ‘always_inline’ attribute, in a function’s declaration or
     definition, specifies to inline all calls to that function (unless
     something about the function makes inlining impossible).  This
     applies to all calls to that function in a compilation unit where
     it has this attribute.  *Note Inline Function Definitions::.

‘gnu_inline’
     The ‘gnu_inline’ attribute, in a function’s declaration or
     definition, specifies to handle the ‘inline’ keywprd the way GNU C
     originally implemented it, many years before ISO C said anything
     about inlining.  *Note Inline Function Definitions::.

   For full documentation of attributes, see the GCC manual.  *Note
Attribute Syntax: (gcc)Attribute Syntax.

Appendix E Signals
******************

Some program operations bring about an error condition called a
“signal”.  These signals terminate the program, by default.

   There are various different kinds of signals, each with a name.  We
have seen several such error conditions through this manual:

‘SIGSEGV’
     This signal is generated when a program tries to read or write
     outside the memory that is allocated for it, or to write memory
     that can only be read.  The name is an abbreviation for
     “segmentation violation”.

‘SIGFPE’
     This signal indicates a fatal arithmetic error.  The name is an
     abbreviation for “floating-point exception”, but covers all types
     of arithmetic errors, including division by zero and overflow.

‘SIGBUS’
     This signal is generated when an invalid pointer is dereferenced,
     typically the result of dereferencing an uninintalized pointer.  It
     is similar to ‘SIGSEGV’, except that ‘SIGSEGV’ indicates invalid
     access to valid memory, while ‘SIGBUS’ indicates an attempt to
     access an invalid address.

   These kinds of signal allow the program to specify a function as a
“signal handler”.  When a signal has a handler, it doesn’t terminate the
program; instead it calls the handler.

   There are many other kinds of signal; here we list only those that
come from run-time errors in C operations.  The rest have to do with the
functioning of the operating system.  The GNU C Library Reference Manual
gives more explanation about signals (*note The GNU C Library:
(libc)Program Signal Handling.).

Appendix F GNU Free Documentation License
*****************************************

                     Version 1.3, 3 November 2008

     Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
     >http://fsf.org/<

     Everyone is permitted to copy and distribute verbatim copies
     of this license document, but changing it is not allowed.

  0. PREAMBLE

     The purpose of this License is to make a manual, textbook, or other
     functional and useful document “free” in the sense of freedom: to
     assure everyone the effective freedom to copy and redistribute it,
     with or without modifying it, either commercially or
     noncommercially.  Secondarily, this License preserves for the
     author and publisher a way to get credit for their work, while not
     being considered responsible for modifications made by others.

     This License is a kind of “copyleft”, which means that derivative
     works of the document must themselves be free in the same sense.
     It complements the GNU General Public License, which is a copyleft
     license designed for free software.

     We have designed this License in order to use it for manuals for
     free software, because free software needs free documentation: a
     free program should come with manuals providing the same freedoms
     that the software does.  But this License is not limited to
     software manuals; it can be used for any textual work, regardless
     of subject matter or whether it is published as a printed book.  We
     recommend this License principally for works whose purpose is
     instruction or reference.

  1. APPLICABILITY AND DEFINITIONS

     This License applies to any manual or other work, in any medium,
     that contains a notice placed by the copyright holder saying it can
     be distributed under the terms of this License.  Such a notice
     grants a world-wide, royalty-free license, unlimited in duration,
     to use that work under the conditions stated herein.  The
     “Document”, below, refers to any such manual or work.  Any member
     of the public is a licensee, and is addressed as “you”.  You accept
     the license if you copy, modify or distribute the work in a way
     requiring permission under copyright law.

     A “Modified Version” of the Document means any work containing the
     Document or a portion of it, either copied verbatim, or with
     modifications and/or translated into another language.

     A “Secondary Section” is a named appendix or a front-matter section
     of the Document that deals exclusively with the relationship of the
     publishers or authors of the Document to the Document’s overall
     subject (or to related matters) and contains nothing that could
     fall directly within that overall subject.  (Thus, if the Document
     is in part a textbook of mathematics, a Secondary Section may not
     explain any mathematics.)  The relationship could be a matter of
     historical connection with the subject or with related matters, or
     of legal, commercial, philosophical, ethical or political position
     regarding them.

     The “Invariant Sections” are certain Secondary Sections whose
     titles are designated, as being those of Invariant Sections, in the
     notice that says that the Document is released under this License.
     If a section does not fit the above definition of Secondary then it
     is not allowed to be designated as Invariant.  The Document may
     contain zero Invariant Sections.  If the Document does not identify
     any Invariant Sections then there are none.

     The “Cover Texts” are certain short passages of text that are
     listed, as Front-Cover Texts or Back-Cover Texts, in the notice
     that says that the Document is released under this License.  A
     Front-Cover Text may be at most 5 words, and a Back-Cover Text may
     be at most 25 words.

     A “Transparent” copy of the Document means a machine-readable copy,
     represented in a format whose specification is available to the
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     straightforwardly with generic text editors or (for images composed
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     available drawing editor, and that is suitable for input to text
     formatters or for automatic translation to a variety of formats
     suitable for input to text formatters.  A copy made in an otherwise
     Transparent file format whose markup, or absence of markup, has
     been arranged to thwart or discourage subsequent modification by
     readers is not Transparent.  An image format is not Transparent if
     used for any substantial amount of text.  A copy that is not
     “Transparent” is called “Opaque”.

     Examples of suitable formats for Transparent copies include plain
     ASCII without markup, Texinfo input format, LaTeX input format,
     SGML or XML using a publicly available DTD, and standard-conforming
     simple HTML, PostScript or PDF designed for human modification.
     Examples of transparent image formats include PNG, XCF and JPG.
     Opaque formats include proprietary formats that can be read and
     edited only by proprietary word processors, SGML or XML for which
     the DTD and/or processing tools are not generally available, and
     the machine-generated HTML, PostScript or PDF produced by some word
     processors for output purposes only.

     The “Title Page” means, for a printed book, the title page itself,
     plus such following pages as are needed to hold, legibly, the
     material this License requires to appear in the title page.  For
     works in formats which do not have any title page as such, “Title
     Page” means the text near the most prominent appearance of the
     work’s title, preceding the beginning of the body of the text.

     The “publisher” means any person or entity that distributes copies
     of the Document to the public.

     A section “Entitled XYZ” means a named subunit of the Document
     whose title either is precisely XYZ or contains XYZ in parentheses
     following text that translates XYZ in another language.  (Here XYZ
     stands for a specific section name mentioned below, such as
     “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.)
     To “Preserve the Title” of such a section when you modify the
     Document means that it remains a section “Entitled XYZ” according
     to this definition.

     The Document may include Warranty Disclaimers next to the notice
     which states that this License applies to the Document.  These
     Warranty Disclaimers are considered to be included by reference in
     this License, but only as regards disclaiming warranties: any other
     implication that these Warranty Disclaimers may have is void and
     has no effect on the meaning of this License.

  2. VERBATIM COPYING

     You may copy and distribute the Document in any medium, either
     commercially or noncommercially, provided that this License, the
     copyright notices, and the license notice saying this License
     applies to the Document are reproduced in all copies, and that you
     add no other conditions whatsoever to those of this License.  You
     may not use technical measures to obstruct or control the reading
     or further copying of the copies you make or distribute.  However,
     you may accept compensation in exchange for copies.  If you
     distribute a large enough number of copies you must also follow the
     conditions in section 3.

     You may also lend copies, under the same conditions stated above,
     and you may publicly display copies.

  3. COPYING IN QUANTITY

     If you publish printed copies (or copies in media that commonly
     have printed covers) of the Document, numbering more than 100, and
     the Document’s license notice requires Cover Texts, you must
     enclose the copies in covers that carry, clearly and legibly, all
     these Cover Texts: Front-Cover Texts on the front cover, and
     Back-Cover Texts on the back cover.  Both covers must also clearly
     and legibly identify you as the publisher of these copies.  The
     front cover must present the full title with all words of the title
     equally prominent and visible.  You may add other material on the
     covers in addition.  Copying with changes limited to the covers, as
     long as they preserve the title of the Document and satisfy these
     conditions, can be treated as verbatim copying in other respects.

     If the required texts for either cover are too voluminous to fit
     legibly, you should put the first ones listed (as many as fit
     reasonably) on the actual cover, and continue the rest onto
     adjacent pages.

