Environment

As last chapter was mapped to chapter 3 of specification similarly this chapter is mapped to chapter 5 of specification. Please refer to these sections simultaneously.

We store source code in two different files with two different extensions. One regular expression for source code is *.c and the other is *.h. These files are stored in hard disk. When compiled it may produce *.o files optionally. Your program may also produce *.a, *.so, a.out (this name may be different for you if you provide -o switch to gcc. At least one *.a or *.so or a.out or its equivalent will be produced on unix systems. On Windows systems you may produce *.lib, *.dll or *.exe. *.lib, *.dll and *.exe map directly to their counterparts in Unix as *.a, *.so and a.out. These files are called static library, dynamic library, and executables respectively.

An implementation translates C source files and executes C programs in two data- processing-system environments, which will be called the translation environment and the execution environment in this International Standard. Their characteristics define and constrain the results of executing conforming C programs constructed according to the syntactic and semantic rules for conforming implementations.

Just to ease the words translation environment is the machine where the program is being compiled and execution environment is the machine where the executables are/will be executed.

Conceptual Model

Translation Environment

Program Structure

A C program need not all be translated at the same time. The text of the program is kept in units called source files, (or preprocessing files) in International Standard. A source file together with all the headers and source files included via the preprocessing directive #include is known as a preprocessing translation unit. After preprocessing, a preprocessing translation unit is called a translation unit. Previously translated translation units may be preserved individually or in libraries. The separate translation units of a program communicate by (for example) calls to functions whose identifiers have external linkage, manipulation of objects whose identifiers have external linkage, or manipulation of data files. Translation units may be separately translated and then later linked to produce an executable program.

A normal C file is preprocessing translation unit. while a file produced by output of gcc -E filename.c is a translation unit. For example, you can have two source files and three headers. par1.c, part2.c, part1.h, part2.h and common.h. Now these may be individually compiled to part1.o and part2.o and then linked to have a final program output.

Forward references: linkages of identifiers (Linkages of identifiers), external definitions (External definitions), preprocessing directives (Preprocessing Directives).

Translation Phases

The precedence among the syntax rules of translation is specified by the following phases. [1]

  1. Physical source file multibyte characters are mapped, in an implementation-defined-manner, to the source character set (introducing newline characters for end-of-line indicators) if necessary. Trigraph sequences are replaced by corresponding single-character internal representations.

    Typically source file reside on HDD in source character set described in Character Sets. Sometimes they may also reside in other storage mediums also for example, floppy disk, USB drive etc. Implementation defines how multibyte characters will map to source character set. Different operating systems typically stored end-of-line in different ways. All these are converted to newline characters. Trigraph sequences are converted to their equivalents. For example, consider following:

    printf("??<\n");
    

    process it with command gcc -E -trigraphs test.c to get following:

    # 1 "test.c"
    # 1 "<built-in>"
    # 1 "<command-line>"
    # 1 "test.c"
    printf("{\n");
    
  2. Each instance of a backslash character (\) immediately followed by a new-line character is deleted, splicing physical source lines to form logical source lines. Only the last backslash on any physical source line shall be eligible for being part of such a splice. A source file that is not empty shall end in a new-line character, which shall not be immediately preceded by a backslash character before any such splicing takes place.

    Consider following:

    processing it though preprocessor like gcc -E test.c will yield

    # 1 "test.c"
    # 1 "<built-in>"
    # 1 "<command-line>"
    # 1 "test.c"
    printf("line 1 line 2");
    

    Now let us consider two files test1.c and test2.c.

    printf("line 1" \
    

    and

    #include "test1.c"
    "line 2 \
    line 3");
    

    process test2.c to get following:

    # 1 "test1.c"
    # 1 "<built-in>"
    # 1 "<command-line>"
    # 1 "test1.c"
    # 1 "test.c" 1
    printf("line 1"
    # 2 "test1.c" 2
    "line 2 line 3");
    

    If you omit newline at end of file then gcc will issue you a warning.

  3. The source file is decomposed into preprocessing tokens [2] and sequences of white-space characters (including comments). A source file shall not end in a partial preprocessing token or in a partial comment. Each comment is replaced by one space character. New-line characters are retained. Whether each nonempty sequence of white-space characters other than new-line is retained or replaced by one space character is implementation-defined.

    Modifying above example like:

    #include "test1.c" // a comment
    "line 2 \
    line 3");
    

    will yield:

    # 1 "test1.c"
    # 1 "<built-in>"
    # 1 "<command-line>"
    # 1 "test1.c"
    # 1 "test.c" 1
    printf("line 1"
    # 2 "test1.c" 2
    "line 2 line 3");
    

    Two important points to note here are that new-lines are retained which is important for next step and comments are replaced by one space character. new-lines are needed to separate preprocessing directives and comments are needed to be replaced by one character else strange things may happen. Consider int/*a comment*/main() being rendered as intmain() for example. For understanding the meaning of last sentence consider the following program:

    #include <stdio.h>
    
    int main()
    {
      #define makestr(a) #a
    
      char *p = makestr(x          y);
    
      puts(p);
    }
    

    and the output is:

    x y
    

    so we can clearly say that gcc replaces multiple whitespace characters by one.

  4. Preprocessing directives are executed, macro invocations are expanded, and _Pragma unary operator expressions are executed. If a character sequence that matches the syntax of a universal character name is produced by token concatenation, the behavior is undefined. A #include preprocessing directive causes the named header or source file to be processed from phase 1 through phase 4, recursively. All preprocessing directives are then deleted.

    For example:

    #define MAX 5
    
    #define MIN(a,b) ((a)<(b)?(a):(b))
    
    printf("%d", MAX)
    
    printf(%d, MIN(5,7));
    

    will become:

    # 1 "test.c"
    # 1 "<built-in>"
    # 1 "<command-line>"
    # 1 "test.c"
    
    
    
    
    printf("%d", 5)
    
    printf(%d, ((5)<(7)?(5):(7)));
    

    The #include preprocessing directives are processed in-depth first order. Once a header has been fully processed, processing resumes in the file that included it. 15 levels of nesting can be done for header files(Translation limits) Before processing the header, the macros __FILE__ and __LINE__ are set (and they are reset when processing resumes in the file containing the header).

  5. Each source character set member and escape sequence in character constants and string literals is converted to the corresponding member of the execution character set; if there is no corresponding member, it is converted to an implementation-defined member other than the null (wide) character. [3]

    For most of the machines both source and execution characters sets are ASCII while some mainframes use EBCDIC as their character set.

