float.h man page
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.
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 floatingpoint numbers and values that provide information about an implementation's floatingpoint arithmetic.
The following parameters are used to define the model for each floatingpoint type:
 s
Sign (±1).
 b
Base or radix of exponent representation (an integer >1).
 e
Exponent (an integer between a minimum $e\_\text{min}$ and a maximum $e\_\text{max}$).
 p
Precision (the number of baseb digits in the significand).
 $f\_k$
Nonnegative integers less than b (the significand digits).
A floatingpoint number x is defined by the following model:
$x\text{}=\text{}sb\text{^}e\text{}\text{}\underset{k=1}{\overset{p}{\Sigma}}\text{}\text{}f\_k\text{}\text{}b\text{^}\text{}k,\text{}e\_\text{min}\text{}\text{}\le \text{}e\text{}\le \text{}e\_\text{max}\text{}$
In addition to normalized floatingpoint numbers ($f\_1$>0 if x≠0), floating types may be able to contain other kinds of floatingpoint numbers, such as subnormal floatingpoint numbers (x≠0, e=$e\_\text{min}$, $f\_1$=0) and unnormalized floatingpoint numbers (x≠0, e>$e\_\text{min}$, $f\_1$=0), and values that are not floatingpoint numbers, such as infinities and NaNs. A NaN is an encoding signifying NotaNumber. A quiet NaN propagates through almost every arithmetic operation without raising a floatingpoint exception; a signaling NaN generally raises a floatingpoint exception when occurring as an arithmetic operand.
An implementation may give zero and nonnumeric 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 floatingpoint operations ('+', '', '*', '/') and of the functions in <math.h> and <complex.h> that return floatingpoint results is implementationdefined, as is the accuracy of the conversion between floatingpoint 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 floatingpoint types. The floatingpoint model representation is provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
The rounding mode for floatingpoint addition is characterized by the implementationdefined 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 implementationdefined 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 implementationdefined 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 implementationdefined behavior.
The <float.h> header shall define the following values as constant expressions with implementationdefined 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 baseFLT_RADIX digits in the floatingpoint significand, p.
FLT_MANT_DIG
DBL_MANT_DIG
LDBL_MANT_DIG
 *

Number of decimal digits, n, such that any floatingpoint number in the widest supported floating type with $p\_\text{max}$ radix b digits can be rounded to a floatingpoint number with n decimal digits and back again without change to the value.
$\begin{array}{l}p\_\text{max}\text{}\text{}log\_10\text{}\text{}b\\ ceiling\text{}1\text{}+\text{}p\_\text{max}\text{}\text{}log\_10\text{}\text{}bceiling\end{array}\text{}\text{}\begin{array}{l}\text{if}\text{}b\text{}is\text{}a\text{}power\text{}of\text{}10\\ otherwise\end{array}$
 DECIMAL_DIG
10
 *

Number of decimal digits, q, such that any floatingpoint number with q decimal digits can be rounded into a floatingpoint number with p radix b digits and back again without change to the q decimal digits.
$\begin{array}{l}p\text{}log\_10\text{}\text{}b\\ floor\text{}(p\text{}\text{}1)\text{}log\_10\text{}\text{}b\text{}floor\end{array}\text{}\text{}\begin{array}{l}\text{if}\text{}b\text{}is\text{}a\text{}power\text{}of\text{}10\\ otherwise\end{array}$
 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 floatingpoint number, $e\_\text{min}$.
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 floatingpoint numbers.
$ceiling\text{}log\_10\text{}\text{}b\text{^}\text{}e\_\text{min}\text{}\text{}\text{^}\text{}1\text{}\text{}ceiling$
 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 floatingpoint number, $e\_\text{max}$.
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 floatingpoint numbers.
$floor\text{}log\_10\text{}\left(\right(1\text{}\text{}b\text{^}\text{}p\left)\text{}b\text{^}e\text{}\_\text{max}\text{}\text{}\right)\text{}floor$
 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 implementationdefined values that are greater than or equal to those shown:
 *

Maximum representable finite floatingpoint number.
$(1\text{}\text{}b\text{^}\text{}p\text{})\text{}b\text{^}e\text{}\_\text{max}\text{}$
 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 implementationdefined (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 floatingpoint type, $b\text{^}\text{}1\text{}\text{}p$.
 FLT_EPSILON
1E5
 DBL_EPSILON
1E9
 LDBL_EPSILON
1E9
 *

Minimum normalized positive floatingpoint number, $b\text{^}\text{}e\_\text{min}\text{}\text{}\text{^}\text{}1$.
 FLT_MIN
1E37
 DBL_MIN
1E37
 LDBL_MIN
1E37
The following sections are informative.
Application Usage
None.
Rationale
All known hardware floatingpoint formats satisfy the property that the exponent range is larger than the number of mantissa digits. The ISO C standard permits a floatingpoint 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 floatingpoint format, and it introduces boundary cases that portable programs should not have to be concerned with (for example, a nonintegral 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.12008 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.kernel.org/doc/manpages/reporting_bugs.html .