     If you publish or distribute Opaque copies of the Document
     numbering more than 100, you must either include a machine-readable
     Transparent copy along with each Opaque copy, or state in or with
     each Opaque copy a computer-network location from which the general
     network-using public has access to download using public-standard
     network protocols a complete Transparent copy of the Document, free
     of added material.  If you use the latter option, you must take
     reasonably prudent steps, when you begin distribution of Opaque
     copies in quantity, to ensure that this Transparent copy will
     remain thus accessible at the stated location until at least one
     year after the last time you distribute an Opaque copy (directly or
     through your agents or retailers) of that edition to the public.

     It is requested, but not required, that you contact the authors of
     the Document well before redistributing any large number of copies,
     to give them a chance to provide you with an updated version of the
     Document.

  4. MODIFICATIONS

     You may copy and distribute a Modified Version of the Document
     under the conditions of sections 2 and 3 above, provided that you
     release the Modified Version under precisely this License, with the
     Modified Version filling the role of the Document, thus licensing
     distribution and modification of the Modified Version to whoever
     possesses a copy of it.  In addition, you must do these things in
     the Modified Version:

       A. Use in the Title Page (and on the covers, if any) a title
          distinct from that of the Document, and from those of previous
          versions (which should, if there were any, be listed in the
          History section of the Document).  You may use the same title
          as a previous version if the original publisher of that
          version gives permission.

       B. List on the Title Page, as authors, one or more persons or
          entities responsible for authorship of the modifications in
          the Modified Version, together with at least five of the
          principal authors of the Document (all of its principal
          authors, if it has fewer than five), unless they release you
          from this requirement.

       C. State on the Title page the name of the publisher of the
          Modified Version, as the publisher.

       D. Preserve all the copyright notices of the Document.

       E. Add an appropriate copyright notice for your modifications
          adjacent to the other copyright notices.

       F. Include, immediately after the copyright notices, a license
          notice giving the public permission to use the Modified
          Version under the terms of this License, in the form shown in
          the Addendum below.

       G. Preserve in that license notice the full lists of Invariant
          Sections and required Cover Texts given in the Document’s
          license notice.

       H. Include an unaltered copy of this License.

       I. Preserve the section Entitled “History”, Preserve its Title,
          and add to it an item stating at least the title, year, new
          authors, and publisher of the Modified Version as given on the
          Title Page.  If there is no section Entitled “History” in the
          Document, create one stating the title, year, authors, and
          publisher of the Document as given on its Title Page, then add
          an item describing the Modified Version as stated in the
          previous sentence.

       J. Preserve the network location, if any, given in the Document
          for public access to a Transparent copy of the Document, and
          likewise the network locations given in the Document for
          previous versions it was based on.  These may be placed in the
          “History” section.  You may omit a network location for a work
          that was published at least four years before the Document
          itself, or if the original publisher of the version it refers
          to gives permission.

       K. For any section Entitled “Acknowledgements” or “Dedications”,
          Preserve the Title of the section, and preserve in the section
          all the substance and tone of each of the contributor
          acknowledgements and/or dedications given therein.

       L. Preserve all the Invariant Sections of the Document, unaltered
          in their text and in their titles.  Section numbers or the
          equivalent are not considered part of the section titles.

       M. Delete any section Entitled “Endorsements”.  Such a section
          may not be included in the Modified Version.

       N. Do not retitle any existing section to be Entitled
          “Endorsements” or to conflict in title with any Invariant
          Section.

       O. Preserve any Warranty Disclaimers.

     If the Modified Version includes new front-matter sections or
     appendices that qualify as Secondary Sections and contain no
     material copied from the Document, you may at your option designate
     some or all of these sections as invariant.  To do this, add their
     titles to the list of Invariant Sections in the Modified Version’s
     license notice.  These titles must be distinct from any other
     section titles.

     You may add a section Entitled “Endorsements”, provided it contains
     nothing but endorsements of your Modified Version by various
     parties—for example, statements of peer review or that the text has
     been approved by an organization as the authoritative definition of
     a standard.

     You may add a passage of up to five words as a Front-Cover Text,
     and a passage of up to 25 words as a Back-Cover Text, to the end of
     the list of Cover Texts in the Modified Version.  Only one passage
     of Front-Cover Text and one of Back-Cover Text may be added by (or
     through arrangements made by) any one entity.  If the Document
     already includes a cover text for the same cover, previously added
     by you or by arrangement made by the same entity you are acting on
     behalf of, you may not add another; but you may replace the old
     one, on explicit permission from the previous publisher that added
     the old one.

     The author(s) and publisher(s) of the Document do not by this
     License give permission to use their names for publicity for or to
     assert or imply endorsement of any Modified Version.

  5. COMBINING DOCUMENTS

     You may combine the Document with other documents released under
     this License, under the terms defined in section 4 above for
     modified versions, provided that you include in the combination all
     of the Invariant Sections of all of the original documents,
     unmodified, and list them all as Invariant Sections of your
     combined work in its license notice, and that you preserve all
     their Warranty Disclaimers.

     The combined work need only contain one copy of this License, and
     multiple identical Invariant Sections may be replaced with a single
     copy.  If there are multiple Invariant Sections with the same name
     but different contents, make the title of each such section unique
     by adding at the end of it, in parentheses, the name of the
     original author or publisher of that section if known, or else a
     unique number.  Make the same adjustment to the section titles in
     the list of Invariant Sections in the license notice of the
     combined work.

     In the combination, you must combine any sections Entitled
     “History” in the various original documents, forming one section
     Entitled “History”; likewise combine any sections Entitled
     “Acknowledgements”, and any sections Entitled “Dedications”.  You
     must delete all sections Entitled “Endorsements.”

  6. COLLECTIONS OF DOCUMENTS

     You may make a collection consisting of the Document and other
     documents released under this License, and replace the individual
     copies of this License in the various documents with a single copy
     that is included in the collection, provided that you follow the
     rules of this License for verbatim copying of each of the documents
     in all other respects.

     You may extract a single document from such a collection, and
     distribute it individually under this License, provided you insert
     a copy of this License into the extracted document, and follow this
     License in all other respects regarding verbatim copying of that
     document.

  7. AGGREGATION WITH INDEPENDENT WORKS

     A compilation of the Document or its derivatives with other
     separate and independent documents or works, in or on a volume of a
     storage or distribution medium, is called an “aggregate” if the
     copyright resulting from the compilation is not used to limit the
     legal rights of the compilation’s users beyond what the individual
     works permit.  When the Document is included in an aggregate, this
     License does not apply to the other works in the aggregate which
     are not themselves derivative works of the Document.

     If the Cover Text requirement of section 3 is applicable to these
     copies of the Document, then if the Document is less than one half
     of the entire aggregate, the Document’s Cover Texts may be placed
     on covers that bracket the Document within the aggregate, or the
     electronic equivalent of covers if the Document is in electronic
     form.  Otherwise they must appear on printed covers that bracket
     the whole aggregate.

  8. TRANSLATION

     Translation is considered a kind of modification, so you may
     distribute translations of the Document under the terms of section
     4.  Replacing Invariant Sections with translations requires special
     permission from their copyright holders, but you may include
     translations of some or all Invariant Sections in addition to the
     original versions of these Invariant Sections.  You may include a
     translation of this License, and all the license notices in the
     Document, and any Warranty Disclaimers, provided that you also
     include the original English version of this License and the
     original versions of those notices and disclaimers.  In case of a
     disagreement between the translation and the original version of
     this License or a notice or disclaimer, the original version will
     prevail.

     If a section in the Document is Entitled “Acknowledgements”,
     “Dedications”, or “History”, the requirement (section 4) to
     Preserve its Title (section 1) will typically require changing the
     actual title.

  9. TERMINATION

     You may not copy, modify, sublicense, or distribute the Document
     except as expressly provided under this License.  Any attempt
     otherwise to copy, modify, sublicense, or distribute it is void,
     and will automatically terminate your rights under this License.

     However, if you cease all violation of this License, then your
     license from a particular copyright holder is reinstated (a)
     provisionally, unless and until the copyright holder explicitly and
     finally terminates your license, and (b) permanently, if the
     copyright holder fails to notify you of the violation by some
     reasonable means prior to 60 days after the cessation.