  6. Adjacent string literal tokens are concatenated.

    For example, consider:

    #include <stdio.h>
    
    #define STR1 "hello "
    #define STR2 "world"
    int main()
    {
      puts(STR1 STR2);
    }
    

    and the output is:

    hello world
    

    Note that this rule only applies to string literals not to character array or pointers because they contain null terminating character.

  7. White-space characters separating tokens are no longer significant. Each preprocessing token is converted into a token. The resulting tokens are syntactically and semantically analyzed and translated as a translation unit.

  8. All external object and function references are resolved. Library components are linked to satisfy external references to functions and objects not defined in the current translation. All such translator output is collected into a program image which contains information needed for execution in its execution environment.

    These steps are typically carried out by the linker ld.

Forward references: universal character names (Universal character names), lexical elements (Universal character names), preprocessing directives (Preprocessing Directives), trigraph sequences (Trigraph sequences), external definitions (External definitions).

[1]Implementations behave as if these separate phases occur, even though many are typically folded together in practice.
[2]the process of dividing a source file’s characters into preprocessing tokens is context-dependent. For example, see the handling of < within a #include preprocessing directive.
[3]An implementation need not convert all non-corresponding source characters to the same execution character.

Diagnostics

A conforming implementation shall produce at least one diagnostic message (identified in an implementation-defined manner) if a preprocessing translation unit or translation unit contains a violation of any syntax rule or constraint, even if the behavior is also explicitly specified as undefined or implementation-defined. Diagnostic messages need not be produced in other circumstances. [4]

Note that it is a requirement imposed on implementation. Nothing about what these messages will contain. Implementations are also free to provide more than one message to assist the programmer locate the source of error and by other means as well like pointing out the line number and column number in program text.

[4]The intent is that an implementation should identify the nature of, and where possible localize, each violation. Of course, an implementation is free to produce any number of diagnostics as long as a valid program is still correctly translated. It may also successfully translate an invalid program.

Execution Environment

Two execution environments are defined: freestanding and hosted. In both cases, program startup occurs when a designated C function is called by the execution environment. All objects with static storage duration shall be initialized (set to their initial values) before program startup. The manner and timing of such initialization are otherwise unspecified. Program termination returns control to the execution environment.

freestanding typically means embedded systems though not in standard.

Forward references: storage durations of objects (4.2.4), initialization (4.7.8).

Freestanding Environment

In a freestanding environment (in which C program execution may take place without any benefit of an operating system), the name and type of the function called at program startup are implementation-defined. Any library facilities available to a freestanding program, other than the minimal set required by clause 4, are implementation-defined.

The effect of program termination in a freestanding environment is implementation-defined.

For example, consider the BIOS of PC which runs without an operating system. The startup function name need not be main. Since, such freestanding systems have scarce resources the requirement for conformance is only limited to a minimal set of library facilities. Sometimes it may not be even possible to stop the program running in a freestanding environment. Consider a PC without an operating system. BIOS will take over and how will it terminate. You will need to power off the system manually.

Hosted Environment

A hosted environment need not be provided, but shall conform to the following specifications if present.

Program Startup

The function called at program startup is named main. The implementation declares no prototype for this function. It shall be defined with a return type of int and with no parameters:

int main(void) { /* ... */ }

or with two parameters (referred to here as argc and argv, though any names may be used, as they are local to the function in which they are declared):

int main(int argc, char *argv[]) { /* ... */ }

or equivalent; [5] or in some other implementation defined manner. The function main must have external linkage. Also, the implementation or compiler should not have main function in any of the headers or libraries. Some implementations also provide a third argument called environment pointer or envp which contains environment variables of the systems.

If they are declared, the parameters to the main function shall obey the following constraints:

  • The value of argc shall be nonnegative.
  • argv[argc] shall be a null pointer.
  • If the value of argc is greater than zero, the array members argv[0] through argv[argc-1] inclusive shall contain pointers to strings, which are given implementation-defined values by the host environment prior to program startup. The intent is to supply to the program information determined prior to program startup from elsewhere in the hosted environment. If the host environment is not capable of supplying strings with letters in both uppercase and lowercase, the implementation shall ensure that the strings are received in lowercase.
  • If the value of argc is greater than zero, the string pointed to by argv[0] represents the program name; argv[0][0] shall be the null character if the program name is not available from the host environment. If the value of argc is greater than one, the strings pointed to by argv[1] through argv[argc-1] represent the program parameters.
  • The parameters argc and argv and the strings pointed to by the argv array shall be modifiable by the program, and retain their last-stored values between program startup and program termination.

Let us see a program to summarize this:

#include <stdio.h>
#include <stdlib.h>

int main(int argc, char *argv[])
{
  for(int i=0; i<argc; i++)
    printf("%s\n", argv[i]);

  if(argv[argc]==NULL)
    printf("argv[argc] is NULL pointer.\n");

  return 0;
}

and the output is:

./a.out
1
2
3
4
5 6
argv[argc] is NULL pointer.
[5]Thus, int can be replaced by a typedef name defined as int, or the type of argv can be written as char ** argv, and so on.

Program Execution

In a hosted environment, a program may use all the functions, macros, type definitions, and objects described in the library clause (clause 7).

Program Termination

If the return type of the main function is a type compatible with int, a return from the initial call to the main function is equivalent to calling the exit function with the value returned by the main function as its argument; [6] reaching the } that terminates the main function returns a value of 0. If the return type is not compatible with int, the termination status returned to the host environment is unspecified.

[6]the lifetimes of objects with automatic storage duration declared in main will have ended in the former case, even where they would not have in the latter.

Forward references: definition of terms (Definitions of terms), the exit function (The exit function).

Program Execution

  1. The semantic descriptions in this International Standard describe the behavior of an abstract machine in which issues of optimization are irrelevant.

    Optimization is very important from compilers aspect. However, it is of no concern for standard. The abstract machine in picture here has never been fully treated in the specification. There has been only one formally verified compiler with a subset of C. [Blazy]

  2. Accessing a volatile object, modifying an object, modifying a file, or calling a function that does any of those operations are all side effects, [7] which are changes in the state of the execution environment. Evaluation of an expression may produce side effects. At certain specified points in the execution sequence called sequence points, all side effects of previous evaluations shall be complete and no side effects of subsequent evaluations shall have taken place. (A summary of the sequence points is given in appendix C).

    There is hardly anything you can do without causing side effects. No useful program can be written without causing side effects. The C library treats all I/O as operations on files. The state of a program in execution includes information about current flow of control. Access of a volatile object does not guarantee a change in state, however, it has to be treated as side effect.

