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.\" 30.Dd July 13, 2014 31.Dt ERF 3 32.Os 33.Sh NAME 34.Nm erf , 35.Nm erff , 36.Nm erfl , 37.Nm erfc , 38.Nm erfcf , 39.Nm erfcl 40.Nd error function operators 41.Sh LIBRARY 42.Lb libm 43.Sh SYNOPSIS 44.In math.h 45.Ft double 46.Fn erf "double x" 47.Ft float 48.Fn erff "float x" 49.Ft "long double" 50.Fn erfl "long double x" 51.Ft double 52.Fn erfc "double x" 53.Ft float 54.Fn erfcf "float x" 55.Ft "long double" 56.Fn erfcl "long double x" 57.Sh DESCRIPTION 58These functions calculate the error function of 59.Fa x . 60.Pp 61The 62.Fn erf , 63.Fn erff , 64and 65.Fn erfl 66functions calculate the error function of x; where 67.Bd -ragged -offset indent 68.if n \{\ 69erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. 70\} 71.if t \{\ 72erf\|(x) := 73(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. 74\} 75.Ed 76.Pp 77The 78.Fn erfc , 79.Fn erfcf , 80and 81.Fn erfcl 82functions calculate the complementary error function of 83.Fa x ; 84that is 85.Fn erfc 86subtracts the result of the error function 87.Fn erf x 88from 1.0. 89.Sh SEE ALSO 90.Xr math 3 91.Sh HISTORY 92The 93.Fn erf 94and 95.Fn erfc 96functions appeared in 97.Bx 4.3 . 98