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.TH COMPLEX.H 3HEAD "Dec 17, 2003"
.SH NAME
complex.h, complex \- complex arithmetic
.SH SYNOPSIS
.LP
.nf
#include <\fBcomplex.h\fR>
.fi

.SH DESCRIPTION
.sp
.LP
The <\fBcomplex.h\fR> header defines the following macros:
.sp
.ne 2
.na
\fB\fBcomplex\fR\fR
.ad
.RS 16n
Expands to \fB_Complex\fR.
.RE

.sp
.ne 2
.na
\fB\fB_Complex_I\fR\fR
.ad
.RS 16n
Expands to a constant expression of type const float \fB_Complex\fR, with the
value of the imaginary unit (that is, a number i such that i^2=\(mi1).
.RE

.sp
.ne 2
.na
\fB\fBimaginary\fR\fR
.ad
.RS 16n
Expands to \fB_Imaginary\fR.
.RE

.sp
.ne 2
.na
\fB\fB_Imaginary_I\fR\fR
.ad
.RS 16n
Expands to a constant expression of type \fBconst float _Imaginary\fR with the
value of the imaginary unit.
.RE

.sp
.ne 2
.na
\fB\fBI\fR\fR
.ad
.RS 16n
Expands to either \fB_Imaginary_I\fR or \fB_Complex_I\fR. If \fB_Imaginary_I\fR
is  not defined, \fBI\fR expands to \fB_Complex_I\fR.
.RE

.sp
.LP
An application can undefine and then, if appropriate, redefine the
\fBcomplex\fR, \fBimaginary\fR, and \fBI\fR macros.
.SH USAGE
.sp
.LP
Values are interpreted as radians, not degrees.
.SH ATTRIBUTES
.sp
.LP
See \fBattributes\fR(5) for descriptions of the following attributes:
.sp

.sp
.TS
box;
c | c
l | l .
ATTRIBUTE TYPE	ATTRIBUTE VALUE
_
Interface Stability	Standard
.TE

.SH SEE ALSO
.sp
.LP
\fBcabs\fR(3M), \fBcacos\fR(3M), \fBcacosh\fR(3M), \fBcarg\fR(3M),
\fBcasin\fR(3M), \fBcasinh\fR(3M), \fBcatan\fR(3M), \fBcatanh\fR(3M),
\fBccos\fR(3M), \fBccosh\fR(3M), \fBcexp\fR(3M), \fBcimag\fR(3M),
\fBclog\fR(3M), \fBconj\fR(3M), \fBcpow\fR(3M), \fBcproj\fR(3M),
\fBcreal\fR(3M), \fBcsin\fR(3M), \fBcsinh\fR(3M), \fBcsqrt\fR(3M),
\fBctan\fR(3M), \fBctanh\fR(3M), \fBattributes\fR(5), \fBstandards\fR(5)
.SH NOTES
.sp
.LP
The choice of \fBI\fR instead of \fBi\fR for the imaginary unit concedes to the
widespread use of the identifier \fBi\fR for other purposes. The application
can use a different identifier, say \fBj\fR, for the imaginary unit by
following the inclusion of the <\fBcomplex.h\fR> header with:
.sp
.in +2
.nf
#undef I
#define j _Imaginary_I
.fi
.in -2

.sp
.LP
An \fBI\fR suffix to designate imaginary constants is not required, as
multiplication by \fBI\fR provides a sufficiently convenient and more generally
useful notation for imaginary terms. The corresponding real type for the
imaginary unit is \fBfloat\fR, so that use of \fBI\fR for algorithmic or
notational convenience does not result in widening types.
.sp
.LP
On systems with imaginary types, the application has the ability to control
whether use of the macro \fBI\fR introduces an imaginary type, by explicitly
defining \fBI\fR to be \fB_Imaginary_I\fR or \fB_Complex_I\fR.
.sp
.LP
Disallowing imaginary types is useful for some applications intended to run on
implementations without support for such types.
.sp
.LP
The macro \fB_Imaginary_I\fR provides a test for whether imaginary types are
supported. The \fBcis()\fR function \fB(cos(x) + I*sin(x))\fR was considered
but rejected because its implementation is easy and straightforward, even
though some implementations could compute sine and cosine more efficiently in
tandem.