|
HTML rendering created 2024-06-26 by Michael Kerrisk, author of The Linux Programming Interface. For details of in-depth Linux/UNIX system programming training courses that I teach, look here. Hosting by jambit GmbH. |
|
|
PROLOG | NAME | SYNOPSIS | DESCRIPTION | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT |
|
|
|
float.h(0P) POSIX Programmer's Manual float.h(0P)
This manual page is part of the POSIX Programmer's Manual. The
Linux implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.
float.h — floating types
#include <float.h>
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.1‐2017 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 kp=Σ1 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:
-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 <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 decimal 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.
None.
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.
None.
complex.h(0p), math.h(0p), stdio.h(0p), stdlib.h(0p), wchar.h(0p)
Portions of this text are reprinted and reproduced in electronic
form from IEEE Std 1003.1-2017, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The
Open Group Base Specifications Issue 7, 2018 Edition, Copyright
(C) 2018 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 .
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 .
IEEE/The Open Group 2017 float.h(0P)
Pages that refer to this page: math.h(0p), double_t(3type), ilogb(3p), logb(3p), strtod(3p), wcstod(3p)
|
HTML rendering created 2024-06-26 by Michael Kerrisk, author of The Linux Programming Interface. For details of in-depth Linux/UNIX system programming training courses that I teach, look here. Hosting by jambit GmbH. |
|