C Language Facilities Implemented By the Library
************************************************

Some of the facilities implemented by the C library really should be thought of as parts of the C language itself.  These facilities ought to be documented in the C Language Manual, not in the library manual; but since we don't have the language manual yet, and documentation for these features has been written, we are publishing it here.

Explicitly Checking Internal Consistency
========================================

When you're writing a program, it's often a good idea to put in checks at strategic places for ``impossible'' errors or violations of basic assumptions.  These checks are helpful in debugging problems due to misunderstandings between different parts of the program.

The assert macro, defined in the header file assert.h, provides a convenient way to abort the program while printing a message about where in the program the error was detected.

Once you think your program is debugged, you can disable the error checks performed by the assert macro by recompiling with the macro NDEBUG defined.  This means you don't actually have to change the program source code to disable these checks.

But disabling these consistency checks is undesirable unless they make the program significantly slower.  All else being equal, more error checking is good no matter who is running the program.  A wise user would rather have a program crash, visibly, than have it return nonsense without indicating anything might be wrong.

 -- Macro: void assert (int EXPRESSION)
     Verify the programmer's belief that EXPRESSION should be nonzero at this point in the program.

     If NDEBUG is not defined, assert tests the value of EXPRESSION.  If it is false (zero), assert aborts the program (see Aborting a Program) after printing a message of the form:

          FILE:LINENUM: Assertion `EXPRESSION' failed.

     on the standard error stream stderr (see Standard Streams). The filename and line number are taken from the C preprocessor macros __FILE__ and __LINE__ and specify where the call to assert was written.

     If the preprocessor macro NDEBUG is defined at the point where assert.h is included, the assert macro is defined to do absolutely nothing.

     Warning: Even the argument expression EXPRESSION is not evaluated if NDEBUG is in effect.  So never use assert with arguments that involve side effects.  For example, assert (++i > 0); is a bad idea, because i will not be incremented if NDEBUG is defined.

Usage note: The assert facility is designed for detecting internal inconsistency; it is not suitable for reporting invalid input or improper usage by the user of the program.

The information in the diagnostic messages printed by the assert macro is intended to help you, the programmer, track down the cause of a bug, but is not really useful for telling a user of your program why his or her input was invalid or why a command could not be carried out.  So you can't use assert to print the error messages for these eventualities.

What's more, your program should not abort when given invalid input, as assert would do---it should exit with nonzero status (see Exit Status) after printing its error messages, or perhaps read another command or move on to the next input file.

See Error Messages, for information on printing error messages for problems that do not represent bugs in the program.

Variadic Functions
==================

ANSI C defines a syntax for declaring a function to take a variable number or type of arguments.  (Such functions are referred to as varargs functions or variadic functions.)  However, the language itself provides no mechanism for such functions to access their non-required arguments; instead, you use the variable arguments macros defined in stdarg.h.

This section describes how to declare variadic functions, how to write them, and how to call them properly.

Compatibility Note: Many older C dialects provide a similar, but incompatible, mechanism for defining functions with variable numbers of arguments, using varargs.h.

Why Variadic Functions are Used
-------------------------------

Ordinary C functions take a fixed number of arguments.  When you define a function, you specify the data type for each argument.  Every call to the function should supply the expected number of arguments, with types that can be converted to the specified ones.  Thus, if the function foo is declared with int foo (int, char *); then you must call it with two arguments, a number (any kind will do) and a string pointer.

But some functions perform operations that can meaningfully accept an unlimited number of arguments.

In some cases a function can handle any number of values by operating on all of them as a block.  For example, consider a function that allocates a one-dimensional array with malloc to hold a specified set of values.  This operation makes sense for any number of values, as long as the length of the array corresponds to that number.  Without facilities for variable arguments, you would have to define a separate function for each possible array size.

The library function printf (see Formatted Output) is an example of another class of function where variable arguments are useful.  This function prints its arguments (which can vary in type as well as number) under the control of a format template string.

These are good reasons to define a variadic function which can handle as many arguments as the caller chooses to pass.

