1CPROJ(3P) POSIX Programmer's Manual CPROJ(3P)
2
6 This manual page is part of the POSIX Programmer's Manual. The Linux
7 implementation of this interface may differ (consult the corresponding
8 Linux manual page for details of Linux behavior), or the interface may
9 not be implemented on Linux.
10
12 cproj, cprojf, cprojl — complex projection functions
13
15 #include <complex.h>
16 double complex cproj(double complex z);
18 float complex cprojf(float complex z);
19 long double complex cprojl(long double complex z);
20
22 The functionality described on this reference page is aligned with the
23 ISO C standard. Any conflict between the requirements described here
24 and the ISO C standard is unintentional. This volume of POSIX.1‐2017
25 defers to the ISO C standard.
26 These functions shall compute a projection of z onto the Riemann
28 sphere: z projects to z, except that all complex infinities (even those
29 with one infinite part and one NaN part) project to positive infinity
30 on the real axis. If z has an infinite part, then cproj(z) shall be
31 equivalent to:
32 INFINITY + I * copysign(0.0, cimag(z))
35
37 These functions shall return the value of the projection onto the Rie‐
38 mann sphere.
39
41 No errors are defined.
42 The following sections are informative.
44
46 None.
47
49 None.
50
52 Two topologies are commonly used in complex mathematics: the complex
53 plane with its continuum of infinities, and the Riemann sphere with its
54 single infinity. The complex plane is better suited for transcendental
55 functions, the Riemann sphere for algebraic functions. The complex
56 types with their multiplicity of infinities provide a useful (though
57 imperfect) model for the complex plane. The cproj() function helps
58 model the Riemann sphere by mapping all infinities to one, and should
59 be used just before any operation, especially comparisons, that might
60 give spurious results for any of the other infinities. Note that a com‐
61 plex value with one infinite part and one NaN part is regarded as an
62 infinity, not a NaN, because if one part is infinite, the complex value
63 is infinite independent of the value of the other part. For the same
64 reason, cabs() returns an infinity if its argument has an infinite part
65 and a NaN part.
66
68 None.
69
71 carg(), cimag(), conj(), creal()
72 The Base Definitions volume of POSIX.1‐2017, <complex.h>
74
76 Portions of this text are reprinted and reproduced in electronic form
77 from IEEE Std 1003.1-2017, Standard for Information Technology -- Por‐
78 table Operating System Interface (POSIX), The Open Group Base Specifi‐
79 cations Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of
80 Electrical and Electronics Engineers, Inc and The Open Group. In the
81 event of any discrepancy between this version and the original IEEE and
82 The Open Group Standard, the original IEEE and The Open Group Standard
83 is the referee document. The original Standard can be obtained online
84 at http://www.opengroup.org/unix/online.html .
85 Any typographical or formatting errors that appear in this page are
87 most likely to have been introduced during the conversion of the source
88 files to man page format. To report such errors, see https://www.ker‐
89 nel.org/doc/man-pages/reporting_bugs.html .
90IEEE/The Open Group 2017 CPROJ(3P)