```float.h(0P)               POSIX Programmer's Manual              float.h(0P)
```

## PROLOG         top

```       This manual page is part of the POSIX Programmer's Manual.  The Linux
implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior), or
the interface may not be implemented on Linux.

delim \$\$
```

## NAME         top

```       float.h — floating types
```

## SYNOPSIS         top

```       #include <float.h>
```

## DESCRIPTION         top

```       The functionality described on this reference page is aligned with
the ISO C standard. Any conflict between the requirements described
here and the ISO C standard is unintentional. This volume of
POSIX.1‐2008 defers to the ISO C standard.

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:

x  " "  =  " "  sb"^" e" "  " "  sum from k=1 to p^  " "  f_ k" "  "
"  b"^" " "-k ,
" "  e_ min" "  " "  <=  " "  e  " "  <=  " "  e_ max" "

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
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 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 floating-point exception when occurring as an arithmetic
operand.

An implementation may give zero and non-numeric values, such as
infinities and NaNs, a sign, or may leave them unsigned. Wherever
such values are unsigned, any requirement in POSIX.1‐2008 to retrieve
the sign shall produce an unspecified sign and any requirement to set
the sign shall be ignored.

The accuracy of the floating-point operations ('+', '−', '*', '/')
and of the functions in <math.h> and <complex.h> that return
floating-point results is implementation-defined, as is the accuracy
of the conversion between floating-point internal representations and
string representations performed by the functions in <stdio.h>,
<stdlib.h>, and <wchar.h>.  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 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
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:

−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
implementation-defined behavior.

The <float.h> header shall define the following values 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.

*  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.

lpile { p_ max" "  " "  log_ 10" "  " "  b above left ceiling  "
"  1  " "  +  " "  p_ max" "  " "  log_ 10" "  " "  b right
ceiling }
" "   " "  lpile {if " " b " " is " " a " " power " " of " " 10
above otherwise}

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.

lpile { p  " "  log_ 10" "  " "  b above left floor  " "  (p  " "
-  " "  1)  " "  log_ 10" "  " "  b  " "  right floor }
" "   " "  lpile {if " " b " " is " " a " " power " " of " " 10
above otherwise}

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.

left ceiling  " "  log_ 10" "  " "  b"^" " "{ e_ min" "  " " "^"
" "-1 } ^  " "  right ceiling

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

Additionally, FLT_MAX_EXP shall be at least as large as
FLT_MANT_DIG, DBL_MAX_EXP shall be at least as large as
DBL_MANT_DIG, and LDBL_MAX_EXP shall be at least as large as
LDBL_MANT_DIG; which has the effect that FLT_MAX, DBL_MAX, and
LDBL_MAX are integral.

*  Maximum integer such that 10 raised to that power is in the range
of representable finite floating-point numbers.

left floor  " "  log_ 10" " ( ( 1  " "  -  " "  b"^" " "-p )  " "
b"^" e" "_ max" "^ )  " "  right floor

FLT_MAX_10_EXP
+37

DBL_MAX_10_EXP
+37

LDBL_MAX_10_EXP
+37

The <float.h> header shall define the following values as constant
expressions with implementation-defined values that are greater than
or equal to those shown:

*  Maximum representable finite floating-point number.

(1  " "  -  " "  b"^" " "-p^)  " "  b"^" e" "_ max" "

FLT_MAX       1E+37

DBL_MAX       1E+37

LDBL_MAX      1E+37

The <float.h> header shall define the following values 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" "  " " "^" " "-1 }\$.

FLT_MIN       1E−37

DBL_MIN       1E−37

LDBL_MIN      1E−37

The following sections are informative.
```

## APPLICATION USAGE         top

```       None.
```

## RATIONALE         top

```       All known hardware floating-point formats satisfy the property that
the exponent range is larger than the number of mantissa digits. The
ISO C standard permits a floating-point format where this property is
not true, such that the largest finite value would not be integral;
however, it is unlikely that there will ever be hardware support for
such a floating-point format, and it introduces boundary cases that
portable programs should not have to be concerned with (for example,
a non-integral DBL_MAX means that ceil() would have to worry about
overflow). Therefore, this standard imposes an additional requirement
that the largest representable finite value is integral.
```

## FUTURE DIRECTIONS         top

```       None.
```

```       complex.h(0p), math.h(0p), stdio.h(0p), stdlib.h(0p), wchar.h(0p)
```

```       Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The Open
Group Base Specifications Issue 7, Copyright (C) 2013 by the
Institute of Electrical and Electronics Engineers, Inc and The Open
Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
applied.) 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.unix.org/online.html .