     Moreover, your license from a particular copyright holder is
     reinstated permanently if the copyright holder notifies you of the
     violation by some reasonable means, this is the first time you have
     received notice of violation of this License (for any work) from
     that copyright holder, and you cure the violation prior to 30 days
     after your receipt of the notice.

     Termination of your rights under this section does not terminate
     the licenses of parties who have received copies or rights from you
     under this License.  If your rights have been terminated and not
     permanently reinstated, receipt of a copy of some or all of the
     same material does not give you any rights to use it.

  10. FUTURE REVISIONS OF THIS LICENSE

     The Free Software Foundation may publish new, revised versions of
     the GNU Free Documentation License from time to time.  Such new
     versions will be similar in spirit to the present version, but may
     differ in detail to address new problems or concerns.  See
     >http://www.gnu.org/copyleft/<.

     Each version of the License is given a distinguishing version
     number.  If the Document specifies that a particular numbered
     version of this License “or any later version” applies to it, you
     have the option of following the terms and conditions either of
     that specified version or of any later version that has been
     published (not as a draft) by the Free Software Foundation.  If the
     Document does not specify a version number of this License, you may
     choose any version ever published (not as a draft) by the Free
     Software Foundation.  If the Document specifies that a proxy can
     decide which future versions of this License can be used, that
     proxy’s public statement of acceptance of a version permanently
     authorizes you to choose that version for the Document.

  11. RELICENSING

     “Massive Multiauthor Collaboration Site” (or “MMC Site”) means any
     World Wide Web server that publishes copyrightable works and also
     provides prominent facilities for anybody to edit those works.  A
     public wiki that anybody can edit is an example of such a server.
     A “Massive Multiauthor Collaboration” (or “MMC”) contained in the
     site means any set of copyrightable works thus published on the MMC
     site.

     “CC-BY-SA” means the Creative Commons Attribution-Share Alike 3.0
     license published by Creative Commons Corporation, a not-for-profit
     corporation with a principal place of business in San Francisco,
     California, as well as future copyleft versions of that license
     published by that same organization.

     “Incorporate” means to publish or republish a Document, in whole or
     in part, as part of another Document.

     An MMC is “eligible for relicensing” if it is licensed under this
     License, and if all works that were first published under this
     License somewhere other than this MMC, and subsequently
     incorporated in whole or in part into the MMC, (1) had no cover
     texts or invariant sections, and (2) were thus incorporated prior
     to November 1, 2008.

     The operator of an MMC Site may republish an MMC contained in the
     site under CC-BY-SA on the same site at any time before August 1,
     2009, provided the MMC is eligible for relicensing.

ADDENDUM: How to use this License for your documents
====================================================

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and license
notices just after the title page:

       Copyright (C)  YEAR  YOUR NAME.
       Permission is granted to copy, distribute and/or modify this document
       under the terms of the GNU Free Documentation License, Version 1.3
       or any later version published by the Free Software Foundation;
       with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
       Texts.  A copy of the license is included in the section entitled ``GNU
       Free Documentation License''.

   If you have Invariant Sections, Front-Cover Texts and Back-Cover
Texts, replace the “with...Texts.” line with this:

         with the Invariant Sections being LIST THEIR TITLES, with
         the Front-Cover Texts being LIST, and with the Back-Cover Texts
         being LIST.

   If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

   If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of free
software license, such as the GNU General Public License, to permit
their use in free software.

Index of Symbols and Keywords
*****************************

* Menu:

* #define:                               Object-like Macros.
                                                            (line  9940)
* #elif:                                 elif.              (line 11278)
* #else:                                 else.              (line 11260)
* #endif:                                ifdef.             (line 11091)
* #error:                                Diagnostics.       (line 11345)
* #if:                                   Conditional Syntax.
                                                            (line 11085)
* #ifdef:                                ifdef.             (line 11091)
* #ifndef:                               ifdef.             (line 11126)
* #include:                              include Syntax.    (line  9652)
* #line:                                 Line Control.      (line 11390)
* #undef:                                Undefining and Redefining Macros.
                                                            (line 10598)
* #warning:                              Diagnostics.       (line 11356)
* _Alignas:                              Type Alignment.    (line 13082)
* _Alignof:                              Type Alignment.    (line 13034)
* _Complex:                              Complex Data Types.
                                                            (line  3099)
* _Static_assert:                        Static Assertions. (line 12983)
* __aligned__:                           Type Alignment.    (line 13082)
* __alignof__:                           Type Alignment.    (line 13034)
* __attribute__:                         Attributes.        (line 13298)
* __auto_type:                           Auto Type.         (line  7296)
* __complex__:                           Complex Data Types.
                                                            (line  3099)
* __label__:                             Local Labels.      (line  6808)
* auto:                                  auto and register. (line  7512)
* bool:                                  Boolean Type.      (line  3002)
* break:                                 break Statement.   (line  6241)
* case:                                  switch Statement.  (line  6477)
* char:                                  Basic Integers.    (line  2876)
* CHAR_MAX:                              Maximum and Minimum Values.
                                                            (line 11518)
* const:                                 const.             (line  7553)
* continue:                              continue Statement.
                                                            (line  6429)
* DBL_DECIMAL_DIG:                       Floating Type Specs.
                                                            (line 11590)
* DBL_HAS_SUBNORM:                       Floating Type Specs.
                                                            (line 11590)
* DBL_MAX:                               Floating Type Specs.
                                                            (line 11590)
* DBL_MIN:                               Floating Type Specs.
                                                            (line 11590)
* DBL_TRUE_MIN:                          Floating Type Specs.
                                                            (line 11590)
* default:                               switch Statement.  (line  6477)
* do:                                    do-while Statement.
                                                            (line  6223)
* double:                                Floating-Point Data Types.
                                                            (line  3050)
* else:                                  if-else Statement. (line  6080)
* extern:                                Extern Declarations.
                                                            (line  7431)
* float:                                 Floating-Point Data Types.
                                                            (line  3050)
* FLT_DECIMAL_DIG:                       Floating Type Specs.
                                                            (line 11590)
* FLT_HAS_SUBNORM:                       Floating Type Specs.
                                                            (line 11590)
* FLT_MAX:                               Floating Type Specs.
                                                            (line 11590)
* FLT_MIN:                               Floating Type Specs.
                                                            (line 11590)
* FLT_TRUE_MIN:                          Floating Type Specs.
                                                            (line 11590)
* for:                                   for Statement.     (line  6293)
* goto:                                  goto Statement.    (line  6686)
* if:                                    if Statement.      (line  6061)
* inline:                                Inline Function Definitions.
                                                            (line  8875)
* int:                                   Basic Integers.    (line  2876)
* INT_MAX:                               Maximum and Minimum Values.
                                                            (line 11518)
* LDBL_DECIMAL_DIG:                      Floating Type Specs.
                                                            (line 11590)
* LDBL_HAS_SUBNORM:                      Floating Type Specs.
                                                            (line 11590)
* LDBL_MAX:                              Floating Type Specs.
                                                            (line 11590)
* LDBL_MIN:                              Floating Type Specs.
                                                            (line 11590)
* LDBL_TRUE_MIN:                         Floating Type Specs.
                                                            (line 11590)
* LLONG_MAX:                             Maximum and Minimum Values.
                                                            (line 11518)
* long double:                           Floating-Point Data Types.
                                                            (line  3050)
* long int:                              Basic Integers.    (line  2876)
* long long int:                         Basic Integers.    (line  2876)
* LONG_MAX:                              Maximum and Minimum Values.
                                                            (line 11518)
* main:                                  The main Function. (line  8439)
* register:                              auto and register. (line  7512)
* restrict:                              restrict Pointers. (line  7669)
* return:                                return Statement.  (line  6163)
* SCHAR_MAX:                             Maximum and Minimum Values.
                                                            (line 11518)
* short int:                             Basic Integers.    (line  2876)
* SHRT_MAX:                              Maximum and Minimum Values.
                                                            (line 11518)
* signed:                                Signed and Unsigned Types.
                                                            (line  2918)
* sizeof:                                Type Size.         (line  3726)
* static:                                Static Local Variables.
                                                            (line  7403)
* static >1<:                            Static Functions.  (line  7909)
* struct:                                Structures.        (line  4461)
* switch:                                switch Statement.  (line  6477)
* typedef:                               Defining Typedef Names.
                                                            (line  5942)
* typeof:                                Auto Type.         (line  7296)
* UCHAR_MAX:                             Maximum and Minimum Values.
                                                            (line 11518)
* UINT_MAX:                              Maximum and Minimum Values.
                                                            (line 11518)
* ULLONG_MAX:                            Maximum and Minimum Values.
                                                            (line 11518)
* ULONG_MAX:                             Maximum and Minimum Values.
                                                            (line 11518)
* union:                                 Unions.            (line  5022)
* unsigned:                              Signed and Unsigned Types.
                                                            (line  2918)
* USHRT_MAX:                             Maximum and Minimum Values.
                                                            (line 11518)
* void:                                  The Void Type.     (line  3154)
* volatile:                              volatile.          (line  7617)
* while:                                 while Statement.   (line  6196)

