# cproj(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.1‐2017 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:

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

```       None.
```

## APPLICATION USAGE         top

```       None.
```

## 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.
```

## FUTURE DIRECTIONS         top

```       None.
```

```       carg(3p), cimag(3p), conj(3p), creal(3p)

The Base Definitions volume of POSIX.1‐2017, complex.h(0p)
```

```       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 .