float (0p) - Linux Manuals
float: floating types
PROLOG
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float.h --- floating types
SYNOPSIS
#include <float.h>
DESCRIPTION
The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2008 defers to the ISO C standard.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:
x " " = " " sb"^" e" " " " sum from k=1 to p^ " " f_ k" " " " b"^" " "-k ,
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 { p " " log_ 10" " " " b above
left floor " " (p " " - " " 1) " " log_ 10" " " " b " " right floor }
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 ) " "
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 .
APPLICATION USAGE
None.
RATIONALE
All known hardware floating-point formats satisfy the property that the
exponent range is larger than the number of mantissa digits. The ISO C standard
permits a floating-point format where this property is not true, such that
the largest finite value would not be integral; however, it is unlikely
that there will ever be hardware support for such a floating-point format,
and it introduces boundary cases that portable programs should not have
to be concerned with (for example, a non-integral DBL_MAX means that
ceil()
would have to worry about overflow). Therefore, this standard imposes
an additional requirement that the largest representable finite value
is integral.
FUTURE DIRECTIONS
None.
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group.
(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) 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.unix.org/online.html .