Concept Index
*************

* Menu:

* # operator:                            Stringification.   (line 10178)
* ## operator:                           Concatenation.     (line 10257)
* ?: side effect:                        Conditional Branches.
                                                            (line  2474)
* \a:                                    Character Constants.
                                                            (line  3468)
* \b:                                    Character Constants.
                                                            (line  3468)
* \e:                                    Character Constants.
                                                            (line  3468)
* \f:                                    Character Constants.
                                                            (line  3468)
* \n:                                    Character Constants.
                                                            (line  3468)
* \r:                                    Character Constants.
                                                            (line  3468)
* \t:                                    Character Constants.
                                                            (line  3468)
* \v:                                    Character Constants.
                                                            (line  3468)
* _ in variables in macros:              Macros and Auto Type.
                                                            (line 10879)
* _Complex keyword:                      Complex Data Types.
                                                            (line  3099)
* _Complex_I:                            Imaginary Constants.
                                                            (line  3412)
* __attribute__((packed)):               Packed Structures. (line  4738)
* __complex__ keyword:                   Complex Data Types.
                                                            (line  3099)
* accessing array elements:              Accessing Array Elements.
                                                            (line  5419)
* addition operator:                     Basic Arithmetic.  (line  1514)
* address of a label:                    Labels as Values.  (line  6878)
* address-of operator:                   Address of Data.   (line  3811)
* aliasing (of storage):                 Aliasing.          (line 13108)
* alignment of type:                     Type Alignment.    (line 13034)
* allocating memory dynamically:         Dynamic Memory Allocation.
                                                            (line  4581)
* allocation file-scope variables:       Allocating File-Scope.
                                                            (line  7479)
* argument promotions:                   Argument Promotions.
                                                            (line  9248)
* arguments:                             Macro Arguments.   (line 10082)
* arguments in macro definitions:        Macro Arguments.   (line 10082)
* arithmetic operators:                  Arithmetic.        (line  1484)
* arithmetic, pointer:                   Pointer Arithmetic.
                                                            (line  4104)
* array:                                 Arrays.            (line  5400)
* array as parameters:                   Arrays as Parameters.
                                                            (line  7939)
* array elements, accessing:             Accessing Array Elements.
                                                            (line  5419)
* array example:                         Array Example.     (line  1033)
* array fields, flexible:                Flexible Array Fields.
                                                            (line  4915)
* array of length zero:                  Zero Length.       (line  4893)
* array of variable length:              Arrays of Variable Length.
                                                            (line  5793)
* array parameters, variable-length:     Variable-Length Array Parameters.
                                                            (line  8585)
* array types, incomplete:               Incomplete Array Types.
                                                            (line  5593)
* array values, constructing:            Constructing Array Values.
                                                            (line  5758)
* array, declaring:                      Declaring an Array.
                                                            (line  5458)
* array, declaring >1<:                  Declaring Arrays and Pointers.
                                                            (line  7071)
* array, layout in memory:               Multidimensional Arrays.
                                                            (line  5727)
* array, multidimensional:               Multidimensional Arrays.
                                                            (line  5675)
* arrays and pointers:                   Pointers and Arrays.
                                                            (line  4211)
* assigning function pointers:           Assigning Function Pointers.
                                                            (line  8390)
* assigning structures:                  Structure Assignment.
                                                            (line  4987)
* assignment expressions:                Assignment Expressions.
                                                            (line  1976)
* assignment in subexpressions:          Assignment in Subexpressions.
                                                            (line  2231)
* assignment type conversions:           Assignment Type Conversions.
                                                            (line  9192)
* assignment, modifying:                 Modifying Assignment.
                                                            (line  2093)
* assignment, simple:                    Simple Assignment. (line  2020)
* associativity and ordering:            Associativity and Ordering.
                                                            (line  2704)
* attributes:                            Attributes.        (line 13298)
* auto declarations:                     auto and register. (line  7512)
* backspace:                             Character Constants.
                                                            (line  3468)
* base conversion (floating point):      Round-Trip Base Conversion.
                                                            (line 12489)
* bell character:                        Character Constants.
                                                            (line  3468)
* binary integer constants:              Integer Constants. (line  3278)
* binary operator grammar:               Binary Operator Grammar.
                                                            (line  2589)
* bit fields:                            Bit Fields.        (line  4765)
* bitwise operators:                     Bitwise Operations.
                                                            (line  1906)
* block:                                 Blocks.            (line  6102)
* block scope:                           Scope.             (line  9322)
* boolean type:                          Boolean Type.      (line  3002)
* branch cuts:                           Complex Arithmetic.
                                                            (line 12452)
* branches of conditional expression:    Conditional Branches.
                                                            (line  2448)
* break statement:                       break Statement.   (line  6241)
* bytes:                                 Storage.           (line   957)
* call-by-value:                         Function Call Semantics.
                                                            (line  8268)
* calling function pointers:             Calling Function Pointers.
                                                            (line  8418)
* calling functions:                     Function Calls.    (line  8236)
* carriage return in source:             Whitespace.        (line  1260)
* case labels in initializers:           Designated Inits.  (line  7214)
* case of letters in identifiers:        Identifiers.       (line  1372)
* case ranges:                           Case Ranges.       (line  6647)
* cast:                                  Explicit Type Conversion.
                                                            (line  9146)
* cast to a union:                       Cast to Union.     (line  5129)
* character constants:                   Character Constants.
                                                            (line  3452)
* character set:                         Characters.        (line  1232)
* CHAR_BIT:                              Integer Representations.
                                                            (line 11437)
* cloning:                               Label Value Caveats.
                                                            (line  6947)
* combining variable declarations:       Combining Variable Declarations.
                                                            (line  7114)
* comma operator:                        Comma Operator.    (line  2492)
* command-line parameters:               Command-line Parameters.
                                                            (line  8498)
* commenting out code:                   Deleted Code.      (line 11320)
* comments:                              Comments.          (line  1292)
* common type:                           Common Type.       (line  9294)
* comparison, pointer:                   Pointer Comparison.
                                                            (line  4064)
* comparisons:                           Numeric Comparisons.
                                                            (line  1776)
* compatible types:                      Compatible Types.  (line  9080)
* compilation module:                    Compilation.       (line 12681)
* compiler options for integer overflow: Signed Overflow.   (line  1638)
* compiling:                             Compile Example.   (line   925)
* complete example program:              Complete Program.  (line   787)
* complex arithmetic in floating-point calculations: Complex Arithmetic.
                                                            (line 12415)
* complex conjugation:                   Complex Data Types.
                                                            (line  3136)
* complex constants:                     Imaginary Constants.
                                                            (line  3400)
* complex numbers:                       Complex Data Types.
                                                            (line  3099)
* compound statement:                    Blocks.            (line  6102)
* computed gotos:                        Labels as Values.  (line  6878)
* computed includes:                     Computed Includes. (line  9841)
* concatenation:                         Concatenation.     (line 10257)
* conditional expression:                Conditional Expression.
                                                            (line  2415)
* conditional group:                     ifdef.             (line 11099)
* conditionals:                          Conditionals.      (line 11028)
* conjunction operator:                  Logical Operators. (line  2307)
* conjunction, bitwise:                  Bitwise Operations.
                                                            (line  1906)
* const fields:                          const Fields.      (line  4859)
* const variables and fields:            const.             (line  7553)
* constant data types, integer:          Integer Const Type.
                                                            (line  3291)
* constants:                             Constants.         (line  3237)
* constants, character:                  Character Constants.
                                                            (line  3452)
* constants, floating-point:             Floating Constants.
                                                            (line  3332)
* constants, imaginary:                  Imaginary Constants.
                                                            (line  3400)
* constants, integer:                    Integer Constants. (line  3245)
* constants, string:                     String Constants.  (line  3500)
* constants, wide character:             Wide Character Constants.
                                                            (line  3640)
* constants, wide string:                Wide String Constants.
