<float.h>(P)						     POSIX Programmer's Manual						      <float.h>(P)

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  num-
       bers,  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 float-
       ing-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 direc-
       tives; 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 evalu-
       ated  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 oper-
	      ations 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 Technol-
       ogy -- 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 .

IEEE
/The Open Group						       2003							      <float.h>(P)