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junkcode/tterribe@email.unc.edu-nmbrthry/[ccan] Mathematics Module.mbox

+From tterribe@email.unc.edu Wed Mar 18 15:38:26 2009
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+Date: Wed, 18 Mar 2009 01:08:26 -0400
+From: "Timothy B. Terriberry" <tterribe@email.unc.edu>
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+Subject: Re: [ccan] Mathematics Module
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+Some of this stuff seems a little trivial to include, but if we're going
+to do so...
+
+The result of nCr is guaranteed to be an integer after each iteration,
+and so there's a) no reason to keep a separate numerator and denominator
+and b) no reason to do a minimum of nine (9!) divisions every iteration.
+Only a single gcd() is needed, and even that can often be skipped,
+requiring only 2-3 divisions per iteration. This is illustrated in
+choose.c (attached). You can easily add the check for the smaller r (_m
+in this implementation), upgrade the types to long, etc., as desired. If
+one really cared about speed, the divisions could be entirely replaced
+by multiplications and a small lookup table, since m and n are known to
+have a very limited range (or the result will overflow).
+
+Also included are a gcd() implementation without tail recursion and
+egcd(), the "extended" gcd, as well as a nice illustration of the use of
+egcd, a Chinese Remainder Theorem solver for systems of linear
+congruences. I don't have time to format these into a nice module with
+test cases right now, but feel free to take what you want and throw the
+rest in "junk". The code is (C) 1998-2001, except crt.c, which is (C)
+1999-2001, 2007. I'm releasing it here under the LGPLv2 license.
+
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