Hp Algorithm to create random numbers

[Albert Chan]

(08-25-2024 12:02 PM)DavidM Wrote:  In your second example, it appears that you may have inadvertently left out the "6" when executing "0.002567 RDZ":
0.00257 RDZ RAND => 0.163041130928
0.002567 RDZ RAND => 0.377640130928

The only reason I figured that out was that I did the same exact thing when testing this after reading your post -- it had me confused for a minute or so until I subsequently typed it in correctly on a second try.

Assuming 1E-16 ≤ seed < 1, we know original state must end in 001

--> state * 2851130928467 ≡ 163041130928467 (mod 10^15)

1/2851130928467 ≡ -46007610876197 ≡ 953992389123803 (mod 10^15)      (*)

--> state ≡ 163041130928467 * 953992389123803 ≡ 002570000000001 (mod 10^15)
--> seed = 0.00257

---

(*) Calculations based on Euclidean GCD calculations, then scale-up for mod inverse, see here

1E15            --> -floor(446607260/9707247377 * 1E15) = -46007610876197
2851130928467 +
2104175036550 -
746955891917 +
610263252716 -
136692639201 +
63492695912 -
9707247377 --> +floor(13843/300885 * 9707247377) = 446607260, 9.71E9*6.35E10 ≈ 6.2E20
5249211650 -
4458035727 +
791175923 -
502156112 +
289019811 -
213136301 +
75883510 -
61369281 +
14514229 -
3312365 +
1264769 -
782827 +
481942 -
300885 --> -floor(-19/413 * 300885) = 13843, 3.01E5*4.82E5 ≈ 1.4E10
181057 +
119828 -
61229 +
58599 -
2630 +
739 -
413 --> -floor(1/21 * 413) = -19, 413*739 = 305207
326 +
87 -
65 +
22 -
21 --> 1/1 ≡ 1 (mod 21), 21*22 = 462
1 = gcd