cprojf(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.1‐2008 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.1‐2008, complex.h(0p)

COPYRIGHT         top

       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1, 2013 Edition, Standard for Information
       Technology -- Portable Operating System Interface (POSIX), The Open
       Group Base Specifications Issue 7, Copyright (C) 2013 by the
       Institute of Electrical and Electronics Engineers, Inc and The Open
       Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
       applied.) 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.unix.org/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                 2013                           CPROJ(3P)