Another wp34s program - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: General Forum (/forum-4.html) +--- Thread: Another wp34s program (/thread-8733.html) Another wp34s program - Gerson W. Barbosa - 07-25-2017 01:53 PM This is a somewhat belated Pi Approximation Day celebration, which took place last Saturday. This is simple implementation of a 22-century old algorithm (lines 001 through 021), followed by a minor tweaking to improve accuracy. Perhaps a Free42 version would have been more appropriate here, but I chose wp34s for convenience. 0001 **LBL A 0002 STO 00 0003 STO 01 0004 # 003 0005 [sqrt] 0006 STO+ X 0007 FILL 0008 # 004 0009 RCL/ L 0010 / 0011 [times] 0012 [sqrt] 0013 DSE 00 0014 SKIP 001 0015 SKIP 006 0016 STO 02 0017 || 0018 STO+ X 0019 FILL 0020 RCL 02 0021 BACK 010 0022 RCL+ X 0023 + 0024 # 004 0025 RCL[times] 01 0026 RCL+ L 0027 # [gamma]EM 0028 # 005 0029 [times] 0030 +/- 0031 e[^x] 0032 + 0033 +/- 0034 2[^x] 0035 INC X 0036 / 0037 # 003 0038 / 0039 END Usage: n A, where n is the number of iterations. You might want to set double mode on (DBLON). ------------------- PS: The expression involving the EM constant is just an approximation of the pattern below:    0   █..█                                                                                                                                   1   ███.████                                                                                                                           2   █......███...                                                                                                                 3   █....█....███.██.                                                                                                          4   █....█..██.█.███████.                                                                                                  5   █....█..████████....█..██                                                                                          6   █....█.█....█...██..███.█████                                                                                   7   █....█.█....█.██.█.......█...████                                                                          8   █....█.█....█.████.███..█..██.█.██.██                                                                  9   █....█.█....██........███.█.█████..█████.                                                        10   █....█.█....██......██.█.███.█..██..████...█.    11   █....█.█....██......███████..██....██.█.█████..█.   12   █....█.█....██.....█....█.....█..██.██.█████..█.█....   13   █....█.█....██.....█....█.█.█..██.....█.█.██....██...█..█   14   █....█.█....██.....█....█.██..██.█...██████......█.█.█..█.██.   15   █....█.█....██.....█....█.██.█.██.███..█..█.██....███...█.██....█   16   █....█.█....██.....█....█.██.██..█.█.█.█.███████..██...██.██......█.█   17   █....█.█....██.....█....█.██.██..█████..█..█..█████.████████........██.█.   18   █....█.█....██.....█....█.██.██.█....██..█.██..█...██████............█...█.██    19   █....█.█....██.....█....█.██.██.█...█...██..█.█..██.█.██.██..█........█...█..██.​.                                         20   █....█.█....██.....█....█.██.██.█...█..█.██..██.█.█████..█.███.█.......██..█.███​██..█    21   █....█.█....██.....█....█.██.██.█...█..██...██.███.█..██...██.██.█.....█.███.█..​..██..███   22   █....█.█....██.....█....█.██.██.█...█..██..█.████..██....█..█.█.██.█...█.██.█.██​.█..██.██..██   23   █....█.█....██.....█....█.██.██.█...█..██..██.█.....█..██..█.██.█.██.█.█.██.█..█​...█.█.........█.   24   █....█.█....██.....█....█.██.██.█...█..██..██.█.█.█..█.████.█..██.█.███..██.█...​█....█.██..██.█..████   25   █....█.█....██.....█....█.██.██.█...█..██..██.█.██..██..███████..██.██..█.█.█...​.██...█.........██..█..█. 12     1000010100001100000100001 12*4+4=52     -5=47     -2=45     -5=40     -1=39     -6=33     -5=28                            (2*a + b)         ----------------------------------------------                                1          1 + ---------------------------------------              2^52 + 2^47 + 2^45 + 2^40 + 2^39 + 2^33