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.\"     from: @(#)erf.3	6.4 (Berkeley) 4/20/91
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.Dd $Mdocdate: May 31 2007 $
.Dt ERFC 3
.Os
.Sh NAME
.Nm erf ,
.Nm erff ,
.Nm erfc ,
.Nm erfcf
.Nd error function operators
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn erf "double x"
.Ft float
.Fn erff "float x"
.Ft double
.Fn erfc "double x"
.Ft float
.Fn erfcf "float x"
.Sh DESCRIPTION
These functions calculate the error function of
.Fa x .
.Pp
The
.Fn erf
calculates the error function of x, and
the
.Fn erff
function is a single precision version of
.Fn erf .
The error function is defined as:
.Bd -filled -offset indent
.if n \{\
erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
.if t \{\
erf\|(x) :=
(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
.Ed
.Pp
The
.Fn erfc
function calculates the complementary error function of
.Fa x ;
that is
.Fn erfc
subtracts the result of the error function
.Fn erf x
from 1.0.
This is useful, since for large
.Fa x
places disappear.
The
.Fn erfcf
function is a single precision version of
.Fn erfc .
.Sh SEE ALSO
.Xr math 3
.Sh HISTORY
The
.Fn erf
and
.Fn erfc
functions appeared in
.Bx 4.3 .