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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.
.\"
.Dd November 3, 2021
.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
.Ss Natural logarithm Function
.Cl
clog natural logarithm
.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
cpow power function
csin sine
csinh hyperbolic sine
ctan tangent
ctanh hyperbolic tangent
.El
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr ieee 3 ,
.Xr math 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 power functions,
.Fn cpowf, cpow ,
and
.Fn cpowl ,
are implemented, but the code was neither reviewed nor tested.
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