Stabilize piecewise-constant weight normalization

[FlorianPfaff]

Summary

• normalize piecewise-constant weights after scaling by their largest finite entry
• prevent overflow when individually finite weights have a non-finite arithmetic mean
• preserve the relative weight ratios and unit-integral density
• add a focused regression using the active backend's maximum finite floating-point value

Bug

PiecewiseConstantDistribution.__init__() normalized weights through

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

A vector can contain valid, nonnegative, individually finite weights whose mean overflows during accumulation. For example, [finfo.max, finfo.max / 2] has a well-defined 2:1 ratio, but the direct mean becomes infinity on NumPy. Dividing by that value collapses both density weights to zero, so the resulting object is not a normalized probability density.

Fix

Divide all weights by their largest entry before computing the mean. The scaled values lie in [0, 1], so the mean remains finite while the relative weights are unchanged. The final density is mathematically identical for ordinary inputs.

Validation

• isolated pre-fix reproduction returns [0.0, 0.0]
• isolated corrected calculation returns [2 / (3π), 1 / (3π)]
• regression verifies both the expected 2:1 density ratio and unit integral
• modified source and regression modules pass python -m py_compile
• branch is two commits ahead of current main and zero behind
• final diff is 8 changed production lines plus one 21-line regression

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

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	20.08s
✅ JSON	prettier	7	0	0	0	0.85s
✅ JSON	v8r	7		0	0	3.87s
✅ MARKDOWN	markdownlint	68	0	0	0	1.58s
✅ MARKDOWN	markdown-table-formatter	68	0	0	0	0.67s
✅ PYTHON	black	1490	182	0	0	78.6s
✅ PYTHON	isort	1490	328	0	0	2.08s
✅ REPOSITORY	betterleaks	yes		no	no	1.64s
✅ REPOSITORY	checkov	yes		no	no	47.34s
✅ REPOSITORY	gitleaks	yes		no	no	13.29s
✅ REPOSITORY	git_diff	yes		no	no	0.24s
✅ REPOSITORY	secretlint	yes		no	no	48.91s
✅ REPOSITORY	syft	yes		no	no	4.87s
✅ REPOSITORY	trivy-sbom	yes		no	no	5.18s
✅ REPOSITORY	trufflehog	yes		no	no	29.9s
✅ YAML	prettier	11	0	0	0	0.65s
✅ YAML	v8r	11		0	0	10.55s
✅ YAML	yamllint	11		0	0	0.54s

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