'\" e
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.\"     from: @(#)erf.3	6.4 (Berkeley) 4/20/91
.\"
.Dd $Mdocdate: August 26 2017 $
.Dt ERFC 3
.Os
.Sh NAME
.Nm erf ,
.Nm erff ,
.Nm erfl ,
.Nm erfc ,
.Nm erfcf ,
.Nm erfcl
.Nd error function operators
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn erf "double x"
.Ft float
.Fn erff "float x"
.Ft long double
.Fn erfl "long double x"
.Ft double
.Fn erfc "double x"
.Ft float
.Fn erfcf "float x"
.Ft long double
.Fn erfcl "long double x"
.Sh DESCRIPTION
These functions calculate the error function of
.Fa x .
.Pp
The
.Fn erf
function calculates the error function of x, and
the
.Fn erff
and
.Fn erfl
functions are single and double precision versions of
.Fn erf .
The error function is defined as:
.Bd -unfilled -offset indent
.EQ
roman erf left ( x right ) =
2 over sqrt pi int from 0 to x e sup {- t sup 2} dt
.EN
.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
and
.Fn erfcl
functions are single and double precision version of
.Fn erfc .
.Sh SEE ALSO
.Xr exp 3
.Sh HISTORY
The
.Fn erf
and
.Fn erfc
functions appeared in
.Bx 4.3 .