Some functions such as open take a fixed set of arguments, but occasionally ignore the last few.  Strict adherence to ANSI C requires these functions to be defined as variadic; in practice, however, the GNU C compiler and most other C compilers let you define such a function to take a fixed set of arguments---the most it can ever use---and then only declare the function as variadic (or not declare its arguments at all!).

How Variadic Functions are Defined and Used
-------------------------------------------

Defining and using a variadic function involves three steps:

  * Define the function as variadic, using an ellipsis (...) in the argument list, and using special macros to access the variable arguments.  See Receiving Arguments.

  * Declare the function as variadic, using a prototype with an ellipsis (...), in all the files which call it. See Variadic Prototypes.

  * Call the function by writing the fixed arguments followed by the additional variable arguments.  See Calling Variadics.

Syntax for Variable Arguments
.............................

A function that accepts a variable number of arguments must be declared with a prototype that says so.   You write the fixed arguments as usual, and then tack on ... to indicate the possibility of additional arguments.  The syntax of ANSI C requires at least one fixed argument before the ....  For example,

     int
     func (const char *a, int b, ...)
     {
       ...
     }

outlines a definition of a function func which returns an int and takes two required arguments, a const char * and an int.  These are followed by any number of anonymous arguments.

Portability note: For some C compilers, the last required argument must not be declared register in the function definition.  Furthermore, this argument's type must be self-promoting: that is, the default promotions must not change its type.  This rules out array and function types, as well as float, char (whether signed or not) and short int (whether signed or not).  This is actually an ANSI C requirement.

Receiving the Argument Values
.............................

Ordinary fixed arguments have individual names, and you can use these names to access their values.  But optional arguments have no names---nothing but ....  How can you access them?

The only way to access them is sequentially, in the order they were written, and you must use special macros from stdarg.h in the following three step process:

 1. You initialize an argument pointer variable of type va_list using va_start.  The argument pointer when initialized points to the first optional argument.

 2. You access the optional arguments by successive calls to va_arg. The first call to va_arg gives you the first optional argument, the next call gives you the second, and so on.

     You can stop at any time if you wish to ignore any remaining optional arguments.  It is perfectly all right for a function to access fewer arguments than were supplied in the call, but you will get garbage values if you try to access too many arguments.

 3. You indicate that you are finished with the argument pointer variable by calling va_end.

     (In practice, with most C compilers, calling va_end does nothing and you do not really need to call it.  This is always true in the GNU C compiler.  But you might as well call va_end just in case your program is someday compiled with a peculiar compiler.)

See Argument Macros, for the full definitions of va_start, va_arg and va_end.

Steps 1 and 3 must be performed in the function that accepts the optional arguments.  However, you can pass the va_list variable as an argument to another function and perform all or part of step 2 there.

You can perform the entire sequence of the three steps multiple times within a single function invocation.  If you want to ignore the optional arguments, you can do these steps zero times.

You can have more than one argument pointer variable if you like.  You can initialize each variable with va_start when you wish, and then you can fetch arguments with each argument pointer as you wish. Each argument pointer variable will sequence through the same set of argument values, but at its own pace.

Portability note: With some compilers, once you pass an argument pointer value to a subroutine, you must not keep using the same argument pointer value after that subroutine returns.  For full portability, you should just pass it to va_end.  This is actually an ANSI C requirement, but most ANSI C compilers work happily regardless.

How Many Arguments Were Supplied
................................

There is no general way for a function to determine the number and type of the optional arguments it was called with.  So whoever designs the function typically designs a convention for the caller to tell it how many arguments it has, and what kind.  It is up to you to define an appropriate calling convention for each variadic function, and write all calls accordingly.

One kind of calling convention is to pass the number of optional arguments as one of the fixed arguments.  This convention works provided all of the optional arguments are of the same type.

A similar alternative is to have one of the required arguments be a bit mask, with a bit for each possible purpose for which an optional argument might be supplied.  You would test the bits in a predefined sequence; if the bit is set, fetch the value of the next argument, otherwise use a default value.

A required argument can be used as a pattern to specify both the number and types of the optional arguments.  The format string argument to printf is one example of this (see Formatted Output Functions).

