1.\" Copyright (c) 2011 David Schultz <das@FreeBSD.org> 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.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.\" $FreeBSD$ 26.\" 27.Dd March 6, 2011 28.Dt CEXP 3 29.Os 30.Sh NAME 31.Nm cexp , 32.Nm cexpf 33.Nd complex exponential functions 34.Sh LIBRARY 35.Lb libm 36.Sh SYNOPSIS 37.In complex.h 38.Ft double complex 39.Fn cexp "double complex z" 40.Ft float complex 41.Fn cexpf "float complex z" 42.Sh DESCRIPTION 43The 44.Fn cexp 45and 46.Fn cexpf 47functions compute the complex exponential of 48.Fa z , 49also known as 50.Em cis Ns ( Ns 51.Fa z Ns ) . 52.Sh RETURN VALUES 53For real numbers 54.Fa x 55and 56.Fa y , 57.Fn cexp 58behaves according to Euler's formula: 59.Bd -ragged -offset indent 60.Fn cexp "x + I*y" 61= 62.Po Sy e Ns ** Ns 63.Fa x * 64.Em cos Ns Po Ns 65.Fa y Ns Pc Pc + Po Ns 66.Sy I 67* 68.Sy e Ns ** Ns 69.Fa x 70* 71.Em sin Ns Po Ns 72.Fa y Ns Pc Pc 73.Ed 74.Pp 75Generally speaking, infinities, zeroes and \*(Nas are handled as would 76be expected from this identity given the usual rules of floating-point 77arithmetic. 78However, care is taken to avoid generating \*(Nas when they are not deserved. 79For example, mathematically we expect that 80.Fo cimag 81.Fn cexp "x + I*0" Fc 82= 0 regardless of the value of 83.Fa x , 84and 85.Fn cexp 86preserves this identity even if 87.Fa x 88is \*(If or \*(Na. 89Likewise, 90.Fn cexp "-\*(If + I*y" 91= 0 and 92.Fo creal 93.Fn cexp "\*(If + I*y" Fc 94= \*(If 95for any 96.Fa y 97(even though the latter property is only mathematically true for 98representable 99.Fa y . ) 100If 101.Fa y 102is not finite, the sign of the result is indeterminate. 103.Sh SEE ALSO 104.Xr complex 3 , 105.Xr exp 3 , 106.Xr math 3 , 107.Sh STANDARDS 108The 109.Fn cexp 110and 111.Fn cexpf 112functions conform to 113.St -isoC-99 . 114