                                                            (line  3675)
* constructing array values:             Constructing Array Values.
                                                            (line  5758)
* constructors, structure:               Structure Constructors.
                                                            (line  5164)
* continuation of lines:                 Line Continuation. (line  1449)
* continue statement:                    continue Statement.
                                                            (line  6429)
* controlling macro:                     Once-Only Headers. (line  9830)
* conversion between pointers and integers: Pointer-Integer Conversion.
                                                            (line  4413)
* conversions, type:                     Type Conversions.  (line  9140)
* counting vowels and punctuation:       switch Example.    (line  6547)
* crash:                                 Stack.             (line   604)
* declararing functions:                 Function Declarations.
                                                            (line  8142)
* declaration of variables:              Variable Declarations.
                                                            (line  7038)
* declarations inside expressions:       Statement Exprs.   (line  6970)
* declarations, combining:               Combining Variable Declarations.
                                                            (line  7114)
* declarations, extern:                  Extern Declarations.
                                                            (line  7431)
* declaring an array:                    Declaring an Array.
                                                            (line  5458)
* declaring arrays and pointers:         Declaring Arrays and Pointers.
                                                            (line  7071)
* declaring function pointers:           Declaring Function Pointers.
                                                            (line  8327)
* decrement operator:                    Increment/Decrement.
                                                            (line  2149)
* decrementing pointers:                 Pointer Increment/Decrement.
                                                            (line  4283)
* defined:                               defined.           (line 11221)
* defining functions:                    Function Definitions.
                                                            (line  7792)
* dereferencing pointers:                Pointer Dereference.
                                                            (line  3897)
* designated initializers:               Designated Inits.  (line  7214)
* diagnostic:                            Diagnostics.       (line 11345)
* digraphs:                              Digraphs.          (line 13278)
* directive line:                        Directives.        (line  9484)
* directive name:                        Directives.        (line  9484)
* directives:                            Directives.        (line  9484)
* disjunction operator:                  Logical Operators. (line  2307)
* disjunction, bitwise:                  Bitwise Operations.
                                                            (line  1906)
* division by zero:                      Division and Remainder.
                                                            (line  1769)
* division operator:                     Basic Arithmetic.  (line  1514)
* do–while statement:                    do-while Statement.
                                                            (line  6223)
* downward funargs:                      Nested Functions.  (line  8751)
* drawbacks of pointer arithmetic:       Pointer Arithmetic Drawbacks.
                                                            (line  4381)
* Duff’s device:                         Duffs Device.      (line  6606)
* dynamic memory allocation:             Dynamic Memory Allocation.
                                                            (line  4581)
* elements of arrays:                    Arrays.            (line  5400)
* empty macro arguments:                 Macro Arguments.   (line 10143)
* enumeration types:                     Enumeration Types. (line  5863)
* enumerator:                            Enumeration Types. (line  5863)
* environment variables:                 Environment Variables.
                                                            (line  8536)
* equal operator:                        Numeric Comparisons.
                                                            (line  1776)
* error recovery (floating point):       Error Recovery.    (line 11985)
* escape (ASCII character):              Character Constants.
                                                            (line  3468)
* escape sequence:                       Character Constants.
                                                            (line  3452)
* exact floating-point arithmetic:       Exact Floating-Point.
                                                            (line 11755)
* exact specification of floating-point constants: Exact Floating Constants.
                                                            (line 12060)
* example program, complete:             Complete Program.  (line   787)
* exception flags (floating point):      Exception Flags.   (line 11732)
* executable file:                       Compile Example.   (line   925)
* execution control expressions:         Execution Control Expressions.
                                                            (line  2301)
* exit status:                           Values from main.  (line  8466)
* EXIT_FAILURE:                          Values from main.  (line  8477)
* EXIT_SUCCESS:                          Values from main.  (line  8477)
* expansion of arguments:                Argument Prescan.  (line 10945)
* explicit type conversion:              Explicit Type Conversion.
                                                            (line  9146)
* expression statement:                  Expression Statement.
                                                            (line  6034)
* expression, conditional:               Conditional Expression.
                                                            (line  2415)
* expressions containing statements:     Statement Exprs.   (line  6970)
* expressions, execution control:        Execution Control Expressions.
                                                            (line  2301)
* extern declarations:                   Extern Declarations.
                                                            (line  7431)
* extern inline function:                Inline Function Definitions.
                                                            (line  8943)
* failure:                               Values from main.  (line  8466)
* Fibonacci function, iterative:         Iterative Fibonacci.
                                                            (line   639)
* Fibonacci function, recursive:         Recursive Fibonacci.
                                                            (line   429)
* field offset:                          Field Offset.      (line  4658)
* fields in structures:                  Structures.        (line  4461)
* file-scope variables:                  File-Scope Variables.
                                                            (line  7370)
* file-scope variables, allocating:      Allocating File-Scope.
                                                            (line  7479)
* first-class object:                    Limitations of C Arrays.
                                                            (line  5629)
* flexible array fields:                 Flexible Array Fields.
                                                            (line  4915)
* floating arithmetic exception flags:   Exception Flags.   (line 11732)
* floating overflow:                     Exception Flags.   (line 11732)
* floating point example:                Float Example.     (line   981)
* floating underflow:                    Special Float Values.
                                                            (line 11665)
* floating underflow >1<:                Exception Flags.   (line 11732)
* floating-point arithmetic invalid optimizations: Invalid Optimizations.
                                                            (line 11700)
* floating-point arithmetic with complex numbers: Complex Arithmetic.
                                                            (line 12415)
* floating-point arithmetic, exact:      Exact Floating-Point.
                                                            (line 11755)
* floating-point constants:              Floating Constants.
                                                            (line  3332)
* floating-point constants, exact specification of: Exact Floating Constants.
                                                            (line 12060)
* floating-point error recovery:         Error Recovery.    (line 11985)
* floating-point fused multiply-add:     Fused Multiply-Add.
                                                            (line 11948)
* floating-point infinity:               Handling Infinity. (line 12099)
* floating-point machine epsilon:        Machine Epsilon.   (line 12295)
* floating-point NaN:                    Handling NaN.      (line 12138)
* floating-point representations:        Floating Representations.
                                                            (line 11552)
* floating-point round-trip base conversion: Round-Trip Base Conversion.
                                                            (line 12489)
* floating-point rounding control:       Rounding Control.  (line 12248)
* floating-point rounding issues:        Rounding Issues.   (line 11828)
* floating-point scaling by powers of the base: Scaling by the Base.
                                                            (line 12220)
* floating-point signed zeros:           Signed Zeros.      (line 12206)
* floating-point significance loss:      Significance Loss. (line 11872)
* floating-point types:                  Floating-Point Data Types.
                                                            (line  3050)
* floating-point values, special:        Special Float Values.
                                                            (line 11624)
* for statement:                         for Statement.     (line  6293)
* formfeed:                              Character Constants.
                                                            (line  3468)
* formfeed in source:                    Whitespace.        (line  1260)
* forward declaration:                   Static Functions.  (line  7923)
* forward function declarations:         Forward Function Declarations.
                                                            (line  7891)
* full expression:                       Sequence Points.   (line  2738)
* function body:                         Function Body.     (line   504)
* function call semantics:               Function Call Semantics.
                                                            (line  8268)
* function calls:                        Function Calls.    (line  8236)
* function declarations:                 Function Declarations.
                                                            (line  8142)
* function declarations, forward:        Forward Function Declarations.
                                                            (line  7891)
* function definitions:                  Function Definitions.
                                                            (line  7792)
* function definitions, inline:          Inline Function Definitions.
                                                            (line  8875)
* function definitions, old-style:       Old-Style Function Definitions.
                                                            (line  9014)
* function header:                       Function Header.   (line   490)
* function parameter lists, variable length: Variable Number of Arguments.
                                                            (line  8648)
* function parameter variables:          Function Parameter Variables.
                                                            (line  7809)
* function pointers:                     Function Pointers. (line  8312)
* function pointers, assigning:          Assigning Function Pointers.
                                                            (line  8390)
* function pointers, calling:            Calling Function Pointers.
                                                            (line  8418)
* function pointers, declaring:          Declaring Function Pointers.
