Someone posted this on sci.math.symbolic, which I've never seen
before, and is the most detailed list I've see of the algorithms used
by Mathematica.

http://reference.wolfram.com/mathematica/note/SomeNotesOnInternalImplementation.html

On a somewhat different topic, it was pointed out that

Mark Sofroniou (one of the numerical algorithm developers at Wolfram
Research) and Giulia Spaletta (a numerical analyst at the University
of Bologna) published a paper that details the specifics of
significance arithmetic as it is implemented in Mathematica:

"Precise numerical computation"
The Journal of Logic and Algebraic Programming
Volume 64, Issue 1, Pages 113-134 (July 2005)

Dave

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