    Functional language like Lisp, Erlang, Haskell etc designed to be side effect free. This helps in proving mathematical properties of a program.

    Expressions may also be evaluated for its result value. Consider following:

    #include <stdio.h>
    
    int main(void)
    {
      int i=0;
    
      printf("Enter an integer.\n");
      scanf("%d", &i);
    
      if(i%2==0)
        printf("Number entered is intger.\n");
    
      return 0;
    }
    

    here you can see that the value of expression i%2 can alter the flow of program. The definition of sequence points is given here and possible sequence points are discussed later in appendix C.

  3. Sequenced before is an asymmetric, transitive, pair-wise relation between evaluations executed by a single thread, which induces a partial order among those evaluations. Given any two evaluations A and B, if A is sequenced before B, then the execution of A shall precede the execution of B. (Conversely, if A is sequenced before B, then B is sequenced after A.) If A is not sequenced before or after B, then A and B are unsequenced. Evaluations A and B are indeterminately sequenced when A is sequenced either before or after B, but it is unspecified which. [8]) The presence of a sequence point between the evaluation of expressions A and B implies that every value computation and side effect associated with A is sequenced before every value computation and side effect associated with B. (A summary of the sequence points is given in annex :math:`S(text{iso.C}).)

  4. In the abstract machine, all expressions are evaluated as specified by the semantics. An actual implementation need not evaluate part of an expression if it can deduce that its value is not used and that no needed side effects are produced (including any caused by calling a function or accessing a volatile object).

    The directions from specification here allow the implementation to optimize the machine code as they want. Note that this may result to certain items not discussed in specification. Any code which is translated and part of final machine code, but is never executed, is known as dead code. Similarly, a piece of code, which does not affect output of a program, is known as redundant code.

  5. When the processing of the abstract machine is interrupted by receipt of a signal, only the values of objects as of the previous sequence point may be relied on. Objects that may be modified between the previous sequence point and the next sequence point need not have received their correct values yet.

    As you may know about modern processors have pipelines so before a signal is pipelined more sequence points may be pipelined, however, we cannot rely on that.

  6. The least requirements on a conforming implementation are:

    • At sequence points, volatile objects are stable in the sense that previous accesses are complete and subsequent accesses have not yet occurred.
    • At program termination, all data written into files shall be identical to the result that execution of the program according to the abstract semantics would have produced.
    • The input and output dynamics of interactive devices shall take place as specified in Files. The intent of these requirements is that unbuffered or line-buffered output appear as soon as possible, to ensure that prompting messages actually appear prior to a program waiting for input.
  7. What constitutes an interactive device is implementation-defined.

  8. More stringent correspondences between abstract and actual semantics may be defined by each implementation.

  9. EXAMPLE 1 An implementation might define a one-to-one correspondence between abstract and actual semantics: at every sequence point, the values of the actual objects would agree with those specified by the abstract semantics. The keyword volatile would then be redundant.

    volatile can only be redundant if the implementation is able to tell the order of evaluation of an expression containing volatile objects.

  10. Alternatively, an implementation might perform various optimizations within each translation unit, such that the actual semantics would agree with the abstract semantics only when making function calls across translation unit boundaries. In such an implementation, at the time of each function entry and function return where the calling function and the called function are in different translation units, the values of all externally linked objects and of all objects accessible via pointers therein would agree with the abstract semantics. Furthermore, at the time of each such function entry the values of the parameters of the called function and of all objects accessible via pointers therein would agree with the abstract semantics. In this type of implementation, objects referred to by interrupt service routines activated by the signal function would require explicit specification of volatile storage, as well as other implementation-defined restrictions.

    Requirement that the code declare all object accessed by interrupt service routines as volatile is difficult to achieve in practice because such routines can be invoked in many ways.

  11. EXAMPLE 2 In executing the fragment

    char c1, c2;
    /* ... */
    c1 = c1 + c2;
    

    the “integer promotions” require that the abstract machine promote the value of each variable to int size and then add the two ints and truncate the sum. Provided the addition of two chars can be done without overflow, or with overflow wrapping silently to produce the correct result, the actual execution need only produce the same result, possibly omitting the promotions.

  12. EXAMPLE 3 Similarly, in the fragment

    float f1, f2;
    double d;
    /* ... */
    f1 = f2 * d;
    

    the multiplication may be executed using single-precision arithmetic if the implementation can ascertain that the result would be the same as if it were executed using double-precision arithmetic (for example, if d were replaced by the constant 2.0, which has type double).

  13. EXAMPLE 4 Implementations employing wide registers have to take care to honor appropriate semantics. Values are independent of whether they are represented in a register or in memory. For example, an implicit spilling of a register is not permitted to alter the value. Also, an explicit store and load is required to round to the precision of the storage type. In particular, casts and assignments are required to perform their specified conversion. For the fragment

    double d1, d2;
    float f;
    d1 = f = expression;
    d2 = (float) expression;
    

    the values assigned to d1 and d2 are required to have been converted to float.

  14. EXAMPLE 5 Rearrangement for floating-point expressions is often restricted because of limitations in precision as well as range. The implementation cannot generally apply the mathematical associative rules for addition or multiplication, nor the distributive rule, because of roundoff error, even in the absence of overflow and underflow. Likewise, implementations cannot generally replace decimal constants in order to rearrange expressions. In the following fragment, rearrangements suggested by mathematical rules for real numbers are often not valid (see F.8).

    double x, y, z;
    /* ... */
    x = (x * y) * z; // not equivalent to x *= y * z;
    z = (x - y) + y; // not equivalent to z = x;
    z = x + x * y;   // not equivalent to z = x * (1.0 + y);
    y = x / 5.0;     // not equivalent to y = x * 0.2;
    
  15. EXAMPLE 6 To illustrate the grouping behavior of expressions, in the following fragment

    int a, b;
    /* ... */
    a = a + 32760 + b + 5;
    

    the expression statement behaves exactly the same as:

    a = (((a + 32760) + b) + 5);
    

    due to the associativity and precedence of these operators. Thus, the result of the sum (a + 32760) is next added to b, and that result is then added to 5 which results in the value assigned to a. On a machine in which overflows produce an explicit trap and in which the range of values representable by an int is [-32768, +32767], the implementation cannot rewrite this expression as a = ((a + b) + 32765); since if the values for a and b were, respectively, -32754 and -15, the sum a + b would produce a trap while the original expression would not; nor can the expression be rewritten either as:

    a = ((a + 32765) + b);
    

    or:

    a = (a + (b + 32765));
    

    since the values for a and b might have been, respectively, 4 and -8 or -17 and 12. However, on a machine in which overflow silently generates some value and where positive and negative overflows cancel, the above expression statement can be rewritten by the implementation in any of the above ways because the same result will occur.