                                                            (line  8327)
* function prototype:                    Function Declarations.
                                                            (line  8155)
* function prototype scope:              Scope.             (line  9322)
* function scope:                        Scope.             (line  9322)
* function-like macros:                  Function-like Macros.
                                                            (line 10035)
* functions:                             Functions.         (line  7784)
* functions that accept variable-length arrays: Variable-Length Array Parameters.
                                                            (line  8585)
* functions with array parameters:       Arrays as Parameters.
                                                            (line  7939)
* functions, nested:                     Nested Functions.  (line  8751)
* functions, static:                     Static Functions.  (line  7909)
* fused multiply-add in floating-point computations: Fused Multiply-Add.
                                                            (line 11948)
* global variables:                      File-Scope Variables.
                                                            (line  7370)
* goto statement:                        goto Statement.    (line  6686)
* goto with computed label:              Labels as Values.  (line  6878)
* grammar, binary operator:              Binary Operator Grammar.
                                                            (line  2589)
* greater-or-equal operator:             Numeric Comparisons.
                                                            (line  1776)
* greater-than operator:                 Numeric Comparisons.
                                                            (line  1776)
* guard macro:                           Once-Only Headers. (line  9830)
* handler (for signal):                  Signals.           (line 13369)
* header file:                           Header Files.      (line  9617)
* hexademical floating-point constants:  Exact Floating Constants.
                                                            (line 12070)
* identifiers:                           Identifiers.       (line  1366)
* identifiers >1<:                       Preprocessing Tokens.
                                                            (line  9528)
* IEEE 754-2008 Standard:                Floating Representations.
                                                            (line 11552)
* if statement:                          if Statement.      (line  6061)
* if...else statement:                   if-else Statement. (line  6080)
* imaginary constants:                   Imaginary Constants.
                                                            (line  3400)
* including just once:                   Once-Only Headers. (line  9801)
* incomplete array types:                Incomplete Array Types.
                                                            (line  5593)
* incomplete types:                      Incomplete Types.  (line  5244)
* increment operator:                    Increment/Decrement.
                                                            (line  2149)
* incrementing pointers:                 Pointer Increment/Decrement.
                                                            (line  4283)
* infinity in floating-point arithmetic: Handling Infinity. (line 12099)
* initializers:                          Initializers.      (line  7143)
* initializers with labeled elements:    Designated Inits.  (line  7214)
* inline function definitions:           Inline Function Definitions.
                                                            (line  8875)
* inline functions, omission of:         Inline Function Definitions.
                                                            (line  8936)
* integer arithmetic:                    Integer Arithmetic.
                                                            (line  1542)
* integer constant data types:           Integer Const Type.
                                                            (line  3291)
* integer constants:                     Integer Constants. (line  3245)
* integer overflow:                      Integer Overflow.  (line  1591)
* integer overflow, compiler options:    Signed Overflow.   (line  1638)
* integer ranges:                        Maximum and Minimum Values.
                                                            (line 11518)
* integer representations:               Integer Representations.
                                                            (line 11431)
* integer types:                         Integer Types.     (line  2869)
* internal block:                        Blocks.            (line  6123)
* intptr_t:                              Pointer Arithmetic Low Level.
                                                            (line  4275)
* invalid optimizations in floating-point arithmetic: Invalid Optimizations.
                                                            (line 11700)
* iteration:                             Loop Statements.   (line  6184)
* iterative Fibonacci function:          Iterative Fibonacci.
                                                            (line   639)
* K&R-style function definitions:        Old-Style Function Definitions.
                                                            (line  9014)
* keyword:                               Identifiers.       (line  1375)
* label:                                 goto Statement.    (line  6686)
* labeled elements in initializers:      Designated Inits.  (line  7214)
* labels as values:                      Labels as Values.  (line  6878)
* layout of structures:                  Structure Layout.  (line  4678)
* left-associative:                      Binary Operator Grammar.
                                                            (line  2589)
* length-zero arrays:                    Zero Length.       (line  4893)
* less-or-equal operator:                Numeric Comparisons.
                                                            (line  1776)
* less-than operator:                    Numeric Comparisons.
                                                            (line  1776)
* lexical syntax:                        Lexical Syntax.    (line  1191)
* limitations of C arrays:               Limitations of C Arrays.
                                                            (line  5629)
* line continuation:                     Line Continuation. (line  1449)
* line control:                          Line Control.      (line 11372)
* linefeed in source:                    Whitespace.        (line  1260)
* linking object files:                  Compilation.       (line 12715)
* local labels:                          Local Labels.      (line  6808)
* local variables:                       Local Variables.   (line  7325)
* local variables in macros:             Macros and Auto Type.
                                                            (line 10861)
* logical operators:                     Logical Operators. (line  2307)
* loop statements:                       Loop Statements.   (line  6184)
* low level pointer arithmetic:          Pointer Arithmetic Low Level.
                                                            (line  4243)
* lvalues:                               Lvalues.           (line  2055)
* machine epsilon (floating point):      Machine Epsilon.   (line 12295)
* macro argument expansion:              Argument Prescan.  (line 10945)
* macro arguments and directives:        Directives Within Macro Arguments.
                                                            (line 10642)
* macros:                                Macros.            (line  9912)
* macros in include:                     Computed Includes. (line  9841)
* macros with arguments:                 Macro Arguments.   (line 10082)
* macros with variable arguments:        Variadic Macros.   (line 10335)
* macros, local labels:                  Local Labels.      (line  6808)
* macros, local variables in:            Macros and Auto Type.
                                                            (line 10861)
* macros, types of arguments:            Auto Type.         (line  7296)
* main function:                         The main Function. (line  8439)
* make rules:                            Compilation.       (line 12681)
* manifest constants:                    Object-like Macros.
                                                            (line  9934)
* maximum integer values:                Maximum and Minimum Values.
                                                            (line 11518)
* memory allocation, dynamic:            Dynamic Memory Allocation.
                                                            (line  4581)
* memory organization:                   Storage.           (line   957)
* minimum integer values:                Maximum and Minimum Values.
                                                            (line 11518)
* modifying assignment:                  Modifying Assignment.
                                                            (line  2093)
* modulus:                               Division and Remainder.
                                                            (line  1712)
* multidimensional arrays:               Multidimensional Arrays.
                                                            (line  5675)
* multiplication operator:               Basic Arithmetic.  (line  1514)
* NaN in floating-point arithmetic:      Handling NaN.      (line 12138)
* NaNs-always-propagate rule:            Handling NaN.      (line 12171)
* negation operator:                     Basic Arithmetic.  (line  1514)
* negation operator, logical:            Logical Operators. (line  2307)
* negation, bitwise:                     Bitwise Operations.
                                                            (line  1906)
* nested block:                          Blocks.            (line  6123)
* nested functions:                      Nested Functions.  (line  8751)
* newline:                               Character Constants.
                                                            (line  3468)
* newline in source:                     Whitespace.        (line  1260)
* not a number:                          Handling NaN.      (line 12138)
* not-equal operator:                    Numeric Comparisons.
                                                            (line  1776)
* null directive:                        Null Directive.    (line 11417)
* null pointers:                         Null Pointers.     (line  3931)
* null statement:                        Null Statement.    (line  6672)
* numbers, preprocessing:                Preprocessing Tokens.
                                                            (line  9540)
* numeric comparisons:                   Numeric Comparisons.
                                                            (line  1776)
* object file:                           Compilation.       (line 12681)
* object-like macro:                     Object-like Macros.
                                                            (line  9934)
* offset of structure fields:            Field Offset.      (line  4658)
* old-style function definitions:        Old-Style Function Definitions.
                                                            (line  9014)
* omitting types in declarations:        Omitting Types.    (line  7528)
* operand execution ordering:            Reordering of Operands.
                                                            (line  2680)
* operand ordering:                      Ordering of Operands.
                                                            (line  2802)
* operand promotions:                    Operand Promotions.
                                                            (line  9280)
* operator precedence:                   Binary Operator Grammar.
                                                            (line  2589)
* operator, addition:                    Basic Arithmetic.  (line  1514)
* operator, comma:                       Comma Operator.    (line  2492)
* operator, decrement:                   Increment/Decrement.
                                                            (line  2149)
* operator, division:                    Basic Arithmetic.  (line  1514)
* operator, equal:                       Numeric Comparisons.
                                                            (line  1776)
* operator, greater-or-equal:            Numeric Comparisons.
                                                            (line  1776)
* operator, greater-than:                Numeric Comparisons.
