HP Forum Archive 19

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Happy Pi Day Message #1 Posted by Egan Ford on 14 Mar 2009, 12:09 p.m. For the last few weekends I have been exploring faster and faster ways to compute Pi to 1000 digits on the 71B. The 71B is an incredible machine. I am always amazed at what this little hand-held computer can do. If you are more interested in newer calculators, then check out my 50g Pi programs: Example: Pi Shootout Sidebar: P2F Vieta Accelerated NOTE: This is a subset of a larger article I will finish someday. I will have more results, hopefully before the next Pi day (22/7). Draft Subject: 1000 Digits of Pi on Pre-1990 Hand-Held Calculators and Computers The genesis of this article originated with the following statement from Gene Wright, "Looks like the race to 1000 digits on a machine prior to 1990 now belongs to TI? Can we beat the 5.81 hours on the TI95 with the HP71B?" (http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=53988) As of early 2009 this challenge has remained unanswered--until now... I've spent the last few weekends exploring various ways to meet this challenge. The most amazing result is Ron Knapp's RPN code running on the 71B (entry 5). The quest to best 5.81 hours could have ended in 1985 with a HP-41 Translator Pac equipped 71B! Algorithm Platform Language Memory Digits Time(s) ------------- -------- -------- ------ ------ ------- 1. Atan Stormer1 HP-71B Forth 3360 B 1002 3172 (0.88 hr) (53.87 min) 2. Atan Stormer HP-71B Forth 3360 B 1002 3434 (0.95 hr) (57.23 min) 3. Atan Machin1 HP-71B Forth 3360 B 1003 3561 (0.99 hr) (59.35 min) 4. Atan Machin HP-71B Forth 3360 B 1003 3825 (1.06 hr) (63.75 min) 5. Atan Machin2 HP-71B RPN 220 R? 1001 6034 (1.68 hr) 6. Spigot HP-71B Forth 17.1 K 1002 6720 (1.87 hr) 7. Atan Machin3 TI-95 AOS 1001 ~20916 (5.81 hr) 8. Atan Machin2 HP-41CX RPN 1540 B 1001 ~30600 (8.50 hr) 11000 decimal digits represented as base 220. 2Ron Knapp implementation. 3Bob Fruit implementation. Table 1 Summary of Results < 9 Hours Entries 1 and 3 are the same as 2 and 4 respectively, just timed differently. All four were computed base 220 to get the most out of the 20-bit Saturn architecture, however entries 1 and 3 stopped the clock after 168 base 220 digits were computed, whereas entries 2 and 4 stopped the clock after the number was converted to base 10. Since it takes ~3.5 minutes just to display the results and without any clear rules on the subject I opted to report both. I expect that most will agree that 1000 decimal digits of Pi must be represented as 1000 decimal digits making entry 2 the fasted pre-1990 hand-held leader. Entries 5 and 8 are based on Ron Knapp's original program published in 1981 (V8N6P69 of the PPC Calculator Journal). Output and Code HP-71B Arctan Forth HP-71B Spigot Forth HP-71B Arctan RPN TI-95 Arctan AOS HP-41CX Arctan RPN 1. HP-71B Arctan Forth Output of entries 2 and 4 (1 and 3 are the same but have different times reported. (see above)): 3. 