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Compiled tree of Oasis Linux based on own branch at <https://hacktivis.me/git/oasis/> git clone https://anongit.hacktivis.me/git/oasis-root.git

cproj.3p (3528B)

    

  1. '\" et
  2. .TH CPROJ "3P" 2017 "IEEE/The Open Group" "POSIX Programmer's Manual"
  3. .\"
  4. .SH PROLOG
  5. This manual page is part of the POSIX Programmer's Manual.
  6. The Linux implementation of this interface may differ (consult
  7. the corresponding Linux manual page for details of Linux behavior),
  8. or the interface may not be implemented on Linux.
  9. .\"
  10. .SH NAME
  11. cproj,
  12. cprojf,
  13. cprojl
  14. \(em complex projection functions
  15. .SH SYNOPSIS
  16. .LP
  17. .nf
  18. #include <complex.h>
  19. .P
  20. double complex cproj(double complex \fIz\fP);
  21. float complex cprojf(float complex \fIz\fP);
  22. long double complex cprojl(long double complex \fIz\fP);
  23. .fi
  24. .SH DESCRIPTION
  25. The functionality described on this reference page is aligned with the
  26. ISO\ C standard. Any conflict between the requirements described here and the
  27. ISO\ C standard is unintentional. This volume of POSIX.1\(hy2017 defers to the ISO\ C standard.
  28. .P
  29. These functions shall compute a projection of
  30. .IR z
  31. onto the Riemann sphere:
  32. .IR z
  33. projects to
  34. .IR z ,
  35. except that all complex infinities (even those with one infinite part
  36. and one NaN part) project to positive infinity on the real axis. If
  37. .IR z
  38. has an infinite part, then
  39. .IR cproj (\c
  40. .IR z )
  41. shall be equivalent to:
  42. .sp
  43. .RS 4
  44. .nf
  46. INFINITY + I * copysign(0.0, cimag(z))
  47. .fi
  48. .P
  49. .RE
  50. .SH "RETURN VALUE"
  51. These functions shall return the value of the projection onto the
  52. Riemann sphere.
  53. .SH ERRORS
  54. No errors are defined.
  55. .LP
  56. .IR "The following sections are informative."
  57. .SH EXAMPLES
  58. None.
  59. .SH "APPLICATION USAGE"
  60. None.
  61. .SH RATIONALE
  62. Two topologies are commonly used in complex mathematics: the complex
  63. plane with its continuum of infinities, and the Riemann sphere with its
  64. single infinity. The complex plane is better suited for transcendental
  65. functions, the Riemann sphere for algebraic functions. The complex
  66. types with their multiplicity of infinities provide a useful (though
  67. imperfect) model for the complex plane. The
  68. \fIcproj\fR()
  69. function helps model the Riemann sphere by mapping all infinities to
  70. one, and should be used just before any operation, especially
  71. comparisons, that might give spurious results for any of the other
  72. infinities. Note that a complex value with one infinite part and one
  73. NaN part is regarded as an infinity, not a NaN, because if one part is
  74. infinite, the complex value is infinite independent of the value of the
  75. other part. For the same reason,
  76. \fIcabs\fR()
  77. returns an infinity if its argument has an infinite part and a NaN
  78. part.
  79. .SH "FUTURE DIRECTIONS"
  80. None.
  81. .SH "SEE ALSO"
  82. .IR "\fIcarg\fR\^(\|)",
  83. .IR "\fIcimag\fR\^(\|)",
  84. .IR "\fIconj\fR\^(\|)",
  85. .IR "\fIcreal\fR\^(\|)"
  86. .P
  87. The Base Definitions volume of POSIX.1\(hy2017,
  88. .IR "\fB<complex.h>\fP"
  89. .\"
  90. .SH COPYRIGHT
  91. Portions of this text are reprinted and reproduced in electronic form
  92. from IEEE Std 1003.1-2017, Standard for Information Technology
  93. -- Portable Operating System Interface (POSIX), The Open Group Base
  94. Specifications Issue 7, 2018 Edition,
  95. Copyright (C) 2018 by the Institute of
  96. Electrical and Electronics Engineers, Inc and The Open Group.
  97. In the event of any discrepancy between this version and the original IEEE and
  98. The Open Group Standard, the original IEEE and The Open Group Standard
  99. is the referee document. The original Standard can be obtained online at
  100. http://www.opengroup.org/unix/online.html .
  101. .PP
  102. Any typographical or formatting errors that appear
  103. in this page are most likely
  104. to have been introduced during the conversion of the source files to
  105. man page format. To report such errors, see
  106. https://www.kernel.org/doc/man-pages/reporting_bugs.html .