Reduce Boost dependency footprint

[andrjohns]

Summary

Including Boost headers outside of their Math library tends to pull in a surprising amount of other Boost headers.

For example, for the single lexical_cast call in init_threadpool_tbb() the total Boost footprint is:

• Boost.Config
• Boost.TypeTraits
• Boost.Container
• Boost.Core
• Boost.Detail
• Boost.Exception
• Boost.ThrowException
• Boost.Limits
• Boost.Move
• Boost.StaticAssert
• Boost.Version
• Boost.LexicalCast

This PR removes three different types of Boost dependencies:

1. boost/lexical_cast (init_threadpool_tbb): Replaced with a std::from_chars + try/catch
2. boost/optional (hypergeometric_2F1): Replaced with std::optional
3. boost/random (_rng functions): Replaced with std:: equivalents (e.g., std::bernoulli_distribution bernoulli_rng)

Tests

N/A - Existing tests should still pass.

Note that this triggered an edge-case with the expected-value (chi-square) testing for distributions, where too few values were sampled for particular bins. The testing util was updated to just merge bins if the expected counts were too low.

Side Effects

Possibility of changes to existing _rng outputs with same seed value

Release notes

Replaced Boost dependencies with standard library equivalents

Checklist

• Copyright holder: Andrew Johnson

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[WardBrian]

Funny, I was just talking to someone today about decreasing our reliance on boost/random

Can we add any new libraries to the trim list

math/lib/upgrade-boost.sh

Lines 117 to 120 in cc6ba8b

	# unused libraries, focusing on larger ones
	UNUSED="leaf nowide pfr json static_string stl_interfaces phoenix msm redis mysql log \
	geometry hana asio multiprecision beast qvm gil xpressive process parser charconv \
	wave atomic polygon metaparse interprocess yap thread compute url test proto"

after this?

[SteveBronder]

You can add this hook to your claude and it stops it from doing these multi line comments

https://gist.github.com/SteveBronder/8c2f141fed4511447a8ad5939157857e

Generally I have seen that if you let it start writing a lot of these it uses them as an excuse to do bad code. The comment can also be wrong since it is untested which can lead to other agents down the road getting confused here.

[andrjohns]

Oh super cool, immediately stolen

[SteveBronder]

Cool!

[SteveBronder]

From the tests it seems like the changes in stan have to happen first before we can merge this