Another possibility is to pass an ``end marker'' value as the last optional argument.  For example, for a function that manipulates an arbitrary number of pointer arguments, a null pointer might indicate the end of the argument list.  (This assumes that a null pointer isn't otherwise meaningful to the function.)  The execl function works in just this way; see Executing a File.

Calling Variadic Functions
..........................

You don't have to write anything special when you call a variadic function. Just write the arguments (required arguments, followed by optional ones) inside parentheses, separated by commas, as usual.  But you should prepare by declaring the function with a prototype, and you must know how the argument values are converted.

In principle, functions that are defined to be variadic must also be declared to be variadic using a function prototype whenever you call them.  (see Variadic Prototypes, for how.)  This is because some C compilers use a different calling convention to pass the same set of argument values to a function depending on whether that function takes variable arguments or fixed arguments.

In practice, the GNU C compiler always passes a given set of argument types in the same way regardless of whether they are optional or required.  So, as long as the argument types are self-promoting, you can safely omit declaring them.  Usually it is a good idea to declare the argument types for variadic functions, and indeed for all functions. But there are a few functions which it is extremely convenient not to have to declare as variadic---for example, open and printf.

Since the prototype doesn't specify types for optional arguments, in a call to a variadic function the default argument promotions are performed on the optional argument values.  This means the objects of type char or short int (whether signed or not) are promoted to either int or unsigned int, as appropriate; and that objects of type float are promoted to type double.  So, if the caller passes a char as an optional argument, it is promoted to an int, and the function should get it with va_arg (AP, int).

Conversion of the required arguments is controlled by the function prototype in the usual way: the argument expression is converted to the declared argument type as if it were being assigned to a variable of that type.

Argument Access Macros
......................

Here are descriptions of the macros used to retrieve variable arguments. These macros are defined in the header file stdarg.h.

 -- Data Type: va_list
     The type va_list is used for argument pointer variables.

 -- Macro: void va_start (va_list AP, LAST_REQUIRED)
     This macro initializes the argument pointer variable AP to point to the first of the optional arguments of the current function; LAST_REQUIRED must be the last required argument to the function.

     See Old Varargs, for an alternate definition of va_start found in the header file varargs.h.

 -- Macro: TYPE va_arg (va_list AP, TYPE)
     The va_arg macro returns the value of the next optional argument, and modifies the value of AP to point to the subsequent argument. Thus, successive uses of va_arg return successive optional arguments.

     The type of the value returned by va_arg is TYPE as specified in the call.  TYPE must be a self-promoting type (not char or short int or float) that matches the type of the actual argument.

 -- Macro: void va_end (va_list AP)
     This ends the use of AP.  After a va_end call, further va_arg calls with the same AP may not work.  You should invoke va_end before returning from the function in which va_start was invoked with the same AP argument.

     In the GNU C library, va_end does nothing, and you need not ever use it except for reasons of portability.

Example of a Variadic Function
------------------------------

Here is a complete sample function that accepts a variable number of arguments.  The first argument to the function is the count of remaining arguments, which are added up and the result returned.  While trivial, this function is sufficient to illustrate how to use the variable arguments facility.

          [file add.c.texi not included]

Old-Style Variadic Functions
............................

Before ANSI C, programmers used a slightly different facility for writing variadic functions.  The GNU C compiler still supports it; currently, it is more portable than the ANSI C facility, since support for ANSI C is still not universal.  The header file which defines the old-fashioned variadic facility is called varargs.h.

Using varargs.h is almost the same as using stdarg.h. There is no difference in how you call a variadic function; see Calling Variadics.  The only difference is in how you define them.  First of all, you must use old-style non-prototype syntax, like this:

     tree
     build (va_alist)
          va_dcl
     {

Secondly, you must give va_start just one argument, like this:

       va_list p;
       va_start (p);

These are the special macros used for defining old-style variadic functions:

 -- Macro: va_alist
     This macro stands for the argument name list required in a variadic function.

 -- Macro: va_dcl
     This macro declares the implicit argument or arguments for a variadic function.

 -- Macro: void va_start (va_list AP)
     This macro, as defined in varargs.h, initializes the argument pointer variable AP to point to the first argument of the current function.

