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.Dd June 23, 2024 29.Dt ERF 3 30.Os 31.Sh NAME 32.Nm erf , 33.Nm erff , 34.Nm erfl , 35.Nm erfc , 36.Nm erfcf , 37.Nm erfcl 38.Nd error function operators 39.Sh LIBRARY 40.Lb libm 41.Sh SYNOPSIS 42.In math.h 43.Ft double 44.Fn erf "double x" 45.Ft float 46.Fn erff "float x" 47.Ft "long double" 48.Fn erfl "long double x" 49.Ft double 50.Fn erfc "double x" 51.Ft float 52.Fn erfcf "float x" 53.Ft "long double" 54.Fn erfcl "long double x" 55.Sh DESCRIPTION 56These functions calculate the error function of 57.Fa x . 58.Pp 59The 60.Fn erf , 61.Fn erff , 62and 63.Fn erfl 64functions calculate the error function of x; where 65.Bd -ragged -offset indent 66.if n \{\ 67erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. 68\} 69.if t \{\ 70erf\|(x) := 71(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. 72\} 73.Ed 74.Pp 75The 76.Fn erfc , 77.Fn erfcf , 78and 79.Fn erfcl 80functions calculate 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. 87.Sh SEE ALSO 88.Xr math 3 89.Sh STANDARDS 90The 91.Fn erf , 92.Fn erff , 93.Fn erfl , 94.Fn erfc , 95.Fn erfcf 96and 97.Fn erfcl 98functions conform to 99.St -isoC-99 . 100.Sh HISTORY 101The 102.Fn erf 103and 104.Fn erfc 105functions appeared in 106.Bx 4.3 . 107