change the magic number 16807 to 16811

[blueloveTH]

Checklist

• The new code additions passed the tests (npm test).
• The linter ran and found no issues (npm run-script lint).

Description

I detected a problem in the combination of ink v1.0.0 and ink.js v2.0.0.
If the length of a shuffle list is 7, it will always return the first element.
Such as:

{~1|2|3|4|5|6|7}
LIST lst = (a),(b),(c),(d),(e),(f),(g)
{LIST_RANDOM(lst)}

which always get 1 and a. However, the problem disappears for other lengths such as 6 or 8. It made me confused.

So I inferred that there is a magic number.
By checking the source, I identified it is 16807.

This number is a multiple of 7.
If this.seed * 16807 < 2147483647, PRNG.next() % 7 should always be zero.
In the implmentation of LIST_RANDOM, it uses PRNG.next() % list.Count.
So I think this is why we always get the first element on length == 7.

My solution is to replace 16807 with 16811. The latter is a prime.
I tested on our usecases to confirm that this modification solves the magical problem.

[blueloveTH]

Update the assertion value under 16811 to pass npm run test.

    expect(story.Continue()).toEqual("14\n");
    expect(story.Continue()).toEqual("-10\n");

[smwhr]

Thanks for your contribution @blueloveTH !

16807 is actually a number that's usually recommended as the a in the PRNG we use (see original paper here) because it has "good random properties" while still cycling and now that you point it out, I think we have an error in the algorithm, there should be a -1 somewhere to break the %7 = 0 chain.

[smwhr]

-    expect(story.Continue()).toEqual("15\n");
-    expect(story.Continue()).toEqual("-24\n");
+    expect(story.Continue()).toEqual("27\n");
+    expect(story.Continue()).toEqual("8\n");

[smwhr]

-    return (this.seed = (this.seed * 16807) % 2147483647);
+    return (this.seed = (this.seed * 48271) % 2147483647);

[smwhr]

After further investigation :

• the %7 problem happens when the story seed is low enough
• we ported as is

storySeed = (new Random (timeSeed)).Next () % 100;

which makes the seed low enough

• since 1993, everyone recommends using 48271 instead of 16807
• 48271 works well in the local tests I did

So if that's ok with you @blueloveTH, I commented your code with the value expected for the tests with 48271.

@y-lohse @ephread I think we could merge this one (because that's a quick fix) while work is being done in #552

[blueloveTH]

Thanks for your investigation @smwhr !
Through your explanation, I have roughly understood the idea of this PRNG algorithm. 48271 is a well-chosen prime number with good random properties. It should work better!

[y-lohse]

Happy to merge this if we do the changes suggested by @smwhr , thanks for the investigation :)

[smwhr]

Closing this one in favour of #952
Thanks @blueloveTH for the initial push in the right direction !