Erlang process rings and calculation examples.

Ring of processes can be used to do meaningful calculations. Following code first makes a simple process ring. Next is demonstration of calculation of Fibonacci numbers using proc rings.The last part does matrix multiplication on a process ring using map reduce kind of functionality. It is inspired by excellent Unix Systems programming book by Robbins and Robbins.

Fun with Erlang processes. Sieve of Eratosthenes reload.

Implementation with different perspective. Thanks to Lab specs from this Berkeley course. I could start 350,000k processes on my laptop. Quite amazing.
BTW I am happy that I wrote the whole program in 20 mins and never changed the design or variable names :).

This course has some innovative assignments which can be fun to learn Erlang.

Mobius function in Erlang and tail recursion.

Quite amazed that a(7) is calculated within reasonable time on my Laptop.
Mobius
Problem statement at Lab1

Tail recursion Fibonacci series in Erlang

Tail Recursion

To write a tail recursive Fibonacci function realize that
F(N) = F(N-1) + F(N-2)
or
F(N) – F(N-1) = F(N-2)
+F(N-1)F(N-2) = F(N-3)
+…
+…
+F(3)F(2) = F(1)
+F(2)-F(1) = F(0)
summing
F(N) = F(N-2) + F(N-3) + … + F(1).
So if we build bottom up ( starting from F(1) ) and pass along F(x-1) to next evaluator we can write something like this.

Erlang and other functional languages are optimized for tail recursion. For N = 30000 it takes less than 1 second. The output is

40> fib:tail_fib(30000).
19042435673462438748500976847175750289440229160233351927339118405204480186334015645055143398261496313746462680414406888563083850055603657740310619718198928947929714143392611469024656483449308262883553198933244095314211154154992091797602074463528140839868820995278353905648288837152313373027428854185240413783027711286633757969372040908765210791301308580029711548762449082301005924550510739921757619046520758565496789221479488666755003743310233657785468581172290594106719323822488426939495282624863879804823433580368865101421394820075152979549683792374577393739322534253197906408052835666632294594746231582662471400644413562679254958577024910666071579523303451450946146257104747680494709535303873170941360441070608298973557161576179154452597979156423104216263957464979391384795077776802220903280507441173996382043335563718339746079992910866064915575335104024807245751118439261465938737435400906452921221950182080802222425495979798360155543925506967015199518087285324593383106768125389304520074812290917762161886588827498280610810822465270583563165461870332006766892853289064108716831003373140279469873515791937818813311730631598182284185088271567688145937352301045235975775773020943043219385055860977483758405710290689324827232264711764535072320524460794310182118123596860236873652311505866805337193988771190119249007146948018269266890839670763428439803797619997277495037186709314163025002517931570189746371535583338167311069714442117594249205335071056156021946875125079852527025692388149215738852678414311054134673189054756417329343835627008097464090777161594425231447628244538155235479823484280828211200123364800921054859912826037993416371331219320802877870621652274274055589610283029854803174083544724718537899241236095404192279020272447418684679370227402528647994025074622898979976020050188417240022841627206728268332714031918425926456735992885333231061710728748826343932659120248598624328091977111801912944766477151447946700560546331072939089300111940726307703614437570659002484903687932986802608471264963787687346537867990076178754102947570311603469155639656251741377370527939576204761062778787204147618092117298450330734362424727526929866990579109160833088283172902879404924552053341676871020564428965625197786475714178722790924502254309036099846112536054591472032328610197564612082721780744990528315966049849573721693792522422092581795964686565434131541986140174294029712869929862854977368424716877840011451671913530003046545949819735541406974644240548424223168510129071794673854353523261978303125929015512989365527148799170257784751281336875223872113775025438350069062195274622603396899781365549348864571497551478878118904611702461750432531088204376795938097567317727492635935829258365408798322192087007729393423987582746351829830094251347938735003228340958634427646690840161210376166938629256998526391558231633766722647996682253101712726212412624235022052083580878207362495285609075370175950936209203296396133158100856830402131795376685034739511683268944576010713654081421402139240433124176338564116781672718660204243410578107448350922382911422776392596604843613363249096976615289605560504888576679637894907321262819343064074072292852810008735030166384995583608311575003838363929289695277384460009524233645207501072908339297207542817706168495104863771430406629765848254332195528600597603096820437009518170202336340203155532165253867793143379779540139686156253945102218152870536304518915450505952816631474675547601150248774744132600968205177569420521185408816770837936929397875845902556398904551764798693457966997222411410793322578669246604930181716937997162033983970515680889491634015415706720634017788159791039491983692312288346995656628327281417729616620150857623498510566989499732965501831068077284636242566331648610154267522174969956975625641432960977430447386352301805864334746626727999006347499781808199454631735554537634501766333664975587446502786336815175496282486579000619566287148530031086028832461183428326743067726448788524471794732311923719919657564733666635736914165955519414277810815184739323543624018353230063906315546823899171266301160317057659159557147266475106287152896374741152827340604749976637445019436550883817123366371700151833823549085265974692171108015534545792779599849353262389399495697200913516918439732000228694570291432171593573987852520820892629643193994930717134922008259407909355368688143395960892072815580780644503591827372210002964806675603957877251591707452763488603236282733806567159751676791156620944411073680772393239340471410656291176117419045659992967115355217979048501104941609800772173489683902945095455704099078764834461244496409227713993666712592073827190209728044264621300740096880024707175736923914461453529301910823646960139692371080693155736430614664199607193379205760879701795897587049507166953821566051918235226718274866495575892337125236123266169077819623329213543228128185812980249098463788539080406688131346475708872012964394222370520940734889027980641129302128565024614313620556259765850003643999654616285213969666661963897824720677971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Sieve of Eratosthenes

Sieve of Eratosthenes in DrRacket

Book review perfect rigor

Finished reading Pefect Rigor by Masha Gesson. Here are the new things I learnt from the book.

  • Jews were discriminated in erstwhile CCCP.
  • IMO students were forced to do physical training and read beyond Mathematics thanks to Andrey Kolmogorov. Who apparently was openly gay.
  • Grigory Perelmen had some good reasons to not accept Fields medal and Clay institutes millennium awards.

Further remarks

  • Author has the most pessimistic facial expressions. Reminds me of Jerry Sienfeld’s girlfriend in one of the episodes.
  • Whole book is written from second/third hand interviews.
  • Who needs stupid Fields medal or million dollar from Clay institute when you can bend the frigging time-space curves on its head and be master of universe. (no seriously).