                                                            (line  1776)
* operator, increment:                   Increment/Decrement.
                                                            (line  2149)
* operator, less-or-equal:               Numeric Comparisons.
                                                            (line  1776)
* operator, less-than:                   Numeric Comparisons.
                                                            (line  1776)
* operator, multiplication:              Basic Arithmetic.  (line  1514)
* operator, negation:                    Basic Arithmetic.  (line  1514)
* operator, not-equal:                   Numeric Comparisons.
                                                            (line  1776)
* operator, postdecrement:               Postincrement/Postdecrement.
                                                            (line  2192)
* operator, postincrement:               Postincrement/Postdecrement.
                                                            (line  2192)
* operator, remainder:                   Division and Remainder.
                                                            (line  1712)
* operator, subtraction:                 Basic Arithmetic.  (line  1514)
* operators:                             Operators/Punctuation.
                                                            (line  1395)
* operators, arithmetic:                 Arithmetic.        (line  1484)
* operators, assignment:                 Assignment Expressions.
                                                            (line  1976)
* operators, bitwise:                    Bitwise Operations.
                                                            (line  1906)
* operators, comparison:                 Numeric Comparisons.
                                                            (line  1776)
* operators, logical:                    Logical Operators. (line  2307)
* operators, shift:                      Shift Operations.  (line  1804)
* operators, shift >1<:                  Shift Operations.  (line  1804)
* optimization and ordering:             Optimization and Ordering.
                                                            (line  2835)
* order of execution:                    Order of Execution.
                                                            (line  2674)
* ordering and optimization:             Optimization and Ordering.
                                                            (line  2835)
* ordering and postincrement:            Postincrement and Ordering.
                                                            (line  2776)
* ordering of operands:                  Reordering of Operands.
                                                            (line  2680)
* ordering of operands >1<:              Ordering of Operands.
                                                            (line  2802)
* overflow, compiler options:            Signed Overflow.   (line  1638)
* overflow, floating:                    Exception Flags.   (line 11732)
* overflow, integer:                     Integer Overflow.  (line  1591)
* overlaying structures:                 Overlaying Structures.
                                                            (line  4957)
* packed structures:                     Packed Structures. (line  4738)
* parameter forward declaration:         Variable-Length Array Parameters.
                                                            (line  8624)
* parameter list:                        Function Parameter Variables.
                                                            (line  7809)
* parameter variables in functions:      Function Parameter Variables.
                                                            (line  7809)
* parameters lists, variable length:     Variable Number of Arguments.
                                                            (line  8648)
* parameters, command-line:              Command-line Parameters.
                                                            (line  8498)
* parentheses in macro bodies:           Operator Precedence Problems.
                                                            (line 10704)
* pitfalls of macros:                    Macro Pitfalls.    (line 10668)
* pointer arithmetic:                    Pointer Arithmetic.
                                                            (line  4104)
* pointer arithmetic, drawbacks:         Pointer Arithmetic Drawbacks.
                                                            (line  4381)
* pointer arithmetic, low level:         Pointer Arithmetic Low Level.
                                                            (line  4243)
* pointer comparison:                    Pointer Comparison.
                                                            (line  4064)
* pointer dereferencing:                 Pointer Dereference.
                                                            (line  3897)
* pointer increment and decrement:       Pointer Increment/Decrement.
                                                            (line  4283)
* pointer type conversion:               Aliasing.          (line 13108)
* pointer-integer conversion:            Pointer-Integer Conversion.
                                                            (line  4413)
* pointers:                              Pointers.          (line  3797)
* pointers and arrays:                   Pointers and Arrays.
                                                            (line  4211)
* pointers to functions:                 Function Pointers. (line  8312)
* pointers, declaring:                   Declaring Arrays and Pointers.
                                                            (line  7071)
* pointers, null:                        Null Pointers.     (line  3931)
* pointers, restrict-qualified:          restrict Pointers. (line  7669)
* pointers, void:                        Void Pointers.     (line  4001)
* postdecrement expression:              Postincrement/Postdecrement.
                                                            (line  2192)
* postincrement and ordering:            Postincrement and Ordering.
                                                            (line  2776)
* postincrement expression:              Postincrement/Postdecrement.
                                                            (line  2192)
* precedence, operator:                  Binary Operator Grammar.
                                                            (line  2589)
* predecrement expression:               Increment/Decrement.
                                                            (line  2149)
* predefined macros:                     Predefined Macros. (line 10428)
* preincrement expression:               Increment/Decrement.
                                                            (line  2149)
* preprocessing:                         Preprocessing.     (line  9440)
* preprocessing directives:              Directives.        (line  9484)
* preprocessing numbers:                 Preprocessing Tokens.
                                                            (line  9540)
* preprocessing tokens:                  Preprocessing Tokens.
                                                            (line  9519)
* prescan of macro arguments:            Argument Prescan.  (line 10945)
* primitive types:                       Primitive Types.   (line  2860)
* printf:                                Complete Explanation.
                                                            (line   854)
* problems with macros:                  Macro Pitfalls.    (line 10668)
* promotion of arguments:                Argument Promotions.
                                                            (line  9248)
* prototype of a function:               Function Declarations.
                                                            (line  8155)
* punctuation:                           Operators/Punctuation.
                                                            (line  1395)
* QNaN:                                  Special Float Values.
                                                            (line 11638)
* quote directories:                     Search Path.       (line  9793)
* ranges in case statements:             Case Ranges.       (line  6647)
* ranges of integer types:               Maximum and Minimum Values.
                                                            (line 11518)
* recursion:                             Function Body.     (line   504)
* recursion, drawbacks of:               Stack.             (line   594)
* recursive Fibonacci function:          Recursive Fibonacci.
                                                            (line   429)
* redefining macros:                     Undefining and Redefining Macros.
                                                            (line 10598)
* referencing structure fields:          Referencing Fields.
                                                            (line  4539)
* register declarations:                 auto and register. (line  7512)
* remainder operator:                    Division and Remainder.
                                                            (line  1712)
* reordering of operands:                Reordering of Operands.
                                                            (line  2680)
* repeated inclusion:                    Once-Only Headers. (line  9801)
* reporting errors:                      Diagnostics.       (line 11345)
* reporting warnings:                    Diagnostics.       (line 11345)
* representation of floating-point numbers: Floating Representations.
                                                            (line 11552)
* representation of integers:            Integer Representations.
                                                            (line 11431)
* reserved words:                        Identifiers.       (line  1375)
* restrict pointers:                     restrict Pointers. (line  7669)
* return (ASCII character):              Character Constants.
                                                            (line  3468)
* return statement:                      return Statement.  (line  6163)
* returning values from main:            Values from main.  (line  8466)
* round-trip base conversion:            Round-Trip Base Conversion.
                                                            (line 12489)
* rounding:                              Rounding.          (line 11777)
* rounding control (floating point):     Rounding Control.  (line 12248)
* rounding issues (floating point):      Rounding Issues.   (line 11828)
* scaling floating point by powers of the base: Scaling by the Base.
                                                            (line 12220)
* scope:                                 Scope.             (line  9322)
* segmentation fault:                    Stack.             (line   604)
* self-reference:                        Self-Referential Macros.
                                                            (line 10888)
* semantics of function calls:           Function Call Semantics.
                                                            (line  8268)
* semicolons (after macro calls):        Swallowing the Semicolon.
                                                            (line 10755)
* sequence points:                       Sequence Points.   (line  2738)
* shift count:                           Shift Operations.  (line  1804)
* shift operators:                       Shift Operations.  (line  1804)
* side effect in ?::                     Conditional Branches.
                                                            (line  2474)
* side effects (in macro arguments):     Duplication of Side Effects.
                                                            (line 10808)
* SIGBUS:                                Signals.           (line 13369)
* SIGFPE:                                Signals.           (line 13369)
* signal:                                Signals.           (line 13369)
* signed types:                          Signed and Unsigned Types.
                                                            (line  2918)
* signed zeros in floating-point arithmetic: Signed Zeros.  (line 12206)
* significance loss (floating point):    Significance Loss. (line 11872)
* SIGSEGV:                               Signals.           (line 13369)
* simple assignment:                     Simple Assignment. (line  2020)
* size of type:                          Type Size.         (line  3726)
* SNaN:                                  Special Float Values.
                                                            (line 11638)
