.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved 
.TH "<float.h>" P 2003 POSIX
.\" <float.h> 
.SH NAME
float.h \- floating types
.SH SYNOPSIS
.LP
\fB#include <float.h>\fP
.SH DESCRIPTION
.LP
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.
.LP
The following parameters are used to define the model for each floating-point
type:
.TP 7
\fIs\fP
Sign (\(+-1).
.TP 7
\fIb\fP
Base or radix of exponent representation (an integer >1).
.TP 7
\fIe\fP
Exponent (an integer between a minimum \fIe\fP_min and a maximum \fIe\fP_max).
.TP 7
\fIp\fP
Precision (the number of base-\fIb\fP digits in the significand).
.TP 7
\fIf\fP_k
Non-negative integers less than \fIb\fP (the significand digits).
.sp
.LP
A floating-point number \fIx\fP is defined by the following model:
.LP
.LP
In addition to normalized floating-point numbers (\fIf\fP_1>0 if \fIx\fP!=0),
floating types may be able to contain other
kinds of floating-point numbers, such as subnormal floating-point
numbers ( \fIx\fP!=0, \fIe\fP= \fIe\fP_min, \fIf\fP_1=0) and
unnormalized floating-point numbers ( \fIx\fP!=0, \fIe\fP> \fIe\fP_min,
\fIf\fP_1=0), and values that are not floating-point
numbers, such as infinities and NaNs. A \fINaN\fP is an encoding signifying
Not-a-Number. A \fIquiet NaN\fP propagates through
almost every arithmetic operation without raising a floating-point
exception; a \fIsignaling NaN\fP generally raises a
floating-point exception when occurring as an arithmetic operand.
.LP
The accuracy of the floating-point operations ( \fB'+'\fP , \fB'-'\fP
, \fB'*'\fP , \fB'/'\fP ) and of the library
functions in \fI<math.h>\fP and \fI<complex.h>\fP that return floating-point
results is implementation-defined. The
implementation may state that the accuracy is unknown.
.LP
All integer values in the \fI<float.h>\fP header, except FLT_ROUNDS,
shall be constant expressions suitable for use in
\fB#if\fP 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.
.LP
The rounding mode for floating-point addition is characterized by
the implementation-defined value of FLT_ROUNDS:
.TP 7
-1
Indeterminable.
.TP 7
\ 0
Toward zero.
.TP 7
\ 1
To nearest.
.TP 7
\ 2
Toward positive infinity.
.TP 7
\ 3
Toward negative infinity.
.sp
.LP
All other values for FLT_ROUNDS characterize implementation-defined
rounding behavior.
.LP
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:
.TP 7
-1
Indeterminable.
.TP 7
\ 0
Evaluate all operations and constants just to the range and precision
of the type.
.TP 7
\ 1
Evaluate operations and constants of type \fBfloat\fP and \fBdouble\fP
to the range and precision of the \fBdouble\fP type;
evaluate \fBlong double\fP operations and constants to the range and
precision of the \fBlong double\fP type.
.TP 7
\ 2
Evaluate all operations and constants to the range and precision of
the \fBlong double\fP type.
.sp
.LP
All other negative values for FLT_EVAL_METHOD characterize implementation-defined
behavior.
.LP
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.
.IP " *" 3
Radix of exponent representation, \fIb\fP.
.TP 7
FLT_RADIX
.RS
2
.RE
.sp
.LP
.IP " *" 3
Number of base-FLT_RADIX digits in the floating-point significand,
\fIp\fP.
.TP 7
FLT_MANT_DIG
.TP 7
DBL_MANT_DIG
.TP 7
LDBL_MANT_DIG
.sp
.LP
.IP " *" 3
Number of decimal digits, \fIn\fP, such that any floating-point number
in the widest supported floating type with \fIp\fP_max
radix \fIb\fP digits can be rounded to a floating-point number with
\fIn\fP decimal digits and back again without change to the
value.
.LP
.TP 7
DECIMAL_DIG
.RS
10
.RE
.sp
.LP
.IP " *" 3
Number of decimal digits, \fIq\fP, such that any floating-point number
with \fIq\fP decimal digits can be rounded into a
floating-point number with \fIp\fP radix \fIb\fP digits and back again
without change to the \fIq\fP decimal digits.
.LP
.TP 7
FLT_DIG
.RS
6
.RE
.TP 7
DBL_DIG
.RS
10
.RE
.TP 7
LDBL_DIG
.RS
10
.RE
.sp
.LP
.IP " *" 3
Minimum negative integer such that FLT_RADIX raised to that power
minus 1 is a normalized floating-point number, \fIe\fP_min.
.TP 7
FLT_MIN_EXP
.TP 7
DBL_MIN_EXP
.TP 7
LDBL_MIN_EXP
.sp
.LP
.IP " *" 3
Minimum negative integer such that 10 raised to that power is in the
range of normalized floating-point numbers.
.LP
.TP 7
FLT_MIN_10_EXP
.RS
-37
.RE
.TP 7
DBL_MIN_10_EXP
.RS
-37
.RE
.TP 7
LDBL_MIN_10_EXP
.RS
-37
.RE
.sp
.LP
.IP " *" 3
Maximum integer such that FLT_RADIX raised to that power minus 1 is
a representable finite floating-point number, \fIe\fP_max.
.TP 7
FLT_MAX_EXP
.TP 7
DBL_MAX_EXP
.TP 7
LDBL_MAX_EXP
.sp
.LP
.IP " *" 3
Maximum integer such that 10 raised to that power is in the range
of representable finite floating-point numbers.
.LP
.TP 7
FLT_MAX_10_EXP
.RS
+37
.RE
.TP 7
DBL_MAX_10_EXP
.RS
+37
.RE
.TP 7
LDBL_MAX_10_EXP
.RS
+37
.RE
.sp
.LP
.LP
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:
.IP " *" 3
Maximum representable finite floating-point number.
.LP
.TP 7
FLT_MAX
.RS
1E+37
.RE
.TP 7
DBL_MAX
.RS
1E+37
.RE
.TP 7
LDBL_MAX
.RS
1E+37
.RE
.sp
.LP
.LP
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:
.IP " *" 3
The difference between 1 and the least value greater than 1 that is
representable in the given floating-point type, \fIb\fP**1-\fIp\fP.
.TP 7
FLT_EPSILON
.RS
1E-5
.RE
.TP 7
DBL_EPSILON
.RS
1E-9
.RE
.TP 7
LDBL_EPSILON
.RS
1E-9
.RE
.sp
.LP
.IP " *" 3
Minimum normalized positive floating-point number, \fIb\fP**\fIe\fP_min.
.TP 7
FLT_MIN
.RS
1E-37
.RE
.TP 7
DBL_MIN
.RS
1E-37
.RE
.TP 7
LDBL_MIN
.RS
1E-37
.RE
.sp
.LP
.LP
\fIThe following sections are informative.\fP
.SH APPLICATION USAGE
.LP
None.
.SH RATIONALE
.LP
None.
.SH FUTURE DIRECTIONS
.LP
None.
.SH SEE ALSO
.LP
\fI<complex.h>\fP , \fI<math.h>\fP
.SH 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 .