CPROJ(P)						     POSIX Programmer's Manual							  CPROJ(P)

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  com-
       plex  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 Technol-
       ogy -- 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(P)