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 .

IEEE/The Open Group                                   2003                                              CPROJ(P)