⚡ Thunderbolt: softmax_v6 — 8x unrolled phases with single-FMA exp256

[bugparty]

💡 What:
Added a new AVX2 kernel, softmax_v6, heavily optimizing the prior versions by:

1. Converting the range reduction x - n*ln2 from dual FMAs to a single FMA to exploit softmax shift-invariance.
2. Mixing loop unrolling: the simple max and normalize phases are unrolled 8x to perfectly match execution unit latency (e.g. max_ps 4-cycle latency), while the register-heavy exp phase is kept at 4x unroll to avoid YMM spilling.

🎯 Why:
The prior softmax_v5 was bottlenecked during the max/normalize phases by unrolling only 4x. Additionally, perfectly accurate ln2 approximation required multiple FMA instructions which bottlenecked port execution while the shift-invariant properties of softmax can tolerate the slight approximation.

🏗️ How:

• Added exp256_ps_v3 inside ml_kernels/include/ml_kernels/softmax.h utilizing single FMA range reduction.
• Upgraded the max search to use 8 independent accumulator chains (max0 through max7).
• Upgraded the normalization phase to compute and store 8 vectors (64 elements) per iteration.
• Created test_softmax_v6 in test_naive_ops.cpp verifying the output is within the 1e-4 target tolerance.
• Bound and recorded this test into the BenchmarkRegistry.

📊 Impact:

• Microbenchmark verified N=1048576 fixed memory runs improved from 4.19 GFLOP/s to 4.48 GFLOP/s, a ~7% throughput improvement, transitioning these phases directly from latency-bound to port execution bound.

🖥️ Tested on:

• Haswell+ (AVX2 + FMA target) via CI GitHub runner VM (Ubuntu).

🔬 How to reproduce:

mkdir build && cd build && cmake .. && make ml_kernel_bench
DISABLE_CPU_BINDING=1 ./ml_kernels/ml_kernel_bench --sizes 1048576 --filter 'softmax_v6'

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PR created automatically by Jules for task 14084203667146761558 started by @bugparty

Summary by CodeRabbit

Release Notes

• New Features

  • Introduced an optimized softmax kernel implementation with enhanced performance characteristics and computational efficiency.

• Documentation

  • Added comprehensive performance benchmarking documentation and optimization insights for the softmax implementation, including comparative benchmark analysis.

• Tests

  • Added extensive test coverage for the new softmax variant, including precision validation and correctness verification across multiple input scenarios.

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[coderabbitai]

📝 Walkthrough

Walkthrough

This PR introduces softmax_v6, a new AVX2-vectorized softmax kernel optimized with a specialized exp range-reduction helper, along with corresponding unit tests, benchmark registration, and performance documentation comparing against prior versions.

Changes

Softmax v6 AVX2 Implementation

Layer / File(s)	Summary
AVX2 exp and softmax_v6 functions ml_kernels/include/ml_kernels/softmax.h	exp256_ps_v3 performs log2-scale range reduction and computes the reduced exponent argument using a single FNMADD. softmax_v6 pipelines max reduction (8-way unroll), exponentiation and sum accumulation (4-way unroll), vector-to-scalar sum reduction, and output normalization (8-way unroll).
Test implementation and integration ml_kernels/src/test_naive_ops.cpp	test_softmax_v6() expands input to 72 elements, verifies per-element agreement with softmax_naive within 1e-4 tolerance, and confirms output probability sum ≈ 1.0. Test is wired into main() for execution.
Benchmark registration ml_kernels/src/kernel_bench.cpp	SoftmaxV6Benchmark inherits SoftmaxBenchmark, invokes ml_kernels::softmax_v6, and is registered for discovery and performance measurement against other softmax variants.
Performance documentation .julius/thunderbolt.md	Dated entry (2024-06-13) documents shift-invariant range reduction using single FMA, mixed unrolling strategy (heavier for max/normalize phases, lighter for exp/polynomial to avoid spilling), benchmark evidence vs v5, and action items for future work.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~25 minutes

Possibly related PRs

• bugparty/cpu_math_kernels_pri#31: The direct predecessor PR introducing exp256_ps_v2 and softmax_v5, which softmax_v6 and exp256_ps_v3 extend with refined range reduction and unrolling tuning.

Poem

🐰 A kernel rebirth, softmax reborn,
With AVX SIMD worn in a mathematical form—
Exp reduces swift with a single FMA dance,
Eight lanes unroll where probabilities prance! ✨

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 30.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately reflects the main change: introducing softmax_v6 with 8x unrolled phases and single-FMA exp256 optimization, which is the core deliverable across all modified files.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch thunderbolt/softmax_v6-14084203667146761558

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[coderabbitai]

🧹 Nitpick comments (1)

ml_kernels/src/test_naive_ops.cpp (1)

186-216: 💤 Low value

Consider adding a test case with a non-multiple-of-8 size to exercise scalar tail handling.

The current test with 72 elements exercises the main loops and 8-element cleanup paths, but doesn't cover the scalar tail (lines 617-621, 648-650 in softmax.h). Adding a test case with, e.g., 75 elements would improve coverage of edge-case handling.

🤖 Prompt for AI Agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@ml_kernels/src/test_naive_ops.cpp` around lines 186 - 216, The test currently
only covers multiples of 8; change test_softmax_v6 to exercise the scalar tail
by using a non-multiple-of-8 length (for example replace input.resize(72, 1.0f)
with input.resize(75, 1.0f) or add a new test function test_softmax_v6_tail that
sets input.size() to 75), then run ml_kernels::softmax_naive and
ml_kernels::softmax_v6 as before and assert elementwise closeness and sum==1 to
validate the scalar tail handling in softmax_v6/softmax_naive.

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Nitpick comments:
In `@ml_kernels/src/test_naive_ops.cpp`:
- Around line 186-216: The test currently only covers multiples of 8; change
test_softmax_v6 to exercise the scalar tail by using a non-multiple-of-8 length
(for example replace input.resize(72, 1.0f) with input.resize(75, 1.0f) or add a
new test function test_softmax_v6_tail that sets input.size() to 75), then run
ml_kernels::softmax_naive and ml_kernels::softmax_v6 as before and assert
elementwise closeness and sum==1 to validate the scalar tail handling in
softmax_v6/softmax_naive.

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ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: 90950ab1-ef6f-43c4-bd68-422c7b9382a7

📥 Commits

Reviewing files that changed from the base of the PR and between acca01e and fc3831e.

📒 Files selected for processing (4)

• .jules/thunderbolt.md
• ml_kernels/include/ml_kernels/softmax.h
• ml_kernels/src/kernel_bench.cpp
• ml_kernels/src/test_naive_ops.cpp