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. All advertising materials mentioning features or use of this software
13.\" must display the following acknowledgement:
14.\" This product includes software developed by the University of
15.\" California, Berkeley and its contributors.
16.\" 4. Neither the name of the University nor the names of its contributors
17.\" may be used to endorse or promote products derived from this software
18.\" without specific prior written permission.
19.\"
20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30.\" SUCH DAMAGE.
31.\"
32.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91
33.\" $Id: erf.3,v 1.3 1993/08/14 13:42:38 mycroft Exp $
34.\"
35.Dd April 20, 1991
36.Dt ERF 3
37.Os BSD 4.3
38.Sh NAME
39.Nm erf ,
40.Nm erfc
41.Nd error function operators
42.Sh SYNOPSIS
43.Fd #include <math.h>
44.Ft double
45.Fn erf "double x"
46.Ft double
47.Fn erfc "double x"
48.Sh DESCRIPTION
49These functions calculate the error function of
50.Fa x .
51.Pp
52The
53.Fn erf
54calculates the error function of x; where
55.Bd -filled -offset indent
56.if n \{\
57erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
58.if t \{\
59erf\|(x) :=
60(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
61.Ed
62.Pp
63The
64.Fn erfc
65function calculates the complementary error function of
66.Fa x ;
67that is
68.Fn erfc
69subtracts the result of the error function
70.Fn erf x
71from 1.0.
72This is useful, since for large
73.Fa x
74places disappear.
75.Sh SEE ALSO
76.Xr math 3
77.Sh HISTORY
78The
79.Fn erf
80and
81.Fn erfc
82functions appeared in
83.Bx 4.3 .
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. All advertising materials mentioning features or use of this software
13.\" must display the following acknowledgement:
14.\" This product includes software developed by the University of
15.\" California, Berkeley and its contributors.
16.\" 4. Neither the name of the University nor the names of its contributors
17.\" may be used to endorse or promote products derived from this software
18.\" without specific prior written permission.
19.\"
20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30.\" SUCH DAMAGE.
31.\"
32.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91
33.\" $Id: erf.3,v 1.3 1993/08/14 13:42:38 mycroft Exp $
34.\"
35.Dd April 20, 1991
36.Dt ERF 3
37.Os BSD 4.3
38.Sh NAME
39.Nm erf ,
40.Nm erfc
41.Nd error function operators
42.Sh SYNOPSIS
43.Fd #include <math.h>
44.Ft double
45.Fn erf "double x"
46.Ft double
47.Fn erfc "double x"
48.Sh DESCRIPTION
49These functions calculate the error function of
50.Fa x .
51.Pp
52The
53.Fn erf
54calculates the error function of x; where
55.Bd -filled -offset indent
56.if n \{\
57erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
58.if t \{\
59erf\|(x) :=
60(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
61.Ed
62.Pp
63The
64.Fn erfc
65function calculates the complementary error function of
66.Fa x ;
67that is
68.Fn erfc
69subtracts the result of the error function
70.Fn erf x
71from 1.0.
72This is useful, since for large
73.Fa x
74places disappear.
75.Sh SEE ALSO
76.Xr math 3
77.Sh HISTORY
78The
79.Fn erf
80and
81.Fn erfc
82functions appeared in
83.Bx 4.3 .