float.h

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 _

<float.h>(P) <float.h>(P)

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 float-
ing-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 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 direc-
tives; 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 evalu-
ated 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 dou-
ble operations and constants to the range and precision of the
long double type.

2 Evaluate all operations and constants to the range and preci-
sion of the long double type.

All other negative values for FLT_EVAL_METHOD characterize implementa-
tion-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 deci-
mal 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.