Last Piece of Pi

So, last spring I did a series of posts on making a Pi spigot. Unfortunately, the project foundered a bit, as it turned out that only Rakudo had the subsignatures needed to make the code pretty, but only Niecza had the big integers needed to make the code work.

Fast forward to today. Now both Rakudo and Niecza can handle the best version of the code with no problem!

Let me emphasize that again. A year ago, neither implementation had those two features. Eight months ago, each had one. Today both have both. What’s more, Rakudo seems to have made some pretty impressive speed improvements.

I think the awkward situation with Rakudo Star has helped obscure the fantastic good news in Perl 6. Right now we have two distinct Perl 6 implementations, each of which is markedly better than anything available a year ago. While there are still some rough edges, both implementations are making visible progress every single day.

Okay, enough cheerleading. Time to finish the Pi story. It turned out there was one last complication. I had never actually tried to use the code to generate an infinite stream of Pi. I always stopped at 40 digits. Confident that the algorithm must work, I tweaked the output to just continue generating digits until you stopped the program with control-C. And I ran it using Niecza, and it printed

3.14159265358979323846264338327950288419716
9399375105820974944592307816406286208998628
0348253421170679821480865

And then it just sat there, calculating. After a few minutes I stopped it and tried it in Rakudo, and got the exact same result.

Well, after adding a few debugging says here and there, I found the problem. The extr sub was returning NaN. It turns out that both compilers have issues with dividing huge numbers. Here’s the division operation that was causing the problem:

826855066209083067690330954944954674053
707782399091459328155002954168455127712
564546723209828068849110223672691692080
858850302237001093531862737473606364113
314687502675869281622802970765988449203
963736097729699655628829895255493809983
868753943269929165690008254816168624365
041070395716948346309925280258763697273
816643106559428329680316113883598846477
019844021876290510680558354153412094804
165563855909020631086890050609449881578
622437959410200560054513816596644762131
226627968813825552929967132893776980417
525678140579476414867767644626389410380
794467097761379794479928269796859019439
705966555011741254554959832606241504043
482378842096776403191455346497512084739
323724281071973237937801014210278895804
940475966938880398182275335278425442994
287812050560074302564177393567873480740
249095636709741437469651121924884638352
523975466249955052660310789169884060356
70777782797813415527343750 / 7640045443
915776552858245682965495041201868477244
923723289802372673948570989301189643881
881673616027696317656701576457227272117
067947294675092324411286583110995372015
785893970194452345100095389207557064515
618905243737091067059065039684867000766
465399984513882758095027633673968549038
659642193965599458094646356792444696562
299054844575814305259223023977803302735
242307789179027935107449661143998428584
590618630170775872761731454567203230484
311106708425828778192240791257477924515
937573923664112071637127786446287936043
637833776529791999568414593746973068229
015816020732598109749879566833692821582
816119454436978125677364775318707235283
939392855143663977524974469973442065855
128922452382372338686111634084367257050
255499210918328304009454606504169283500
652033488755998721320134300149134205253
095344802815192912405314659633341062491
389270940370884860337596933277382049709
5584869384765625

Turns out the bottom number is bigger than can be presented by a Num, so the division operation ends up becoming N / Inf, which is NaN. This is a bit obscured in Rakudo because the division operation actually returns a Rat (which should be illegal according to the spec!), but then .floor is called on the result, which tries to convert to Num before doing the floor operation.

This opens several questions, like: Should Perl 6’s Int / Int operator be modified to try to cope with this sort of case?

But for the Pi problem, the good news is this: every time the extr sub is called, its result is fed to .floor. That means we simply needed to replace / with div and get rid of the .floors.

And with that, the code easily produces 2,000+ digits of Pi using either Rakudo or Niecza!