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.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 .

Any typographical or formatting errors that appear

in this page are most likely

to have been introduced during the conversion of the source files to

man page format. To report such errors, see

https://www.kernel.org/doc/man-pages/reporting_bugs.html .