cproj(3p) — Linux manual page


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

PROLOG         top

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

NAME         top

       cproj, cprojf, cprojl — complex projection functions

SYNOPSIS         top

       #include <complex.h>

       double complex cproj(double complex z);
       float complex cprojf(float complex z);
       long double complex cprojl(long double complex z);

DESCRIPTION         top

       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         top

       These functions shall return the value of the projection onto the
       Riemann sphere.

ERRORS         top

       No errors are defined.

       The following sections are informative.

EXAMPLES         top




RATIONALE         top

       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.



SEE ALSO         top

       carg(3p), cimag(3p), conj(3p), creal(3p)

       The Base Definitions volume of POSIX.1‐2017, complex.h(0p)

COPYRIGHT         top

       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(3P)

Pages that refer to this page: complex.h(0p)carg(3p)cimag(3p)conj(3p)creal(3p)