float.h (0p)  Linux Man Pages
float.h: floating types
NAME
float.h  floating types
SYNOPSIS
DESCRIPTION
The characteristics of floating types are defined in terms of a model that describes a representation of floatingpoint numbers and values that provide information about an implementation's floatingpoint arithmetic.
The following parameters are used to define the model for each floatingpoint 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 baseb digits in the significand).
 f_k

Nonnegative integers less than b (the significand digits).
A floatingpoint number x is defined by the following model:
In addition to normalized floatingpoint numbers (f_1>0 if x!=0), floating types may be able to contain other kinds of floatingpoint numbers, such as subnormal floatingpoint numbers ( x!=0, e= e_min, f_1=0) and unnormalized floatingpoint numbers ( x!=0, e> e_min, f_1=0), and values that are not floatingpoint numbers, such as infinities and NaNs. A NaN is an encoding signifying NotaNumber. A quiet NaN propagates through almost every arithmetic operation without raising a floatingpoint exception; a signaling NaN generally raises a floatingpoint exception when occurring as an arithmetic operand.
The accuracy of the floatingpoint operations ( '+', '', '*', '/' ) and of the library functions in <math.h> and <complex.h> that return floatingpoint results is implementationdefined. 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 floatingpoint types. The floatingpoint model representation is provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
The rounding mode for floatingpoint addition is characterized by the implementationdefined 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 implementationdefined 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 implementationdefined 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 implementationdefined behavior.
The values given in the following list shall be defined as constant expressions with implementationdefined 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 baseFLT_RADIX digits in the floatingpoint significand, p.
 FLT_MANT_DIG
 DBL_MANT_DIG
 LDBL_MANT_DIG

 *
 Number of decimal digits, n, such that any floatingpoint number in the widest supported floating type with p_max radix b digits can be rounded to a floatingpoint number with n decimal digits and back again without change to the value.
 DECIMAL_DIG

 10
 *
 Number of decimal digits, q, such that any floatingpoint number with q decimal digits can be rounded into a floatingpoint 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 floatingpoint 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 floatingpoint 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 floatingpoint 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 floatingpoint 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 implementationdefined values that are greater than or equal to those shown:
 *
 Maximum representable finite floatingpoint 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 implementationdefined (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 floatingpoint type, b**1p.
 FLT_EPSILON

 1E5
 DBL_EPSILON

 1E9
 LDBL_EPSILON

 1E9
 *
 Minimum normalized positive floatingpoint number, b**e_min.
 FLT_MIN

 1E37
 DBL_MIN

 1E37
 LDBL_MIN

 1E37
The following sections are informative.
APPLICATION USAGE
RATIONALE
FUTURE DIRECTIONS
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) 20012003 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 .