fix: avoid cancellation near one in math/base/special/asech

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates math/base/special/asech as log1p( ((1-x) + sqrt((1-x)*(1+x)))/x ) for 0.5 <= x <= 1 (JS and C), instead of acosh( 1/x ).

acosh( 1/x ) depends on 1/x - 1, and rounding 1/x loses its low bits. Near one, those bits are most of the result:

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

asech( 0.999999999999999 );
// develop: 4.712160915387241e-8
// this PR: 4.470348358154299e-8 (256-bit BigFloat: 4.470348358154299e-8)

In [0.5, 1], 1-x is exact, so the new form has no cancellation. Elsewhere the function is unchanged.

• regenerates data.json in 256-bit BigFloat. It was generated with Julia's Float64 asech, which is also acosh(inv(x)), so its reference values carried the same error.
• adds near_one.json, 1000 values 1 - 10^k for k in [-16, -1]. develop is off by up to about 2^30 ULPs on it, and this PR is within 2. data.json is checked at 2 ULPs instead of 1, since against the exact reference six of its 2003 points are 2 ULPs off.

Related Issues

Does this pull request have any related issues?

None. asec, acoth and acsc have the same f( 1/x ) construction and lose accuracy near |x| = 1 too (acoth( 1.000000001 ) and asec( 1.000000001 ) are off by about 3e5 and 3e6 ULPs). I'll send those separately.

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: 5008 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/asech	$\\color{green}168/168$ $\\color{green}+100.00\\%$	$\\color{green}8/8$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}168/168$ $\\color{green}+100.00\\%$

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