| @@ -1,93 +1,93 @@ | | | @@ -1,93 +1,93 @@ |
1 | .\" Copyright (c) 1985, 1991 Regents of the University of California. | | 1 | .\" Copyright (c) 1985, 1991 Regents of the University of California. |
2 | .\" All rights reserved. | | 2 | .\" All rights reserved. |
3 | .\" | | 3 | .\" |
4 | .\" Redistribution and use in source and binary forms, with or without | | 4 | .\" Redistribution and use in source and binary forms, with or without |
5 | .\" modification, are permitted provided that the following conditions | | 5 | .\" modification, are permitted provided that the following conditions |
6 | .\" are met: | | 6 | .\" are met: |
7 | .\" 1. Redistributions of source code must retain the above copyright | | 7 | .\" 1. Redistributions of source code must retain the above copyright |
8 | .\" notice, this list of conditions and the following disclaimer. | | 8 | .\" notice, this list of conditions and the following disclaimer. |
9 | .\" 2. Redistributions in binary form must reproduce the above copyright | | 9 | .\" 2. Redistributions in binary form must reproduce the above copyright |
10 | .\" notice, this list of conditions and the following disclaimer in the | | 10 | .\" notice, this list of conditions and the following disclaimer in the |
11 | .\" documentation and/or other materials provided with the distribution. | | 11 | .\" documentation and/or other materials provided with the distribution. |
12 | .\" 3. Neither the name of the University nor the names of its contributors | | 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 | | 13 | .\" may be used to endorse or promote products derived from this software |
14 | .\" without specific prior written permission. | | 14 | .\" without specific prior written permission. |
15 | .\" | | 15 | .\" |
16 | .\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND | | 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 | | 17 | .\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
18 | .\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | | 18 | .\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
19 | .\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE | | 19 | .\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE |
20 | .\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | | 20 | .\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
21 | .\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | | 21 | .\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
22 | .\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | | 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 | | 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 | | 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 | | 25 | .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
26 | .\" SUCH DAMAGE. | | 26 | .\" SUCH DAMAGE. |
27 | .\" | | 27 | .\" |
28 | .\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 | | 28 | .\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 |
29 | .\" $NetBSD: erf.3,v 1.13 2014/11/17 16:53:23 christos Exp $ | | 29 | .\" $NetBSD: erf.3,v 1.14 2015/11/07 18:17:51 nros Exp $ |
30 | .\" | | 30 | .\" |
31 | .Dd November 17, 2014 | | 31 | .Dd November 7, 2015 |
32 | .Dt ERF 3 | | 32 | .Dt ERF 3 |
33 | .Os | | 33 | .Os |
34 | .Sh NAME | | 34 | .Sh NAME |
35 | .Nm erf , | | 35 | .Nm erf , |
36 | .Nm erff , | | 36 | .Nm erff , |
37 | .Nm erfl , | | 37 | .Nm erfl , |
38 | .Nm erfc , | | 38 | .Nm erfc , |
39 | .Nm erfcf , | | 39 | .Nm erfcf , |
40 | .Nm erfcl | | 40 | .Nm erfcl |
41 | .Nd error function operators | | 41 | .Nd error function operators |
42 | .Sh LIBRARY | | 42 | .Sh LIBRARY |
43 | .Lb libm | | 43 | .Lb libm |
44 | .Sh SYNOPSIS | | 44 | .Sh SYNOPSIS |
45 | .In math.h | | 45 | .In math.h |
46 | .Ft double | | 46 | .Ft double |
47 | .Fn erf "double x" | | 47 | .Fn erf "double x" |
48 | .Ft float | | 48 | .Ft float |
49 | .Fn erff "float x" | | 49 | .Fn erff "float x" |
50 | .Ft long double | | 50 | .Ft long double |
51 | .Fn erff "long double x" | | 51 | .Fn erfl "long double x" |
52 | .Ft double | | 52 | .Ft double |
53 | .Fn erfc "double x" | | 53 | .Fn erfc "double x" |
54 | .Ft float | | 54 | .Ft float |
55 | .Fn erfcf "float x" | | 55 | .Fn erfcf "float x" |
56 | .Ft long double | | 56 | .Ft long double |
57 | .Fn erfcl "long double x" | | 57 | .Fn erfcl "long double x" |
58 | .Sh DESCRIPTION | | 58 | .Sh DESCRIPTION |
59 | These functions calculate the error function of | | 59 | These functions calculate the error function of |
60 | .Fa x . | | 60 | .Fa x . |
61 | .Pp | | 61 | .Pp |
62 | The | | 62 | The |
63 | .Fn erf | | 63 | .Fn erf |
64 | calculates the error function of x; where | | 64 | calculates the error function of x; where |
65 | .Bd -filled -offset indent | | 65 | .Bd -filled -offset indent |
66 | .if n \{\ | | 66 | .if n \{\ |
67 | erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} | | 67 | erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} |
68 | .if t \{\ | | 68 | .if t \{\ |
69 | erf\|(x) := | | 69 | erf\|(x) := |
70 | (2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} | | 70 | (2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} |
71 | .Ed | | 71 | .Ed |
72 | .Pp | | 72 | .Pp |
73 | The | | 73 | The |
74 | .Fn erfc | | 74 | .Fn erfc |
75 | function calculates the complementary error function of | | 75 | function calculates the complementary error function of |
76 | .Fa x ; | | 76 | .Fa x ; |
77 | that is | | 77 | that is |
78 | .Fn erfc | | 78 | .Fn erfc |
79 | subtracts the result of the error function | | 79 | subtracts the result of the error function |
80 | .Fn erf x | | 80 | .Fn erf x |
81 | from 1.0. | | 81 | from 1.0. |
82 | This is useful, since for large | | 82 | This is useful, since for large |
83 | .Fa x | | 83 | .Fa x |
84 | places disappear. | | 84 | places disappear. |
85 | .Sh SEE ALSO | | 85 | .Sh SEE ALSO |
86 | .Xr math 3 | | 86 | .Xr math 3 |
87 | .Sh HISTORY | | 87 | .Sh HISTORY |
88 | The | | 88 | The |
89 | .Fn erf | | 89 | .Fn erf |
90 | and | | 90 | and |
91 | .Fn erfc | | 91 | .Fn erfc |
92 | functions appeared in | | 92 | functions appeared in |
93 | .Bx 4.3 . | | 93 | .Bx 4.3 . |