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+'\" et
+.TH CPROJ "3P" 2017 "IEEE/The Open Group" "POSIX Programmer's Manual"
+.\"
+.SH PROLOG
+This manual page is part of the POSIX Programmer's Manual.
+The Linux implementation of this interface may differ (consult
+the corresponding Linux manual page for details of Linux behavior),
+or the interface may not be implemented on Linux.
+.\"
+.SH NAME
+cproj,
+cprojf,
+cprojl
+\(em complex projection functions
+.SH SYNOPSIS
+.LP
+.nf
+#include <complex.h>
+.P
+double complex cproj(double complex \fIz\fP);
+float complex cprojf(float complex \fIz\fP);
+long double complex cprojl(long double complex \fIz\fP);
+.fi
+.SH DESCRIPTION
+The functionality described on this reference page is aligned with the
+ISO\ C standard. Any conflict between the requirements described here and the
+ISO\ C standard is unintentional. This volume of POSIX.1\(hy2017 defers to the ISO\ C standard.
+.P
+These functions shall compute a projection of
+.IR z
+onto the Riemann sphere:
+.IR z
+projects to
+.IR z ,
+except that all complex infinities (even those with one infinite part
+and one NaN part) project to positive infinity on the real axis. If
+.IR z
+has an infinite part, then
+.IR cproj (\c
+.IR z )
+shall be equivalent to:
+.sp
+.RS 4
+.nf
+
+INFINITY + I * copysign(0.0, cimag(z))
+.fi
+.P
+.RE
+.SH "RETURN VALUE"
+These functions shall return the value of the projection onto the
+Riemann sphere.
+.SH ERRORS
+No errors are defined.
+.LP
+.IR "The following sections are informative."
+.SH EXAMPLES
+None.
+.SH "APPLICATION USAGE"
+None.
+.SH RATIONALE
+Two topologies are commonly used in complex mathematics: the complex
+plane with its continuum of infinities, and the Riemann sphere with its
+single infinity. The complex plane is better suited for transcendental
+functions, the Riemann sphere for algebraic functions. The complex
+types with their multiplicity of infinities provide a useful (though
+imperfect) model for the complex plane. The
+\fIcproj\fR()
+function helps model the Riemann sphere by mapping all infinities to
+one, and should be used just before any operation, especially
+comparisons, that might give spurious results for any of the other
+infinities. Note that a complex value with one infinite part and one
+NaN part is regarded as an infinity, not a NaN, because if one part is
+infinite, the complex value is infinite independent of the value of the
+other part. For the same reason,
+\fIcabs\fR()
+returns an infinity if its argument has an infinite part and a NaN
+part.
+.SH "FUTURE DIRECTIONS"
+None.
+.SH "SEE ALSO"
+.IR "\fIcarg\fR\^(\|)",
+.IR "\fIcimag\fR\^(\|)",
+.IR "\fIconj\fR\^(\|)",
+.IR "\fIcreal\fR\^(\|)"
+.P
+The Base Definitions volume of POSIX.1\(hy2017,
+.IR "\fB<complex.h>\fP"
+.\"
+.SH COPYRIGHT
+Portions of this text are reprinted and reproduced in electronic form
+from IEEE Std 1003.1-2017, Standard for Information Technology
+-- Portable Operating System Interface (POSIX), The Open Group Base
+Specifications Issue 7, 2018 Edition,
+Copyright (C) 2018 by the Institute of
+Electrical and Electronics Engineers, Inc and The Open Group.
+In the event of any discrepancy between this version and the original IEEE and
+The Open Group Standard, the original IEEE and The Open Group Standard
+is the referee document. The original Standard can be obtained online at
+http://www.opengroup.org/unix/online.html .
+.PP
+Any typographical or formatting errors that appear
+in this page are most likely
+to have been introduced during the conversion of the source files to
+man page format. To report such errors, see
+https://www.kernel.org/doc/man-pages/reporting_bugs.html .