#include <float.h>
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:
A floating-point number x is defined by the following model:
x " " = " " sb"^" e" " " " sum from k=1 to p^ " " f_ k" " " " b"^" " "-k ,
" " e_ min" " " " <= " " e " " <= " " e_ max" "
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.
An implementation may give zero and non-numeric values, such as infinities and NaNs, a sign, or may leave them unsigned. Wherever such values are unsigned, any requirement in POSIX.1-2008 to retrieve the sign shall produce an unspecified sign and any requirement to set the sign shall be ignored.
The accuracy of the floating-point operations ('+', '-', '*', '/') and of the functions in <math.h> and <complex.h> that return floating-point results is implementation-defined, as is the accuracy of the conversion between floating-point internal representations and string representations performed by the functions in <stdio.h>, <stdlib.h>, and <wchar.h>. 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:
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:
All other negative values for FLT_EVAL_METHOD characterize implementation-defined behavior.
The <float.h> header shall define the following values as constant expressions with implementation-defined values that are greater or equal in magnitude (absolute value) to those shown, with the same sign.
lpile { p_ max" " " " log_ 10" " " " b above
left ceiling " " 1 " " + " " p_ max" " " " log_ 10" " " " b right ceiling }
" " " " lpile {if " " b " " is " " a " " power " " of " " 10 above otherwise}
lpile { p " " log_ 10" " " " b above
left floor " " (p " " - " " 1) " " log_ 10" " " " b " " right floor }
" " " " lpile {if " " b " " is " " a " " power " " of " " 10 above otherwise}
left ceiling " " log_ 10" " " " b"^" " "{ e_ min" " " " "^" " "-1 } ^ " " right ceiling
Additionally, FLT_MAX_EXP shall be at least as large as FLT_MANT_DIG, DBL_MAX_EXP shall be at least as large as DBL_MANT_DIG, and LDBL_MAX_EXP shall be at least as large as LDBL_MANT_DIG; which has the effect that FLT_MAX, DBL_MAX, and LDBL_MAX are integral.
left floor " " log_ 10" " ( ( 1 " " - " " b"^" " "-p ) " "
b"^" e" "_ max" "^ ) " " right floor
The <float.h> header shall define the following values as constant expressions with implementation-defined values that are greater than or equal to those shown:
(1 " " - " " b"^" " "-p^) " " b"^" e" "_ max" "
The <float.h> header shall define the following values as constant expressions with implementation-defined (positive) values that are less than or equal to those shown:
The following sections are informative.
Any typographical or formatting errors that appear in this page are most likely to have been introduced during the conversion of the source files to man page format. To report such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .