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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CPROJ 3
5.Os BSD 4
6.Sh NAME
7.Nm cproj
8.Nd projection onto the Riemann sphere
9.Sh SYNOPSIS
10.Fd #include <complex.h>
11.Ft double complex
12.Fn cproj "double complex z"
13.Ft long double complex
14.Fn cprojl "long double complex z"
15.Ft float complex
16.Fn cprojf "float complex z"
17.Sh DESCRIPTION
18.Fn cproj "z"
19computes the projection of a complex floating-point number
20.Fa z
21onto the Riemann sphere: for any finite
22.Fa z ,
23.Fn cproj "z"
24= z, but all complex infinities (including infinities with one NaN part)
25project to positive infinity on the real axis.
26.Pp
27Specifically, if
28.Fa z
29= x + iy has an infinite part (one of x or y is infinity), then
30.Fn cproj "z"
31is equivalent to INFINITY + I*copysign(0.0,cimag(z)).
32.Sh NOTE
33.Fn cproj
34projects onto the C99 "Riemann Sphere", which may not agree with the mathematical
35notion of the Riemann Sphere; in particular, it has two infinites (inf � 0i) and
36four zeroes (�0 � 0i).
37.Sh SEE ALSO
38.Xr complex 3
39.Sh STANDARDS
40The
41.Fn cproj
42function conforms to ISO/IEC 9899:1999(E).