test: migrate math/base/special/ellipj to ULP-based assertions

[Devansh-18155]

Resolves a part of #11352

Description

What is the purpose of this pull request?

This pull request:

• Migrates tests for @stdlib/math/base/special/ellipj from relative tolerance testing to ULP difference testing using @stdlib/assert/is-almost-same-value.

Related Issues

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This pull request has the following related issues:

• Resolves a part of [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352

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• Read, understood, and followed the contributing guidelines.

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I used AI assistance to calculate minimum required ULP values.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/ellipj	$\\color{red}701/713$ $\\color{green}+98.32\\%$	$\\color{red}32/34$ $\\color{green}+94.12\\%$	$\\color{green}7/7$ $\\color{green}+100.00\\%$	$\\color{red}701/713$ $\\color{green}+98.32\\%$

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

[kgryte]

@Devansh-18155 How did you derive these ULP diffs? Given the previous deltas (e.g., 18*EPS), I am surprised by these large ULP differences.

[kgryte]

This same comment applies to several other test assertions.

[Devansh-18155]

@kgryte ,Large ULP diffs because the previous test checks difference (18 * EPS), while isAlmostSameValue checks ULP, As an deltas of 2.3 * EPS which makes approx 4750 ULP.
I derived it by checking max ULP diff across dataset and we can keep this limits!

[kgryte]

This still doesn't seem right. 1 unit of epsilon is roughly equal to 1 ULP, so, again, this large divergence is surprising. Can you provide exact test values demonstrating the large ULP difference?

[Devansh-18155]

@kgryte ,

Taken a test case from medium_positive_modulus.json :

• u : 5.006645997054875
• m : 0.8826190324290656
• Computed sn : -0.000761851982413601
• Expected sn : -0.000761851982414116
• Difference : 5.15 e-16 ( approx 2.3 EPS)

The value is small (0.0007), 1 ULP is 1.08e-19. So difference is 2.3 * EPS in terms, it takes 4750 ULPs.

1 ULP =1 EPS but, if the numbers are closer to zero the ULP shrinks as well.

[kgryte]

Oh, I see. The tolerances were previously computed incorrectly. They should have been scaled by the expected value.

[kgryte]

Left initial comments.

[kgryte]

LGTM