fix: use expm1 in stats/base/dists/exponential/cdf

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates stats/base/dists/exponential/cdf as -expm1( -lambda*x ) instead of 1 - exp( -lambda*x ) (JS, factory and C).

Subtracting exp(-lambda*x) from 1 cancels when lambda*x is small, and gives 0 for lambda*x < 2^-53:

var cdf = require( '@stdlib/stats/base/dists/exponential/cdf' );

cdf( 1.0e-20, 1.0 );
// develop: 0.0
// this PR: 1.0e-20

cdf( 1.0e-10, 1.0 );
// develop: 1.000000082740371e-10
// this PR: 9.999999999500001e-11

weibull/cdf and planck/cdf already use -expm1(...).

Tests: there's a new test/fixtures/julia/small_x.json (x log-spaced over [1e-300, 0.1], lambda in [0.1, 10.1]). runner.jl evaluates 1 - exp(-lambda*x) in 2048-bit BigFloat. The new tests in test.cdf.js, test.factory.js and test.native.js pass at 1 ULP. On develop, 999 of those assertions fail. The existing R fixture still passes at 0 ULP.

Related Issues

Does this pull request have any related issues?

None. Related to #15763 (exponential/quantile).

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

No.

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)
• Research and understanding

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 1 - exp(...).

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/exponential/cdf	$\\color{green}275/275$ $\\color{green}+0.00\\%$	$\\color{green}20/20$ $\\color{green}+0.00\\%$	$\\color{green}4/4$ $\\color{green}+0.00\\%$	$\\color{green}275/275$ $\\color{green}+0.00\\%$

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

[0PrashantYadav0]

Suggested change

	if ( x < 0.0 ) {
	if ( x <= 0.0 ) {

Non-blocking: cdf( -0.0, 1.0 ) now returns -0.0 (develop returns 0.0), since -expm1( +0.0 ) is -0.0. Should x = -0 short-circuit here? Same in lib/factory.js:67 and src/main.c:44.

[Abhist17]

Yes, done in 33192b4. x <= 0.0 now short-circuits to 0.0 in lib/main.js, lib/factory.js and src/main.c, so cdf( -0.0, 1.0 ) is +0 again. I added a -0/+0 test to test.cdf.js, test.factory.js and test.native.js checked with isPositiveZero. It fails without the change, and each file passes 2,015 with it (native rebuilt locally).