```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.1‐2008 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.1‐2008, complex.h(0p)
```

```       Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The Open
Group Base Specifications Issue 7, Copyright (C) 2013 by the
Institute of Electrical and Electronics Engineers, Inc and The Open
Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
applied.) 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.unix.org/online.html .