1993-03-21 12:45:37 +03:00
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.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. All advertising materials mentioning features or use of this software
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.\" must display the following acknowledgement:
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.\" This product includes software developed by the University of
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.\" California, Berkeley and its contributors.
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.\" 4. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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1993-08-01 11:32:48 +04:00
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.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91
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1999-08-16 02:23:53 +04:00
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.\" $NetBSD: erf.3,v 1.9 1999/08/15 22:23:54 kleink Exp $
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1993-03-21 12:45:37 +03:00
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.\"
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.Dd April 20, 1991
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.Dt ERF 3
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1997-03-30 03:10:55 +04:00
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.Os
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1993-03-21 12:45:37 +03:00
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.Sh NAME
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.Nm erf ,
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1999-08-16 02:23:53 +04:00
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.Nm erff ,
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.Nm erfc ,
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.Nm erfcf
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1993-03-21 12:45:37 +03:00
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.Nd error function operators
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1998-02-05 21:45:17 +03:00
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.Sh LIBRARY
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.Lb libm
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1993-03-21 12:45:37 +03:00
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.Sh SYNOPSIS
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.Fd #include <math.h>
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.Ft double
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.Fn erf "double x"
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1997-03-30 03:10:55 +04:00
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.Ft float
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1995-04-14 22:39:53 +04:00
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.Fn erff "float x"
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1993-03-21 12:45:37 +03:00
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.Ft double
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.Fn erfc "double x"
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1995-04-14 22:39:53 +04:00
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.Ft float
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.Fn erfcf "float x"
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1993-03-21 12:45:37 +03:00
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.Sh DESCRIPTION
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These functions calculate the error function of
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.Fa x .
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.Pp
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The
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.Fn erf
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calculates the error function of x; where
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.Bd -filled -offset indent
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.if n \{\
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erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
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.if t \{\
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1999-07-02 19:37:33 +04:00
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erf\|(x) :=
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1993-03-21 12:45:37 +03:00
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(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
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.Ed
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.Pp
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The
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.Fn erfc
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function calculates the complementary error function of
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.Fa x ;
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that is
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.Fn erfc
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subtracts the result of the error function
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.Fn erf x
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from 1.0.
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This is useful, since for large
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.Fa x
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places disappear.
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.Sh SEE ALSO
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.Xr math 3
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.Sh HISTORY
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The
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.Fn erf
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and
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.Fn erfc
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functions appeared in
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.Bx 4.3 .
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