2011-03-07 03:09:24 +00:00
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.\" Copyright (c) 2011 David Schultz <das@FreeBSD.org>
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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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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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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.\" $FreeBSD$
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.\"
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.Dd March 6, 2011
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.Dt CEXP 3
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.Os
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.Sh NAME
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.Nm cexp ,
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.Nm cexpf
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.Nd complex exponential functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In complex.h
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.Ft double complex
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.Fn cexp "double complex z"
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.Ft float complex
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.Fn cexpf "float complex z"
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.Sh DESCRIPTION
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The
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.Fn cexp
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and
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.Fn cexpf
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functions compute the complex exponential of
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.Fa z ,
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also known as
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.Em cis Ns ( Ns
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2012-05-11 20:06:46 +00:00
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.Fa z Ns ) .
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2011-03-07 03:09:24 +00:00
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.Sh RETURN VALUES
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For real numbers
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.Fa x
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and
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.Fa y ,
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.Fn cexp
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behaves according to Euler's formula:
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.Bd -ragged -offset indent
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.Fn cexp "x + I*y"
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=
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2012-09-11 17:40:06 +00:00
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.Po Sy e Ns ** Ns
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2011-03-07 03:09:24 +00:00
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.Fa x *
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2012-09-11 17:40:06 +00:00
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.Em cos Ns Po Ns
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.Fa y Ns Pc Pc + Po Ns
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2011-03-07 03:09:24 +00:00
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.Sy I
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*
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.Sy e Ns ** Ns
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.Fa x
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*
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2012-09-11 17:40:06 +00:00
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.Em sin Ns Po Ns
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.Fa y Ns Pc Pc
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2011-03-07 03:09:24 +00:00
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.Ed
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.Pp
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Generally speaking, infinities, zeroes and \*(Nas are handled as would
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be expected from this identity given the usual rules of floating-point
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arithmetic.
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However, care is taken to avoid generating \*(Nas when they are not deserved.
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For example, mathematically we expect that
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.Fo cimag
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.Fn cexp "x + I*0" Fc
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= 0 regardless of the value of
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.Fa x ,
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and
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.Fn cexp
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preserves this identity even if
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.Fa x
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is \*(If or \*(Na.
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Likewise,
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.Fn cexp "-\*(If + I*y"
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= 0 and
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.Fo creal
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.Fn cexp "\*(If + I*y" Fc
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= \*(If
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for any
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.Fa y
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(even though the latter property is only mathematically true for
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representable
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.Fa y . )
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If
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.Fa y
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is not finite, the sign of the result is indeterminate.
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.Sh SEE ALSO
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.Xr complex 3 ,
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.Xr exp 3 ,
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2014-12-27 08:22:58 +00:00
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.Xr math 3
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2011-03-07 03:09:24 +00:00
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.Sh STANDARDS
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The
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.Fn cexp
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and
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.Fn cexpf
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functions conform to
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.St -isoC-99 .
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