141592653589793238462643383279502884197169399375105820974944592307816406286208 998628034825342117067982148086513282306647093844609550582231725359408128481117 450284102701938521105559644622948954930381964428810975665933446128475648233786 783165271201909145648566923460348610454326648213393607260249141273724587006606 315588174881520920962829254091715364367892590360011330530548820466521384146951 941511609433057270365759591953092186117381932611793105118548074462379962749567 351885752724891227938183011949129833673362440656643086021394946395224737190702 179860943702770539217176293176752384674818467669405132000568127145263560827785 771342757789609173637178721468440901224953430146549585371050792279689258923542 019956112129021960864034418159813629774771309960518707211349999998372978049951 059731732816096318595024459455346908302642522308253344685035261931188171010003 137838752886587533208381420617177669147303598253490428755468731159562863882353 787593751957781857780532171226806613001927876611195909216420198938 TIME: 3824.81 SEC 3. 141592653589793238462643383279502884197169399375105820974944592307816406286208 998628034825342117067982148086513282306647093844609550582231725359408128481117 450284102701938521105559644622948954930381964428810975665933446128475648233786 783165271201909145648566923460348610454326648213393607260249141273724587006606 315588174881520920962829254091715364367892590360011330530548820466521384146951 941511609433057270365759591953092186117381932611793105118548074462379962749567 351885752724891227938183011949129833673362440656643086021394946395224737190702 179860943702770539217176293176752384674818467669405132000568127145263560827785 771342757789609173637178721468440901224953430146549585371050792279689258923542 019956112129021960864034418159813629774771309960518707211349999998372978049951 059731732816096318595024459455346908302642522308253344685035261931188171010003 137838752886587533208381420617177669147303598253490428755468731159562863882353 787593751957781857780532171226806613001927876611195909216420198937 TIME: 3433.92 SEC Code: : PIATAN ; 79 6 / CONSTANT MAXL 1002 CONSTANT N N 6 / 1 + CONSTANT M 5 CONSTANT S M S * CONSTANT E CREATE A E NALLOT CREATE B E NALLOT CREATE XX E NALLOT CREATE YY E NALLOT VARIABLE D VARIABLE F VARIABLE FF VARIABLE G VARIABLE H : 1D. <# # #> TYPE ; : 06D. <# # # # # # # #> TYPE ; : MPSET OVER ! DUP E + SWAP S + DO 0 I ! S +LOOP ; : MPCOPY 2DUP - SWAP DUP E + SWAP DO I @ OVER I + ! S +LOOP 2DROP ; : UD+ ROT + ROT ROT + ; : MPDIV D ! DUP DUP M 0 DO DUP @ 0= IF S + ELSE LEAVE THEN LOOP DUP E - ROT = IF 2DROP 0 ELSE 0 SWAP ROT E + SWAP DO I @ SWAP D @ UM/MOD I ! S +LOOP DROP 1 THEN ; : MPMULT D ! DUP DUP E + S - M 0 DO DUP @ 0= IF S - ELSE LEAVE THEN LOOP > IF DROP ELSE 0 SWAP DUP E + S - DO I @ D @ UM* ROT 0 D+ SWAP I ! S NEGATE +LOOP DROP THEN ; : MPSUB 2DUP - D ! 0 SWAP DUP E + S - DO I D @ + DUP H ! @ 0 I @ 0 D- ROT 0 UD+ H @ ! S NEGATE +LOOP 2DROP ; : MPADD 2DUP - D ! 0 SWAP DUP E + S - DO I D @ + DUP H ! @ 0 I @ 0 D+ ROT 0 D+ SWAP H @ ! S NEGATE +LOOP 2DROP ; : MPATAN F ! G ! 1 FF ! XX 1 MPSET XX F @ MPDIV DROP G @ XX MPCOPY F @ 1024 < IF F @ DUP * F ! 