
CPROJ(P) POSIX Programmer's Manual CPROJ(P)
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 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 con
tinuum 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 imper
fect) 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 IEEE Std 1003.12001,
<complex.h>
COPYRIGHT
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) 20012003 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 orig
inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 CPROJ(P) 
