1CPROJ(P)                   POSIX Programmer's Manual                  CPROJ(P)
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NAME

6       cproj, cprojf, cprojl - complex projection functions
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SYNOPSIS

9       #include <complex.h>
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11       double complex cproj(double complex z);
12       float complex cprojf(float complex z);
13       long double complex cprojl(long double complex z);
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DESCRIPTION

17       These  functions  shall  compute  a  projection  of  z onto the Riemann
18       sphere: z projects to z, except that all complex infinities (even those
19       with  one  infinite part and one NaN part) project to positive infinity
20       on the real axis. If z has an infinite part, then cproj(  z)  shall  be
21       equivalent to:
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24              INFINITY + I * copysign(0.0, cimag(z))
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RETURN VALUE

27       These  functions shall return the value of the projection onto the Rie‐
28       mann sphere.
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ERRORS

31       No errors are defined.
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33       The following sections are informative.
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EXAMPLES

36       None.
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APPLICATION USAGE

39       None.
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RATIONALE

42       Two topologies are commonly used in complex  mathematics:  the  complex
43       plane with its continuum of infinities, and the Riemann sphere with its
44       single infinity. The complex plane is better suited for  transcendental
45       functions,  the  Riemann  sphere  for  algebraic functions. The complex
46       types with their multiplicity of infinities provide  a  useful  (though
47       imperfect)  model  for  the  complex plane.  The cproj() function helps
48       model the Riemann sphere by mapping all infinities to one,  and  should
49       be  used  just before any operation, especially comparisons, that might
50       give spurious results for any of the other infinities. Note that a com‐
51       plex  value  with  one infinite part and one NaN part is regarded as an
52       infinity, not a NaN, because if one part is infinite, the complex value
53       is  infinite  independent  of the value of the other part. For the same
54       reason, cabs() returns an infinity if its argument has an infinite part
55       and a NaN part.
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FUTURE DIRECTIONS

58       None.
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SEE ALSO

61       carg()  ,  cimag()  , conj() , creal() , the Base Definitions volume of
62       IEEE Std 1003.1-2001, <complex.h>
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65       Portions of this text are reprinted and reproduced in  electronic  form
66       from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
67       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
68       Specifications  Issue  6,  Copyright  (C) 2001-2003 by the Institute of
69       Electrical and Electronics Engineers, Inc and The Open  Group.  In  the
70       event of any discrepancy between this version and the original IEEE and
71       The Open Group Standard, the original IEEE and The Open Group  Standard
72       is  the  referee document. The original Standard can be obtained online
73       at http://www.opengroup.org/unix/online.html .
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77IEEE/The Open Group                  2003                             CPROJ(P)
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