erf.3   [plain text]


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.\"     from: @(#)erf.3	6.4 (Berkeley) 4/20/91
.\"	$Id: erf.3,v 1.4 2004/12/20 21:35:45 scp Exp $
.\"
.Dd January 30, 2003
.Dt ERF 3
.Os BSD 4.3
.Sh NAME
.Nm erf ,
.Nm erfc
.Nd error function operators
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn erf "double x"
.Ft long double
.Fn erfl "long double x"
.Ft float
.Fn erff "float x"
.Ft double
.Fn erfc "double x"
.Ft long double
.Fn erfcl "long double x"
.Ft float
.Fn erfcf "float x"
.Sh DESCRIPTION
These functions calculate the error function of
.Fa x .
.Pp
The
.Fn erf
function calculates the error function of x; where
.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
computes the difference of the error function
.Fn erf x
from 1.0.
This is useful, since for large
.Fa x
use of
.Fn erfc
avoids loss of precision due to cancellation.
.Sh SPECIAL VALUES
.Fn erf "±0"
returns ±0.
.Pp
.Fn erf "±infinity"
returns ±1.
.Pp
.Fn erfc "-infinity"
returns 2.
.Pp
.Fn erfc "+infinity"
returns +0.
.Sh SEE ALSO
.Xr math 3
.Sh STANDARDS
The
.Fn erf
and
.Fn erfc
functions conform to ISO/IEC 9899:1999(E).