Implement dual LUT scheme for int16 reciprocal/rsqrt operations

[3l1]

Summary:
Dual LUT Strategy (from Bolt reference)

1. Range LUT: Covers full int16 range, LOW resolution at small values
2. Resolution LUT: Scaled input (x*128), HIGH resolution for codes 0-256

Interpolation Weights

• x <= 255: Use resolution_lut (high accuracy for small values)
• x >= 256: Use range_lut (works fine for large values)
• Transition at 255/256 to avoid interpolation artifacts

Next Steps

• Full test suite validation
• Performance benchmarking
• Reduce number of rescale ops

Reviewed By: digantdesai

Differential Revision: D87120925

[pytorch-bot]

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❌ 4 New Failures, 1 Unrelated Failure

As of commit 5060a1c with merge base 5a64056 ():

NEW FAILURES - The following jobs have failed:

• Lint / lintrunner / linux-job (gh)
  >>> Lint for backends/arm/test/ops/test_rsqrt.py:
• Lint / lintrunner-mypy / linux-job (gh)
  >>> Lint for backends/arm/_passes/__init__.py:
• pull / unittest-arm-backend-with-no-fvp (test_pytest_models) / linux-job (gh)
  RuntimeError: Command docker exec -t efbae420b172aa620d4755db402af4989a6f80c23b429bb1b46dd4901378052d /exec failed with exit code 1
• pull / unittest-arm-backend-with-no-fvp (test_pytest_ops) / linux-job (gh)
  RuntimeError: Command docker exec -t 864779b2e111a8b95370012afedf33715fc2df2ec4fb74df7453a328d2a0df3b /exec failed with exit code 1

UNSTABLE - The following job is marked as unstable, possibly due to flakiness on trunk:

• pull / android / run-emulator (gh) (#16137)

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[meta-codesync]

@3l1 has exported this pull request. If you are a Meta employee, you can view the originating Diff in D87120925.

[digantdesai]

Review automatically exported from Phabricator review in Meta.

[3l1]

@pytorchbot label "release notes: none"

[3l1]

NOTE: I have pending changes before merging !!