  16. EXAMPLE 7 The grouping of an expression does not completely determine its evaluation. In the following fragment

    #include <stdio.h>
    int sum;
    char *p;
    /* ... */
    sum = sum * 10 - '0' + (*p++ = getchar());
    

    the expression statement is grouped as if it were written as:

    sum = (((sum * 10) - '0') + ((*(p++)) = (getchar())));
    

    but the actual increment of p can occur at any time between the previous sequence point and the next sequence point (the ;), and the call to getchar can occur at any point prior to the need of its returned value.

  17. EXAMPLE 7 The grouping of an expression does not completely determine its evaluation. In the following fragment

    #include <stdio.h>
    int sum;
    char *p;
    /* ... */
    sum = sum * 10 - '0' + (*p++ = getchar());
    

    the expression statement is grouped as if it were written as sum = (((sum * 10) - '0') + ((*(p++)) = (getchar()))); but the actual increment of p can occur at any time between the previous sequence point and the next sequence point (the ;), and the call to getchar can occur at any point prior to the need of its returned value.

[7]The IEC 60559 standard for binary floating-point arithmetic requires certain user-accessible status flags and control modes. Floating-point operations implicitly set the status flags; modes affect result values of floating-point operations. Implementations that support such floating-point state are required to regard changes to it as side effects - see appendix for details. The floating-point environment library <fenv.h> provides a programming facility for indicating when these side effects matter, freeing the implementations in other cases.
[8]The executions of unsequenced evaluations can interleave. Indeterminately sequenced evaluations cannot interleave, but can be executed in any order.

Forward references: expressions (Expressions), type qualifiers (Type qualifiers), statements (Statements and blocks), the signal function (The signal function), files (Files).

[Blazy]Sandrine Blazy, Zaynah Dargaye, Xavier Leroy, Formal Verification of a C Compiler Front-end FM‘06: 14th Symposium on Formal Methods 4085 (2006) pp.460-475

Multi-threaded executions and data races

  1. Under a hosted implementation, a program can have more than one thread of execution (or thread) running concurrently. The execution of each thread proceeds as defined by the remainder of this standard. The execution of the entire program consists of an execution of all of its threads. [9] Under a freestanding implementation, it is implementation-defined whether a program can have more than one thread of execution.

  2. The value of an object visible to a thread T at a particular point is the initial value of the object, a value stored in the object by T , or a value stored in the object by another thread, according to the rules below.

  3. NOTE 1 In some cases, there may instead be undefined behavior. Much of this section is motivated by the desire to support atomic operations with explicit and detailed visibility constraints. However, it also implicitly supports a simpler view for more restricted programs.

  4. Two expression evaluations conflict if one of them modifies a memory location and the other one reads or modifies the same memory location.

  5. The library defines a number of atomic operations (7.17) and operations on mutexes (7.26.4) that are specially identified as synchronization operations. These operations play a special role in making assignments in one thread visible to another. A synchronization operation on one or more memory locations is either an acquire operation, a release operation, both an acquire and release operation, or a consume operation. A synchronization operation without an associated memory location is a fence and can be either an acquire fence, a release fence, or both an acquire and release fence. In addition, there are relaxed atomic operations, which are not synchronization operations, and atomic read-modify-write operations, which have special characteristics.

  6. NOTE 2 For example, a call that acquires a mutex will perform an acquire operation on the locations composing the mutex. Correspondingly, a call that releases the same mutex will perform a release operation on those same locations. Informally, performing a release operation on A forces prior side effects on other memory locations to become visible to other threads that later perform an acquire or consume operation on A. We do not include relaxed atomic operations as synchronization operations although, like synchronization operations, they cannot contribute to data races.

  7. All modifications to a particular atomic object M occur in some particular total order, called the modification order of M. If A and B are modifications of an atomic object M, and A happens before B, then A shall precede B in the modification order of M, which is defined below.

  8. NOTE 3 This states that the modification orders must respect the “happens before” relation.

  9. NOTE 4 There is a separate order for each atomic object. There is no requirement that these can be combined into a single total order for all objects. In general this will be impossible since different threads may observe modifications to different variables in inconsistent orders.

  10. A release sequence headed by a release operation A on an atomic object M is a maximal contiguous sub-sequence of side effects in the modification order of M, where the first operation is A and every subsequent operation either is performed by the same thread that performed the release or is an atomic read-modify-write operation.

  11. Certain library calls synchronize with other library calls performed by another thread. In particular, an atomic operation A that performs a release operation on an object M synchronizes with an atomic operation B that performs an acquire operation on M and reads a value written by any side effect in the release sequence headed by A.

  12. NOTE 5 Except in the specified cases, reading a later value does not necessarily ensure visibility as described below. Such a requirement would sometimes interfere with efficient implementation.

  13. NOTE 6 The specifications of the synchronization operations define when one reads the value written by another. For atomic variables, the definition is clear. All operations on a given mutex occur in a single total order. Each mutex acquisition “reads the value written” by the last mutex release.

  14. An evaluation A carries a dependency [10] to an evaluation B if:

    • the value of A is used as an operand of B, unless:
      • B is an invocation of the kill_dependency macro,
      • A is the left operand of a && or || operator,
      • A is the left operand of a ? : operator, or
      • A is the left operand of a , operator;

    or,

    • A writes a scalar object or bit-field M, B reads from M the value written by A, and A is sequenced before B, or
    • for some evaluation X, A carries a dependency to X and X carries a dependency to B.
  15. An evaluation A is dependency-ordered before [11] an evaluation B if:

    • A performs a release operation on an atomic object M, and, in another thread, B performs a consume operation on M and reads a value written by any side effect in the release sequence headed by A, or
    • for some evaluation X, A is dependency-ordered before X and X carries a dependency to B.
  16. An evaluation A inter-thread happens before an evaluation B if A synchronizes with B, A is dependency-ordered before B, or, for some evaluation X:

    • A synchronizes with X and X is sequenced before B,
    • A is sequenced before X and X inter-thread happens before B, or
    • A inter-thread happens before X and X inter-thread happens before B.
  17. NOTE 7 The “inter-thread happens before” relation describes arbitrary concatenations of “sequenced before”, “synchronizes with”, and “dependency-ordered before” relationships, with two exceptions. The first exception is that a concatenation is not permitted to end with “dependency-ordered before” followed by “sequenced before”. The reason for this limitation is that a consume operation participating in a “dependency-ordered before” relationship provides ordering only with respect to operations to which this consume operation actually carries a dependency. The reason that this limitation applies only to the end of such a concatenation is that any subsequent release operation will provide the required ordering for a prior consume operation. The second exception is that a concatenation is not permitted to consist entirely of “sequenced before”. The reasons for this limitation are (1) to permit “inter-thread happens before” to be transitively closed and (2) the “happens before” relation, defined below, provides for relationships consisting entirely of “sequenced before”.

