<float.h>

The Open Group Base Specifications Issue 6
IEEE Std 1003.1-2001
Copyright © 2001 The IEEE and The Open Group, All Rights reserved.

NAME

float.h - floating types

SYNOPSIS

#include <float.h>

DESCRIPTION

^[CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std 1003.1-2001 defers to the ISO C standard.

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.

The following parameters are used to define the model for each floating-point type:

s

Sign (±1).

b

Base or radix of exponent representation (an integer >1).

e

Exponent (an integer between a minimum e_min and a maximum e_max).

p

Precision (the number of base-b digits in the significand).

f_k

Non-negative integers less than b (the significand digits).

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

In addition to normalized floating-point numbers (f₁>0 if x!=0), floating types may be able to contain other kinds of floating-point numbers, such as subnormal floating-point numbers ( x!=0, e= e_min, f₁=0) and unnormalized floating-point numbers ( x!=0, e> e_min, f₁=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.

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. 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:

-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 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:

-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 defined as 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.

DECIMAL_DIG

10

Number of decimal digits, 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.

FLT_DIG

6

DBL_DIG

10

LDBL_DIG

10

Minimum negative integer such that FLT_RADIX raised to that power minus 1 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.

FLT_MIN_10_EXP

-37

DBL_MIN_10_EXP

-37

LDBL_MIN_10_EXP

-37

Maximum integer such that FLT_RADIX raised to that power minus 1 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.

FLT_MAX_10_EXP

+37

DBL_MAX_10_EXP

+37

LDBL_MAX_10_EXP

+37

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

Maximum representable finite floating-point number.

FLT_MAX

1E+37

DBL_MAX

1E+37

LDBL_MAX

1E+37

The values given in the following list shall be defined as 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