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 .