  18. An evaluation A happens before an evaluation B if A is sequenced before B or A inter-thread happens before B.

  19. A visible side effect A on an object M with respect to a value computation B of M satisfies the conditions:

    • A happens before B, and
    • there is no other side effect X to M such that A happens before X and X happens before B.

    The value of a non-atomic scalar object M, as determined by evaluation B, shall be the value stored by the visible side effect A.

  20. NOTE 8 If there is ambiguity about which side effect to a non-atomic object is visible, then there is a data race and the behavior is undefined.

  21. NOTE 9 This states that operations on ordinary variables are not visibly reordered. This is not actually detectable without data races, but it is necessary to ensure that data races, as defined here, and with suitable restrictions on the use of atomics, correspond to data races in a simple interleaved (sequentially consistent) execution.

  22. The visible sequence of side effects on an atomic object M, with respect to a value computation B of M, is a maximal contiguous sub-sequence of side effects in the modification order of M, where the first side effect is visible with respect to B, and for every subsequent side effect, it is not the case that B happens before it. The value of an atomic object M, as determined by evaluation B, shall be the value stored by some operation in the visible sequence of M with respect to B. Furthermore, if a value computation A of an atomic object M happens before a value computation B of M, and the value computed by A corresponds to the value stored by side effect X, then the value computed by B shall either equal the value computed by A, or be the value stored by side effect Y, where Y follows X in the modification order of M.

  23. NOTE 10 This effectively disallows compiler reordering of atomic operations to a single object, even if both operations are “relaxed” loads. By doing so, we effectively make the “cache coherence” guarantee provided by most hardware available to C atomic operations.

  24. NOTE 11 The visible sequence depends on the “happens before” relation, which in turn depends on the values observed by loads of atomics, which we are restricting here. The intended reading is that there must exist an association of atomic loads with modifications they observe that, together with suitably chosen modification orders and the “happens before” relation derived as described above, satisfy the resulting constraints as imposed here.

  25. The execution of a program contains a data race if it contains two conflicting actions in different threads, at least one of which is not atomic, and neither happens before the other. Any such data race results in undefined behavior.

  26. NOTE 12 It can be shown that programs that correctly use simple mutexes and memory_order_seq_cst operations to prevent all data races, and use no other synchronization operations, behave as though the operations executed by their constituent threads were simply interleaved, with each value computation of an object being the last value stored in that interleaving. This is normally referred to as “sequential consistency”. However, this applies only to data-race-free programs, and data-race-free programs cannot observe most program transformations that do not change single-threaded program semantics. In fact, most single-threaded program transformations continue to be allowed, since any program that behaves differently as a result must contain undefined behavior.

  27. NOTE 13 Compiler transformations that introduce assignments to a potentially shared memory location that would not be modified by the abstract machine are generally precluded by this standard, since such an assignment might overwrite another assignment by a different thread in cases in which an abstract machine execution would not have encountered a data race. This includes implementations of data member assignment that overwrite adjacent members in separate memory locations. We also generally preclude reordering of atomic loads in cases in which the atomics in question may alias, since this may violate the “visible sequence” rules.

  28. NOTE 14 Transformations that introduce a speculative read of a potentially shared memory location may not preserve the semantics of the program as defined in this standard, since they potentially introduce a data race. However, they are typically valid in the context of an optimizing compiler that targets a specific machine with well-defined semantics for data races. They would be invalid for a hypothetical machine that is not tolerant of races or provides hardware race detection.

[9]The execution can usually be viewed as an interleaving of all of the threads. However, some kinds of atomic operations, for example, allow executions inconsistent with a simple interleaving as described below.
[10]The “carries a dependency” relation is a subset of the “sequenced before” relation, and is similarly strictly intra-thread.
[11]The “dependency-ordered before” relation is analogous to the “synchronizes with” relation, but uses release/consume in place of release/acquire.

Environmental considerations

Character Sets

  1. Two sets of characters and their associated collating sequences shall be defined: the set in which source files are written (the source character set), and the set interpreted in the execution environment (the execution character set). Each set is further divided into a basic character set, whose contents are given by this subclause, and a set of zero or more locale-specific members (which are not members of the basic character set) called extended characters. The combined set is also called the extended character set. The values of the members of the execution character set are implementation-defined.

  2. In a character constant or string literal, members of the execution character set shall be represented by corresponding members of the source character set or by escape sequences consisting of the backslash followed by one or more characters. A byte with all bits set to 0, called the null character, shall exist in the basic execution character set; it is used to terminate a character string.

  3. Both the basic source and basic execution character sets shall have the following members: the 26 uppercase letters of the Latin alphabet:

    A B C D E F G H I J K L: M N O P Q R S T U V W X Y Z
    

    the 26 lowercase letters of the Latin alphabet:

    a b c d e f g h i j k l m n o p q r s t u v w x y z
    

    the 10 decimal digits:

    0 1 2 3 4 5 6 7 8 9
    

    the following 29 graphic characters:

    ~ ! # % ^ & * ( ) - _ = + \ | [ ] { } ; : ' " , < . > / ?
    

    the space character, and control characters representing horizontal tab, vertical tab, and form feed. The representation of each member of the source and execution basic character sets shall fit in a byte. In both the source and execution basic character sets, the value of each character after 0 in the above list of decimal digits shall be one greater than the value of the previous. In source files, there shall be some way of indicating the end of each line of text; this International Standard treats such an end-of-line indicator as if it were a single new-line character. In the basic execution character set, there shall be control characters representing alert, backspace, carriage return, and new line. If any other characters are encountered in a source file (except in an identifier, a character constant, a string literal, a header name, a comment, or a preprocessing token that is never converted to a token), the behavior is undefined.

    These character sets are also described in The C Character Set .

