[math-fun] record computation of Pi ,
I should expect floating point to have been equally useless for the mere kilodigit efforts of the early Mersenne prime chasers. I now realize I have no idea how they did it. Ah, I forgot about C.R.T.. The Chudnovskys used it for a gigadigit on their Porkroast 1. It enabled them to punt the huge common divisors that hampered my effort. --rwg Date: 2016-12-12 00:07 From: Joerg Arndt <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com> * Bill Gosper <billgosper@gmail.com> [Dec 12. 2016 08:38]:
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Or is floating point still so much faster than fixed that they sacrificed several digits per "word" to redundant exponents, like the old Mersenne finders? --rwg
For this (giga-digits) precision floating point is useless. They certainly used (a variant of) the "three primes" NTTs, doing CRT at the very end. Sadly, the information given by the program author is rather sketchy. E.g., I'd like to know whether Montgomery multiplication is used. The computation IS an impressive feat, even though the guy had a machine with a droolworthy 1.2 TB of RAM. Best regards, jj
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Bill Gosper