1.\" Copyright (c) 1985, 1991 Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 3. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 29.\" $NetBSD: erf.3,v 1.12 2003/08/07 16:44:47 agc Exp $ 30.\" 31.Dd April 20, 1991 32.Dt ERF 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 LIBRARY 41.Lb libm 42.Sh SYNOPSIS 43.In math.h 44.Ft double 45.Fn erf "double x" 46.Ft float 47.Fn erff "float x" 48.Ft double 49.Fn erfc "double x" 50.Ft float 51.Fn erfcf "float x" 52.Sh DESCRIPTION 53These functions calculate the error function of 54.Fa x . 55.Pp 56The 57.Fn erf 58calculates the error function of x; where 59.Bd -filled -offset indent 60.if n \{\ 61erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} 62.if t \{\ 63erf\|(x) := 64(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} 65.Ed 66.Pp 67The 68.Fn erfc 69function calculates the complementary error function of 70.Fa x ; 71that is 72.Fn erfc 73subtracts the result of the error function 74.Fn erf x 75from 1.0. 76This is useful, since for large 77.Fa x 78places disappear. 79.Sh SEE ALSO 80.Xr math 3 81.Sh HISTORY 82The 83.Fn erf 84and 85.Fn erfc 86functions appeared in 87.Bx 4.3 . 88