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

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

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

Near one the result is small, and acos( 1/x ) takes it from 1 - 1/x, whose low bits are lost to the rounding of 1/x:

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

asec( 1.000000001 );
// develop: 4.472136140385348e-5
// this PR: 4.472136138149279e-5 (256-bit BigFloat: 4.472136138149279e-5)

For x >= 1, tan( asec(x) ) = sqrt(x^2-1), and x-1 is exact for 1 <= x <= 2. Near -1 the result is close to π, so the relative error there was already small, and that side is unchanged.

• regenerates the fixtures in 256-bit BigFloat (they came from Julia's Float64 asec). The existing sets still pass at their current tolerances.
• adds near_one.json, 1000 values 1 + 10^k for k in [-15, -1], which pass at 2 ULPs.

Related Issues

Does this pull request have any related issues?

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

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/asec	$\\color{green}166/166$ $\\color{green}+100.00\\%$	$\\color{green}8/8$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}166/166$ $\\color{green}+100.00\\%$

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