[Cfp-interest 3346] Re: The 'cproj' routine - 7.3.9.5

[Damian McGuckin]

The following is proposed. Any comments are welcome.

Thanks - Damian

"7.3.9.5#2 The cproj functions"

The cproj functions map z to itself except where z has an infinite real or 
imaginary part (even if the other part is a NaN) in which case cproj(z)
is equivalent to

  	CMPLX(INFINITY, copysign(0.0, cimag(z))))

"7.3.9.5#3 The cproj functions"

The cproj functions return their argument unless that argument has an 
infinite part in which case they return a complex floating value with 
infinite real part and zero imaginary part.

"Background Rationale"

The cproj functions capture the spirit of the mathematical mapping onto 
the complex plane extended by a single point at infinity. They perform the 
simple task of mapping any argument with an infinite part into one of two 
canonical values that compare equal, mapping any other argument to itself.

The current statements in 7.3.9.5 #2 and #3 about the Riemann sphere are 
incorrect. The Riemann sphere is a mathematically related topic, which may 
explain its historical presence in 7.3.9.5, but the Riemann sphere is not 
the subject of the cproj functions.  This change removes the references to
the Riemann sphere.

This proposal requires no implementation changes.