Stabilize piecewise-constant weight normalization

[FlorianPfaff]

Summary

• scale finite nonnegative piecewise-constant weights by their maximum before normalization
• preserve relative interval mass while avoiding overflow in the raw mean and the mean * 2π denominator
• add a backend-aware regression using the active floating-point dtype's maximum finite value

Bug

PiecewiseConstantDistribution normalized constructor weights with

mean_weight = mean(w)
self.w = w / (mean_weight * 2.0 * pi)

Valid individually finite weights near the dtype maximum can overflow while computing the mean or while multiplying the mean by 2π. The resulting infinite denominator collapses every stored density weight to zero. For example, [finfo.max, finfo.max / 2] should retain a 2:1 mass ratio, but the current implementation produces [0, 0].

Fix

Divide all weights by their maximum finite value first. The scaled values lie in [0, 1], so their mean and subsequent normalization remain finite while the relative weights are unchanged.

Validation

• isolated numerical reproduction: the previous formula yields [0, 0] for [finfo.max, finfo.max / 2]
• the scale-first formula yields densities [2/(3π), 1/(3π)] and integrates to one
• regression derives the maximum finite value from the active backend dtype and checks the expected normalized density
• modified source and regression modules pass Python bytecode compilation
• branch is two commits ahead of current main, zero behind; final diff is 8 production-line changes plus one focused 23-line regression

The full multi-backend test matrix is delegated to GitHub Actions.

[github-actions]

✅MegaLinter analysis: Success

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✅ PYTHON	black	1490	182	0	0	96.91s
✅ PYTHON	isort	1490	328	0	0	2.69s
✅ REPOSITORY	betterleaks	yes		no	no	2.44s
✅ REPOSITORY	checkov	yes		no	no	54.4s
✅ REPOSITORY	gitleaks	yes		no	no	15.19s
✅ REPOSITORY	git_diff	yes		no	no	0.14s
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✅ REPOSITORY	trufflehog	yes		no	no	32.31s
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[FlorianPfaff]

Closing as duplicate of #4295. The latter carries the same piecewise-constant normalization repair on the preferred branch.