* space character in source:             Whitespace.        (line  1260)
* special floating-point values:         Special Float Values.
                                                            (line 11624)
* stack:                                 Stack.             (line   594)
* stack frame:                           Stack.             (line   594)
* stack frame >1<:                       Stack.             (line   594)
* stack overflow:                        Stack.             (line   594)
* standard output:                       Complete Explanation.
                                                            (line   857)
* statement, break:                      break Statement.   (line  6241)
* statement, continue:                   continue Statement.
                                                            (line  6429)
* statement, do–while:                   do-while Statement.
                                                            (line  6223)
* statement, expression:                 Expression Statement.
                                                            (line  6034)
* statement, for:                        for Statement.     (line  6293)
* statement, goto:                       goto Statement.    (line  6686)
* statement, if:                         if Statement.      (line  6061)
* statement, if...else:                  if-else Statement. (line  6080)
* statement, null:                       Null Statement.    (line  6672)
* statement, return:                     return Statement.  (line  6163)
* statement, switch:                     switch Statement.  (line  6477)
* statement, while:                      while Statement.   (line  6196)
* statements:                            Statements.        (line  6017)
* statements inside expressions:         Statement Exprs.   (line  6970)
* statements, loop:                      Loop Statements.   (line  6184)
* static assertions:                     Static Assertions. (line 12983)
* static function, declaration:          Static Functions.  (line  7923)
* static functions:                      Static Functions.  (line  7909)
* static local variables:                Static Local Variables.
                                                            (line  7403)
* sticky exception flags (floating point): Exception Flags. (line 11732)
* storage organization:                  Storage.           (line   957)
* string:                                Strings.           (line  5508)
* string constants:                      String Constants.  (line  3500)
* stringification:                       Stringification.   (line 10178)
* structure assignment:                  Structure Assignment.
                                                            (line  4987)
* structure constructors:                Structure Constructors.
                                                            (line  5164)
* structure field offset:                Field Offset.      (line  4658)
* structure fields, constant:            const Fields.      (line  4859)
* structure fields, referencing:         Referencing Fields.
                                                            (line  4539)
* structure layout:                      Structure Layout.  (line  4678)
* structures:                            Structures.        (line  4461)
* structures, overlaying:                Overlaying Structures.
                                                            (line  4957)
* structures, unnamed:                   Unnamed Types as Fields.
                                                            (line  5203)
* subexpressions, assignment in:         Assignment in Subexpressions.
                                                            (line  2231)
* subnormal numbers:                     Special Float Values.
                                                            (line 11665)
* subtraction operator:                  Basic Arithmetic.  (line  1514)
* success:                               Values from main.  (line  8466)
* switch statement:                      switch Statement.  (line  6477)
* symbolic constants:                    Object-like Macros.
                                                            (line  9934)
* system header files:                   Header Files.      (line  9624)
* tab (ASCII character):                 Character Constants.
                                                            (line  3468)
* tab character in source:               Whitespace.        (line  1260)
* tentative definition:                  Allocating File-Scope.
                                                            (line  7492)
* thunks:                                Nested Functions.  (line  8751)
* token:                                 Lexical Syntax.    (line  1191)
* token concatenation:                   Concatenation.     (line 10257)
* token pasting:                         Concatenation.     (line 10257)
* truncation:                            Integer Conversion.
                                                            (line  2989)
* truth value:                           Numeric Comparisons.
                                                            (line  1776)
* two’s-complement representation:       Integer Representations.
                                                            (line 11444)
* twosum:                                Error Recovery.    (line 12010)
* type alignment:                        Type Alignment.    (line 13034)
* type conversion, pointer:              Aliasing.          (line 13108)
* type conversions:                      Type Conversions.  (line  9140)
* type designator:                       Type Designators.  (line  3190)
* type size:                             Type Size.         (line  3726)
* type tags:                             Type Tags.         (line  5316)
* type, boolean:                         Boolean Type.      (line  3002)
* type, void:                            The Void Type.     (line  3154)
* typedef names:                         Defining Typedef Names.
                                                            (line  5942)
* types of integer constants:            Integer Const Type.
                                                            (line  3291)
* types, compatible:                     Compatible Types.  (line  9080)
* types, complex:                        Complex Data Types.
                                                            (line  3099)
* types, enumeration:                    Enumeration Types. (line  5863)
* types, floating-point:                 Floating-Point Data Types.
                                                            (line  3050)
* types, incomplete:                     Incomplete Types.  (line  5244)
* types, integer:                        Integer Types.     (line  2869)
* types, primitive:                      Primitive Types.   (line  2860)
* types, signed:                         Signed and Unsigned Types.
                                                            (line  2918)
* types, unsigned:                       Signed and Unsigned Types.
                                                            (line  2918)
* uintptr_t:                             Pointer-Integer Conversion.
                                                            (line  4413)
* undefining macros:                     Undefining and Redefining Macros.
                                                            (line 10598)
* underflow, floating:                   Special Float Values.
                                                            (line 11665)
* underflow, floating >1<:               Exception Flags.   (line 11732)
* underscores in variables in macros:    Macros and Auto Type.
                                                            (line 10879)
* Unicode:                               Characters.        (line  1232)
* Unicode character codes:               Unicode Character Codes.
                                                            (line  3604)
* union, casting to a:                   Cast to Union.     (line  5129)
* unions:                                Unions.            (line  5022)
* unions, unnamed:                       Unnamed Types as Fields.
                                                            (line  5203)
* universal character names:             Unicode Character Codes.
                                                            (line  3604)
* unnamed structures:                    Unnamed Types as Fields.
                                                            (line  5203)
* unnamed unions:                        Unnamed Types as Fields.
                                                            (line  5203)
* unsafe macros:                         Duplication of Side Effects.
                                                            (line 10808)
* unsigned types:                        Signed and Unsigned Types.
                                                            (line  2918)
* UTF-8 String Constants:                UTF-8 String Constants.
                                                            (line  3586)
* variable declarations:                 Variable Declarations.
                                                            (line  7038)
* variable declarations, combining:      Combining Variable Declarations.
                                                            (line  7114)
* variable number of arguments:          Variadic Macros.   (line 10335)
* variable-length array parameters:      Variable-Length Array Parameters.
                                                            (line  8585)
* variable-length arrays:                Arrays of Variable Length.
                                                            (line  5793)
* variable-length parameter lists:       Variable Number of Arguments.
                                                            (line  8648)
* variables:                             Variables.         (line  7016)
* variables, const:                      const.             (line  7553)
* variables, file-scope:                 File-Scope Variables.
                                                            (line  7370)
* variables, global:                     File-Scope Variables.
                                                            (line  7370)
* variables, local:                      Local Variables.   (line  7325)
* variables, local, in macros:           Macros and Auto Type.
                                                            (line 10861)
* variables, static local:               Static Local Variables.
                                                            (line  7403)
* variables, volatile:                   volatile.          (line  7617)
* variadic function:                     Variable Number of Arguments.
                                                            (line  8648)
* variadic macros:                       Variadic Macros.   (line 10335)
* va_copy:                               Variable Number of Arguments.
                                                            (line  8716)
* va_end:                                Variable Number of Arguments.
                                                            (line  8659)
* va_list:                               Variable Number of Arguments.
                                                            (line  8659)
* va_start:                              Variable Number of Arguments.
                                                            (line  8659)
* vertical tab:                          Character Constants.
                                                            (line  3468)
* vertical tab in source:                Whitespace.        (line  1260)
* void pointers:                         Void Pointers.     (line  4001)
* void type:                             The Void Type.     (line  3154)
* volatile variables and fields:         volatile.          (line  7617)
* while statement:                       while Statement.   (line  6196)
* whitespace characters in source files: Whitespace.        (line  1260)
* wide character constants:              Wide Character Constants.
                                                            (line  3640)
* wide string constants:                 Wide String Constants.
                                                            (line  3675)
* wrapper #ifndef:                       Once-Only Headers. (line  9801)
* zero, division by:                     Division and Remainder.
                                                            (line  1769)
* zero-length arrays:                    Zero Length.       (line  4893)
* zero-origin indexing:                  Array Example.     (line  1062)