# NEW202303.TXT

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ON 20230306@10:14:48 AM at page:
On a web page you were interested in at:
http://techref.massmind.org/Techref/method/math.htm#44991.4269444444
James Newton[JMN-EFP-786] See also:
https://http://www.reenigne.org/blog/multiplying-faster-with-squares/
Multiplying Faster with Squares (Lookup). Because:<BR>(a+b)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> + 2ab
<BR>(a-b)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> - 2ab
<BR>
Subtracting these gives:
<BR>4ab = (a+b)<sup>2</sup> - (a-b)<sup>2</sup>
<BR>
Or:
<BR>ab = (a+b)<sup>2</sup>/4 - (a-b)<sup>2</sup>/4
<BR>which reduces the difficult parts from an x*y to an x<sup>2</sup>/4. With only one variable (and enough ram) lookup tables are suddenly back in frame. Add some amazing tricks based on the fact that a-b and a+b are always both even or both odd, and you can actually do very fast multiplies on a processor without mul.

ON 20230306@11:04:23 AM at page:
On a web page you were interested in at:
http://techref.massmind.org/Techref/method/math.htm#
James Newton[JMN-EFP-786] edited the page. Difference:
http://techref.massmind.org/techref/diff.asp?url=\Techref\method\math.htm&version=1

ON 20230315@3:20:22 PM at page:
On a web page you were interested in at:
http://techref.massmind.org/Techref/io/stepper/THB6064/gallery.htm#
James Newton[JMN-EFP-786] edited the page. Difference:
http://techref.massmind.org/techref/diff.asp?url=\Techref\io\stepper\THB6064\gallery.htm&version=0

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 file: /Techref/new202303.txt, 1KB, , updated: 2023/3/15 15:20, local time: 2023/6/3 21:35, TOP NEW HELP FIND:  3.235.40.122:LOG IN

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