The other argument macros, va_arg and va_end, are the same in varargs.h as in stdarg.h; see Argument Macros for details.

It does not work to include both varargs.h and stdarg.h in the same compilation; they define va_start in conflicting ways.

Null Pointer Constant
=====================

The null pointer constant is guaranteed not to point to any real object. You can assign it to any pointer variable since it has type void *.  The preferred way to write a null pointer constant is with NULL.

 -- Macro: void * NULL
     This is a null pointer constant.

You can also use 0 or (void *)0 as a null pointer constant, but using NULL is cleaner because it makes the purpose of the constant more evident.

If you use the null pointer constant as a function argument, then for complete portability you should make sure that the function has a prototype declaration.  Otherwise, if the target machine has two different pointer representations, the compiler won't know which representation to use for that argument.  You can avoid the problem by explicitly casting the constant to the proper pointer type, but we recommend instead adding a prototype for the function you are calling.

Important Data Types
====================

The result of subtracting two pointers in C is always an integer, but the precise data type varies from C compiler to C compiler.  Likewise, the data type of the result of sizeof also varies between compilers. ANSI defines standard aliases for these two types, so you can refer to them in a portable fashion.  They are defined in the header file stddef.h.

 -- Data Type: ptrdiff_t
     This is the signed integer type of the result of subtracting two pointers.  For example, with the declaration char *p1, *p2;, the expression p2 - p1 is of type ptrdiff_t.  This will probably be one of the standard signed integer types (short int, int or long int), but might be a nonstandard type that exists only for this purpose.

 -- Data Type: size_t
     This is an unsigned integer type used to represent the sizes of objects. The result of the sizeof operator is of this type, and functions such as malloc (see Unconstrained Allocation) and memcpy (see Copying and Concatenation) accept arguments of this type to specify object sizes.

     Usage Note: size_t is the preferred way to declare any arguments or variables that hold the size of an object.

In the GNU system size_t is equivalent to either unsigned int or unsigned long int.  These types have identical properties on the GNU system, and for most purposes, you can use them interchangeably.  However, they are distinct as data types, which makes a difference in certain contexts.

For example, when you specify the type of a function argument in a function prototype, it makes a difference which one you use.  If the system header files declare malloc with an argument of type size_t and you declare malloc with an argument of type unsigned int, you will get a compilation error if size_t happens to be unsigned long int on your system.  To avoid any possibility of error, when a function argument or value is supposed to have type size_t, never declare its type in any other way.

Compatibility Note: Pre-ANSI C implementations generally used unsigned int for representing object sizes and int for pointer subtraction results.  They did not necessarily define either size_t or ptrdiff_t.  Unix systems did define size_t, in sys/types.h, but the definition was usually a signed type.

Data Type Measurements
======================

Most of the time, if you choose the proper C data type for each object in your program, you need not be concerned with just how it is represented or how many bits it uses.  When you do need such information, the C language itself does not provide a way to get it. The header files limits.h and float.h contain macros which give you this information in full detail.

Computing the Width of an Integer Data Type
-------------------------------------------

The most common reason that a program needs to know how many bits are in an integer type is for using an array of long int as a bit vector. You can access the bit at index N with

     vector[N / LONGBITS] & (1 << (N % LONGBITS))

provided you define LONGBITS as the number of bits in a long int.

There is no operator in the C language that can give you the number of bits in an integer data type.  But you can compute it from the macro CHAR_BIT, defined in the header file limits.h.

CHAR_BIT
     This is the number of bits in a char---eight, on most systems. The value has type int.

     You can compute the number of bits in any data type TYPE like this:

          sizeof (TYPE) * CHAR_BIT

Range of an Integer Type
------------------------

Suppose you need to store an integer value which can range from zero to one million.  Which is the smallest type you can use?  There is no general rule; it depends on the C compiler and target machine.  You can use the MIN and MAX macros in limits.h to determine which type will work.

Each signed integer type has a pair of macros which give the smallest and largest values that it can hold.  Each unsigned integer type has one such macro, for the maximum value; the minimum value is, of course, zero.

The values of these macros are all integer constant expressions.  The MAX and MIN macros for char and short int types have values of type int.  The MAX and MIN macros for the other types have values of the same type described by the macro---thus, ULONG_MAX has type unsigned long int.