0 FF ! THEN 1 BEGIN 2 + XX F @ MPDIV DROP FF @ 1 = IF XX F @ MPDIV DROP THEN YY XX MPCOPY DUP YY SWAP MPDIV 1 = WHILE DUP 2 AND 0 > IF G @ YY MPSUB ELSE G @ YY MPADD THEN REPEAT DROP ; : MPPRINT XX SWAP MPCOPY XX @ 0 1D. ." ." CR N 0 DO 0 XX ! XX 1000000 MPMULT XX @ 0 06D. I 6 / 1 + MAXL MOD 0= IF CR THEN 6 +LOOP ; : MACHIN A 5 MPATAN A 16 MPMULT B 239 MPATAN B 4 MPMULT A B MPSUB ; : STORMER A 57 MPATAN A 176 MPMULT B 239 MPATAN B 28 MPMULT A B MPADD B 682 MPATAN B 48 MPMULT A B MPSUB B 12943 MPATAN B 96 MPMULT A B MPADD ; : DOIT CLOCK MACHIN A MPPRINT CR CLOCK CR ." TIME: " X<>Y F- STD F. ." SEC" CR CR CLOCK STORMER A MPPRINT CR CLOCK CR ." TIME: " X<>Y F- STD F. ." SEC" CR ; 2. HP-71B Spigot Forth 314159265358979323846264338327950288419716939937510582097494459230781640628620 899862803482534211706798214808651328230664709384460955058223172535940812848111 745028410270193852110555964462294895493038196442881097566593344612847564823378 678316527120190914564856692346034861045432664821339360726024914127372458700660 631558817488152092096282925409171536436789259036001133053054882046652138414695 194151160943305727036575959195309218611738193261179310511854807446237996274956 735188575272489122793818301194912983367336244065664308602139494639522473719070 217986094370277053921717629317675238467481846766940513200056812714526356082778 577134275778960917363717872146844090122495343014654958537105079227968925892354 201995611212902196086403441815981362977477130996051870721134999999837297804995 105973173281609631859502445945534690830264252230825334468503526193118817101000 313783875288658753320838142061717766914730359825349042875546873115956286388235 378759375195778185778053217122680661300192787661119590921642019893 TIME: 6720.22 SEC Code: : SPIGOT ; : 06D. <# # # # # # # #> TYPE ; 79 6 / CONSTANT MAXL 1002 CONSTANT N N 6 / 21 * CONSTANT M 5 CONSTANT S CREATE A M S * NALLOT 1000000 CONSTANT F VARIABLE E VARIABLE K VARIABLE P : SPIGOTM 1 K ! 0, 1 M 1 - DO I SWAP OVER UM* SWAP 2SWAP UM* D+ 200000000000, D+ I 2* 1 - M/MOD ROT A I S * + ! -1 +LOOP F M/MOD 06D. DUP E ! 0 0 M 22 - DO 1 I DO I SWAP OVER UM* SWAP 2SWAP UM* D+ A I S * + DUP P ! @ F UM* D+ I 2* 1 - M/MOD ROT P @ ! -1 +LOOP F M/MOD E @ 0 D+ 06D. DUP E ! 0 1 K +! K @ MAXL MOD 0= IF CR THEN -21 +LOOP 2DROP ; : DOIT CLOCK SPIGOTM CLOCK CR CR ." TIME: " X<>Y F- STD F. ." SEC" CR ; 3. HP-71B Arctan RPN This was originally written by Ron Knapp for the 41. Minor changes were made to address output formatting and timing. Output: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208 99862803482534211706798214808651328230664709384460955058223172535940812848111745 02841027019385211055596446229489549303819644288109756659334461284756482337867831 65271201909145648566923460348610454326648213393607260249141273724587006606315588 17488152092096282925409171536436789259036001133053054882046652138414695194151160 94330572703657595919530921861173819326117931051185480744623799627495673518857527 24891227938183011949129833673362440656643086021394946395224737190702179860943702 77053921717629317675238467481846766940513200056812714526356082778577134275778960 91736371787214684409012249534301465495853710507922796892589235420199561121290219 60864034418159813629774771309960518707211349999998372978049951059731732816096318 59502445945534690830264252230825334468503526193118817101000313783875288658753320 