1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
|
.\" $OpenBSD: erf.3,v 1.14 2013/06/05 03:40:26 tedu Exp $
.\" Copyright (c) 1985, 1991 Regents of the University of California.
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\" 3. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91
.\"
.Dd $Mdocdate: June 5 2013 $
.Dt ERFC 3
.Os
.Sh NAME
.Nm erf ,
.Nm erff ,
.Nm erfl ,
.Nm erfc ,
.Nm erfcf ,
.Nm erfcl
.Nd error function operators
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn erf "double x"
.Ft float
.Fn erff "float x"
.Ft long double
.Fn erfl "long double x"
.Ft double
.Fn erfc "double x"
.Ft float
.Fn erfcf "float x"
.Ft long double
.Fn erfcl "long double x"
.Sh DESCRIPTION
These functions calculate the error function of
.Fa x .
.Pp
The
.Fn erf
calculates the error function of x, and
the
.Fn erff
and
.Fn erfl
functions are single and double precision versions of
.Fn erf .
The error function is defined as:
.Bd -filled -offset indent
.if n \{\
erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
.if t \{\
erf\|(x) :=
(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
.Ed
.Pp
The
.Fn erfc
function calculates the complementary error function of
.Fa x ;
that is
.Fn erfc
subtracts the result of the error function
.Fn erf x
from 1.0.
This is useful, since for large
.Fa x
places disappear.
The
.Fn erfcf
and
.Fn erfcl
functions are single and double precision version of
.Fn erfc .
.Sh SEE ALSO
.Xr exp 3
.Sh HISTORY
The
.Fn erf
and
.Fn erfc
functions appeared in
.Bx 4.3 .
|
