122 lines
3.0 KiB
Groff
122 lines
3.0 KiB
Groff
.\" 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 .
|