fix: evaluate the upper tail without cancellation in stats/base/dists/laplace/logcdf

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates the upper tail of stats/base/dists/laplace/logcdf without cancellation (JS, factory and C).

Above the mean the function computed ln(1/2) + log1p( 1 - exp(-z) ). That's ln(1/2) + ln(2 - exp(-z)), which cancels and rounds to 0 once exp(-z) is below an ULP of 2:

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

logcdf( 50.0, 0.0, 1.0 );
// develop: 0
// this PR: -9.643749239819589e-23

logcdf( 3.0, 0.0, 1.0 );
// develop and this PR: -0.025208618236919594

It now uses the equivalent log1p( -exp(-z)/2 ), which has no subtraction. The lower branch and x = mu are unchanged.

Fixtures and tolerances. The fixtures came from Distributions.jl's logcdf, which evaluates the same expression in Float64, and the tests asserted them at 0 ULP. So develop was being checked for bit-equality with a reference that has the same cancellation. gen now evaluates the log CDF in 2048-bit BigFloat, and all three fixtures were regenerated. Measured against them:

fixture	this PR: p99 / max ULP	develop: p99 / max ULP
positive_mean	1 / 1	1 / 1
negative_mean	1 / 1	1 / 1
large_variance	3 / 155	803 / ~4.3e18 (0)

The tolerances are set from those numbers: 1, 1 and 160 ULP. The 160 is not slack in the formula. Far above the mean the result is about -exp(-z)/2, so the rounding of z = (x-mu)/b gets amplified by z, and large_variance reaches z ≈ 120. Any double-precision evaluation hits that; there's a comment on the assertion saying so. test.logcdf.js / test.factory.js / test.native.js pass 3,013 / 3,018 / 3,013.

Related Issues

Does this pull request have any related issues?

None.

Questions

Any questions for reviewers of this pull request?

[stdlib-bot]

Hello! Thank you for your contribution to stdlib.

We noticed that the contributing guidelines acknowledgment is missing from your pull request. Here's what you need to do:

1. Please read our contributing guidelines.

2. Update your pull request description to include this checked box:

   - [x] Read, understood, and followed the [contributing guidelines](https://github.com/stdlib-js/stdlib/blob/develop/CONTRIBUTING.md)

This acknowledgment confirms that you've read the guidelines, which include:

• The developer's certificate of origin
• Your agreement to license your contributions under the project's terms

We can't review or accept contributions without this acknowledgment.

Thank you for your understanding and cooperation. We look forward to reviewing your contribution!

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/laplace/logcdf	$\\color{green}293/293$ $\\color{green}+100.00\\%$	$\\color{green}23/23$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}293/293$ $\\color{green}+100.00\\%$

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