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.Dd November 3, 2021
.Dt CEXP 3
.Os
.Sh NAME
.Nm cexp ,
.Nm cexpf ,
.Nm cexpl
.Nd complex exponential functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn cexp "double complex z"
.Ft float complex
.Fn cexpf "float complex z"
.Ft long double complex
.Fn cexpl "long double complex z"
.Sh DESCRIPTION
The
.Fn cexp ,
.Fn cexpf ,
and
.Fn cexpl
functions compute the complex exponential of
.Fa z ,
also known as
.Em cis Ns ( Ns
.Fa z Ns ) .
.Sh RETURN VALUES
For real numbers
.Fa x
and
.Fa y ,
.Fn cexp
behaves according to Euler's formula:
.Bd -ragged -offset indent
.Fn cexp "x + I*y"
=
.Po Sy e Ns ** Ns
.Fa x *
.Em cos Ns Po Ns
.Fa y Ns Pc Pc + Po Ns
.Sy I
*
.Sy e Ns ** Ns
.Fa x
*
.Em sin Ns Po Ns
.Fa y Ns Pc Pc
.Ed
.Pp
Generally speaking, infinities, zeroes and \*(Nas are handled as would
be expected from this identity given the usual rules of floating-point
arithmetic.
However, care is taken to avoid generating \*(Nas when they are not deserved.
For example, mathematically we expect that
.Fo cimag
.Fn cexp "x + I*0" Fc
= 0 regardless of the value of
.Fa x ,
and
.Fn cexp
preserves this identity even if
.Fa x
is \*(If or \*(Na.
Likewise,
.Fn cexp "-\*(If + I*y"
= 0 and
.Fo creal
.Fn cexp "\*(If + I*y" Fc
= \*(If
for any
.Fa y
(even though the latter property is only mathematically true for
representable
.Fa y . )
If
.Fa y
is not finite, the sign of the result is indeterminate.
.Sh SEE ALSO
.Xr complex 3 ,
.Xr exp 3 ,
.Xr math 3
.Sh STANDARDS
The
.Fn cexp ,
.Fn cexpf ,
and
.Fn cexpl
functions conform to
.St -isoC-99 .