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.\" 4. 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.\" $FreeBSD$ 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 58and the 59.Fn erff 60functions calculate the error function of x; where 61.Bd -ragged -offset indent 62.if n \{\ 63erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. 64\} 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\} 69.Ed 70.Pp 71The 72.Fn erfc 73and the 74.Fn erfcf 75functions calculate the complementary error function of 76.Fa x ; 77that is 78.Fn erfc 79subtracts the result of the error function 80.Fn erf x 81from 1.0. 82This is useful, since for large 83.Fa x 84places disappear. 85.Sh SEE ALSO 86.Xr math 3 87.Sh HISTORY 88The 89.Fn erf 90and 91.Fn erfc 92functions appeared in 93.Bx 4.3 . 94