float.h(1) 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 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.
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.

COPYRIGHT

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

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