'\" et
.TH CPROJ "3P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
.SH PROLOG
This manual page is part of the POSIX Programmer's Manual.
The Linux implementation of this interface may differ (consult
the corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.

.SH NAME
cproj,
cprojf,
cprojl
\(em complex projection functions
.SH SYNOPSIS
.LP
.nf
#include <complex.h>
.P
double complex cproj(double complex \fIz\fP);
float complex cprojf(float complex \fIz\fP);
long double complex cprojl(long double complex \fIz\fP);
.fi
.SH DESCRIPTION
The functionality described on this reference page is aligned with the
ISO\ C standard. Any conflict between the requirements described here and the
ISO\ C standard is unintentional. This volume of POSIX.1\(hy2008 defers to the ISO\ C standard.
.P
These functions shall compute a projection of
.IR z
onto the Riemann sphere:
.IR z
projects to
.IR z ,
except that all complex infinities (even those with one infinite part
and one NaN part) project to positive infinity on the real axis. If
.IR z
has an infinite part, then
.IR cproj (\c
.IR z )
shall be equivalent to:
.sp
.RS 4
.nf
\fB
INFINITY + I * copysign(0.0, cimag(z))
.fi \fR
.P
.RE
.SH "RETURN VALUE"
These functions shall return the value of the projection onto the
Riemann sphere.
.SH ERRORS
No errors are defined.
.LP
.IR "The following sections are informative."
.SH EXAMPLES
None.
.SH "APPLICATION USAGE"
None.
.SH RATIONALE
Two topologies are commonly used in complex mathematics: the complex
plane with its continuum of infinities, and the Riemann sphere with its
single infinity. The complex plane is better suited for transcendental
functions, the Riemann sphere for algebraic functions. The complex
types with their multiplicity of infinities provide a useful (though
imperfect) model for the complex plane. The
\fIcproj\fR()
function helps model the Riemann sphere by mapping all infinities to
one, and should be used just before any operation, especially
comparisons, that might give spurious results for any of the other
infinities. Note that a complex value with one infinite part and one
NaN part is regarded as an infinity, not a NaN, because if one part is
infinite, the complex value is infinite independent of the value of the
other part. For the same reason,
\fIcabs\fR()
returns an infinity if its argument has an infinite part and a NaN
part.
.SH "FUTURE DIRECTIONS"
None.
.SH "SEE ALSO"
.IR "\fIcarg\fR\^(\|)",
.IR "\fIcimag\fR\^(\|)",
.IR "\fIconj\fR\^(\|)",
.IR "\fIcreal\fR\^(\|)"
.P
The Base Definitions volume of POSIX.1\(hy2008,
.IR "\fB<complex.h>\fP"
.SH COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group.
(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
event of any discrepancy between this version and the original IEEE and
The Open Group Standard, the original IEEE and The Open Group Standard
is the referee document. The original Standard can be obtained online at
http://www.unix.org/online.html .

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