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84 lines
2.8 KiB
Plaintext
84 lines
2.8 KiB
Plaintext
.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved
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.TH "CPROJ" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual"
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.\" cproj
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.SH NAME
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cproj, cprojf, cprojl \- complex projection functions
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.SH SYNOPSIS
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.LP
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\fB#include <complex.h>
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.br
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.sp
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double complex cproj(double complex\fP \fIz\fP\fB);
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.br
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float complex cprojf(float complex\fP \fIz\fP\fB);
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.br
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long double complex cprojl(long double complex\fP \fIz\fP\fB);
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.br
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\fP
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.SH DESCRIPTION
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.LP
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These functions shall compute a projection of \fIz\fP onto the Riemann
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sphere: \fIz\fP projects to \fIz\fP, except that all
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complex infinities (even those with one infinite part and one NaN
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part) project to positive infinity on the real axis. If \fIz\fP
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has an infinite part, then \fIcproj\fP( \fIz\fP) shall be equivalent
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to:
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.sp
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.RS
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.nf
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\fBINFINITY + I * copysign(0.0, cimag(z))
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\fP
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.fi
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.RE
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.SH RETURN VALUE
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.LP
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These functions shall return the value of the projection onto the
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Riemann sphere.
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.SH ERRORS
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.LP
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No errors are defined.
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.LP
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\fIThe following sections are informative.\fP
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.SH EXAMPLES
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.LP
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None.
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.SH APPLICATION USAGE
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.LP
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None.
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.SH RATIONALE
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.LP
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Two topologies are commonly used in complex mathematics: the complex
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plane with its continuum of infinities, and the Riemann
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sphere with its single infinity. The complex plane is better suited
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for transcendental functions, the Riemann sphere for algebraic
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functions. The complex types with their multiplicity of infinities
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provide a useful (though imperfect) model for the complex plane.
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The \fIcproj\fP() function helps model the Riemann sphere by mapping
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all infinities to one, and should be used just before any
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operation, especially comparisons, that might give spurious results
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for any of the other infinities. Note that a complex value with
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one infinite part and one NaN part is regarded as an infinity, not
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a NaN, because if one part is infinite, the complex value is
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infinite independent of the value of the other part. For the same
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reason, \fIcabs\fP()
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returns an infinity if its argument has an infinite part and a NaN
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part.
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.SH FUTURE DIRECTIONS
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.LP
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None.
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.SH SEE ALSO
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.LP
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\fIcarg\fP() , \fIcimag\fP() , \fIconj\fP() , \fIcreal\fP() , the
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Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI<complex.h>\fP
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.SH COPYRIGHT
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Portions of this text are reprinted and reproduced in electronic form
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from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
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-- Portable Operating System Interface (POSIX), The Open Group Base
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Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
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Electrical and Electronics Engineers, Inc and The Open Group. In the
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event of any discrepancy between this version and the original IEEE and
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The Open Group Standard, the original IEEE and The Open Group Standard
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is the referee document. The original Standard can be obtained online at
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http://www.opengroup.org/unix/online.html .
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