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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
       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
       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(3P)