math function speed

[mccaugh at uiucdcsm.UUCP]

 A numerical-analyst named McConnell makes chronic contributions to the APL
 Conference Proceedings...in particular, I believe the 1983 edition has an
 article by him definiteively addressing the "square-root" problem. It is
 really quite informative.
 Our own Prof. Gear presents a convincing strategy in his "Computer Organ-
 ization and Programming" (2nd edition) for speeding up square-root compu-
 tation on the IBM-360/370 (he presents the strategy without proof: I have
 a proof in case anyone is interested); not that it is necessarily optimal,
 but it is a "speed-up".
 No, Newton's (actually, Newton-Raphson's) Method is not "optimal": it only
 converges quadratically; for a really nice cubically-converging version,
 look at Franz's "Elements of Numerical Analysis". However, fewer itera-
 tions are bought at the price of more ocmputations per iteration.....