(02-14-2018 07:24 PM)John Keith Wrote: (02-12-2018 03:40 AM)Gerson W. Barbosa Wrote: For real fun, I would try a 2500-year-old algorithm (with a small adjustment for speed) on my 50g. No problem waiting three hours for the glorious thousand digits :-)
http://www.hpmuseum.org/cgi-sys/cgiwrap/...443#189221
There is also a 4-minute alternative (certainly more than 10 minutes on the 49G). Both programs require the LongFloat library, though.
I know it's "cheating", but LongFloat's built-in function FPI returns 1000 digits of PI in about 42 seconds on the HP50, about 1.1s on the emulator. :-)
Less than 74 seconds on my HP 49G. But this is not about getting it fast, it's about testing a method that was available in India at least sinced the late 14th century. I believe the continued fraction which works as a correction to the very slowly convergent Madhava-Leibniz series (a.k.a. Gregory series), was known to Madhava. 20 terms of the series and 20 terms of the continued fraction would have yielded 30 correct digits, but the latter might be not practical for manual calculation, or they just thought it was not worth the effort.
By using this method, a thousand digits can be computed in less than four hours (3h51m09s) on a 49G. I don't think they would have found that too slow back then :-)
1000
Code:
%%HP: T(3)A(D)F(.);
\<< 1. + DUP 'DIGITS' STO 4. + 3. / IP R\<-\->F DUPDUP FADD OVER FSQ 4. R\<-\->F
FMULT OVER DUP FADD DUPDUP FADD SWAP 1. R\<-\->F FSUB 0. R\<-\->F DUP 1. 8. ROLL
R\<-\->F
START UNROT OVER FINV FSUB OVER 2. R\<-\->F FSUB FINV FADD 6. ROLLD 4. ROLLD
OVER FADD PICK3 SWAP FDIV 4. ROLLD UNROT DUP2 SWAP FSUB 5. ROLL 6. PICK FADD FDIV
UNROT OVER 1. R\<-\->F FSUB DUP FADD FSUB UNROT 4. R\<-\->F FSUB UNROT 5. ROLLD
UNROT 6. ROLL 6. ROLL
NEXT 4. PICK FADD FINV FADD 4. R\<-\->F FMULT 5. ROLLD 4. DROPN
\>>
EVAL
-->
31415926535897932384626433832795028841971693993751058209749445923078164062862
089986280348253421170679821480865132823066470938446095505822317253594081284811
174502841027019385211055596446229489549303819644288109756659334461284756482337
867831652712019091456485669234603486104543266482133936072602491412737245870066
063155881748815209209628292540917153643678925903600113305305488204665213841469
519415116094330572703657595919530921861173819326117931051185480744623799627495
673518857527248912279381830119491298336733624406566430860213949463952247371907
021798609437027705392171762931767523846748184676694051320005681271452635608277
857713427577896091736371787214684409012249534301465495853710507922796892589235
420199561121290219608640344181598136297747713099605187072113499999983729780499
510597317328160963185950244594553469083026425223082533446850352619311881710100
031378387528865875332083814206171776691473035982534904287554687311595628638823
537875937519577818577805321712268066130019278766111959092164201989.E-1000
s: 13868.7266
That's about the time it takes the HP 50g to get the equivalent algebraic expression. Expanding it would take much, much longer.
1000
Code:
« PUSH RAD -105 CF -3 CF 4 + 3 IDIV2 DROP DUPDUP + OVER SQ 4 * OVER DUP + DUPDUP + SWAP 1 - 0 DUP 1
8 ROLL
START UNROT OVER INV - OVER 2 - INV + 6 ROLLD 4 ROLLD OVER + PICK3 SWAP / 4 ROLLD UNROT DUP2
SWAP - 5 ROLL 6 PICK + / UNROT OVER 1 - DUP + - UNROT 4 - UNROT 5 ROLLD UNROT 6 ROLL 6 ROLL
NEXT 4
PICK + INV + 4 * 5 ROLLD 4 DROPN POP
»
EVAL
-->
Code:
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2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)
+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)
+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672
)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668)+2672)+668
)+2672)+668)+2672)+668)+2672)+668)+2672))*4'
EXPAND
-->
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980089432434864965104974017069056/
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714122045000936522301890676982272649077234522014303978345842413157035790893429
82462406016044012038707143579375
1000 SWAP
FXND DUP SIZE R->I ALOG OVER - PICK3 * SWAP IQUOT + ->STR DUP HEAD -51
FC? { "." } { "," } IFTE + SWAP TAIL + 1 ROT 2 + SUB
EVAL
-->
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
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031378387528865875332083814206171776691473035982534904287554687311595628638823
537875937519577818577805321712268066130019278766111959092164201989
Edited to (try to) fix some formatting
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