fix: evaluate the lower tail from p in stats/base/dists/laplace/quantile

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates the lower tail of stats/base/dists/laplace/quantile from p itself (JS, factory and C).

The function computed mu - b*signum(p-0.5)*ln(1 - 2|p-0.5|). For p < 0.5, 1 - 2|p-0.5| is 2p, but forming 0.5 - p first rounds away the low-order bits of a small p. Precision degrades below p ~ 1e-8, and for p < 2^-54 the result is -Infinity:

var quantile = require( '@stdlib/stats/base/dists/laplace/quantile' );

quantile( 1.0e-20, 0.0, 1.0 );
// develop: -Infinity
// this PR: -45.35855467932097 (= ln(2e-20))

quantile( 1.0e-10, 0.0, 1.0 );
// develop: -22.332703666640143
// this PR: -22.33270374938051

It now returns mu + b*ln(2p) for p < 0.5, and mu - b*ln(2(1-p)) otherwise. Both products are exact, and 1 - p is exact for p >= 0.5. The upper tail was already accurate, since p - 0.5 is exact there. This also drops the signum and abs dependencies.

Tests: runner.jl gains a gen_tails function. It evaluates the textbook formula mu - b*sign(p-0.5)*ln(1 - 2|p-0.5|) in 2048-bit BigFloat and writes tails.json:

• 500 points with p log-spaced over [1e-300, 0.1],
• 500 points with 1-p log-spaced over [1e-16, 0.1].

mu is 0, so the test isolates the tail and not the rounding of mu + .... The new tests in test.quantile.js, test.factory.js and test.native.js pass at the existing 1-ULP tolerance. On develop, 498 of them fail. The existing fixtures still pass unchanged.

Related Issues

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None.

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Other

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Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
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Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

This PR was written primarily by Claude Code. I found the bug by scanning stats/base/dists for ln( 1.0 - ... ).

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/laplace/quantile	$\\color{green}303/303$ $\\color{green}+100.00\\%$	$\\color{green}27/27$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}303/303$ $\\color{green}+100.00\\%$

The above coverage report was generated for the changes in this PR.