Experiment: Switch RNG from ecuyer1988 to mixmax

[WardBrian]

Submission Checklist

• Run unit tests: ./runTests.py src/test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary

Experiment to see how viable it is to change RNGs, see #3167 and discussion.

Also needs https://github.com/stan-dev/stanc3/tree/experiment/mixmax-rng

Intended Effect

How to Verify

Side Effects

Documentation

Copyright and Licensing

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Simons Foundation

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[WardBrian]

This seems fine up to the performance tests, which don't yet pass on the stanc3_bin_url parameter so can't be run yet.

I had to revert some of the tests to using ecuyer1988 in e026895 because a fair number of tests here seem to have "magic" seeds and assert on certain values, and I cannot tell if those values were derived somehow of if the existing output was just frozen in the tests

[WardBrian]

Interesting: Up at the performance-tests-cmdstan level, this change had two models fail https://jenkins.flatironinstitute.org/blue/organizations/jenkins/Stan%2FCmdStan%20Performance%20Tests/detail/downstream_tests/391/pipeline

One of them is a data generation model which heavily uses RNGs, so it is expected that it would likely change. The other is low_dim_gauss_mix_collapse (here)

[WardBrian]

Closing for now, if we ever wanted to make this change it seems like we'd just need to update the magic numbers in a few of our tests