Avoid hangs and debug asserts on invalid parameters for Zipf

[mstoeckl]

• Added a CHANGELOG.md entry

Summary

The Zipf distribution sampler could panic (at debug_assert!(t > F::zero());) when given invalid parameters (like s = inf); or hang in an infinite loop when sampling. This change rejects parameter combinations for which the generalized Zipf distribution is not well defined, and slightly modifies Zipf::new() so that sampling avoids the debug assert and produces the correct value when s = inf.

Motivation

This another simple panic / hang issue that I found by fuzzing input parameters.

Details

The normalization constant (sum from i=1 to n of 1/i^s) of the generalized Zipf distribution needs to be positive and finite for the distribution to be well defined. if s <= 1 and n = inf, then the sum in the constant diverges.

If s = inf, then each term of the constant is 0, so the specific formula in Wikipedia will not work; however, the Zipf distribution approaches the distribution concentrated on i=1 as s -> inf. The previous implementation computed a nan in Zipf::new which triggered the debug assertion (or an infinite loop), but a small change avoids both.

(Edit: originally this PR rejected the case s = inf, but after posting it I changed my mind; in general, if a limiting distribution exists and is close enough to the distribution at the largest finite parameters, then producing that limiting distribution is safe and avoids having the library user write a special case to produce effectively that limiting distribution.)

[dhardy]

I think inv_cdf also needs a special case for s = inf? Perhaps not if it's safe to assume that p <= 1. Maybe that should be a debug_assert.

[mstoeckl]

I think inv_cdf also needs a special case for s = inf? Perhaps not if it's safe to assume that p <= 1. Maybe that should be a debug_assert.

It should be OK. The range of possible inputs for p in inv_cdf should be [0,1]; anything outside this is not a probability value. Zipf::sample is the only caller and provides it a sample from StandardUniform (in [0,1)).