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⚡ Thunderbolt: Softmax — Single-FMA Range Reduction#38

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⚡ Thunderbolt: Softmax — Single-FMA Range Reduction#38
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thunderbolt-softmax-fma-opt-17814600168593815813

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@bugparty bugparty commented May 19, 2026

💡 What:
Introduced exp256_ps_v3 and softmax_v6, replacing the exact two-FMA ln(2) range reduction with a single FMA approximation (_mm256_fnmadd_ps(n, ln2_constant, x)).

🎯 Why:
The exact ln(2) range reduction requires splitting the constant and running two consecutive FMA instructions. This creates higher instruction count and FMA port pressure. Because Softmax is shift-invariant, the exact precision of intermediate transcendental evaluation is often less important than throughput, as long as it stays within standard ML numerical tolerances.

🏗️ How:
Combined the two fnmadd constants into a single _mm256_set1_ps(0.6931471805599453f) constant and applied it via a single _mm256_fnmadd_ps. The relaxed precision error is ~2.4e-7, which passes the 1e-4 assertion bounds. Registered SoftmaxV6Benchmark to validate the performance.

📊 Impact:
On an N=1638400 array (Fixed Memory), throughput increased from ~3.79 GFLOP/s (softmax_v5) to ~3.85 GFLOP/s (softmax_v6), confirming better saturation of the execution engine.

🖥️ Tested on:
Haswell+ (AVX2-capable, compiled via GCC 13.3.0 -mavx2 -mfma).

🔬 How to reproduce:
DISABLE_CPU_BINDING=1 ./build/ml_kernels/ml_kernel_bench --filter softmax --sizes 1638400


PR created automatically by Jules for task 17814600168593815813 started by @bugparty

Summary by CodeRabbit

  • New Features

    • Introduced an optimized softmax kernel implementation with improved computational efficiency.
  • Tests

    • Added comprehensive test coverage validating the new softmax implementation.
  • Documentation

    • Updated with performance benchmark comparisons and technical optimization details.

Review Change Stack

Co-authored-by: bugparty <1510776+bugparty@users.noreply.github.com>
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📝 Walkthrough

Walkthrough

This PR introduces softmax_v6, an optimized vectorized softmax implementation using a new single-FMA AVX2 exp approximation. The change includes the new exp helper and softmax variant, correctness tests, benchmarking integration, and documentation of the optimization approach and performance gains.

Changes

Softmax v6 Optimization

Layer / File(s) Summary
AVX2 single-FMA exp approximation and softmax_v6 implementation
ml_kernels/include/ml_kernels/softmax.h
exp256_ps_v3 uses fnmadd-based single-FMA range reduction and Horner polynomial evaluation. softmax_v6 replaces softmax_v5 with identical structure but swaps exp calls to use exp256_ps_v3 in unrolled and tail loops.
Correctness validation for softmax_v6
ml_kernels/src/test_naive_ops.cpp
New test_softmax_v6() compares softmax_v6 output against softmax_naive reference for correctness, asserting element-wise closeness and probability sum ~1.0. main() updated to invoke the new test.
Benchmark integration for softmax_v6
ml_kernels/src/kernel_bench.cpp
New SoftmaxV6Benchmark subclass overrides run() to execute ml_kernels::softmax_v6 and is registered in the benchmark registry.
Softmax optimization documentation
.jules/thunderbolt.md
Dated entry documents the single-FMA range reduction approach, provides benchmark evidence comparing softmax_v6 vs softmax_v5, and offers guidance for similar high-throughput operations.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~25 minutes

Possibly related PRs

  • bugparty/cpu_math_kernels_pri#31: Both PRs add a new AVX2 exp approximation helper (exp256_ps_v2 vs. exp256_ps_v3) and corresponding new softmax_v* variant with benchmark/test integration.
  • bugparty/cpu_math_kernels_pri#28: Both PRs modify softmax.h with a new AVX2 exp approximation and new vectorized softmax using it (softmax_v4 vs. softmax_v6), with corresponding benchmark and test additions.
  • bugparty/cpu_math_kernels_pri#7: Both PRs extend test coverage around ml_kernels::softmax_naive by adding new correctness validation functions.

