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 .