Section: POSIX Programmer's Manual (0P)
Updated: 2003
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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 floatingpoint numbers
and values that provide information about an implementation's floatingpoint
arithmetic.
The following parameters are used to define the model for each floatingpoint
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 baseb digits in the significand).
 f_k

Nonnegative integers less than b (the significand digits).
A floatingpoint number x is defined by the following model:
In addition to normalized floatingpoint numbers (f_1>0 if x!=0),
floating types may be able to contain other
kinds of floatingpoint numbers, such as subnormal floatingpoint
numbers ( x!=0, e= e_min, f_1=0) and
unnormalized floatingpoint numbers ( x!=0, e> e_min,
f_1=0), and values that are not floatingpoint
numbers, such as infinities and NaNs. A NaN is an encoding signifying
NotaNumber. A quiet NaN propagates through
almost every arithmetic operation without raising a floatingpoint
exception; a signaling NaN generally raises a
floatingpoint exception when occurring as an arithmetic operand.
The accuracy of the floatingpoint operations ( '+', '',
'*', '/' ) and of the library
functions in <math.h> and <complex.h> that return floatingpoint
results is implementationdefined. 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 floatingpoint
types. The floatingpoint model representation is
provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
The rounding mode for floatingpoint addition is characterized by
the implementationdefined 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 implementationdefined
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 implementationdefined 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 implementationdefined
behavior.
The values given in the following list shall be defined as constant
expressions with implementationdefined 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 baseFLT_RADIX digits in the floatingpoint significand,
p.
 FLT_MANT_DIG

 DBL_MANT_DIG

 LDBL_MANT_DIG

 *

Number of decimal digits, n, such that any floatingpoint number
in the widest supported floating type with p_max
radix b digits can be rounded to a floatingpoint number with
n decimal digits and back again without change to the
value.
 DECIMAL_DIG


10
 *

Number of decimal digits, q, such that any floatingpoint number
with q decimal digits can be rounded into a
floatingpoint 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 floatingpoint 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 floatingpoint 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 floatingpoint 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 floatingpoint 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 implementationdefined values that are
greater than or equal to those shown:
 *

Maximum representable finite floatingpoint 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 implementationdefined (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 floatingpoint type, b**1p.
 FLT_EPSILON


1E5
 DBL_EPSILON


1E9
 LDBL_EPSILON


1E9
 *

Minimum normalized positive floatingpoint number, b**e_min.
 FLT_MIN


1E37
 DBL_MIN


1E37
 LDBL_MIN


1E37
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) 20012003 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 .