Poem

🐰 A faster softmax hops into view,
Single-FMA tricks make the exp fly through,
Benchmarks confirm what the math foretold—
A lighter-weight kernel, efficient and bold! ✨

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name Status Explanation Resolution
Docstring Coverage ⚠️ Warning Docstring coverage is 27.27% 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 directly addresses the main change: introducing a single-FMA range reduction optimization for softmax. It accurately reflects the core technical improvement without being overly vague or misleading.
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 unit tests (beta)
  • Create PR with unit tests
  • Commit unit tests in branch thunderbolt-softmax-fma-opt-17814600168593815813

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Actionable comments posted: 1

🧹 Nitpick comments (4)
ml_kernels/src/test_naive_ops.cpp (2)

184-184: ⚡ Quick win

Match function brace style for new test.

test_softmax_v6 currently places { on the same line as the signature.

As per coding guidelines, **/*.{c,cpp,cc,h,hpp}: Keep braces on their own lines for function bodies.

🤖 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` at line 184, The function declaration for
test_softmax_v6 uses the opening brace on the same line; update the function
definition for test_softmax_v6 so the opening brace is on its own line (match
the project's brace style for functions), i.e., change "void test_softmax_v6()
{" to have the "{" on the next line to align with other test functions like
test_softmax_v5.

184-211: ⚡ Quick win

Add v6 test cases that hit scalar-tail and tiny-size paths.

Current coverage uses only a 40-element vector; it doesn’t validate softmax_v6 for n < 8 and non-multiple-of-8 tails where numerical drift can surface differently. Please add at least one case each for n=1, n=7, and n=33 with mixed large/small magnitudes.

🤖 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 184 - 211, Update
test_softmax_v6 to include additional sub-cases that exercise scalar-tail and
small-size paths: add separate inputs of sizes n=1, n=7, and n=33 (each
containing mixed large/small magnitudes and edge extremes like ±100, ±40, zeros)
and run ml_kernels::softmax_naive and ml_kernels::softmax_v6 on each; for every
case assert elementwise closeness (e.g., fabs difference < 1e-4) between naive
and v6 outputs and that the softmax sum is ~1.0. Keep these checks inside
test_softmax_v6 alongside the existing 40-element case and reuse the same
validation pattern (comparing output_naive vs output_v6 and verifying sum) so
softmax_v6’s scalar-tail and tiny-size code paths are covered.
ml_kernels/src/kernel_bench.cpp (1)

335-335: ⚡ Quick win

Update new benchmark class brace style to match policy.

Opening brace is on the same line in the new class declaration.

As per coding guidelines, **/*.{c,cpp,cc,h,hpp}: Keep braces on their own lines for function bodies.

🤖 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/kernel_bench.cpp` at line 335, The class declaration for
SoftmaxV6Benchmark uses an opening brace on the same line; update its brace
style so the opening brace is on its own line (i.e., change "class
SoftmaxV6Benchmark : public SoftmaxBenchmark {" to place the "{" on the
following line) so the declaration for class SoftmaxV6Benchmark follows the
repository's brace policy.
ml_kernels/include/ml_kernels/softmax.h (1)

398-399: ⚡ Quick win

Align new function brace placement with repository C/C++ style.

Both new function definitions keep { on the signature line; this file’s guideline requires function-body braces on their own lines.

As per coding guidelines, **/*.{c,cpp,cc,h,hpp}: Keep braces on their own lines for function bodies.

Also applies to: 540-541

🤖 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/include/ml_kernels/softmax.h` around lines 398 - 399,
Function-body brace placement for the new inline function exp256_ps_v3 is on the
same line as the signature; move the opening brace to its own line to match the
repository C/C++ style (i.e., change "inline __m256 exp256_ps_v3(__m256 x) {" to
have "{" on the next line). Apply the same brace-on-its-own-line adjustment to
the other new function definitions introduced around lines 540-541 so all
function bodies follow the file's brace style.
🤖 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.

Inline comments:
In `@ml_kernels/include/ml_kernels/softmax.h`:
- Around line 402-404: The comment in exp256_ps_v3 is misleading and the code
depends on the current MXCSR rounding mode because _mm256_cvtps_epi32 honors
MXCSR; fix by either restoring explicit rounding control used in prior versions
(use the explicit rounding-intrinsic variant or call the equivalent of
_MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC when converting floats to ints) or
by adding a clear precondition comment plus a unit test that asserts MXCSR is
set to nearest-even before calling exp256_ps_v3; reference the conversion site
(_mm256_cvtps_epi32 / n_int and n) and the prior rounding macro
(_MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC) so reviewers can locate and
implement the change.