83814206171776691473035982534904287554687311595628638823537875937519577818577805 321712268066130019278766111959092164201989 TIME: 6033.60 SEC Code (use RUN TRANS41 to input): LBL "CPI2" X<0? R^ ST* T RCL 05 CLRG + ST+ T ST* Z + 219 RCL 01 X^2 * DSE Y STO 00 RCL 04 R^ RCL 08 LBL 14 TIME ST/ Z + * STO IND 00 HR * + FRC RDN STO IND 00 ENTER^ FC? 00 X<>Y DSE 03 FIX 03 LBL 99 GTO 04 LASTX DSE 00 4 RCL 08 RCL 13 INT GTO 13 STO 09 ST/ Z * R^ 219 1E5 MOD 3 + STO 00 ST/ Y R^ DSE 02 RCL 05 TIME STO 04 INT GTO 05 - HR X^2 LASTX LBL 04 + RCL IND 00 STO 05 FRC RCL 07 X>0? - X<>Y RDN * ISG IND 00 STO IND 00 427 + RCL 06 X>0? LBL E + X<>Y LBL 05 GTO 11 SF 21 STO 02 INT X<>Y RCL 05 CLA 239 RCL 04 RDN + FIX 00 X^2 ST* T / LBL 11 14.114 STO 07 ST* Z STO 01 ISG 00 STO 00 LASTX * CLX GTO 10 SF 29 1E2 STO IND 00 R^ GTO J RCL IND 00 * RDN ENTER^ LBL 09 ACX STO 13 ENTER^ GTO 06 RCL 03 STD RDN LBL 99 LBL 07 STO 00 CF 29 X^2 RCL 08 RCL 01 RCL 10 ISG 00 STO 08 ST/ Z ST/ Z X^2 LBL 15 94E-5 MOD MOD 3 XEQ 16 STO 11 X<>Y X<>Y Y^X ISG 00 14.0139 INT INT LASTX FS? 00 STO 12 ST+ IND 00 X<>Y * GTO 17 25 RDN RCL 04 STO 08 XEQ 16 STO 10 + ST* Z CLX CLA LBL 00 STO 01 * LBL 12 ISG 00 RCL 11 RCL 03 ENTER^ RCL IND 00 GTO 15 ST+ 12 RCL 04 LBL 06 X<>Y ACA RCL 12 * RCL 01 RCL 04 GTO 17 RND ENTER^ ST/ Z ST/ Z LBL 16 STO 00 ISG 00 MOD * RCL IND 00 RCL 07 GTO 02 RDN ENTER^ RCL 04 RCL 02 DSE 02 INT LBL 99 / INT GTO 00 + RCL 08 INT ENTER^ 4096E-7 RCL IND 00 ST/ Z LASTX ST* Z STO 08 - MOD FRC 2 1439.00006 X>0? R^ RCL 04 - STO 02 GTO 08 INT XEQ 18 ST- Z 837E-6 DSE 00 LASTX XEQ 18 * STO 11 LBL 99 FRC RTN RCL 10 115.115 DSE IND 00 RDN LBL 18 * STO 12 ISG 00 + * STO 06 80 RCL 05 X<>Y RCL Y CLX STO 13 + INT X=0? STO 01 5E6 LBL 08 RCL 04 GTO 19 X<>Y STO 07 STO IND 00 ST* T LOG RCL 13 .75 R^ ST* Z INT * STO 06 RCL 04 * LBL 19 ENTER^ LBL J * STO IND 00 RCL 09 GTO 01 RCL 11 ENTER^ RDN X<>Y LBL 02 ST+ 12 ISG 00 ENTER^ X=Y? RCL 06 RCL 12 GTO 07 LBL 99 GTO 20 ST/ Z RND RCL 03 RCL 08 - MOD STO 00 STO 00 ST/ Z 0 X<>Y STO 03 FS?C 00 MOD LBL 21 INT SF 00 GTO 03 X<>Y ARCL X X<>Y LBL 03 CLX INT DSE Y RCL 04 RCL 02 ENTER^ ST+ IND 00 GTO 21 ST* Z INT DSE 02 RDN LBL 20 * ENTER^ FS? 00 + ARCL T ENTER^ ENTER^ GTO 09 ISG 00 ACA LBL 01 LBL 99 LBL 10 GTO 12 CLA RCL 06 2 X<> IND 00 114.013 RTN ST/ Z - RCL 04 STO 00 LBL 17 MOD ST* Z / 215 ADV STO 03 RCL 10 FRC STO 03 ADV RDN ST* Z LASTX CLX 219 INT X<>Y INT LBL 13 STO 00 + * RCL 08 RCL IND 03 RCL IND 00 RCL 05 2 * + 3600 ST- Y ST- L FRC RCL IND 00 * X<>Y CLX LASTX - FIX 02 RCL IND 00 LASTX INT 0 "TIME: " + ST* T ST+ IND 00 X<>Y ARCL X X>0? ST- Y RDN X<0? "} SEC" ISG 01 RDN X<>Y X>0? PRA LBL 99 * RCL 05 GTO 14 END 4. TI-95 Arctan AOS Code: 5. HP-41CX Arctan RPN This was originally written by Ron Knapp. Minor changes were made to address output formatting, timing, and duplicate labels (labels were changed to increase readability). NOTE: The timing was from EMU41, the orginal time was ~8.5 hours. The final article will have a 41CX retiming. Output: 3. 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 TIME: 32.51 SEC Code: 01 LBL "CPI2" 111 STO IND 00 221 X>0? 