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 (con-
       sult 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 infini-
       ties (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 Rie-
       mann 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, Copy-
       right (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.open-
       group.org/unix/online.html .



IEEE/The Open Group                                           2003                                                     CPROJ(3P)