HP-42S (Free42, DM-42) mini-challenge – Wallis Product

[Valentin Albillo]

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Hi, Gerson:

(07-04-2020 04:42 PM)Gerson W. Barbosa Wrote:  Least number of steps then least number of bytes, including a 2-character label, wins.

A pity, should you have included a "fastest running time" win condition this "let's-think-out-of-the-box" concoction o'mine would've surely won, as its running time is about the same regardless of the input:

[19-step, 36-byte program]

01   LBL "WP"
02   STO ST Y
03   N!
04   X^2
05   RCL ST Y
06   STO+ ST X
07   N!
08   /
09   X^2
10   2
11   2
12   RCLx ST T
13   STO+ ST X
14   Y^X
15   *
16   0.5
17   RCL+ ST Z
18   /
19   END

Some Examples (run in Free42)

1 XEQ “WP” -> 2.66666666667
10 -> 3.06770380664
123 -> 3.13523960403

which virtually match your results.

As stated, the time is about the same whatever the argument, i.e., extremely fast, and it leaves the original contents of X when the program is run (i.e., the argument keyed in) in stack Y, Z and T. However, it's limited to those arguments that won't overflow the calculation, mostly the factorials, and a few steps can surely be shaved here and there, but I'm just too sleepy right now. :O

Thanks for the nice mini-challenge, I saw it at 4:00 a.m. and it was just what I needed before going to bed.

Have a nice weekend.
V.