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.
cproj, cprojf, cprojl — complex projection functions
double complex cproj(double complex z);
float complex cprojf(float complex z);
long double complex cprojl(long double complex z);
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:
These functions shall return the value of the projection onto the Riemann
No errors are defined.
INFINITY + I * copysign(0.0, cimag(z))
The following sections are informative.
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
carg(), cimag(), conj(),
The Base Definitions volume of POSIX.1‐2017,
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 .
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