1CPROJ(3P) POSIX Programmer's Manual CPROJ(3P)
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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.
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12 cproj, cprojf, cprojl - complex projection functions
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15 #include <complex.h>
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17 double complex cproj(double complex z);
18 float complex cprojf(float complex z);
19 long double complex cprojl(long double complex z);
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23 These functions shall compute a projection of z onto the Riemann
24 sphere: z projects to z, except that all complex infinities (even those
25 with one infinite part and one NaN part) project to positive infinity
26 on the real axis. If z has an infinite part, then cproj( z) shall be
27 equivalent to:
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30 INFINITY + I * copysign(0.0, cimag(z))
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33 These functions shall return the value of the projection onto the Rie‐
34 mann sphere.
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37 No errors are defined.
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39 The following sections are informative.
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42 None.
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45 None.
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48 Two topologies are commonly used in complex mathematics: the complex
49 plane with its continuum of infinities, and the Riemann sphere with its
50 single infinity. The complex plane is better suited for transcendental
51 functions, the Riemann sphere for algebraic functions. The complex
52 types with their multiplicity of infinities provide a useful (though
53 imperfect) model for the complex plane. The cproj() function helps
54 model the Riemann sphere by mapping all infinities to one, and should
55 be used just before any operation, especially comparisons, that might
56 give spurious results for any of the other infinities. Note that a com‐
57 plex value with one infinite part and one NaN part is regarded as an
58 infinity, not a NaN, because if one part is infinite, the complex value
59 is infinite independent of the value of the other part. For the same
60 reason, cabs() returns an infinity if its argument has an infinite part
61 and a NaN part.
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64 None.
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67 carg(), cimag(), conj(), creal(), the Base Definitions volume of
68 IEEE Std 1003.1-2001, <complex.h>
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71 Portions of this text are reprinted and reproduced in electronic form
72 from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
73 -- Portable Operating System Interface (POSIX), The Open Group Base
74 Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
75 Electrical and Electronics Engineers, Inc and The Open Group. In the
76 event of any discrepancy between this version and the original IEEE and
77 The Open Group Standard, the original IEEE and The Open Group Standard
78 is the referee document. The original Standard can be obtained online
79 at http://www.opengroup.org/unix/online.html .
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83IEEE/The Open Group 2003 CPROJ(3P)