fix: avoid cancellation near multiples of 2π in math/base/special/cosm1

[Abhist17]

Description

What is the purpose of this pull request?

This pull request:

• evaluates math/base/special/cosm1 as -2 sin^2(x/2) outside [-π/4,π/4] (JS and C), instead of cos(x) - 1.

cos(x) - 1 cancels wherever cos(x) is close to one, which is near every multiple of 2π, not only near zero (inside [-π/4,π/4] the polynomial already handles that):

var cosm1 = require( '@stdlib/math/base/special/cosm1' );

cosm1( -6.271126315854843 );
// develop: -0.0000727087547741645
// this PR: -0.00007270875477419403 (256-bit BigFloat: -0.00007270875477419403)

x/2 is exact and sin has its own argument reduction, so the half-angle form has no cancellation. #15609 uses the same identity for versin (versin(x) = -cosm1(x)).

• replaces the test for |x| > π/4, which compared cosm1(x) against cos(x) - 1 (the expression being replaced) at 1 ULP, with fixtures evaluated in 256-bit BigFloat by a new Julia runner. The fixtures cover the same two ranges, [π/4, 4π] and [-4π, -π/4], plus 2000 values within 10^-8 to 10^-1 of ±2πk for k = 1..10. develop is off by up to about 2^30 ULPs on those, and this PR passes all three at 2.

Related Issues

Does this pull request have any related issues?

None.

Questions

Any questions for reviewers of this pull request?

No.

Other

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test.js and test.native.js pass.

Checklist

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• Read, understood, and followed the contributing guidelines.

AI Assistance

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• Code generation (e.g., when writing an implementation or fixing a bug)
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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/cosm1	$\\color{green}245/245$ $\\color{green}+100.00\\%$	$\\color{green}12/12$ $\\color{green}+100.00\\%$	$\\color{green}3/3$ $\\color{green}+100.00\\%$	$\\color{green}245/245$ $\\color{green}+100.00\\%$

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