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.\" Copyright (c) 2004 Stefan Farfeleder
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $FreeBSD$
.\"
.Dd August 7, 2008
.Dt CIMAG 3
.Os
.Sh NAME
.Nm cimag , cimagf , cimagl ,
.Nm conj , conjf , conjl ,
.Nm cproj , cprojf , cprojl ,
.Nm creal , crealf , creall
.Nd "functions to manipulate complex numbers"
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double
.Fn cimag "double complex z"
.Ft float
.Fn cimagf "float complex z"
.Ft "long double"
.Fn cimagl "long double complex z"
.Ft "double complex"
.Fn conj "double complex z"
.Ft "float complex"
.Fn conjf "float complex z"
.Ft "long double complex"
.Fn conjl "long double complex z"
.Ft "double complex"
.Fn cproj "double complex z"
.Ft "float complex"
.Fn cprojf "float complex z"
.Ft "long double complex"
.Fn cprojl "long double complex z"
.Ft double
.Fn creal "double complex z"
.Ft float
.Fn crealf "float complex z"
.Ft "long double"
.Fn creall "long double complex z"
.Sh DESCRIPTION
Let
.Sm off
.Fa a + b * Em i
.Sm on
denote the complex number
.Fa z .
.Pp
The
.Fn creal
functions return the real part
.Fa a ,
and the
.Fn cimag
functions return the imaginary part
.Fa b .
.Pp
The
.Fn conj
functions return the complex conjugate
.Sm off
.Fa a - b * Em i .
.Sm on
.Pp
The
.Fn cproj
functions return the projection onto the Riemann sphere.
If
.Fa z
contains an infinite component, then the result is
.Fa \*(If \*(Pm 0 Ns * Ns Em i ,
where the (zero) imaginary part of the result has the same sign as
.Fa b .
Otherwise, the result is
.Fa z .
.Pp
These functions do not signal any floating point exceptions.
.Sh STANDARDS
The
.Fn cimag ,
.Fn conj ,
.Fn cproj ,
and
.Fn creal
functions conform to
.St -isoC-99 .
.Sh HISTORY
The
.Fn cimag ,
.Fn conj
and
.Fn creal
functions first appeared in
.Fx 5.3 .
The
.Fn cproj
functions appeared in
.Fx 8.0.