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CPROJ(3P)                  POSIX Programmer's Manual                 CPROJ(3P)
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 Rie-
       mann 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 com-
       plex  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 Electri-
       cal  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.ker-
       nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group                  2013                            CPROJ(3P)