  4. A letter is an uppercase letter or a lowercase letter as defined above; in this International Standard the term does not include other characters that are letters in other alphabets.

  5. The universal character name construct provides a way to name other characters.

Forward references: universal character names (Universal character names), character constants (Character constants), preprocessing directives (Preprocessing Directives), string literals (String literals), comments (Comments), string (Introduction).

Trigraph sequences

All occurrences in a source file of the following sequences of three characters (called trigraph sequences [12]) are replaced with the corresponding single character.

Trigraph Equivalent Trigraph Equivalent Trigraph Equivalent
??= # ??’ ^ ??! |
??( [ ??) ] ??< {
??> } ??/ \ ??- ~

This table is also given in The C Character Set . No other trigraph sequences exist. Each ? that does not begin one of the trigraphs listed above is not changed.

EXAMPLE The following source line

printf("Eh???/n");

becomes (after replacement of the trigraph sequence ??/)

printf("Eh?\n");

Multibyte characters

The source character set may contain multibyte characters, used to represent members of the extended character set. The execution character set may also contain multibyte characters, which need not have the same encoding as for the source character set. For both character sets, the following shall hold:

  • The basic character set shall be present and each character shall be encoded as a single byte.
  • The presence, meaning, and representation of any additional members is locale- specific.
  • A multibyte character set may have a state-dependent encoding, wherein each sequence of multibyte characters begins in an initial shift state and enters other locale-specific shift states when specific multibyte characters are encountered in the sequence. While in the initial shift state, all single-byte characters retain their usual interpretation and do not alter the shift state. The interpretation for subsequent bytes in the sequence is a function of the current shift state.
  • A byte with all bits zero shall be interpreted as a null character independent of shift state. Such a byte shall not occur as part of any other multibyte character.

For source files, the following shall hold:

  • An identifier, comment, string literal, character constant, or header name shall begin and end in the initial shift state.

  • An identifier, comment, string literal, character constant, or header name shall consist of a sequence of valid multibyte characters.

    For example, accented characters fall in this category.

Character display semantics

The active position is that location on a display device where the next character output by the fputc function would appear. The intent of writing a printing character (as defined by the isprint function) to a display device is to display a graphic representation of that character at the active position and then advance the active position to the next position on the current line. The direction of writing is locale-specific. If the active position is at the final position of a line (if there is one), the behavior of the display device is unspecified. Following escape sequences are also treated in Escape Sequences.

Alphabetic escape sequences representing nongraphic characters in the execution character set are intended to produce actions on display devices as follows:

\a (alert) Produces an audible or visible alert without changing the active position.

\b (backspace) Moves the active position to the previous position on the current line. If the active position is at the initial position of a line, the behavior of the display device is unspecified.

\f (form feed) Moves the active position to the initial position at the start of the next logical page.

\n (new line) Moves the active position to the initial position of the next line.

\r (carriage return) Moves the active position to the initial position of the current line.

\t (horizontal tab) Moves the active position to the next horizontal tabulation position on the current line. If the active position is at or past the last defined horizontal tabulation position, the behavior of the display device is unspecified.

\v (vertical tab) Moves the active position to the initial position of the next vertical tabulation position. If the active position is at or past the last defined vertical tabulation position, the behavior of the display device is unspecified.

Each of these escape sequences shall produce a unique implementation-defined value which can be stored in a single char object. The external representations in a text file need not be identical to the internal representations, and are outside the scope of this International Standard.

Forward references: the isprint function (The isprint function), the fputc function (The fputc function).

[12]The trigraph sequences enable the input of characters that are not defined in the Invariant Code Set as described in ISO/IEC 646, which is a subset of the seven-bit US ASCII code set.

Signals and interrupts

Functions shall be implemented such that they may be interrupted at any time by a signal, or may be called by a signal handler, or both, with no alteration to earlier, but still active, invocations’ control flow (after the interruption), function return values, or objects with automatic storage duration. All such objects shall be maintained outside the function image (the instructions that compose the executable representation of a function) on a per-invocation basis.

Environmental limits

Both the translation and execution environments constrain the implementation of language translators and libraries. The following summarizes the language-related environmental limits on a conforming implementation; the library-related limits are discussed in chapter 13 onwards.

Translation limits

The implementation shall be able to translate and execute at least one program that contains at least one instance of every one of the following limits: [13]

  • 127 nesting levels of blocks
  • 63 nesting levels of conditional inclusion
  • 12 pointer, array, and function declarators (in any combinations) modifying an arithmetic, structure, union, or incomplete type in a declaration
  • 63 nesting levels of parenthesized declarators within a full declarator
  • 63 nesting levels of parenthesized expressions within a full expression
  • 63 significant initial characters in an internal identifier or a macro name (each universal character name or extended source character is considered a single character)
  • 31 significant initial characters in an external identifier (each universal character name specifying a short identifier of 0000FFFF or less is considered 6 characters, each universal character name specifying a short identifier of 00010000 or more is considered 10 characters, and each extended source character is considered the same number of characters as the corresponding universal character name, if any) [14]
  • 4095 external identifiers in one translation unit
  • 511 identifiers with block scope declared in one block
  • 4095 macro identifiers simultaneously defined in one preprocessing translation unit
  • 127 parameters in one function definition
  • 127 arguments in one function call
  • 127 parameters in one macro definition
  • 127 arguments in one macro invocation
  • 4095 characters in a logical source line
  • 4095 characters in a character string literal or wide string literal (after concatenation)
  • 65535 bytes in an object (in a hosted environment only)
  • 15 nesting levels for #include files
  • 1023 case labels for a switch statement (excluding those for any nested switch statements)
  • 1023 members in a single structure or union
  • 1023 enumeration constants in a single enumeration
  • 63 levels of nested structure or union definitions in a single struct-declaration-list
[13]Implementations should avoid imposing fixed translation limits whenever possible.
[14]See “future language directions” (External names)

Numerical limits

An implementation is required to document all the limits specified in this subclause, which are specified in the headers <limits.h> and <float.h>. Additional limits are specified in <stdint.h>.

Forward references: integer types <stdint.h> (Integer types <stdint.h>).

Sizes of integer types <limits.h>

The values given below shall be replaced by constant expressions suitable for use in #if preprocessing directives. Moreover, except for CHAR_BIT and MB_LEN_MAX, the following shall be replaced by expressions that have the same type as would an expression that is an object of the corresponding type converted according to the integer promotions. Their implementation-defined values shall be equal or greater in magnitude (absolute value) to those shown, with the same sign.