SCHAR_MIN

     This is the minimum value that can be represented by a signed char.

SCHAR_MAX
UCHAR_MAX

     These are the maximum values that can be represented by a signed char and unsigned char, respectively.

CHAR_MIN

     This is the minimum value that can be represented by a char. It's equal to SCHAR_MIN if char is signed, or zero otherwise.

CHAR_MAX

     This is the maximum value that can be represented by a char. It's equal to SCHAR_MAX if char is signed, or UCHAR_MAX otherwise.

SHRT_MIN

     This is the minimum value that can be represented by a signed short int.  On most machines that the GNU C library runs on, short integers are 16-bit quantities.

SHRT_MAX
USHRT_MAX

     These are the maximum values that can be represented by a signed short int and unsigned short int, respectively.

INT_MIN

     This is the minimum value that can be represented by a signed int.  On most machines that the GNU C system runs on, an int is a 32-bit quantity.

INT_MAX
UINT_MAX

     These are the maximum values that can be represented by, respectively, the type signed int and the type unsigned int.

LONG_MIN

     This is the minimum value that can be represented by a signed long int.  On most machines that the GNU C system runs on, long integers are 32-bit quantities, the same size as int.

LONG_MAX
ULONG_MAX

     These are the maximum values that can be represented by a signed long int and unsigned long int, respectively.

LONG_LONG_MIN

     This is the minimum value that can be represented by a signed long long int.  On most machines that the GNU C system runs on, long long integers are 64-bit quantities.

LONG_LONG_MAX
ULONG_LONG_MAX

     These are the maximum values that can be represented by a signed long long int and unsigned long long int, respectively.

WCHAR_MAX

     This is the maximum value that can be represented by a wchar_t. See Wide Char Intro.

The header file limits.h also defines some additional constants that parameterize various operating system and file system limits.  These constants are described in System Configuration.

Floating Type Macros
--------------------

The specific representation of floating point numbers varies from machine to machine.  Because floating point numbers are represented internally as approximate quantities, algorithms for manipulating floating point data often need to take account of the precise details of the machine's floating point representation.

Some of the functions in the C library itself need this information; for example, the algorithms for printing and reading floating point numbers (see I/O on Streams) and for calculating trigonometric and irrational functions (see Mathematics) use it to avoid round-off error and loss of accuracy.  User programs that implement numerical analysis techniques also often need this information in order to minimize or compute error bounds.

The header file float.h describes the format used by your machine.

Floating Point Representation Concepts
......................................

This section introduces the terminology for describing floating point representations.

You are probably already familiar with most of these concepts in terms of scientific or exponential notation for floating point numbers.  For example, the number 123456.0 could be expressed in exponential notation as 1.23456e+05, a shorthand notation indicating that the mantissa 1.23456 is multiplied by the base 10 raised to power 5.

More formally, the internal representation of a floating point number can be characterized in terms of the following parameters:

  * The sign is either -1 or 1.

  * The base or radix for exponentiation, an integer greater than 1.  This is a constant for a particular representation.

  * The exponent to which the base is raised.  The upper and lower bounds of the exponent value are constants for a particular representation.

     Sometimes, in the actual bits representing the floating point number, the exponent is biased by adding a constant to it, to make it always be represented as an unsigned quantity.  This is only important if you have some reason to pick apart the bit fields making up the floating point number by hand, which is something for which the GNU library provides no support.  So this is ignored in the discussion that follows.

  * The mantissa or significand, an unsigned integer which is a part of each floating point number.

  * The precision of the mantissa.  If the base of the representation is B, then the precision is the number of base-B digits in the mantissa.  This is a constant for a particular representation.

     Many floating point representations have an implicit hidden bit in the mantissa.  This is a bit which is present virtually in the mantissa, but not stored in memory because its value is always 1 in a normalized number.  The precision figure (see above) includes any hidden bits.

     Again, the GNU library provides no facilities for dealing with such low-level aspects of the representation.

