http://en.wikipedia.org/wiki/Wallace_tree http://en.wikipedia.org/wiki/Wallace_tree is the implementation used on the Pentium III and http://en.wikipedia.org/wi

http://en.wikipedia.org/wiki/Wallace_tree http://en.wikipedia.org/wiki/Wallace_tree is the implementation used on the Pentium III and http://en.wikipedia.org/wiki/Dadda_tree http://en.wikipedia.org/wiki/Dadda_tree is an improvement on that. The Dadda tree was invented in 1965 [1], so I guess the issue is more in having enough transistors and joining them up fast than in designing the multiply algorithm. Having said that, the following might be some possible references. Glenn Colón-Bonet and Paul Winterrowd, "Multiplier Evolution: A Family of Multiplier VLSI Implementations" -- http://comjnl.oxfordjournals.org/cgi/content/abstract/bxm123v1 http://comjnl.oxfordjournals.org/cgi/content/abstract/bxm123... Shailendra Jain, Vasantha Erraguntla, Sriram R. Vangal, Yatin Hoskote, Nitin Borkar, Tulasi Mandepudi, Karthik VP, "A 90mW/GFlop 3.4GHz Reconfigurable Fused/Continuous Multiply-Accumulator for Floating-Point and Integer Operands in 65nm," VLSI Design, International Conference on, pp. 252-257, 2010 23rd International Conference on VLSI Design, 2010. -- http://www.computer.org/portal/web/csdl/doi/10.1109/VLSI.Design.2010.59 http://www.computer.org/portal/web/csdl/doi/10.1109/VLSI.Des... I would have thought the state-of-the-art is trade secret for Intel and AMD, unless anyone actually depackages their chips to look at the multipliers? Patent applications might be worth looking at, but they are probably incomprehensible. Also, http://www.ece.ucsb.edu/~parhami/ece_252b.htm http://www.ece.ucsb.edu/~parhami/ece_252b.htm looks like a good course web page on VLSI maths, but I don't know. [1] Dadda, L. (1965). "Some schemes for parallel multipliers". Alta Frequenza 34: 349–356.