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.

       delim $$

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.1‐2008 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 $e_ min$ 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" "  " "  sum from k=1 to p^  " "  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.

           lpile { p_ max" "  " "  log_ 10" "  " "  b above left ceiling  "
           "  1  " "  +  " "  p_ max" "  " "  log_ 10" "  " "  b right
           ceiling }
            " "   " "  lpile {if " " b " " is " " a " " power " " of " " 10
           above 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.

           lpile { p  " "  log_ 10" "  " "  b above left floor  " "  (p  " "
           -  " "  1)  " "  log_ 10" "  " "  b  " "  right floor }
            " "   " "  lpile {if " " b " " is " " a " " power " " of " " 10
           above 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.

           left ceiling  " "  log_ 10" "  " "  b"^" " "{ e_ min" "  " " "^"
           " "-1 } ^  " "  right 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 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.

           left floor  " "  log_ 10" " ( ( 1  " "  -  " "  b"^" " "-p )  " "
               b"^" e" "_ max" "^ )  " "  right 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 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, 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 .

       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                 2013                         float.h(0P)

Pages that refer to this page: math.h(0p)ilogb(3p)logb(3p)strtod(3p)wcstod(3p)