[Cfp-interest] Clebsch-Gordan coefficients

David Hough CFP pcfp at oakapple.net
Thu Dec 12 23:13:17 PST 2013


During the discussion of the scaled product reduction operations,
I mentioned Clebsch-Gordan coefficients.   Read all about them here:

http://en.wikipedia.org/wiki/Clebsch-Gordan_coefficients
http://en.wikipedia.org/wiki/Wigner_3-j_symbols

with formulas here:

http://en.wikipedia.org/wiki/Table_of_Clebsch%E2%80%93Gordan_coefficients

>From the explicit formulas we see that they require evaluating the ratios
of products of sums and differences.    The products might get very large,
yet the ratios remain reasonable.

This problem was the motivation for the wraparound exponent treatment of
trapped overflow and underflow in 754-1985.    However the general inability
to portably exploit traps defeated the intent.      754-2008 decided instead
to work at a higher level, specifying an interface for computing scaled
products rather than specifying an implementation mechanism.    This interface 
is robust in the face of the usual run of overflows and underflows arising
in these problems.



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