float.h(0P) | POSIX Programmer's Manual | float.h(0P) |
PROLOG
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.NAME
float.h — floating typesSYNOPSIS
#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 $e\_\mathrm{min}$ and a maximum $e\_\mathrm{max}$ ).
- p
- Precision (the number of base−b digits in the significand).
- $f\_k$ " 6 Non-negative integers less than b (the significand digits).
- −1
- Indeterminable.
- 0
- Toward zero.
- 1
- To nearest.
- 2
- Toward positive infinity.
- 3
- Toward negative infinity.
- −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.
- *
- 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 $p\_\mathrm{max}$ radix b digits can be rounded to a floating-point number with n decimal digits and back again without change to the value.
$\begin{array}{c}p\_\mathrm{max}\mathrm{log}\_10b\\ \u23081+p\_\mathrm{max}\mathrm{log}\_10b\u2309\end{array}\begin{array}{c}\mathrm{if}b\mathrm{is}a\mathrm{power}\mathrm{of}10\\ \mathrm{otherwise}\end{array}$
- 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.
$\begin{array}{c}p\mathrm{log}\_10b\\ \u230a(p-1)\mathrm{log}\_10b\u230b\end{array}\begin{array}{c}\mathrm{if}b\mathrm{is}a\mathrm{power}\mathrm{of}10\\ \mathrm{otherwise}\end{array}$
- 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, $e\_\mathrm{min}$ .
- 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.
$\u2308\mathrm{log}\_10b^e\_\mathrm{min}^-1\u2309$
- 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, $e\_\mathrm{max}$ .
- 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 floating-point numbers.
$\u230a\mathrm{log}\_10\left(\right(1-b^-p)b^e\_\mathrm{max})\u230b$
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:
- FLT_MAX_10_EXP
- +37
- DBL_MAX_10_EXP
- +37
- LDBL_MAX_10_EXP
- +37
- *
- Maximum representable finite floating-point number.
$(1-b^-p)b^e\_\mathrm{max}$
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:
- FLT_MAX
- 1E+37
- DBL_MAX
- 1E+37
- LDBL_MAX
- 1E+37
- *
- 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, $b^e\_\mathrm{min}^-1$ .
- FLT_MIN
- 1E−37
- DBL_MIN
- 1E−37
- LDBL_MIN
- 1E−37
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.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 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 .2013 | IEEE/The Open Group |