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

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates math/base/special/acsc as sign(x) * atan( 1/sqrt((|x|-1)*(|x|+1)) ) for 1 <= |x| <= 2 (JS and C), instead of asin( 1/x ).

The slope of asin is unbounded at one, so near |x| = 1 it amplifies the rounding of 1/x:

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

acsc( 1.000000001 );
// develop: 1.5707516054334927
// this PR: 1.570751605433515 (256-bit BigFloat: 1.570751605433515)

For x >= 1, cot( acsc(x) ) = sqrt(x^2-1), and |x|-1 is exact for 1 <= |x| <= 2. acsc(±1) is still ±π/2. Elsewhere the function is unchanged.

• regenerates the fixtures in 256-bit BigFloat. They came from Julia's Float64 acsc and were checked with strictEqual, so they pinned asin(1/x) bit for bit. They are now checked at 1 ULP, the same as most math/base/special packages.
• adds near_positive_one.json and near_negative_one.json, 1000 values each at ±(1 + 10^k) for k in [-15, -1], which pass at 1 ULP.

Related Issues

Does this pull request have any related issues?

None. Same construction as #16110 (asech), #16111 (acoth) and #16112 (asec).

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/acsc	$\\color{green}187/187$ $\\color{green}+100.00\\%$	$\\color{green}11/11$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}187/187$ $\\color{green}+100.00\\%$

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