HP-41 Challenge: Double Integrals by INTEG Recursion

[Ángel Martin]

(06-01-2016 06:51 PM)Valentin Albillo Wrote:  For the record, this is the HP-71B code to compute the quintuple integral using a Monte-Carlo approach, a straightforward 3-line affair with no Math ROM needed.

>LIST

10 DESTROY ALL @ RANDOMIZE 1 @ B=.7*.8*.9*1.1 @ FOR K=1 TO 4 @ N=10^K
20 S=0 @ FOR I=1 TO N @ X=RND*.7 @ Y=RND*.8 @ Z=RND*.9 @ U=RND @ W=RND*1.1
30 S=S+SQR(6-X*X-Y*Y-Z*Z-U*U-W*W) @ NEXT I @ DISP N,S*B/N @ NEXT K

>RUN

10 1.17631976176
100 1.19138525241
1000 1.18851295632
10000 1.18896583878


The output are the results for 10, 100, 1000 and 10000 random samples, the last having 5 correct digits (save one ulp) and about as fast as the INTEGRAL approach.

Best regards.
V.

Clear and elegant; sometimes I wonder why I bother with RPN and FOCAL - so cumbersome in comparison...

Cheers,
ÁM