| erf.3 (165906) | erf.3 (268593) |
|---|---|
| 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. --- 12 unchanged lines hidden (view full) --- 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 | 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. --- 12 unchanged lines hidden (view full) --- 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: head/lib/msun/man/erf.3 165906 2007-01-09 01:02:06Z imp $ | 29.\" $FreeBSD: head/lib/msun/man/erf.3 268593 2014-07-13 17:05:03Z kargl $ |
| 30.\" | 30.\" |
| 31.Dd April 20, 1991 | 31.Dd July 13, 2014 |
| 32.Dt ERF 3 33.Os 34.Sh NAME 35.Nm erf , 36.Nm erff , | 32.Dt ERF 3 33.Os 34.Sh NAME 35.Nm erf , 36.Nm erff , |
| 37.Nm erfl , |
|
| 37.Nm erfc , | 38.Nm erfc , |
| 38.Nm erfcf | 39.Nm erfcf , 40.Nm erfcl |
| 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" | 41.Nd error function operators 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.In math.h 46.Ft double 47.Fn erf "double x" 48.Ft float 49.Fn erff "float x" |
| 50.Ft "long double" 51.Fn erfl "long double x" |
|
| 48.Ft double 49.Fn erfc "double x" 50.Ft float 51.Fn erfcf "float x" | 52.Ft double 53.Fn erfc "double x" 54.Ft float 55.Fn erfcf "float x" |
| 56.Ft "long double" 57.Fn erfcl "long double x" |
|
| 52.Sh DESCRIPTION 53These functions calculate the error function of 54.Fa x . 55.Pp 56The | 58.Sh DESCRIPTION 59These functions calculate the error function of 60.Fa x . 61.Pp 62The |
| 57.Fn erf 58and the 59.Fn erff | 63.Fn erf , 64.Fn erff , 65and 66.Fn erfl |
| 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 | 67functions calculate the error function of x; where 68.Bd -ragged -offset indent 69.if n \{\ 70erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. 71\} 72.if t \{\ 73erf\|(x) := 74(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. 75\} 76.Ed 77.Pp 78The |
| 72.Fn erfc 73and the 74.Fn erfcf | 79.Fn erfc , 80.Fn erfcf , 81and 82.Fn erfcl |
| 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. | 83functions calculate the complementary error function of 84.Fa x ; 85that is 86.Fn erfc 87subtracts the result of the error function 88.Fn erf x 89from 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 . | 90.Sh SEE ALSO 91.Xr math 3 92.Sh HISTORY 93The 94.Fn erf 95and 96.Fn erfc 97functions appeared in 98.Bx 4.3 . |