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.\" Copyright (c) 2011 Murray Stokely <murray@FreeBSD.org>
.\" 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 ``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 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 October 17, 2011
.Dt COMPLEX 3
.Os
.Sh NAME
.Nm complex
.Nd "complex arithmetic"
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Sh DESCRIPTION
These functions support complex arithmetic in the C math library.
.Sh "LIST OF FUNCTIONS"
Each of the following
.Vt "double complex"
functions has a
.Vt "float complex"
counterpart with an
.Ql f
appended to the name and a
.Vt "long double complex"
counterpart with an
.Ql l
appended.
As an example, the
.Vt "float complex"
and
.Vt "long double complex"
counterparts of
.Ft double
.Fn cabs "double complex z"
are
.Ft float
.Fn cabsf "float complex z"
and
.Ft "long double"
.Fn cabsl "long double complex z" ,
respectively.
.de Cl
.Bl -column "csqrt" "complex absolute value (i.e. norm, modulus, magnitude)"
.Em "Name	Description"
..
.\" Section 7.3.5 - 7.3.7 of ISO C99 standard unimplemented, see BUGS
.\" Section 7.3.8 of ISO C99 standard
.Ss Absolute-value Functions
.Cl
cabs	complex absolute value (i.e. norm, modulus, magnitude)
csqrt	complex square root
.El
.Ss Exponential Function
.Cl
cexp	exponential base e
.El
.\" Section 7.3.9 of ISO C99 standard
.Ss Manipulation Functions
.Cl
carg	compute the argument (i.e. phase angle)
cimag	compute the imaginary part
conj	compute the complex conjugate
cproj	compute projection onto Riemann sphere
creal	compute the real part
.El
.\" Section 7.3.5-6 of ISO C99 standard
.Ss Trigonometric and Hyperbolic Functions
.Cl
cacos	arc cosine
cacosh	arc hyperbolic cosine
casin	arc sine
casinh	arc hyperbolic sine
catan	arc tangent
catanh	arc hyperbolic tangent
ccos	cosine
ccosh	hyperbolic cosine
csin	sine
csinh	hyperbolic sine
ctan	tangent
ctanh	hyperbolic tangent
.El
.Sh SEE ALSO
.Xr math 3 ,
.Xr fenv 3 ,
.Xr ieee 3 ,
.Xr tgmath 3
.Rs
.%T "ISO/IEC 9899:TC3"
.%U http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
.Re
.Sh STANDARDS
The
.In complex.h
functions described here conform to
.St -isoC-99 .
.Sh BUGS
The logarithmic functions
.Fn clog
and the power functions
.Fn cpow
are not implemented.
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