[VA] SRC #012c - Then and Now: Sum

[Albert Chan]

(12-04-2022 08:49 AM)Werner Wrote:  - Why does Albert’s code run so much slower than J-F’s, while doing 31 loops vs 40?

> 20 DIM F(63) @ F(2)=2 @ F(3)=6 @ B=4
> 30 FOR X=3 TO 6 @ FOR Y=B TO B+B-1 @ F(Y)=Y*F(X) @ NEXT Y @ B=B+B @ NEXT X
> 80 FNZ=Z/F(N) @ END DEF
>RUN
 2.086377665      31      0.05

Above patch removed FNB(N) and FNF(N), and build list of F(N) instead.

F(N=63) is enough, since (G-LN2) shrink at O(1/2^n)
For 12 decimal digits, we need at most N=12/LOG10(2) ≈ 40
Z = (G-LN2)/F, with F growing faster than primes, O(n*ln(n)), it needed even less than that.

Cached F doubled program speed (translated to HP71B runtime of about 10s)