1.\" $OpenBSD: erf.3,v 1.11 2007/05/31 19:19:35 jmc Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 30.\" 31.Dd $Mdocdate: May 31 2007 $ 32.Dt ERFC 3 33.Os 34.Sh NAME 35.Nm erf , 36.Nm erff , 37.Nm erfc , 38.Nm erfcf 39.Nd error function operators 40.Sh SYNOPSIS 41.Fd #include <math.h> 42.Ft double 43.Fn erf "double x" 44.Ft float 45.Fn erff "float x" 46.Ft double 47.Fn erfc "double x" 48.Ft float 49.Fn erfcf "float x" 50.Sh DESCRIPTION 51These functions calculate the error function of 52.Fa x . 53.Pp 54The 55.Fn erf 56calculates the error function of x, and 57the 58.Fn erff 59function is a single precision version of 60.Fn erf . 61The error function is defined as: 62.Bd -filled -offset indent 63.if n \{\ 64erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} 65.if t \{\ 66erf\|(x) := 67(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} 68.Ed 69.Pp 70The 71.Fn erfc 72function calculates the complementary error function of 73.Fa x ; 74that is 75.Fn erfc 76subtracts the result of the error function 77.Fn erf x 78from 1.0. 79This is useful, since for large 80.Fa x 81places disappear. 82The 83.Fn erfcf 84function is a single precision version of 85.Fn erfc . 86.Sh SEE ALSO 87.Xr math 3 88.Sh HISTORY 89The 90.Fn erf 91and 92.Fn erfc 93functions appeared in 94.Bx 4.3 . 95