Talk:Addition-chain exponentiation: Difference between revisions
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[[User:Arbautjc|Arbautjc]] ([[User talk:Arbautjc|talk]]) 21:14, 20 July 2015 (UTC)
: I do not think this is valid reasoning.
: The wikipedia mention of [[wp:Addition_chain#Brauer_chain|star chains]] does indeed mention that star chains can fail to produce invalid values. However, the example given is for an exponent of 1227873210934869755325459645562028180483410421970385642998266670782559244925047578059104483100233309036904622010710304861903062287481691063068371652744142574931000480320516175613904206157567455536712489864433925819285983619453998073177028402644441528674227. Here, the addition-chain has 6110 elements while the optimal chain has at most 6109 elements (but apparently no one has been able to prove that they have found an optimal chain for that exponent).
: So by your reasoning, any implementation which limits itself to 64 bit integers is also an invalid implementation because that implementation would not produce an optimal result for an exponent of 1227873210934869755325459645562028180483410421970385642998266670782559244925047578059104483100233309036904622010710304861903062287481691063068371652744142574931000480320516175613904206157567455536712489864433925819285983619453998073177028402644441528674227.
: That said, if you can modify the task in some reasonable way which brings out the flaws of star chains, I would accept your reasoning. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 21:43, 20 July 2015 (UTC)
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