The mantissa of a floating point number actually represents an implicit fraction whose denominator is the base raised to the power of the precision.  Since the largest representable mantissa is one less than this denominator, the value of the fraction is always strictly less than 1.  The mathematical value of a floating point number is then the product of this fraction, the sign, and the base raised to the exponent.

We say that the floating point number is normalized if the fraction is at least 1/B, where B is the base.  In other words, the mantissa would be too large to fit if it were multiplied by the base.  Non-normalized numbers are sometimes called denormal; they contain less precision than the representation normally can hold.

If the number is not normalized, then you can subtract 1 from the exponent while multiplying the mantissa by the base, and get another floating point number with the same value.  Normalization consists of doing this repeatedly until the number is normalized.  Two distinct normalized floating point numbers cannot be equal in value.

(There is an exception to this rule: if the mantissa is zero, it is considered normalized.  Another exception happens on certain machines where the exponent is as small as the representation can hold.  Then it is impossible to subtract 1 from the exponent, so a number may be normalized even if its fraction is less than 1/B.)

Floating Point Parameters
.........................

These macro definitions can be accessed by including the header file float.h in your program.

Macro names starting with FLT_ refer to the float type, while names beginning with DBL_ refer to the double type and names beginning with LDBL_ refer to the long double type.  (Currently GCC does not support long double as a distinct data type, so the values for the LDBL_ constants are equal to the corresponding constants for the double type.)

Of these macros, only FLT_RADIX is guaranteed to be a constant expression.  The other macros listed here cannot be reliably used in places that require constant expressions, such as #if preprocessing directives or in the dimensions of static arrays.

Although the ANSI C standard specifies minimum and maximum values for most of these parameters, the GNU C implementation uses whatever values describe the floating point representation of the target machine.  So in principle GNU C actually satisfies the ANSI C requirements only if the target machine is suitable.  In practice, all the machines currently supported are suitable.

FLT_ROUNDS
     This value characterizes the rounding mode for floating point addition. The following values indicate standard rounding modes:

     -1
          The mode is indeterminable.

     0
          Rounding is towards zero.

     1
          Rounding is to the nearest number.

     2
          Rounding is towards positive infinity.

     3
          Rounding is towards negative infinity.

     Any other value represents a machine-dependent nonstandard rounding mode.

     On most machines, the value is 1, in accordance with the IEEE standard for floating point.

     Here is a table showing how certain values round for each possible value of FLT_ROUNDS, if the other aspects of the representation match the IEEE single-precision standard.

                           0       1              2              3
           1.00000003     1.0     1.0            1.00000012     1.0
           1.00000007     1.0     1.00000012     1.00000012     1.0
          -1.00000003    -1.0    -1.0           -1.0           -1.00000012
          -1.00000007    -1.0    -1.00000012    -1.0           -1.00000012

FLT_RADIX
     This is the value of the base, or radix, of exponent representation. This is guaranteed to be a constant expression, unlike the other macros described in this section.  The value is 2 on all machines we know of except the IBM 360 and derivatives.

FLT_MANT_DIG
     This is the number of base-FLT_RADIX digits in the floating point mantissa for the float data type.  The following expression yields 1.0 (even though mathematically it should not) due to the limited number of mantissa digits:

          float radix = FLT_RADIX;

          1.0f + 1.0f / radix / radix / ... / radix

     where radix appears FLT_MANT_DIG times.

DBL_MANT_DIG
LDBL_MANT_DIG
     This is the number of base-FLT_RADIX digits in the floating point mantissa for the data types double and long double, respectively.

FLT_DIG

     This is the number of decimal digits of precision for the float data type.  Technically, if P and B are the precision and base (respectively) for the representation, then the decimal precision Q is the maximum number of decimal digits such that any floating point number with Q base 10 digits can be rounded to a floating point number with P base B digits and back again, without change to the Q decimal digits.

     The value of this macro is supposed to be at least 6, to satisfy ANSI C.

DBL_DIG
LDBL_DIG

     These are similar to FLT_DIG, but for the data types double and long double, respectively.  The values of these macros are supposed to be at least 10.

FLT_MIN_EXP
     This is the smallest possible exponent value for type float. More precisely, is the minimum negative integer such that the value FLT_RADIX raised to this power minus 1 can be represented as a normalized floating point number of type float.

