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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 dif-
       fer (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 com-
       plex 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  func-
       tions, the Riemann sphere for algebraic functions. The complex types with their multiplicity of infinities pro-
       vide 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, Stan-
       dard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base  Specifica-
       tions  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 Stan-
       dard,  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)