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Calculating a record-breaking 31.4T digits of Pi with GCP

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Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#111

Post by vonmoltke »

StreakyCobra wrote: post #23
hokobomo wrote: post #17

> March 14 (represented as 3/14 in many parts of the world) haha

I wanted to comment the same part, but I wanted to let them the benefit of the doubt, so I went to Wikipedia «date format by country» page [1], and summed up from the table how many people have "MD" vs "DM" in their date format: DM -> 3392/5550 ~= 61.1% MD -> 2158/5550 ~= 38.9% Note: I ignored both green and red regions that have both "DM" and "MD" in their format. So it is definitively not the majority of people. Us…

I treat "some" as an informal expression of relative quantity and "many" as an informal expression of absolute quantity. So it is valid to say many countries use "MD" and many countries use "DM", though most countries use "DM" and only some use "MD".

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#112

Post by ectospheno »

rlanday wrote: post #84
bostonpete wrote: post #36

Earlier quoted context omitted.

The linked NASA article points out that with 40 digits of pi you could compute the circumference of the visible universe to an accuracy equal to the diameter of a hydrogen atom. I'm gonna say there's no practical application that would require even 40 digits, never mind a few hundred

You need more digits than that to accurately compute double-precision trigonometric functions (if the input is close to pi, you need enough accurate digits left after performing range reduction). This paper claims you need 2/pi accurate to 1144 bits which is about 345 decimal digits: https://www.csee.umbc.edu/~phatak/645/supl/Ng-ArgReduction.p...

As a counterpoint, no real computation I've performed on a computer needed to compute the cos of 2^1023 radians. I can't imagine such a scenario either.

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#113

Post by rlanday »

ectospheno wrote: post #112
rlanday wrote: post #84

Earlier quoted context omitted.

You need more digits than that to accurately compute double-precision trigonometric functions (if the input is close to pi, you need enough accurate digits left after performing range reduction). This paper claims you need 2/pi accurate to 1144 bits which is about 345 decimal digits: https://www.csee.umbc.edu/~phatak/645/supl/Ng-ArgReduction.p...

As a counterpoint, no real computation I've performed on a computer needed to compute the cos of 2^1023 radians. I can't imagine such a scenario either.

You can either implement the functions accurately or inaccurately. Implementing them inaccurately is a slippery slope. Intel botched the hardware implementations in their processors not only for large inputs but also for inputs nearish to multiples of pi:

http://notabs.org/fpuaccuracy/index.htm

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#114

Post by Smithalicious »

aaaaaaaaaaab wrote: post #32

Meh, throwing raw power at the problem is not that impressive. Bellard's [1] 2009 record was much more impressive, because he used a clever formula to break the existing record with a mere (albeit beefy) desktop computer: https://bellard.org/pi/pi2700e9/ The record he broke with his desktop PC was made using a supercomputer cluster. [1] If somebody is not familiar with him, he is also the original author of QEMU, ffm…

Wow, I had no idea that the same guy is behind both QEMU and FFMPEG! That's really impressive.

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#115

Post by patrickg_zill »

onion2k wrote: post #15
curiousgal wrote: post #11

Earlier quoted context omitted.

Why would you need to do that? It's not like those digits are useful for anything at all.

I guess it depends on your definition of "useful", but one potential way to use pi would be as a way to transmit compressed data incredibly efficiently. If you could find the data you want to transmit in pi somewhere you'd only need to transmit an offset and a length to send anything than can be represented numerically. The hard part would be finding what you want to send though... ;)

You've kind of re-invented, in a way, using DCT transforms to encode music more efficiently...

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#116

Post by isostatic »

rkangel wrote: post #73
s_gourichon wrote: post #22

Earlier quoted context omitted.

Yes. ISO chooses year-month-day, which puts largest component first and smallest last. This has the nice benefit that treating it as a string and doing alphanumerical sort matches the actual day sort. Ref. https://en.wikipedia.org/wiki/ISO_8601

The main benefit of Y-M-D, is that no-one uses Y-D-M, and the 'Y' component is easily recognisable. So if you use Y-M-D, then everyone knows it's Y-M-D and there is no ambiguity.

I found out recently the x509/tls certa are YYMMDD

200122

For example. Amazing.

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#117

Post by wool_gather »

stephencanon wrote: post #98
wool_gather wrote: post #94

Earlier quoted context omitted.

This is the concept of [a "normal" number][0] (which is a strange choice of word, I think). Apparently pi is not proven to be normal. But the implication as I understand is that, yes, any given sequence that you'd care to look for is there somewhere. [0]: https://en.wikipedia.org/wiki/Normal_number

Almost all numbers are normal, so it seems like a perfectly reasonable choice of terminology =) [On the other hand, almost none of the numbers someone on the street might name are normal, so ...]

Ah, I didn't realize that, thanks! That makes sense now that you say it.

Re: Calculating a record-breaking 31.4T digits of Pi with GCP

#118

Post by stephencanon »

wool_gather wrote: post #117
stephencanon wrote: post #98

Earlier quoted context omitted.

Almost all numbers are normal, so it seems like a perfectly reasonable choice of terminology =) [On the other hand, almost none of the numbers someone on the street might name are normal, so ...]

Ah, I didn't realize that, thanks! That makes sense now that you say it.

Almost all real numbers are a lot of things, though:

   - uncomputable
   - irrational
   - transcendental
   - ...
So it's not really that good of a justification. =)
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