Path: utzoo!attcan!uunet!ncrlnk!ncrcae!ece-csc!mcnc!rutgers!mit-eddie!uw-beaver!uw-june!rik
From: rik@june.cs.washington.edu (Rik Littlefield)
Newsgroups: comp.arch
Subject: Re: Trachtenberg System of Math
Summary: Reference, but don't bother
Message-ID: <6245@june.cs.washington.edu>
Date: 27 Oct 88 05:50:10 GMT
References: <6232@june.cs.washington.edu> <6821@pasteur.Berkeley.EDU>
Organization: U of Washington, Computer Science, Seattle
Lines: 34

In article <6821@pasteur.Berkeley.EDU>, aho@cory.Berkeley.EDU (Alex Ho) writes:
> In article <6232@june.cs.washington.edu> pardo@cs.washington.edu (David Keppel) writes:
> >As a kid I read part of a book called "The Trachtenberg System of
> >Math" or some such.  The basic idea was that there were several rules
> >that could be applied to *all* numbers to do *very* fast (linear in
> >number of digits?) multiplies and multi-row adds. 
> 
> this system sounds pretty interesting.
> do you have a reference to the original source,
> a book or a more recent magazine article, by any
> chance.
> 

I believe you are looking for "The Trachtenberg Speed System of Basic
Mathematics", (translated and adapted) by Ann Cutler and Rudolph McShane,
copyright 1960, published by Doubleday and Company, Garden City, NY,
Library of Congress 60-13513.

Be prepared for disillusionment -- I believe the content is not as
suggested above.  In fact, the Trachtenberg system for multiplication
by arbitrary numbers is still an O(MN) process for M- and N-digit
numbers.  Trachtenberg just computes the partial products for each pair
of digits in such an order that the partial sum-of-products remains a
small number that you can usually keep in your head.  This lets you
write down the product directly, right-to-left, without going through
the usual bother of writing down all the partial products.  Cute, but
it's hard to see how it applies to hardware multipliers.

--Rik

Disclaimer: I got my copy as a gift probably 15 years ago, decided at the
time that it wasn't worth my while, and never did read it all the way
through.  The interpretation above is based on a 3-minute scan of one
chapter.