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 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 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 .