float.h(0P) POSIX Programmer's Manual float.h(0P)PROLOG
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implementation of this interface may differ (consult the corresponding
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NAMEfloat.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 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:
x = sb^e kΣ1 f_k b^ −k, e_min ≤ e ≤ e_max
In addition to normalized floating-point numbers (f_1>0 if x≠0), float‐
ing 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 infini‐
ties 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 representa‐
tions 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 DECI‐
MAL_DIG, FLT_EVAL_METHOD, FLT_RADIX, and FLT_ROUNDS have separate names
for all three floating-point types. The floating-point model represen‐
tation 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 pre‐
cision 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 implementa‐
tion-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.
* 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.
p_max log_10 b if b is a power of 10
⎡ 1 + p_max log_10 b⎤ otherwise
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.
p log_10 b if b is a power of 10
⎣ (p − 1) log_10 b ⎦ otherwise
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.
⎡ log_10 b^ e_min ^ −1 ⎤
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
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.
* Maximum integer such that 10 raised to that power is in the range
of representable finite floating-point numbers.
⎣ log_10 ((1 − b^ −p) b^e _max ) ⎦
FLT_MAX_10_EXP
+37
DBL_MAX_10_EXP
+37
LDBL_MAX_10_EXP
+37
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:
* Maximum representable finite floating-point number.
(1 − b^ −p) b^e _max
FLT_MAX 1E+37
DBL_MAX 1E+37
LDBL_MAX 1E+37
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 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 ^ −1.
FLT_MIN 1E−37
DBL_MIN 1E−37
LDBL_MIN 1E−37
The following sections are informative.
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; how‐
ever, 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-inte‐
gral 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.
SEE ALSO
<complex.h>, <math.h>, <stdio.h>, <stdlib.h>, <wchar.h>
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 Electri‐
cal 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 .
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.ker‐
nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group 2013 float.h(0P)