331 + 02 CLRG 112 RDN 222 GTO 09 332 ISG 00 03 219 113 ENTER 223 DSE 00 333 GTO 13 04 STO 00 114 LBL 99 224 LBL 99 334 114.013 05 TIME 115 RCL 08 225 DSE IND 00 335 STO 00 06 HR 116 ST/ Z 226 ISG 00 336 215 07 STO IND 00 117 MOD 227 RCL 05 337 STO 03 08 FIX 03 118 X<>Y 228 + 338 CLX 09 4 119 INT 229 LBL 09 339 LBL 14 10 STO 09 120 ST+ IND 00 230 STO IND 00 340 RCL IND 03 11 E5 121 RDN 231 R^ 341 + 12 ST/ Y 122 + 232 RCL 04 342 RCL IND 00 13 STO 04 123 STO 01 233 * 343 - 14 X^2 124 RCL 03 234 ENTER 344 0 15 STO 05 125 RCL 04 235 ISG 00 345 X<>Y 16 X<>Y 126 * 236 GTO 08 346 X<0? 17 427 127 ENTER 237 RCL 03 347 X>0? 18 + 128 ISG 00 238 STO 00 348 GTO 15 19 STO 02 129 GTO 03 239 FS?C 00 349 RCL 05 20 239 130 DSE 02 240 GTO 04 350 + 21 X^2 131 GTO 01 241 CLX 351 DSE Y 22 STO 07 132 4096 E-7 242 ENTER 352 LBL 15 23 LASTX 133 STO 08 243 DSE 02 353 STO IND 00 24 E2 134 1439.00006 244 FS? 00 354 RDN 25 * 135 STO 02 245 GTO 10 355 DSE 03 26 STO 13 136 837 E-6 246 LBL 11 356 DSE 00 27 RDN 137 STO 11 247 X<> IND 00 357 GTO 14 28 X^2 138 115.115 248 RCL 04 358 219 29 STO 08 139 STO 12 249 / 359 STO 00 30 94 E-5 140 80 250 FRC 360 TIME 31 STO 11 141 STO 13 251 LASTX 361 HR 32 14.0139 142 5 E6 252 INT 362 RCL IND 00 33 STO 12 143 STO 07 253 RCL 08 363 - 34 25 144 .75 254 * 364 STO IND 00 35 STO 10 145 STO 06 255 FRC 365 RTN 36 LBL 01 146 LBL J 256 LASTX 366 LBL E 37 RCL 11 147 RCL 11 257 INT 367 SF 21 38 ST+ 12 148 ST+ 12 258 ST+ IND 00 368 CLA 39 RCL 12 149 RCL 12 259 RDN 369 FIX 00 40 RND 150 RND 260 X<>Y 370 14.114 41 STO 00 151 STO 00 261 RCL 05 371 STO 00 42 RCL 07 152 STO 03 262 ST* T 372 SF 29 43 RCL 02 153 SF 00 263 ST* Z 373 RCL IND 00 44 INT 154 LBL 04 264 * 374 ARCL X 45 ENTER 155 RCL 02 265 RCL 08 375 ACA 46 ST* Z 156 INT 266 * 376 CLA 47 2 157 ENTER 267 FRC 377 PRBUF 48 - 158 ENTER 268 X<>Y 378 CF 29 49 ST- Z 159 LBL 99 269 LASTX 379 ISG 00 50 * 160 2 270 INT 380 LBL 16 51 RCL 10 161 - 271 R^ 381 XEQ 17 52 * 162 ST* Z 272 + 382 ISG 00 53 STO 06 163 RCL 10 273 RCL 05 383 FS? 00 54 CLX 164 ST* Z 274 - 384 GTO 18 55 STO 01 165 X<>Y 275 + 385 " " 56 X<>Y 166 * 276 X>0? 386 XEQ 17 57 RCL 13 167 2 277 ISG IND 00 387 PRBUF 58 * 168 ST- L 278 X>0? 388 CLA 59 ENTER 169 CLX 279 GTO 12 389 ISG 00 60 GTO 02 170 LASTX 280 RCL 05 390 GTO 16 61 LBL 03 171 ST* T 281 + 391 AVIEW 62 RCL 06 172 ST- Y 282 LBL 12 392 GTO 18 63 ST/ Z 173 RDN 283 ISG 00 393 LBL 17 64 MOD 174 * 284 GTO 11 394 RCL IND 00 65 X<>Y 175 R^ 285 GTO J 395 RCL 04 66 INT 176 ST+ T 286 LBL 10 396 / 67 X<>Y 177 X^2 287 RCL 03 397 INT 68 RCL 04 178 R^ 288 STO 00 398 LASTX 69 ST* Z 179 + 289 RCL 10 399 FRC 70 * 180 + 290 X^2 400 RCL 04 71 ENTER 181 FC? 00 291 3 401 XEQ 19 72 LBL 02 182 GTO 05 292 Y^X 402 " " 73 RCL 06 183 RCL 13 293 LASTX 403 XEQ 19 74 ST/ Z 184 * 294 * 404 RTN 75 MOD 185 3 295 STO 08 405 LBL 19 76 STO 03 186 DSE 02 296 CLX 406 * 77 RDN 187 GTO 06 297 LBL 13 407 RCL Y 78 INT 188 LBL 05 298 RCL IND 00 408 X=0? 79 + 189 RCL 07 299 X<>Y 409 GTO 20 80 RCL 05 190 * 300 RCL 04 410 LOG 81 ST- Y 191 RCL 06 301 ST/ Z 411 INT 82 X<>Y 192 LBL 06 302 * 412 LBL 20 83 RCL IND 00 193 X<>Y 303 ENTER 413 RCL 09 84 + 194 RDN 304 LBL 99 414 X<>Y 85 X>0? 