
<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 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 arith
metic 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 implementa
tiondefined. The implementation may state that the accuracy is unknown.
All integer values in the <float.h> header, except FLT_ROUNDS, shall be constant expres
sions suitable for use in #if preprocessing directives; all floating values shall be con
stant 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 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 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 preci
sion 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 behav
ior.
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 sup
ported floating type with p_max radix b digits can be rounded to a floatingpoint num
ber 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 with
out 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 normal
ized 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 normal
ized 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 orig
inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 <float.h>(P) 
