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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  con-
       tinuum  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 imper-
       fect) 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 orig-
       inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .

IEEE/The Open Group			       2003					 CPROJ(P)
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