feat: add math/base/special/gelu

[AryanSharma48]

Part of #15575

Description

What is the purpose of this pull request?

This pull request:

• adds @stdlib/math/base/special/gelu to evaluate the Gaussian Error Linear Unit (GELU) activation function.
• implements the numerically stable formulation using @stdlib/math/base/special/erfc to prevent catastrophic cancellation for negative values.
• handles IEEE 754 edge cases including signed zeros, NaN, and ±Infinity.
• includes unit tests with 2 ULPs tolerance assertions, benchmarks, usage examples, TypeScript declarations, and documentation.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Add modern scalar ML activation functions (GELU, SiLU) to @stdlib/math/base/special #15575

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.

No.

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

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

I consulted an AI assistant for research and mathematical understanding of the GELU formulation and repository conventions, while the changes were authored in accordance with canonical @stdlib guidelines.

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@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/gelu	$\\color{green}115/115$ $\\color{green}+100.00\\%$	$\\color{green}7/7$ $\\color{green}+100.00\\%$	$\\color{green}1/1$ $\\color{green}+100.00\\%$	$\\color{green}115/115$ $\\color{green}+100.00\\%$

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