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.

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

       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.1‐2008 defers to the ISO C standard.

       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 POSIX.1‐2008, <complex.h>

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 .