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CPROJ(3P) POSIX Programmer's Manual CPROJ(3P)PROLOGThis manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may dif- fer (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.NAMEcproj, cprojf, cprojl - complex projection functionsSYNOPSIS#include<complex.h>doublecomplexcproj(doublecomplexz);floatcomplexcprojf(floatcomplexz);longdoublecomplexcprojl(longdoublecomplexz);DESCRIPTIONThese functions shall compute a projection ofzonto the Riemann sphere:zprojects toz, except that all com- plex infinities (even those with one infinite part and one NaN part) project to positive infinity on the real axis. Ifzhas an infinite part, thencproj(z) shall be equivalent to:INFINITY+I*copysign(0.0,cimag(z))RETURNVALUEThese functions shall return the value of the projection onto the Riemann sphere.ERRORSNo errors are defined.Thefollowingsectionsareinformative.EXAMPLESNone.APPLICATIONUSAGENone.RATIONALETwo 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 func- tions, the Riemann sphere for algebraic functions. The complex types with their multiplicity of infinities pro- vide a useful (though imperfect) model for the complex plane. Thecproj() 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,cabs() returns an infinity if its argument has an infinite part and a NaN part.FUTUREDIRECTIONSNone.SEEALSOcarg(),cimag(),conj(),creal(), the Base Definitions volume of IEEE Std 1003.1-2001,<complex.h>COPYRIGHTPortions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Stan- dard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifica- tions Issue 6, Copyright (C) 2001-2003 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 Stan- dard, 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 . IEEE/The Open Group 2003 CPROJ(3P)