DBL_MIN_EXP
LDBL_MIN_EXP

     These are similar to FLT_MIN_EXP, but for the data types double and long double, respectively.

FLT_MIN_10_EXP
     This is the minimum negative integer such that 10 raised to this power minus 1 can be represented as a normalized floating point number of type float.  This is supposed to be -37 or even less.

DBL_MIN_10_EXP
LDBL_MIN_10_EXP
     These are similar to FLT_MIN_10_EXP, but for the data types double and long double, respectively.

FLT_MAX_EXP
     This is the largest possible exponent value for type float.  More precisely, this is the maximum positive integer such that value FLT_RADIX raised to this power minus 1 can be represented as a floating point number of type float.

DBL_MAX_EXP
LDBL_MAX_EXP
     These are similar to FLT_MAX_EXP, but for the data types double and long double, respectively.

FLT_MAX_10_EXP
     This is the maximum positive integer such that 10 raised to this power minus 1 can be represented as a normalized floating point number of type float.  This is supposed to be at least 37.

DBL_MAX_10_EXP
LDBL_MAX_10_EXP
     These are similar to FLT_MAX_10_EXP, but for the data types double and long double, respectively.

FLT_MAX

     The value of this macro is the maximum number representable in type float.  It is supposed to be at least 1E+37.  The value has type float.

     The smallest representable number is - FLT_MAX.

DBL_MAX
LDBL_MAX

     These are similar to FLT_MAX, but for the data types double and long double, respectively.  The type of the macro's value is the same as the type it describes.

FLT_MIN

     The value of this macro is the minimum normalized positive floating point number that is representable in type float.  It is supposed to be no more than 1E-37.

DBL_MIN
LDBL_MIN

     These are similar to FLT_MIN, but for the data types double and long double, respectively.  The type of the macro's value is the same as the type it describes.

FLT_EPSILON

     This is the minimum positive floating point number of type float such that 1.0 + FLT_EPSILON != 1.0 is true.  It's supposed to be no greater than 1E-5.

DBL_EPSILON
LDBL_EPSILON

     These are similar to FLT_EPSILON, but for the data types double and long double, respectively.  The type of the macro's value is the same as the type it describes.  The values are not supposed to be greater than 1E-9.

IEEE Floating Point
...................

Here is an example showing how the floating type measurements come out for the most common floating point representation, specified by the IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE Std 754-1985).  Nearly all computers designed since the 1980s use this format.

The IEEE single-precision float representation uses a base of 2.  There is a sign bit, a mantissa with 23 bits plus one hidden bit (so the total precision is 24 base-2 digits), and an 8-bit exponent that can represent values in the range -125 to 128, inclusive.

So, for an implementation that uses this representation for the float data type, appropriate values for the corresponding parameters are:

     FLT_RADIX                             2
     FLT_MANT_DIG                         24
     FLT_DIG                               6
     FLT_MIN_EXP                        -125
     FLT_MIN_10_EXP                      -37
     FLT_MAX_EXP                         128
     FLT_MAX_10_EXP                      +38
     FLT_MIN                 1.17549435E-38F
     FLT_MAX                 3.40282347E+38F
     FLT_EPSILON             1.19209290E-07F

Here are the values for the double data type:

     DBL_MANT_DIG                         53
     DBL_DIG                              15
     DBL_MIN_EXP                       -1021
     DBL_MIN_10_EXP                     -307
     DBL_MAX_EXP                        1024
     DBL_MAX_10_EXP                      308
     DBL_MAX         1.7976931348623157E+308
     DBL_MIN         2.2250738585072014E-308
     DBL_EPSILON     2.2204460492503131E-016

Structure Field Offset Measurement
----------------------------------

You can use offsetof to measure the location within a structure type of a particular structure member.

 -- Macro: size_t offsetof (TYPE, MEMBER)
     This expands to a integer constant expression that is the offset of the structure member named MEMBER in a the structure type TYPE. For example, offsetof (struct s, elem) is the offset, in bytes, of the member elem in a struct s.

     This macro won't work if MEMBER is a bit field; you get an error from the C compiler in that case.