195 / 305 RCL 08 415 X=Y? 86 ISG 01 196 STO 01 306 ST/ Z 416 GTO 21 87 LBL 99 197 CLX 307 MOD 417 - 88 X<0? 198 R^ 308 R^ 418 0 89 + 199 ENTER 309 INT 419 LBL 22 90 RCL 01 200 GTO 07 310 LASTX 420 ARCL X 91 RCL 04 201 LBL 08 311 FRC 421 DSE Y 92 ST/ Z 202 RCL 01 312 RDN 422 GTO 22 93 * 203 ST/ Z 313 + 423 LBL 21 94 ENTER 204 MOD 314 X<>Y 424 ARCL T 95 LBL 99 205 X<>Y 315 INT 425 ACA 96 RCL 08 206 INT 316 RCL 04 426 CLA 97 ST/ Z 207 X<>Y 317 ST* T 427 RTN 98 MOD 208 RCL 04 318 ST* Z 428 LBL 18 99 R^ 209 ST* Z 319 * 429 219 100 INT 210 * 320 STO IND 00 430 STO 00 101 LASTX 211 ENTER 321 RDN 431 RCL IND 00 102 FRC 212 LBL 07 322 ENTER 432 3600 103 RDN 213 RCL 01 323 LBL 99 433 * 104 + 214 ST/ Z 324 RCL 08 434 FIX 02 105 X<>Y 215 MOD 325 ST/ Z 435 "TIME: " 106 INT 216 RDN 326 MOD 436 ARCL X 107 RCL 04 217 INT 327 X<>Y 437 >" SEC" 108 ST* T 218 + 328 INT 438 PRA 109 ST* Z 219 RCL IND 00 329 ST+ IND 00 439 END 110 * 220 - 330 RDN Edited: Minor bug in PIATAN Forth that may have left a value on the stack after run. Results and time unaffected, just clean up. Edited: Removed TI-59 article. Edited: 19 Mar 2009, 9:26 a.m. after one or more responses were posted

Re: Happy Pi Day Message #2 Posted by Katie Wasserman on 15 Mar 2009, 11:04 a.m., in response to message #1 by Egan Ford Egan, Wow, you've been a busy guy! I need some time to digest all this, but thank you for all your work on Vieta Accelerated. I didn't know about Kreminski's formula, very interesting. -Katie

Re: Happy Pi Day Message #3 Posted by Palmer O. Hanson, Jr. on 15 Mar 2009, 10:39 p.m., in response to message #1 by Egan Ford Egan: The article that you included with the TI-95 program was originally published as part of the documentation of a TI-59 program on V7N4/5P27-29 of TI PPC Notes back in mid-1982. You can access that at Viktor Toth's site. The procedures described for running the TI-59 program do not apply to the TI-95 program. There is also an error in the article where it states "... There is a linear relationship between the number of decimal places and the running time of the program. ..." Actually, the relationship should be, and usually is very close to a squared relationship. The material in TI PPC Notes includes the TI-59 program. Unfortunately, the program listing is incomplete in that the first forty steps of program II-B are missing. If anyone would like to run the TI-59 program I can provide a listing of the missing steps. The TI-59 program is limited to 460 digits by memory limitations. There was a program published in the French magazine Science et Vie which was substatially slower but which would find 1287 digits of pi. That is particularly impressive since the TI-59's user memory is only 1300 digits. Palmer

Re: Happy Pi Day Message #4 Posted by Egan Ford on 16 Mar 2009, 10:50 a.m., in response to message #3 by Palmer O. Hanson, Jr. Palmer, I was a bit confused myself about the pairing of that article and the source. They were sent to me as a single 3 page PDF. I've removed the article to avoid any ambiguity. Do you have any links, articles, etc... about the TI-95 Pi program and its 5.81 hour result? Any corroborating or anecdotal information would be great. Thanks.

