Most impressive/complex/amazing C-series program?

[Valentin Albillo]

      
Hi, brickviking:

(04-08-2018 02:29 AM)brickviking Wrote:  What's an a.m. routine? I can see some tests in there, and a square root, but the concept's currently beyond me.

The code simply computes Pi using the formula:

      Pi = 2 * 2/sqrt(2) * 2/sqrt(2+sqrt(2)) * 2/sqrt(2+sqrt(2+sqrt(2))) * ...

which converges to the 10-digit representation of Pi (3.141592654) using just 17 terms. The algorithm is very clearly seen in this HP-71B equivalent command-line version

      >FIX 9 @ F=0 @ P=2 @ FOR I=1 TO 17 @ F=SQR(2+F) @ P=2*P/F @ NEXT I @ P

            3.141592654

If you want to see the convergence after each term, this simpler implementation I've independently concocted adds an intermediate stop (R/S) and removes the now unneeded test, decreasing the step count from 17 to 14:

      01-       35  CLx
      02-       36  ENTER
      03-        2   2
     *04-       34  X<>Y
      05-        2   2
      06-       40   +
      07-    43 21  SQR
      08-       10   /
      09-    43 36  LSTx
      10-       34  X<>Y
      11-        2   2
      12-       20   *
      13-       31  R/S
      14- 43,33 04  GTO 04

To run it in any HP-12C, set 9 decimals (f 9), go to the top of program memory (GTO 00), and use R/S to see the converging value after each new term, like this:

      f 9
      GTO 00
      R/S      -> 2.828427126
      R/S      -> 3.061467460
      R/S      -> 3.121445154
      R/S      -> 3.136548492
      R/S      -> 3.140331160
                  ---
      R/S      -> 3.141592648
      R/S      -> 3.141592652
      R/S      -> 3.141592654

After pressing R/S sixteen times the value has converged and there's no need to go on, any subsequent R/S would produce the same value (3.141592654) again.

      Note: the original code in the Code panel has one typo. Step 14 appears like this:

            14-43,33 00 RTN

      but though the keycode is correct, it should read GTO 00 instead of RTN, like this:

            14-43,33 00 GTO 00

      because that's what the keycode indicates and there's no RTN instruction in the HP-12C's instruction set as there's no subroutine (GSB) capability either.

Regards.
V.