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       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

       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 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

       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 .

       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 .