# MINSTD

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This multiplicative congruential pseudo random number generator is called
"The minimal standard generator" or MCG16807.
First described in 1988 Park and Miller paper
[Random number generators: Good ones are hard to find](https://www.cems.uwe.ac.uk/~irjohnso/coursenotes/ufeen8-15-m/p1192-parkmiller.pdf).

Generator _modulus m_ = 2^31-1 is Mersene prime M31.
The _multiplier a_ = 7^5 = 16807 was first suggested by
Lewis, Goodman and Miller in 1969.

Multiplicative congruential [generators of this form](https://en.wikipedia.org/wiki/Lehmer_random_number_generator)
are ascribed to _D. H. Lehmer_ and they are know as Lehmer random number generators.
First described by Hutchinson and independently by Downham and Roberts.

Generator was later criticized by [Marsaglia and Sullivan](https://www.firstpr.com.au/dsp/rand31/p105-crawford.pdf)
(1993). While it is still in use today
(in particular: in [CarbonLib](https://macintoshgarden.org/apps/carbonlib),
in Matlab as [mcg16807](https://www.mathworks.com/help/matlab/ref/randstream.html),
FreeBSD 5 as [rand()](https://github.com/freebsd/freebsd-src/blob/releng/5.0/lib/libc/stdlib/rand.c)
and in C++11 as [function minstd_rand0](https://en.cppreference.com/w/cpp/numeric/random))
Park, Miller and Stockmeyer "officially" since July 1990 advocate 
_a = 48271_ multiplier.

Updated version performs much better in [Spectral test](https://en.wikipedia.org/wiki/Spectral_test)
where performs very well up to 6th dimension.

## Minimalistic code

This code have _no dependencies_ and is not using standard library.
Can be used in [embedded](https://docs.rust-embedded.org/book/) or
[webasm](https://rustwasm.github.io/docs/book/) environments.

## MINSTD / 1990 version

Multiplier 48271

https://oeis.org/A221556

## MINSTD0 / 1988 version

Multiplier 16807

https://oeis.org/A096550

## Spectral test

| multiplier | 2d | 3d |  4d  |  5d   |   6d   |  7d   |  8d  |
| ---------- | -- | ---| ---- | ----  | -----  | ----- | -----|
|16807 |0.3375|0.4412  |0.5752|	0.7361|	0.6454 | 0.5711|0.6096|
|48271 |0.8960|0.8269  |0.8506|	0.7332|	0.8078 | 0.5865|0.4364|
|69621 |0.7836|0.9205  |0.8516|	0.7318|	0.7667 | 0.6628|0.7845|

Value 0.75 or higher is considered good enough to pass spectral
test.

## License

This is free and unencumbered software released into the public domain.

This code can be used under terms of [CC0-1.0](https://creativecommons.org/publicdomain/zero/1.0/) or
the [Unlicense](https://unlicense.org).

![Unlicense logo](https://unlicense.org/pd-icon.png)