.\" Copyright (c) 2011 Murray Stokely <murray@FreeBSD.org>
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.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.