fix: avoid cancellation near |x| = 1 in math/base/special/acoth

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates math/base/special/acoth as sign(x) * log1p( 2/(|x|-1) )/2 for 1 <= |x| <= 2 (JS and C), instead of atanh( 1/x ).

atanh( 1/x ) depends on 1 - |1/x|, and rounding 1/x loses its low bits:

var acoth = require( '@stdlib/math/base/special/acoth' );

acoth( 1.000000001 );
// develop: 10.708206467132994
// this PR: 10.708206467632994 (256-bit BigFloat: 10.708206467632994)

acoth(x) = log( (x+1)/(x-1) )/2 = log1p( 2/(x-1) )/2, and x-1 is exact for 1 <= x <= 2. acoth(±1) still returns ±Infinity. Elsewhere the function is unchanged.

• regenerates the fixtures in 256-bit BigFloat. They were generated with Julia's Float64 acoth, which is also atanh(inv(x)), so the reference values carried the same error. Against the exact values, the medium and large sets need 2 ULPs (they were checked at 1). The large set covers 3 <= |x| <= 28, which this PR doesn't touch, so those 2-ULP differences were already there.
• adds near_positive_one.json and near_negative_one.json, 1000 values each at ±(1 + 10^k) for k in [-15, -1]. They pass at 1 ULP.

Related Issues

Does this pull request have any related issues?

None. It is the same construction as #16110 (asech); asec and acsc follow.

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.

test.js and test.native.js pass.

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

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/acoth	$\\color{green}183/183$ $\\color{green}+100.00\\%$	$\\color{green}11/11$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}183/183$ $\\color{green}+100.00\\%$

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