  • number of bits for smallest object that is not a bit-field (byte)

    CHAR_BIT 8

  • minimum value for an object of type signed char

    SCHAR_MIN -127 // \(-(2^7 - 1)\)

  • maximum value for an object of type signed char

    SCHAR_MAX +127 // \(2^7 - 1\)

  • maximum value for an object of type unsigned char

    UCHAR_MAX 255 // \(2^8 - 1\)

  • minimum value for an object of type char

    CHAR_MIN see below

  • maximum value for an object of type char

    CHAR_MAX see below

  • maximum number of bytes in a multibyte character, for any supported locale

    MB_LEN_MAX 1

  • minimum value for an object of type short int

    SHRT_MIN -32767 // \(-(2^{15} - 1)\)

  • maximum value for an object of type short int

    SHRT_MAX +32767 // \(2^{15} - 1\)

  • maximum value for an object of type unsigned short int

    USHRT_MAX 65535 // \(2^{16} - 1\)

  • minimum value for an object of type int

    INT_MIN -32767 // \(-(2^{15} - 1)\)

  • maximum value for an object of type int

    INT_MAX +32767 // \(2^{15} - 1\)

  • maximum value for an object of type unsigned int

    UINT_MAX 65535 // \(2^{16} - 1\)

  • minimum value for an object of type long int

    LONG_MIN -2147483647 // \(-(2^{31} - 1)\)

  • maximum value for an object of type long int

    LONG_MAX +2147483647 // \(2^{31} - 1\)

  • maximum value for an object of type unsigned long int

    ULONG_MAX 4294967295 // \(2^{32} - 1\)

  • minimum value for an object of type long long int

    LLONG_MIN -9223372036854775807 // \(-(2^{63} - 1)\)

  • maximum value for an object of type long long int

    LLONG_MAX +9223372036854775807 // \(2^{63} - 1\)

  • maximum value for an object of type unsigned long long int

    ULLONG_MAX 18446744073709551615 // \(2^{64} - 1\)

If the value of an object of type char is treated as a signed integer when used in an expression, the value of CHAR_MIN shall be the same as that of SCHAR_MIN and the value of CHAR_MAX shall be the same as that of SCHAR_MAX. Otherwise, the value of CHAR_MIN shall be 0 and the value of CHAR_MAX shall be the same as that of UCHAR_MAX. [15] The value UCHAR_MAX shall equal \(2^{CHAR_BIT} - 1\).

Forward references: representations of types (Representation of Types), conditional inclusion (Conditional Inclusion).

[15]See Types.

Characteristics of floating types ``<float.h>``

The characteristics of floating types are defined in terms of a model that describes a representation of floating-point numbers and values that provide information about an implementation’s floating-point arithmetic. [16] The following parameters are used to define the model for each floating-point type

\(s\) sign
\(b\) base or radix of exponent representation (an integer > 1)
\(e\) exponent (an integer between a minimum emin and a maximum emax )
\(p\) precision (the number of base-b digits in the significand)
\(f_k\) nonnegative integers less than b (the significand digits)

A floating-point number (x) is defined by the following model:

\[x = sb^e \sum_{k=1}^p f_kb^{-k},~e_{min}~\leq~e~\leq~e_{max}\]

In addition to normalized floating-point numbers (\(f_1 > 0\) if \(x \neq 0\)), floating types may be able to contain other kinds of floating-point numbers, such as subnormal floating-point numbers (\(x \neq 0, e = e_{min}, f_1 = 0\)) and unnormalized floating-point numbers (\(x \neq 0, e > e_{min} , f_1 = 0\)), and values that are not floating-point numbers, such as infinities and NaNs. A NaN is an encoding signifying Not-a-Number. A quiet NaN propagates through almost every arithmetic operation without raising a floating-point exception; a signaling NaN generally raises a floating-point exception when occurring as an arithmetic operand. [17]

An implementation may give zero and non-numeric values (such as infinities and NaNs) a sign or may leave them unsigned. Wherever such values are unsigned, any requirement in this International Standard to retrieve the sign shall produce an unspecified sign, and any requirement to set the sign shall be ignored.

The accuracy of the floating-point operations (+, -, *, /) and of the library functions in <math.h> and <complex.h> that return floating-point results is implementation-defined, as is the accuracy of the conversion between floating-point internal representations and string representations performed by the library functions in <stdio.h>, <stdlib.h> and <wchar.h>. The implementation may state that the accuracy is unknown.

All integer values in the <float.h> header, except FLT_ROUNDS, shall be constant expressions suitable for use in #if preprocessing directives; all floating values shall be constant expressions. All except DECIMAL_DIG, FLT_EVAL_METHOD, FLT_RADIX and FLT_ROUNDS have separate names for all three floating-point types. The floating- point model representation is provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.

The rounding mode for floating-point addition is characterized by the implementation- defined value of FLT_ROUNDS: [18]

-1 indeterminable
0 toward zero
1 to nearest
2 toward positive infinity
3 toward negative infinity

All other values for FLT_ROUNDS characterize implementation-defined rounding behavior. The four rounding methods were also described in Terms, Definitions and Symbols.

The values of operations with floating operands and values subject to the usual arithmetic conversions and of floating constants are evaluated to a format whose range and precision may be greater than required by the type. The use of evaluation formats is characterized by the implementation-defined value of FLT_EVAL_METHOD: [19]

-1 indeterminable;
0 evaluate all operations and constants just to the range and precision of the type;
1 evaluate operations and constants of type float and double to the range and precision of the double type, evaluate long double operations and constants to the range and precision of the long double type;
2 evaluate all operations and constants to the range and precision of the long double type.

All other negative values for FLT_EVAL_METHOD characterize implementation-defined behavior.

