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Date: Wed, 18 Nov 2020 15:47:52 +0100
From: Christophe =?ISO-8859-1?Q?Sta=EFesse?= <chastai@skynet.be>
To: ~skeeto/public-inbox@lists.sr.ht
Subject: Improving on QBasic's Random Number Generator
Message-Id: <20201118154752.5854d027b288acf1a685f298@skynet.be>
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Hello,

Interesting article!

> the implementation is a full 32-bit multiply using 16-bit limbs
> (note: the LCG constants listed here are wrong)

It is actually a 24-bit multiplier (a hint is that there are 3 multiplications) ant it computes:
  word[RndVar]*word[RndA] + 65536*word[RndVar+2]*word[RndA] + 65536*word[RndA]*word[RndVar]

The third multiplication is identical to the first. This is a bug. word[RndA] should actually be word[RndA+2].
This is why a=0xfd43fd and not 0x343fd as documented.

There is another bug similar in the addition of c: ... + word[RndC] + 65536*byte[RndC]. byte[RndC] should be byte[RndC+2]. Hence c=0xc39ec3 instead of 0x269ec3.

I checked the original code and RandA and RandC are defined as 32-bit variables initialised with the documented constants.

That said, even the fixed version produces a similarly bad randogram and a quick check seems to confirm that removing the lowest-order byte produces better result.

Cheers,
Christophe.