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Obtaining More Decimal Digits (50g)
Message #1 Posted by Eddie W. Shore on 30 Aug 2012, 12:07 p.m.

http://edspi31415.blogspot.com/2012/08/obtaining-more-digits-with-hp-50g.html

      
Re: Obtaining More Decimal Digits (50g)
Message #2 Posted by Gilles Carpentier on 1 Sept 2012, 5:12 a.m.,
in response to message #1 by Eddie W. Shore

Hi Eddy,

Interesting. Here is a program wich calcultate n digits of PI with the same idea using BMP (Plouffe) formula 

«
  -> n
 «
  0                                            @ initial Value of PI
  n ALOG                                       @ Number of digits to find
  1                                            @ 16^k initial value = 16^0
  0 '2+LOG(8*n)+n*LOG(16)' >NUM CEIL R>I FOR k @ Number of iteration 
   k 1. DISP                                   @ Display iterations
   OVER [ 120 151 47 ]     k PEVAL *           @ Nominator * n ALOG
   OVER 16 * SWAP ROT                          @ 16^k and 16^(k+1) on the stack
   [ 512 1024 712 194 15 ] k PEVAL *           @ Denominator
   IQUOT 4. ROLL + UNROT                       @ Integer quotient and add to ~PI
  NEXT 
  DROP2 
 »
»
'nPi' STO

The idea is that if you expand Plouffe formula :

'(1/(16^k))*((((4/((8*k)+1))-(2/((8*k)+4)))-(1/((8*k)+5)))-(1/((8*k)+6)))' EVAL EXPAND
->
'(k^2*120+151*k+47)/((512*k^4+1024*k^3+712*k^2+194*k+15)*2^(4*k))'

500 nPi gives the 500 first décimal of PI in ~ 3mn on a real calc (few seconds with emu48)(the last 3 digits are wrong)

As you can see here, the BMP formula is very interesting to calculate the n'th dgit of PI in hexadecimal :

Calculate the 1 million PI hexa digit in UserRpl

Edited: 1 Sept 2012, 5:55 a.m.

            
Re: Obtaining More Decimal Digits (50g)
Message #3 Posted by Eddie W. Shore on 13 Sept 2012, 8:34 a.m.,
in response to message #2 by Gilles Carpentier

I kind of get stuck at matching 20 digits for pi. (correct digits of pi are separated)

24 nPi returns 314159265358979323846 1556

30 nPi returns 314159265358979323846 1565762641

36 nPi returns 314159265358979323846 1565762653862973

Eddie

Sorry for the late reply

                  
Re: Obtaining More Decimal Digits (50g)
Message #4 Posted by Gilles Carpentier on 13 Sept 2012, 5:38 p.m.,
in response to message #3 by Eddie W. Shore

Hi

You must be in 'exact mode' (uncheck APPROX in CAS setup) and _no decimal point_ in the numbers used for calculation in the program

36 nPI

3141592653589793238462643383279502869

2500 nPI

3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456027509

Edited: 13 Sept 2012, 5:57 p.m.

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