BSD 4_3_Net_2 release

[unix-history] / usr / src / lib / libm / common_source / erf.3

diff --git a/usr/src/lib/libm/common_source/erf.3 b/usr/src/lib/libm/common_source/erf.3
index 2acd45d..20344ea 100644 (file)
--- a/usr/src/lib/libm/common_source/erf.3
+++ b/usr/src/lib/libm/common_source/erf.3
@@ -1,37 +1,82 @@
-.\" Copyright (c) 1985 Regents of the University of California.
-.\" All rights reserved.  The Berkeley software License Agreement
-.\" specifies the terms and conditions for redistribution.
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.

 .\"
 .\"

-.\"    @(#)erf.3       6.2 (Berkeley) 5/12/86
+.\" 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. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"    This product includes software developed by the University of
+.\"    California, Berkeley and its contributors.
+.\" 4. 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.

 .\"
 .\"

-.TH ERF 3M  "May 12, 1986"
-.UC 6
-.SH NAME
-erf, erfc \- error functions
-.SH SYNOPSIS
-.nf
-.B #include <math.h>
-.PP
-.B double erf(x)
-.B double x;
-.PP
-.B double erfc(x)
-.B double x;
-.fi
-.SH DESCRIPTION
-Erf\|(x) returns the error function of x; where
+.\" 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.
+.\"
+.\"     @(#)erf.3      6.4 (Berkeley) 4/20/91
+.\"
+.Dd April 20, 1991
+.Dt ERF 3
+.Os BSD 4.3
+.Sh NAME
+.Nm erf ,
+.Nm erfc
+.Nd error function operators
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn erf "double x"
+.Ft double
+.Fn erfc "double x"
+.Sh DESCRIPTION
+These functions calculate the error function of
+.Fa x .
+.Pp
+The
+.Fn erf
+calculates the error function of x; where
+.Bd -filled -offset indent

 .if n \{\
 .if n \{\

-.PP

 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. \}
 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. \}

-.PP
-Erfc\|(x) returns 1.0\-erf\|(x).
-.PP
-The entry for erfc is provided because of the extreme loss
-of relative accuracy if erf\|(x) is called for large x
-and the result subtracted from 1.
-(e.g. for x = 10, 12 places are lost).
-.SH SEE ALSO
-math(3M)
+.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.
+.Sh SEE ALSO
+.Xr math 3
+.Sh HISTORY
+The
+.Fn erf
+and
+.Fn erfc
+functions appeared in
+.Bx 4.3 .