float.h(0p) — Linux manual page

PROLOG | NAME | SYNOPSIS | DESCRIPTION | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT

float.h(0P)             POSIX Programmer's Manual            float.h(0P)

PROLOG         top

       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         top

       float.h — floating types

SYNOPSIS         top

       #include <float.h>

DESCRIPTION         top

       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  ≤ ee_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.

APPLICATION USAGE         top

       None.

RATIONALE         top

       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         top

       None.

SEE ALSO         top

       complex.h(0p), math.h(0p), stdio.h(0p), stdlib.h(0p), wchar.h(0p)

COPYRIGHT         top

       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)

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