[Issue 10550] Xorshift32 and Xorshift160 do not generate uniformly-distributed random numbers

[d-bugmail at puremagic.com]

http://d.puremagic.com/issues/show_bug.cgi?id=10550



--- Comment #1 from Joseph Rushton Wakeling <joseph.wakeling at webdrake.net> 2013-07-05 07:35:07 PDT ---
The Xorshift32 non-uniformity can be fixed by correcting the update rule in
popFront(), from:

        static if (bits == 32)
        {
            temp      = seeds_[0] ^ (seeds_[0] << a);
            temp      = temp >> b;
            seeds_[0] = temp ^ (temp << c);
        }

to:

        static if (bits == 32)
        {
            temp      = seeds_[0] ^ (seeds_[0] << a);
            temp      = temp ^ (temp >> b);
            seeds_[0] = temp ^ (temp << c);
        }

See p.3 of http://www.jstatsoft.org/v08/i14/paper -- the current implementation
appears to be a typo when copying the first from the list of possible update
rules.

However, if this change is made, the Xorshift unittests fail for the checks
against the reference edition:

    auto checking = [
        [2463534242UL, 267649, 551450, 53765, 108832, 215250, 435468, 860211,
660133, 263375],
        [362436069UL, 2113136921, 19051112, 3010520417, 951284840, 1213972223,
3173832558, 2611145638, 2515869689, 2245824891],
        [521288629UL, 1950277231, 185954712, 1582725458, 3580567609,
2303633688, 2394948066, 4108622809, 1116800180, 3357585673],
        [88675123UL, 3701687786, 458299110, 2500872618, 3633119408, 516391518,
2377269574, 2599949379, 717229868, 137866584],
        [5783321UL, 93724048, 491642011, 136638118, 246438988, 238186808,
140181925, 533680092, 285770921, 462053907],
        [0UL, 246875399, 3690007200, 1264581005, 3906711041, 1866187943,
2481925219, 2464530826, 1604040631, 3653403911]
    ];

    alias TypeTuple!(Xorshift32, Xorshift64, Xorshift96, Xorshift128,
Xorshift160, Xorshift192) XorshiftTypes;

    foreach (I, Type; XorshiftTypes)
    {
        Type rnd;

        foreach (e; checking[I])
        {
            assert(rnd.front == e);
            rnd.popFront();
        }
    }

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