CPROJ(3)                   POSIX Programmer's Manual                  CPROJ(3)



PROLOG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.

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
       The functionality described on this reference page is aligned with the
       ISO C standard. Any conflict between the requirements described here
       and the ISO C standard is unintentional. This volume of POSIX.1-2017
       defers to the ISO C standard.

       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 POSIX.1-2017, <complex.h>

COPYRIGHT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1-2017, Standard for Information Technology --
       Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 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 .

       Any typographical or formatting errors that appear in this page are
       most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .



IEEE/The Open Group                  2017                             CPROJ(3)
