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 November 3, 2021 28.Dt CEXP 3 29.Os 30.Sh NAME 31.Nm cexp , 32.Nm cexpf , 33.Nm cexpl 34.Nd complex exponential functions 35.Sh LIBRARY 36.Lb libm 37.Sh SYNOPSIS 38.In complex.h 39.Ft double complex 40.Fn cexp "double complex z" 41.Ft float complex 42.Fn cexpf "float complex z" 43.Ft long double complex 44.Fn cexpl "long double complex z" 45.Sh DESCRIPTION 46The 47.Fn cexp , 48.Fn cexpf , 49and 50.Fn cexpl 51functions compute the complex exponential of 52.Fa z , 53also known as 54.Em cis Ns ( Ns 55.Fa z Ns ) . 56.Sh RETURN VALUES 57For real numbers 58.Fa x 59and 60.Fa y , 61.Fn cexp 62behaves according to Euler's formula: 63.Bd -ragged -offset indent 64.Fn cexp "x + I*y" 65= 66.Po Sy e Ns ** Ns 67.Fa x * 68.Em cos Ns Po Ns 69.Fa y Ns Pc Pc + Po Ns 70.Sy I 71* 72.Sy e Ns ** Ns 73.Fa x 74* 75.Em sin Ns Po Ns 76.Fa y Ns Pc Pc 77.Ed 78.Pp 79Generally speaking, infinities, zeroes and \*(Nas are handled as would 80be expected from this identity given the usual rules of floating-point 81arithmetic. 82However, care is taken to avoid generating \*(Nas when they are not deserved. 83For example, mathematically we expect that 84.Fo cimag 85.Fn cexp "x + I*0" Fc 86= 0 regardless of the value of 87.Fa x , 88and 89.Fn cexp 90preserves this identity even if 91.Fa x 92is \*(If or \*(Na. 93Likewise, 94.Fn cexp "-\*(If + I*y" 95= 0 and 96.Fo creal 97.Fn cexp "\*(If + I*y" Fc 98= \*(If 99for any 100.Fa y 101(even though the latter property is only mathematically true for 102representable 103.Fa y . ) 104If 105.Fa y 106is not finite, the sign of the result is indeterminate. 107.Sh SEE ALSO 108.Xr complex 3 , 109.Xr exp 3 , 110.Xr math 3 111.Sh STANDARDS 112The 113.Fn cexp , 114.Fn cexpf , 115and 116.Fn cexpl 117functions conform to 118.St -isoC-99 . 119