# Man Pages

cproj(3p) - phpMan cproj(3p) - phpMan

Command: man perldoc info search(apropos)

```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.

carg(), cimag(), conj(), creal(), the Base Definitions volume of IEEE Std 1003.1-2001, <complex.h>