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+--- Thread: Pi Approximation Day (/thread-15364.html)
Pi Approximation Day - Gerson W. Barbosa - 07-22-2020 11:22 PM
Today is Pi Approximation Day.
To celebrate it, here is an HP 50g program based on a variation of the Wallis Product. Here we use (2/1*4/3*6/5*8/7*...) plus a correction factor in continued fraction form. The number of digits per iteration is slightly less than 21/10, which is being used by the program, so this has to be adjusted. The argument
of the RPL program is the desired number of decimal places. For n = 100, the program returns 98 correct decimal digits; for n = 200, the program gets all of them right. This takes about one minute on the emulator because of the slowness of EXPAND to process long algebraic expressions.
Code:
« PUSH RAD -105 CF -3 CF DUP 10 * 21 / CEIL 0 2 ROT 8 OVER * PICK3 + UNROT 1
FOR i i DUP + DUP 1 - UNROT * OVER / SWAP SQ 4 ROLL 4 PICK + / UNROT -1
STEP SQ UNROT 2 / + / EXPAND FXND DUP SIZE R→I ALOG OVER - PICK3 * SWAP IQUOT
+ →STR DUP HEAD 0 I→R →STR TAIL + SWAP TAIL + 1 ROT 2 + SUB POP
»253 bytes, CKS = # 537h
3,14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745
028410270193852110555964462294895493038196
HP-75C program:
Code:
10 INPUT N
15 C=0
20 D=8*N+2
25 W=2
30 FOR I=N TO 1 STEP -1
35 T=2*I-1
40 W=W*(T+1)/T
45 C=T*T/(C+D)
50 NEXT I
55 C=C+D/2
60 DISP W*W/C