The values given in the following list shall be replaced by constant expressions with implementation-defined values that are greater or equal in magnitude (absolute value) to those shown, with the same sign:

  • radix of exponent representation, \(b\)

    FLT_RADIX 2
  • number of base-FLT_RADIX digits in the floating-point significand, \(p\)

    FLT_MANT_DIG
    DBL_MANT_DIG
    LDBL_MANT_DIG
  • number of decimal digits, \(n\), such that any floating-point number in the widest supported floating type with \(p_{max}\) radix \(b\) digits can be rounded to a floating-point number with \(n\) decimal digits and back again without change to the value,

    \[\begin{split}\left\{ \begin{array}{l l} p_{max} \log_{10} b & \quad \text{if } b \text{ is a power of 10}\\ \lceil 1 + p_{max} \log_{10} b \rceil & \quad \text{otherwise} \end{array}\right.\end{split}\]
    DECIMAL_DIG 10
  • number of decimal digits, : math:q, such that any floating-point number with \(q\) decimal digits can be rounded into a floating-point number with \(p\) radix \(b\) digits and back again without change to the \(q\) decimal digits,

    \[\begin{split}\left\{ \begin{array}{l l} p \log_{10} b & \quad \text{if } b \text{ is a power of 10}\\ \lfloor (p - 1) \log_{10} b \rfloor & \quad \text{otherwise} \end{array}\right.\end{split}\]
    FLT_DIG 6
    DBL_DIG 10
    LDBL_DIG 10
  • minimum negative integer such that FLT_RADIX raised to one less than that power is a normalized floating-point number, \(e_{min}\)

    FLT_MIN_EXP
    DBL_MIN_EXP
    LDBL_MIN_EXP
  • minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers, \(\lceil\log_{10}b^{e_{min}-1}\rceil\)

    FLT_MIN_10_EXP -37
    DBL_MIN_10_EXP -37
    LDBL_MIN_10_EXP -37
  • maximum integer such that FLT_RADIX raised to one less than that power is a representable finite floating-point number, \(e_{max}\)

    FLT_MAX_EXP
    DBL_MAX_EXP
    LDBL_MAX_EXP
  • maximum integer such that 10 raised to that power is in the range of representable finite floating-point numbers, \(\lfloor\log_{10}((1 - b^{-p})b^{e_{max}})\rfloor\)

    FLT_MAX_10_EXP +37
    DBL_MAX_10_EXP +37
    LDBL_MAX_10_EXP +37

The values given in the following list shall be replaced by constant expressions with implementation-defined values that are greater than or equal to those shown:

  • maximum representable finite floating-point number, \((1 - b^{-p})b^{e_{max}}\)

    FLT_MAX 1E+37
    DBL_MAX 1E+37
    LDBL_MAX 1E+37

The values given in the following list shall be replaced by constant expressions with implementation-defined (positive) values that are less than or equal to those shown:

  • the difference between 1 and the least value greater than 1 that is representable in the given floating point type, \(b^{1 - p}\)

    FLT_EPSILON 1E-5
    DBL_EPSILON 1E-9
    LDBL_EPSILON 1E-9
  • minimum normalized positive floating-point number, \(b^{e_{min} - 1}\)

    FLT_MIN 1E-37
    DBL_MIN 1E-37
    LDBL_MIN 1E-37

Recommended practice

Conversion from (at least) double to decimal with DECIMAL_DIG digits and back should be the identity function.

EXAMPLE 1 The following describes an artificial floating-point representation that meets the minimum requirements of this International Standard, and the appropriate values in a <float.h> header for type float:

\[x = s 16^e \sum_{k=1}^6 f_k 16^{-k},~-31 \leq~e~\leq~+32\]
FLT_RADIX                   16
FLT_MANT_DIG                 6
FLT_EPSILON    9.53674316E-07F
FLT_DIG                      6
FLT_MIN_EXP                -31
FLT_MIN        2.93873588E-39F
FLT_MIN_10_EXP             -38
FLT_MAX_EXP                +32
FLT_MAX        3.40282347E+38F
FLT_MAX_10_EXP             +38

EXAMPLE 2 The following describes floating-point representations that also meet the requirements for single-precision and double-precision normalized numbers in IEC 60559, [20] and the appropriate values in a <float.h> header for types float and double:

\[ \begin{align}\begin{aligned}x = s 2^e \sum_{k=1}^24 f_k 2^{-k},~-125 \leq~e~\leq~+128\\x = s 2^e \sum_{k=1}^53 f_k 2^{-k},~-1024 \leq~e~\leq~+1024\end{aligned}\end{align} \]
FLT_RADIX                        2
DECIMAL_DIG                     17
FLT_MANT_DIG                    24
FLT_EPSILON        1.19209290E-07F // decimal constant
FLT_EPSILON               0x1P-23F // hex constant
FLT_DIG                          6
FLT_MIN_EXP                   -125
FLT_MIN            1.17549435E-38F // decimal constant
FLT_MIN                  0X1P-126F // hex consttant
FLT_MIN_10_EXP                 -37
FLT_MAX_EXP                   +128
FLT_MAX            3.40282347E+38F // decimal constant
FLT_MAX            0X1.fffffeP127F // hex constant
FLT_MAX_10_EXP                 +38
DBL_MANT_DIG                    53
DBL_EPSILON 2.2204460492503131E-16 // deciaml constant
DBL_EPSILON                0X1P-52 // hex constant
DBL_DIG                         15
DBL_MIN_EXP                  -1021
DBL_MIN    2.2250738585072014E-308 // deciaml constant
DBL_MIN                  0X1P-1022 // hex constant
DBL_MIN_10_EXP                -307
DBL_MAX_EXP                  +1024
DBL_MAX    1.7976931348623157E+308 // decimal constant
DBL_MAX     0X1.fffffffffffffP1023 // hex constant
DBL_MAX_10_EXP                +308

If a type wider than double were supported, then DECIMAL_DIG would be greater than 17. For example, if the widest type were to use the minimal-width IEC 60559 double-extended format (64 bits of precision), then DECIMAL_DIG would be 21.

Forward references: conditional inclusion (Conditional Inclusion), complex arithmetic <complex.h> (Complex arithmetic <complex.h>, extended multibyte and wide character utilities <wchar.h> (Extended multibyte and wide character utilities <wchar.h>), floating-point environment <fenv.h> (Floating-point environment <fenv.h>), general utilities <stdlib.h> (General utilities <stdlib.h>), input/output <stdio.h> (Input/output <stdio.h>), mathematics <math.h> (Mathematics <math.h>).

[16]The floating-point model is intended to clarify the description of each floating-point characteristic and does not require the floating-point arithmetic of the implementation to be identical.
[17]IEC 60559:1989 specifies quiet and signaling NaNs. For implementations that do not support IEC 60559:1989, the terms quiet NaN and signaling NaN are intended to apply to encodings with similar behavior.
[18]Evaluation of FLT_ROUNDS correctly reflects any execution-time change of rounding mode through the function fesetround in <fenv.h>.
[19]The evaluation method determines evaluation formats of expressions involving all floating types, not just real types. For example, if FLT_EVAL_METHOD is 1, then the product of two float _Complex operands is represented in the double _Complex format, and its parts are evaluated to double.
[20]The floating-point model in that standard sums powers of b from zero, so the values of the exponent limits are one less than shown here.