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NAME

       float.h - floating types

SYNOPSIS

       #include <float.h>

DESCRIPTION

       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:

       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.

       The accuracy of the floating-point operations ( ’+’ , ’-’ , ’*’ , ’/’ )
       and  of  the  library functions in <math.h> and <complex.h> that return
       floating-point results is  implementation-defined.  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  values  given  in  the following list shall be defined 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.

       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.

       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.

       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

        * Maximum integer such that 10 raised to that power is in the range of
          representable finite floating-point numbers.

       FLT_MAX_10_EXP
              +37

       DBL_MAX_10_EXP
              +37

       LDBL_MAX_10_EXP
              +37

       The  values  given  in  the following list shall be defined as constant
       expressions with implementation-defined values that are greater than or
       equal to those shown:

        * Maximum representable finite floating-point number.

       FLT_MAX
              1E+37

       DBL_MAX
              1E+37

       LDBL_MAX
              1E+37

       The  values  given  in  the following list shall be defined 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.

       FLT_MIN
              1E-37

       DBL_MIN
              1E-37

       LDBL_MIN
              1E-37

       The following sections are informative.

APPLICATION USAGE

       None.

RATIONALE

       None.

FUTURE DIRECTIONS

       None.

SEE ALSO

       <complex.h> , <math.h>

COPYRIGHT

       Portions of this text are reprinted and reproduced in  electronic  form
       from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
       Specifications  Issue  6,  Copyright  (C) 2001-2003 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 .