# RANDU

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RANDU is Pseudorandom multiplicative
[congruential generator](https://en.wikipedia.org/wiki/Linear_congruential_generator)
(MCG). This generator was first introduced in the early 1960s; its use soon became widespread
during 1960's and 1970's.
Its part of the IBM Scientific Subroutine Library for IBM System/360 computers.

RANDU uses MCG coeficients _multiplier a_ = 65539 ( 2^16 + 3 ) and _modulus m_ = 2^31 and _constant c_ = 0.
It can be implemented
very quickly on 32-bit hardware in just 2 operations: wrapping multiplication by _a_ and bit
masking of result using AND _0x7fffffff_.

Generated values are positive 31 bit integers. Generator period is 2^29. Lower bits have low randomness
and should not be used separately. Problem with lower bits randomness and not achieving full period is common
for all congruential generators with power of 2 modulus.

RANDU fails the spectral test for dimensions greater than 2.
RANDU produces very [strong banding](https://www.juliabloggers.com/dissecting-randu/)
when used in 3 dimensions. All points in 3d space fall in 15 two-dimensional planes. This effect can be used in GPU
programming for visual effects and take advantage of compute simplicity.

### References

https://en.wikipedia.org/wiki/RANDU

https://oeis.org/A096555

https://en.wikipedia.org/wiki/Linear_congruential_generator

## Spectral test

| 2d  |  3d   |  4d   |  5d  |  6d  |  7d  |  8d  |
| --- | ----  | ----- | ---- | ---- | ---- | ---- |
|0.93 |	0.012 | 0.059 |	0.16 | 0.29 | 0.45 | 0.62 |

Values 0.75 and higher are commonly considered as passing of
the spectral test. While this generator failing higher dimensions
it is a _very strong_ in generating 2d data.

## License

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

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

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