float.h(3)                 POSIX Programmer's Manual                float.h(3)



PROLOG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.

NAME
       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.1-2017
       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  <S_ki_p=g1ma> _f__k  b^ -_k, _e_min  <= _e <= _e_max

       In addition to normalized floating-point numbers (f1>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,
       f1=0) and unnormalized floating-point numbers (_x!=0, _e>_e_min, f1=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  log10  _b           if _b is _a power of 10
           |~ 1 + _p_max  log10  _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 log10  _b              if _b is _a power of 10
           |_ (_p - 1) log10  _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.

           |~ log10  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.

           |_ log10 ((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;
       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 1003.1-2017, 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(3)
