Friday, March 16, 2012

Using LMD2 to Generate a Long Nonzero Pseudorandom Sequence

Borrowing the multiplier from LMD2, we can rapidly create a long (49,327,206,862 outputs, excluding the initial x0=0) sequence of nonzero 32-bit values by simply altering (x0, c0) as follows, while keeping ITERATE_NO_ZERO_CHECK as described in the previous post:

As usual, ITERATE_NO_ZERO_CHECK means:

p = 0xFE001000 * x + c
x <- p MOD 2^32
c <- p / 2^32 (Shift p right by 32.)

Except that, unlike with LMD2:

(x0, c0) = (0, 0xDA6D32BA)


(x1, c1) = (0xDA6D32BA, 0)
(x2, c2) = (0x5F2BA000, 0xD8B865FB)
(x3, c3) = (0x92B865FB, 0x5E6D4EB3)

(Only the "x" values are the pseudorandom outputs.)

Don't forget that 0xFE001000 is easy to multiply by, as described in the previous post.

Someone out there probably has a use for such a sequence. And it's not bad from error detection standpoint, either.

(Blogger's font antics are driving me insane. I've changed to this idiotic font that displays hexadecimal numbers with different number and letter heights. Of course, it's the default. So let's hope it fixes the problem.)

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