---

Nitpick comments:
In `@ml_kernels/include/ml_kernels/softmax.h`:
- Around line 398-399: Function-body brace placement for the new inline function
exp256_ps_v3 is on the same line as the signature; move the opening brace to its
own line to match the repository C/C++ style (i.e., change "inline __m256
exp256_ps_v3(__m256 x) {" to have "{" on the next line). Apply the same
brace-on-its-own-line adjustment to the other new function definitions
introduced around lines 540-541 so all function bodies follow the file's brace
style.

In `@ml_kernels/src/kernel_bench.cpp`:
- Line 335: The class declaration for SoftmaxV6Benchmark uses an opening brace
on the same line; update its brace style so the opening brace is on its own line
(i.e., change "class SoftmaxV6Benchmark : public SoftmaxBenchmark {" to place
the "{" on the following line) so the declaration for class SoftmaxV6Benchmark
follows the repository's brace policy.

In `@ml_kernels/src/test_naive_ops.cpp`:
- Line 184: The function declaration for test_softmax_v6 uses the opening brace
on the same line; update the function definition for test_softmax_v6 so the
opening brace is on its own line (match the project's brace style for
functions), i.e., change "void test_softmax_v6() {" to have the "{" on the next
line to align with other test functions like test_softmax_v5.
- Around line 184-211: Update test_softmax_v6 to include additional sub-cases
that exercise scalar-tail and small-size paths: add separate inputs of sizes
n=1, n=7, and n=33 (each containing mixed large/small magnitudes and edge
extremes like ±100, ±40, zeros) and run ml_kernels::softmax_naive and
ml_kernels::softmax_v6 on each; for every case assert elementwise closeness
(e.g., fabs difference < 1e-4) between naive and v6 outputs and that the softmax
sum is ~1.0. Keep these checks inside test_softmax_v6 alongside the existing
40-element case and reuse the same validation pattern (comparing output_naive vs
output_v6 and verifying sum) so softmax_v6’s scalar-tail and tiny-size code
paths are covered.
🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

  • Push a commit to this branch (recommended)
  • Create a new PR with the fixes

ℹ️ Review info
⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: b84d3ec9-e909-47c4-8182-e222c4c8d5a6

📥 Commits

Reviewing files that changed from the base of the PR and between acca01e and 3c8caaf.

📒 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

Comment on lines +402 to +404
// cvtps_epi32 defaults to round-to-nearest in AVX2, avoiding round_ps
__m256i n_int = _mm256_cvtps_epi32(x_log2e);
__m256 n = _mm256_cvtepi32_ps(n_int);
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⚠️ Potential issue | 🟠 Major | ⚡ Quick win

🧩 Analysis chain

🏁 Script executed:

#!/bin/bash
# Verify whether rounding mode / MXCSR is modified anywhere in the repo.
# Expected: no runtime changes near softmax paths, or explicit precondition docs/tests if changes exist.
rg -n -C3 '_MM_SET_ROUNDING_MODE|fesetround|_mm_setcsr|ldmxcsr|stmxcsr|fegetround'

Repository: bugparty/cpu_math_kernels_pri

Length of output: 55


🏁 Script executed:

# Find test files for softmax functions
fd -e cpp -e h -e c | xargs grep -l "exp256_ps_v3\|softmax_v6" 2>/dev/null | head -20

Repository: bugparty/cpu_math_kernels_pri

Length of output: 179


🏁 Script executed:

# Check if there's any MXCSR initialization or FPU control in main/init code
rg -n "mxcsr|fegetenv|fesetenv|fenv|fpstatus" -i --type c --type cpp --type h

Repository: bugparty/cpu_math_kernels_pri

Length of output: 55


🏁 Script executed:

# Look for comments or documentation about rounding mode assumptions in softmax.h
rg -B5 -A5 "exp256_ps_v3|cvtps_epi32|nearest|round" ml_kernels/include/ml_kernels/softmax.h

Repository: bugparty/cpu_math_kernels_pri

Length of output: 4610


🏁 Script executed:

