HP42s first major program (Double Integral) Best way to approach?

[Albert Chan]

(06-01-2020 01:02 PM)Werner Wrote:  Well, I had to try that out, Albert!
It's more than 10x faster than the integral solution: (which is noticeable on a DM42):

Very nice !

Suggestion:
Your AGM2 code had AGM(a,b) in Y register, instead of expected X
The fix actually made the code shorter, by deleting Line 47, Line 61

To make the name more suggestive, rename "AGM2" as simply "AGM"
With these changes, on Free42, we calculate Pi via AGM, like this.

0.5 SQRT 1 XEQ "AGM" [X^2] [X<>Y] / 2 *
→ 3.141592653589793238462643383279504

Another example, ellipse_perimeter(50, 10):

50 Enter 10 +
50 Enter 10 * SQRT 2 *
XEQ "AGM" /                             ; "diameter" of ellipse = y/x
PI *
→ 210.100445397

Or,

50 Enter 10 XEQ "AGM"
[X<>Y] 10 [X↑2] + [X<>Y] /     ; "diameter" of ellipse = (y+b²)/x
PI *
→ 210.100445397

For the same reason, I would rename "KE" as "EK", since E is in X register

Again, for ellipse_perimeter(50, 10):

Perimeter = 4 a E(e), where a = 50, e = √(1-0.2^2) = √0.96

0.96 SQRT
XEQ "EK"                     ; E(e)
200 *                          ; 4 a
→ 210.100445397

What do you think ?