Hello, yes, speaking of wich, To go from a decimal number to continued fraction there is one simple algorithm that uses only additions. You just need a for-next loop, you start with x0 (supposedly fractional) Start with S0= 0. do Sn+1 = Sn+Xn, until Xn+1 is greater than 1. Output the index n (the partial quotient). X0 = Xn+1 od: In principle this is clean, no inverse to compute. The only drawback of this method is that when the partial quotient is really big then the procedures hangs. But if the number is believed to be non-exotic, well, that's a living. The big advantage is that the computation can be carried out to billions of digits wide with not much overhead, it is a bit slow perhaps but very economical in memory. Does this have ever been attempted on a big number like Pi ?? Question : what is the cost of operations to inverse a number of let's say 22459 billion digits ?? a lot ? it could be improved with this trick. When you have a certain X0 in the process - Evaluate roughly the ratio of 1/X0 = ratio , (let's say to 50 digits) then multiply the big number by that [ ratio ] + 1 , [ ] being the integer part. For all practical purpose the ratio won't be bigger than 20-30 digits. so this is simple in fact, only 1 multiplication by 1 number of limited size. Too simple ? Best regards, Simon Plouffe Le 2016-12-11 à 18:04, Bill Gosper a écrit :

Digits. Feh. What a waste of chips and neurons. The only excuse: Now that they've done it, converting to the continued fraction might be slightly easier than extracting the cf directly. But if you want both, it might be easier to extract the decimal from the cf. Or maybe not, since they probably wrote their own multiprecision routines to use base 10^19 vs 2^64 to dodge the big radix conversion cost. 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

Date: 2016-12-10 17:53 From: Simon Plouffe <simon.plouffe@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>

They made a new computation record of Pi,

http://www.numberworld.org/y-cruncher/records.html

22 459 157 718 361 digits.

This is big.

the digits seems to be rather normal in base 10 and 16.

https://arxiv.org/ftp/arxiv/papers/1612/1612.00489.pdf

also : 22.459157718361 is Pi^E.

Some explanations here : http://pi2e.ch/

best regards, Simon Plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

Why the hate? The guy has a single box somewhere and he decided to calculate this using a few CPU months and a few disks. He calculated some digits of pi probably for fun, and then let people know about it. Would it have been better for him to just let the machine be idle for those months when he wasn't using it to play World of Warcraft or whatever the latest game is? Some people tinker with old automobiles, some people knit, some people recreate 70's microcomputers. "Digits of pi" is something non-mathematicians understand; "terms of the continued fraction of pi" is probably not. I think it's cool, myself. If it leads a dozen people a greater understanding of the mathematics of how it was done, I think it is a net win. -tom On Sun, Dec 11, 2016 at 9:04 AM, Bill Gosper <billgosper@gmail.com> wrote:

Digits. Feh. What a waste of chips and neurons. The only excuse: Now that they've done it, converting to the continued fraction might be slightly easier than extracting the cf directly. But if you want both, it might be easier to extract the decimal from the cf. Or maybe not, since they probably wrote their own multiprecision routines to use base 10^19 vs 2^64 to dodge the big radix conversion cost. 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

Date: 2016-12-10 17:53 From: Simon Plouffe <simon.plouffe@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>

They made a new computation record of Pi,

http://www.numberworld.org/y-cruncher/records.html

22 459 157 718 361 digits.

This is big.

the digits seems to be rather normal in base 10 and 16.

https://arxiv.org/ftp/arxiv/papers/1612/1612.00489.pdf

also : 22.459157718361 is Pi^E.

Some explanations here : http://pi2e.ch/

best regards, Simon Plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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