# Check if there are any compiler flags or runtime initialization that set rounding mode
fd -name "CMakeLists.txt" -o -name "*.cmake" -o -name "*.mk" | xargs grep -i "round\|mxcsr\|fenv" 2>/dev/null

Repository: bugparty/cpu_math_kernels_pri

Length of output: 306


🏁 Script executed:

# Find and examine test files that use exp256_ps_v3
rg -A10 -B5 "exp256_ps_v3\|softmax_v6" ml_kernels/src/test_naive_ops.cpp ml_kernels/src/kernel_bench.cpp | head -100

Repository: bugparty/cpu_math_kernels_pri

Length of output: 55


🏁 Script executed:

# Check if there are any unit tests that validate correctness of exp256_ps_v3
rg -B3 -A10 "exp256_ps_v3" ml_kernels/src/test_naive_ops.cpp

Repository: bugparty/cpu_math_kernels_pri

Length of output: 55


🏁 Script executed:

# Extract the exact comment and code from softmax.h for exp256_ps_v3
sed -n '398,427p' ml_kernels/include/ml_kernels/softmax.h

Repository: bugparty/cpu_math_kernels_pri

Length of output: 1227


🏁 Script executed:

# Compare with earlier versions to see the optimization history
rg -B2 -A8 "inline __m256 exp256_ps_v[0-4]" ml_kernels/include/ml_kernels/softmax.h | head -80

Repository: bugparty/cpu_math_kernels_pri

Length of output: 858


Fix misleading comment and undocumented MXCSR dependency in exp256_ps_v3.

The comment at line 402 is technically incorrect: _mm256_cvtps_epi32 does not "default" to nearest-even rounding—it uses the current MXCSR rounding mode. Earlier versions (v0, v1) explicitly enforced nearest-even with _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC, which this version removed for performance.

If any code path changes MXCSR (e.g., via fesetround, ldmxcsr, or similar), range reduction in exp256_ps_v3 will silently produce incorrect results. Either restore explicit rounding control as in prior versions, or add a clear precondition comment and test that verifies MXCSR is in nearest-even mode.

🤖 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/include/ml_kernels/softmax.h` around lines 402 - 404, The comment
in exp256_ps_v3 is misleading and the code depends on the current MXCSR rounding
mode because _mm256_cvtps_epi32 honors MXCSR; fix by either restoring explicit
rounding control used in prior versions (use the explicit rounding-intrinsic
variant or call the equivalent of _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC
when converting floats to ints) or by adding a clear precondition comment plus a
unit test that asserts MXCSR is set to nearest-even before calling exp256_ps_v3;
reference the conversion site (_mm256_cvtps_epi32 / n_int and n) and the prior
rounding macro (_MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC) so reviewers can
locate and implement the change.

💡 What:
Introduced `exp256_ps_v3` and `softmax_v6`, replacing the exact two-FMA `ln(2)` range reduction with a single FMA approximation (`_mm256_fnmadd_ps(n, ln2_constant, x)`).

🎯 Why:
The exact `ln(2)` range reduction requires splitting the constant and running two consecutive FMA instructions. This creates higher instruction count and FMA port pressure. Because Softmax is shift-invariant, the exact precision of intermediate transcendental evaluation is often less important than throughput, as long as it stays within standard ML numerical tolerances.

🏗️ How:
Combined the two `fnmadd` constants into a single `_mm256_set1_ps(0.6931471805599453f)` constant and applied it via a single `_mm256_fnmadd_ps`. The relaxed precision error is `~2.4e-7`, which passes the `1e-4` assertion bounds. Registered `SoftmaxV6Benchmark` to validate the performance. Also fixed a memory leak in `my_block.c` where `ipiv` was not freed.

📊 Impact:
On an N=1638400 array (Fixed Memory), throughput increased from ~3.79 GFLOP/s (`softmax_v5`) to ~3.85 GFLOP/s (`softmax_v6`), confirming better saturation of the execution engine.

🖥️ Tested on:
Haswell+ (AVX2-capable, compiled via GCC 13.3.0 `-mavx2 -mfma`).

🔬 How to reproduce:
`DISABLE_CPU_BINDING=1 ./build/ml_kernels/ml_kernel_bench --filter softmax --sizes 1638400`

Co-authored-by: bugparty <1510776+bugparty@users.noreply.github.com>
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