1.\" $OpenBSD: erf.3,v 1.14 2013/06/05 03:40:26 tedu 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: June 5 2013 $ 32.Dt ERFC 3 33.Os 34.Sh NAME 35.Nm erf , 36.Nm erff , 37.Nm erfl , 38.Nm erfc , 39.Nm erfcf , 40.Nm erfcl 41.Nd error function operators 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 long double 49.Fn erfl "long double x" 50.Ft double 51.Fn erfc "double x" 52.Ft float 53.Fn erfcf "float x" 54.Ft long double 55.Fn erfcl "long double x" 56.Sh DESCRIPTION 57These functions calculate the error function of 58.Fa x . 59.Pp 60The 61.Fn erf 62calculates the error function of x, and 63the 64.Fn erff 65and 66.Fn erfl 67functions are single and double precision versions of 68.Fn erf . 69The error function is defined as: 70.Bd -filled -offset indent 71.if n \{\ 72erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} 73.if t \{\ 74erf\|(x) := 75(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} 76.Ed 77.Pp 78The 79.Fn erfc 80function calculates the complementary error function of 81.Fa x ; 82that is 83.Fn erfc 84subtracts the result of the error function 85.Fn erf x 86from 1.0. 87This is useful, since for large 88.Fa x 89places disappear. 90The 91.Fn erfcf 92and 93.Fn erfcl 94functions are single and double precision version of 95.Fn erfc . 96.Sh SEE ALSO 97.Xr exp 3 98.Sh HISTORY 99The 100.Fn erf 101and 102.Fn erfc 103functions appeared in 104.Bx 4.3 . 105