phpMan

/* Void Main's man pages */

{ phpMan } else { main(); }

<float.h>(0P) POSIX Programmer's Manual <float.h>(0P)

NAME
float.h - floating types

SYNOPSIS
#include <float.h>

DESCRIPTION
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 (f_1>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, f_1=0) and unnormalized floating-point
numbers ( x!=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 op-
erand.

The accuracy of the floating-point operations ( '+', '-', '*', '/' ) and of the library functions in <math.h> and <com-
plex.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 pre-
processing 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 evalu-
ation 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.

FLT_MIN
1E-37

DBL_MIN
1E-37

LDBL_MIN
1E-37

The following sections are informative.

APPLICATION USAGE
None.

RATIONALE
None.

FUTURE DIRECTIONS
None.