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.Dd November 3, 2021 26.Dt CEXP 3 27.Os 28.Sh NAME 29.Nm cexp , 30.Nm cexpf , 31.Nm cexpl 32.Nd complex exponential functions 33.Sh LIBRARY 34.Lb libm 35.Sh SYNOPSIS 36.In complex.h 37.Ft double complex 38.Fn cexp "double complex z" 39.Ft float complex 40.Fn cexpf "float complex z" 41.Ft long double complex 42.Fn cexpl "long double complex z" 43.Sh DESCRIPTION 44The 45.Fn cexp , 46.Fn cexpf , 47and 48.Fn cexpl 49functions compute the complex exponential of 50.Fa z , 51also known as 52.Em cis Ns ( Ns 53.Fa z Ns ) . 54.Sh RETURN VALUES 55For real numbers 56.Fa x 57and 58.Fa y , 59.Fn cexp 60behaves according to Euler's formula: 61.Bd -ragged -offset indent 62.Fn cexp "x + I*y" 63= 64.Po Sy e Ns ** Ns 65.Fa x * 66.Em cos Ns Po Ns 67.Fa y Ns Pc Pc + Po Ns 68.Sy I 69* 70.Sy e Ns ** Ns 71.Fa x 72* 73.Em sin Ns Po Ns 74.Fa y Ns Pc Pc 75.Ed 76.Pp 77Generally speaking, infinities, zeroes and \*(Nas are handled as would 78be expected from this identity given the usual rules of floating-point 79arithmetic. 80However, care is taken to avoid generating \*(Nas when they are not deserved. 81For example, mathematically we expect that 82.Fo cimag 83.Fn cexp "x + I*0" Fc 84= 0 regardless of the value of 85.Fa x , 86and 87.Fn cexp 88preserves this identity even if 89.Fa x 90is \*(If or \*(Na. 91Likewise, 92.Fn cexp "-\*(If + I*y" 93= 0 and 94.Fo creal 95.Fn cexp "\*(If + I*y" Fc 96= \*(If 97for any 98.Fa y 99(even though the latter property is only mathematically true for 100representable 101.Fa y . ) 102If 103.Fa y 104is not finite, the sign of the result is indeterminate. 105.Sh SEE ALSO 106.Xr complex 3 , 107.Xr exp 3 , 108.Xr math 3 109.Sh STANDARDS 110The 111.Fn cexp , 112.Fn cexpf , 113and 114.Fn cexpl 115functions conform to 116.St -isoC-99 . 117