Re: Happy Pi Day Message #5 Posted by Marcus von Cube, Germany on 16 Mar 2009, 11:45 a.m., in response to message #4 by Egan Ford Could you please repost the link to the removed TI-59 article? My former printout of your post is incomplete and I'd like to read the document. Marcus

Re: Happy Pi Day Message #6 Posted by Egan Ford on 16 Mar 2009, 12:16 p.m., in response to message #5 by Marcus von Cube, Germany Here is the original PDF that was sent to me. It is higher resolution than the images posted here (MoHPC size limitation). http://sense.net/~egan/ti-95pi.pdf

Re: Happy Pi Day Message #7 Posted by Marcus von Cube, Germany on 17 Mar 2009, 4:08 a.m., in response to message #6 by Egan Ford Hi Egan, thanks for the download. I might have caught the PI disease. Marcus

Re: Happy Pi Day Message #8 Posted by Egan Ford on 17 Mar 2009, 7:44 a.m., in response to message #7 by Marcus von Cube, Germany I do not find the number Pi that interesting. A handful of digits can solve many practical problems. E.g. with less than 100 digits you can calculate the circumference of the universe accurate to the radius of a hydrogen atom. What I find interesting is all the different math that can be applied to computing Pi. And, what I find most interesting is the computational methods used to compute Pi, especially on machines with limited resources. As I explore this history I am truly amazed at the ingenuity and determination of the individual programmers. Especially the TI programmers. AFAIK, the 41 and 71 outclass the 59 and 95 in terms of I/O and memory forcing the TI community to think smarter. Fascinating!

Re: Happy Pi Day Message #9 Posted by Palmer O. Hanson, Jr. on 16 Mar 2009, 11:25 p.m., in response to message #4 by Egan Ford Egan: You wrote: Quote: Do you have any links, articles, etc... about the TI-95 Pi program and its 5.81 hour result? Any corroborating or anecdotal information would be great. The following notes accompanied my transmission of the TI-95 program to Gene Wright: Quote: 1. A direct translation would yield bad results if the number of digits asked for was greater than 770. I "fixed" it by changing from using ten digit registers with only the three guard digits available for carries from one register to the next to using nine digit registers with four digits available for the carries. The completed program is a hybrid which uses ten digit registers for up to 770 digits and nine digits for more than 770 digits. This yields about a ten per cent increase in speed for requests for less than 770 digits. Flag 3 controls whether 9 or 10 digit registers are used. 2. It would have been possible to simply print out the nine digit registers, but that made it difficult to check the answers against my pi table which was printed in groups of ten digits so I added a routine at the end which will either print or display the nine digit registers in a ten digit format. I could have used the same routine in another way to simply rearrange the 9 digit information back into the registers as 10 digit information but I didn't. 3. The TI-59 proram used two HIR registers to save two data registers for the calculation. My conversion replaced HIR 07 with data register 470 and HIR 08 with data register 471. 4. The TI-95 does not permit comparisons with the t register without using assembly language techniques. My conversion used data register 472 as a comparison register. Where the t register was used only as a place to park a value for later recovery I used the TI-95 t register as at lines 0408 and 0415. 5. I also used data register 474 to store the number of places desired and data register 473 to store the number of data registers to be used for the number of places desired. 6. In Bob's discussion of his program he says that "There is a linear relationship between the number of decimal places and the running time of the programs." Actually, the relationship is essentially a square relationship with an upward tail at the low end driven by the initialization routines and by the initializations for each iteration. You can see that in the plots. That is all the supporting documentation that there is other than my handwritten programming notes and some run time results where the run time results are included in the graph that accompanied the transmission to Gene. Some years ago I assembled a fairly thorough summary of the work with pi on the TI-59 including references to TI PPC Notes for details. It runs several pages. If you send an e-mail address I will send it to you. Palmer

Re: Happy Pi Day Message #10 Posted by Egan Ford on 17 Mar 2009, 7:29 a.m., in response to message #9 by Palmer O. Hanson, Jr. Thank you very much. I find all of this history very interesting. You've got mail.

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