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.TH complex.h 3HEAD "17 Dec 2003" "SunOS 5.11" "Headers"
.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
.mk
.na
\fB\fBcomplex\fR\fR
.ad
.RS 16n
.rt  
Expands to \fB_Complex\fR.
.RE

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

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

.sp
.ne 2
.mk
.na
\fB\fBI\fR\fR
.ad
.RS 16n
.rt  
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
tab() box;
cw(2.75i) |cw(2.75i) 
lw(2.75i) |lw(2.75i) 
.
ATTRIBUTE TYPEATTRIBUTE VALUE
_
Interface StabilityCommitted
_
StandardSee \fBstandards\fR(5).
.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.