Module randomize::lcg

Functions for Linear Congruential Generators.

An LCG is just one multiply and one add, so it's very fast. However, they're not much in terms of statistical quality, so you need to be using the u128 version if you want the kind of quality it takes to pass a PRNG test suite. Accordingly, the LCGs given here aren't actually supported with a struct to hold the state and all that. It's just the necessary math expression wrapped in a function.

The Period of an LCG is equal to the numeric range of the state type used.

• lcg8 is for u8 and has a period of 2^8
• lcg16 is for u16 and has a period of 2^16
• and so on

Constants

As you might guess, different LCG multipliers give better or worse quality. There's apparently a thing called a Spectral Test you can do to rate the quality of different LCG multipliers, but I don't know much about it. The pcg module has a good multiplier for each LCG size.

Also, the additive value that you pick can affect the output stream as well. This allows some flexibility, because even with a single good multiplier selected you still have many output streams available to you. The main limit here is that the value must be odd, but that's quite a bit of freedom. Again, the pcg module offers some defaults if you'd like.

There are also some LCG implementations here with pre-baked constants. They're based on the generators used in various games you might have played before. They are "just for fun", and not actually any higher quality than normal for an LCG of their size.

Jump Ahead

It's possible to do some funny math and advance an LCG as if you'd gone through N steps in only log(N) time. There is a jump function available for each size LCG offered. If you'd like to jump "backward" instead of forward that also works, since PRNG sequences are looped. Just cast a signed value into an unsigned value (eg: -5i32 as u32) and jump by that much. It has to go forward the "long way", but you arrive at the right value.

Functions

jump_lcg8	Gives the lcg8 output delta steps from now in log(delta) time.
jump_lcg16	Gives the lcg16 output delta steps from now in log(delta) time.
jump_lcg32	Gives the lcg32 output delta steps from now in log(delta) time.
jump_lcg64	Gives the lcg64 output delta steps from now in log(delta) time.
jump_lcg128	Gives the lcg128 output delta steps from now in log(delta) time.
lcg8	The u8 LCG
lcg16	The u16 LCG
lcg32	The u32 LCG
lcg32_colosseum	The LCG from a game with "colosseum" in its name.
lcg64	The u64 LCG
lcg128	The u128 LCG
lcg32_gen4alt	The alternate LCG from the gen4 games.
lcg32_gen3gen4	The LCG from the gen3 and gen4 games.
lcg64_gen5gen6	The LCG from the gen5 and gen6 games.