mt19937.factory does not accept 0 as a seed

[charredUtensil]

Description

Calling mt19937.factory({seed:0}) causes:

factory.js:427 Uncaught TypeError: invalid option. `seed` option must be either a positive integer less than or equal to the maximum unsigned 32-bit integer or an array-like object containing integer values less than or equal to the maximum unsigned 32-bit integer. Option: ``.
    at Function.factory (factory.js:427:1)
    at <anonymous>:1:9

However, the documentation states the valid range for a seed is [0, 4294967295]

I am using the mt19937 and beta libraries to generate pseudorandom values for a map generator. As part of that, I'm actually using mt19937 to generate random seeds that I feed back into mt19937 to generate more independent PRNGs, so it's a bit odd that the range of valid seeds is off by 1 from the range of output values. I suspect the documentation is correct and the generator is wrong.

Related Issues

Related issues # , # , and # .

Questions

No.

Demo

No response

Reproduction

import mt19937 from "@stdlib/random-base-mt19937";
mt19937.factory({seed:0})

### Expected Results

```shell
A working pseudorandom number generator

Actual Results

factory.js:427 Uncaught TypeError: invalid option. `seed` option must be either a positive integer less than or equal to the maximum unsigned 32-bit integer or an array-like object containing integer values less than or equal to the maximum unsigned 32-bit integer. Option: ``.
    at Function.factory (factory.js:427:1)
    at <anonymous>:1:9

Version

0.2.1

Environments

Firefox, Chrome

Browser Version

No response

Node.js / npm Version

No response

Platform

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Checklist

• Read and understood the Code of Conduct.
• Searched for existing issues and pull requests.

[stdlib-bot]

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[kgryte]

@charredUtensil I believe the documentation is wrong here and the implementation correct. It is fairly common for PRNGs to not allow 0 seeds, as this can lead to degenerate starting states. From the original paper,

Since any initial seed except zero lies on the same orbit, the choice of an initial seed does not affect the randomness for the whole period.

and

Before using genrand( ), sgenrand( ) must be called with a nonzero unsigned long integer as a seed.

[kgryte]

Also, unrelated to the documentation bug, I suggest using a different PRNG for seeding (e.g., minstd or minstd-shuffle), in order to ensure that your seeds are independent of your implementation.