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Logarithm
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===Feynman's algorithm=== While at [[Los Alamos National Laboratory]] working on the [[Manhattan Project]], [[Richard Feynman]] developed a bit-processing algorithm to compute the logarithm that is similar to long division and was later used in the [[Connection Machine]]. The algorithm relies on the fact that every real number {{mvar|x}} where {{Math|1 < ''x'' < 2}} can be represented as a product of distinct factors of the form {{Math|1 + 2<sup>β''k''</sup>}}. The algorithm sequentially builds that product {{Mvar|P}}, starting with {{math|''P'' {{=}} 1}} and {{math|''k'' {{=}} 1}}: if {{math|''P'' Β· (1 + 2<sup>β''k''</sup>) < ''x''}}, then it changes {{Mvar|P}} to {{math|''P'' Β· (1 + 2<sup>β''k''</sup>)}}. It then increases <math>k</math> by one regardless. The algorithm stops when {{Mvar|k}} is large enough to give the desired accuracy. Because {{Math|log(''x'')}} is the sum of the terms of the form {{Math|log(1 + 2<sup>β''k''</sup>)}} corresponding to those {{Mvar|k}} for which the factor {{Math|1 + 2<sup>β''k''</sup>}} was included in the product {{Mvar|P}}, {{Math|log(''x'')}} may be computed by simple addition, using a table of {{Math|log(1 + 2<sup>β''k''</sup>)}} for all {{Mvar|k}}. Any base may be used for the logarithm table.<ref>{{citation |first=Danny |last=Hillis |author-link=Danny Hillis |title=Richard Feynman and The Connection Machine |journal=Physics Today |volume= 42|issue= 2|page= 78|date=15 January 1989 |doi=10.1063/1.881196|bibcode=1989PhT....42b..78H}}</ref>
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