NAME
cproj, cprojf, cprojl - complex projection functions
SYNOPSIS
#include <complex.h>
double complex cproj(double complex z);
float complex cprojf(float complex z);
long double complex cprojl(long double complex z);
DESCRIPTION
These functions shall compute a projection of z onto the Riemann
sphere: z projects to 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 z has an infinite part, then cproj( z) shall be
equivalent to:
INFINITY + I * copysign(0.0, cimag(z))
RETURN VALUE
These functions shall return the value of the projection onto the
Riemann sphere.
ERRORS
No errors are defined.
The following sections are informative.
EXAMPLES
None.
APPLICATION USAGE
None.
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 cproj() 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, cabs() returns an infinity if its argument has an infinite part
and a NaN part.
FUTURE DIRECTIONS
None.
SEE ALSO
carg() , cimag() , conj() , creal() , the Base Definitions volume of
IEEE Std 1003.1-2001, <complex.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/online.html .