Originální popis anglicky:
cproj, cprojf, cprojl - complex projection functions
Návod, kniha: POSIX Programmer's Manual
#include <complex.h>
double complex cproj(double complex
z);
float complex cprojf(float complex
z);
long double complex cprojl(long double complex
z);
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))
These functions shall return the value of the projection onto the Riemann
sphere.
No errors are defined.
The following sections are informative.
None.
None.
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.
None.
carg() ,
cimag() ,
conj() ,
creal() , the Base
Definitions volume of IEEE Std 1003.1-2001,
<complex.h>
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 original
Standard can be obtained online at http://www.opengroup.org/unix/online.html
.
