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.TH FLOAT.H 3HEAD "Dec 17, 2003"
.SH NAME
float.h, float \- floating types
.SH SYNOPSIS
.LP
.nf
#include <\fBfloat.h\fR>
.fi

.SH DESCRIPTION
.sp
.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.
.sp
.LP
The following parameters are used to define the model for each floating-point
type:
.sp
.ne 2
.na
\fB\fIs\fR\fR
.ad
.RS 6n
sign (\(+-1)
.RE

.sp
.ne 2
.na
\fB\fIb\fR\fR
.ad
.RS 6n
base or radix of exponent representation (an integer >1)
.RE

.sp
.ne 2
.na
\fB\fIe\fR\fR
.ad
.RS 6n
exponent (an integer between a minimum e(min) and a maximum e(max))
.RE

.sp
.ne 2
.na
\fB\fIp\fR\fR
.ad
.RS 6n
precision (the number of base-\fIb\fR digits in the significand)
.RE

.sp
.ne 2
.na
\fB\fIf\fR(\fIk\fR)\fR
.ad
.RS 6n
non-negative integers less than \fIb\fR (the significand digits)
.RE

.sp
.LP
In addition to normalized floating-point numbers (\fIf\fR(1)>0 if
\fIx\fR\(!=0), floating types might 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 \fBNaN\fR is an encoding signifying Not-a-Number. A \fBquiet NaN\fR
propagates through almost every arithmetic operation without raising a
floating-point exception; a \fBsignaling NaN\fR generally raises a
floating-point exception when occurring as an arithmetic operand.
.sp
.LP
The accuracy of the library functions in \fBmath.h\fR(3HEAD) and
\fBcomplex.h\fR(3HEAD) that return floating-point results is defined on the
\fBlibm\fR(3LIB) manual page.
.sp
.LP
All integer values in the <\fBfloat.h\fR> header, except \fBFLT_ROUNDS\fR, are
constant expressions suitable for use in \fB#if\fR preprocessing directives;
all floating values are constant expressions. All except \fBDECIMAL_DIG\fR,
\fBFLT_EVAL_METHOD\fR, \fBFLT_RADIX\fR, and \fBFLT_ROUNDS\fR have separate
names for all three floating-point types. The floating-point model
representation is provided for all values except \fBFLT_EVAL_METHOD\fR and
\fBFLT_ROUNDS\fR.
.sp
.LP
The rounding mode for floating-point addition is characterized by the value of
\fBFLT_ROUNDS\fR:
.sp
.ne 2
.na
\fB\fB-1\fR\fR
.ad
.RS 6n
Indeterminable.
.RE

.sp
.ne 2
.na
\fB\fB0\fR\fR
.ad
.RS 6n
Toward zero.
.RE

.sp
.ne 2
.na
\fB\fB1\fR\fR
.ad
.RS 6n
To nearest.
.RE

.sp
.ne 2
.na
\fB\fB2\fR\fR
.ad
.RS 6n
Toward positive infinity.
.RE

.sp
.ne 2
.na
\fB\fB3\fR\fR
.ad
.RS 6n
Toward negative infinity.
.RE

.sp
.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 might be greater than required by the type. The use
of evaluation formats is characterized by the architecture-dependent value of
\fBFLT_EVAL_METHOD\fR:
.sp
.ne 2
.na
\fB\fB-1\fR\fR
.ad
.RS 6n
Indeterminable.
.RE

.sp
.ne 2
.na
\fB\fB0\fR\fR
.ad
.RS 6n
Evaluate all operations and constants just to the range and precision of the
type.
.RE

.sp
.ne 2
.na
\fB\fB1\fR\fR
.ad
.RS 6n
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.
.RE

.sp
.ne 2
.na
\fB\fB2\fR\fR
.ad
.RS 6n
Evaluate all operations and constants to the range and precision of the long
double type.
.RE

.sp
.LP
The values given in the following list are defined as constants.
.RS +4
.TP
.ie t \(bu
.el o
Radix of exponent representation, \fIb\fR.
.sp
.in +2
.nf
FLT_RADIX
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Number of base-\fBFLT_RADIX\fR digits in the floating-point significand,
\fIp\fR.
.sp
.in +2
.nf
FLT_MANT_DIG
DBL_MANT_DIG
LDBL_MANT_DIG
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Number of decimal digits, \fIn\fR, such that any floating-point number in the
widest supported floating type with \fIp\fR(max) radix \fIb\fR digits can be
rounded to a floating-point number with \fIn\fR decimal digits and back again
without change to the value.
.sp
.in +2
.nf
DECIMAL_DIG
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Number of decimal digits, \fIq\fR, such that any floating-point number with
\fIq\fR decimal digits can be rounded into a floating-point number with \fIp\fR
radix \fIb\fR digits and back again without change to the \fIq\fR decimal
digits.
.sp
.in +2
.nf
FLT_DIG
DBL_DIG
LDBL_DIG
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Minimum negative integer such that \fBFLT_RADIX\fR raised to that power minus 1
is a normalized floating-point number, e(min).
.sp
.in +2
.nf
FLT_MIN_EXP
DBL_MIN_EXP
LDBL_MIN_EXP
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Minimum negative integer such that 10 raised to that power is in the range of
normalized floating-point numbers.
.sp
.in +2
.nf
FLT_MIN_10_EXP
DBL_MIN_10_EXP
LDBL_MIN_10_EXP
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Maximum integer such that \fBFLT_RADIX\fR raised to that power minus 1 is a
representable finite floating-point number, e(max).
.sp
.in +2
.nf
FLT_MAX_EXP
DBL_MAX_EXP
LDBL_MAX_EXP
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Maximum integer such that 10 raised to that power is in the range of
representable finite floating-point numbers.
.sp
.in +2
.nf
FLT_MAX_10_EXP
DBL_MAX_10_EXP
LDBL_MAX_10_EXP
.fi
.in -2

.RE
.sp
.LP
The values given in the following list are defined as constant expressions with
values that are greater than or equal to those shown:
.RS +4
.TP
.ie t \(bu
.el o
Maximum representable finite floating-point number.
.sp
.in +2
.nf
FLT_MAX
DBL_MAX
LDBL_MAX
.fi
.in -2

.RE
.sp
.LP
The values given in the following list are defined as constant expressions with
implementation-defined (positive) values that are less than or equal to those
shown:
.RS +4
.TP
.ie t \(bu
.el o
The difference between 1 and the least value greater than 1 that is
representable in the given floating-point type, \fIb\fR^1 -\fI p\fR.
.sp
.in +2
.nf
FLT_EPSILON
DBL_EPSILON
LDBL_EPSILON
.fi
.in -2

.RE
.RS +4
.TP
.ie t \(bu
.el o
Minimum normalized positive floating-point number, \fIb\fR^e(min)^-1.
.sp
.in +2
.nf
FLT_MIN
DBL_MIN
LDBL_MIN
.fi
.in -2

.RE
.SH ATTRIBUTES
.sp
.LP
See \fBattributes\fR(5) for descriptions of the following attributes:
.sp

.sp
.TS
box;
c | c
l | l .
ATTRIBUTE TYPE	ATTRIBUTE VALUE
_
Interface Stability	Standard
.TE

.SH SEE ALSO
.sp
.LP
\fBcomplex.h\fR(3HEAD), \fBmath.h\fR(3HEAD), \fBattributes\fR(5),
\fBstandards\fR(5)