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SIMD_SPEEDUP_NOTES.md

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SIMD Speedup Investigation Notes

Date: 2026-01-19 Branch: simd-speedup-exploration

Summary

Successfully implemented a 34% faster AVX2 DCT using 16-bit packed data and vpmaddwd, directly translating libjpeg-turbo's jfdctint-avx2.asm to Rust intrinsics.

Key Results

Performance (DCT, batch of 1000 blocks)

Implementation Time (µs) Throughput (Melem/s) vs scalar
scalar (multiversion) 20.8 48.0 baseline
transpose_i32x8 27.3 36.7 0.76x
avx2_intrinsics (i32) 16.2 61.6 1.28x
avx2_i16_vpmaddwd 12.1 82.3 1.72x

The i16 vpmaddwd implementation is:

  • 34% faster than the i32 AVX2 intrinsics
  • 72% faster than scalar
  • Produces exact match with scalar reference (max diff: 0)

vpmaddwd Optimization

The vpmaddwd instruction is key to libjpeg-turbo's AVX2 DCT performance:

; vpmaddwd computes: result[i] = a[2i] * b[2i] + a[2i+1] * b[2i+1]
; This maps perfectly to DCT patterns like:
;   data2 = tmp13 * (FIX_0_541 + FIX_0_765) + tmp12 * FIX_0_541
;   data6 = tmp13 * FIX_0_541 + tmp12 * (FIX_0_541 - FIX_1_847)

Bugs Fixed

  1. _mm256_set_epi16 element ordering: Arguments are in REVERSE order (e15..e0), so constant vector pairs were swapped. Fixed pw_f130_f054 and pw_mf078_f117.

  2. Reference scalar used wrong variable naming: Libjpeg uses non-standard naming where tmp13 = tmp0 - tmp3 (textbooks call this tmp11) and tmp12 = tmp1 - tmp2 (textbooks call this tmp13). The scalar reference in debug examples was using textbook naming, causing apparent mismatches.

libjpeg-turbo Assembly Analysis

libjpeg-turbo's jfdctint-avx2.asm uses:

  • 16-bit data packed as (row0|row4), (row1|row5), (row2|row6), (row3|row7)
  • 16-bit transpose with vpunpcklwd/hi (faster than 32-bit)
  • vpmaddwd for all multiply-accumulate operations
  • After transpose: (col1|col0), (col3|col2), (col4|col5), (col6|col7)

This layout enables efficient butterfly operations:

  • tmp1_0 = data1_0 + data6_7 processes two butterflies per instruction

Files Modified

  • src/dct.rs: Rewrote forward_dct_8x8_avx2_i16 with new dotranspose and dodct helpers
  • benches/dct.rs: Criterion benchmarks for all DCT variants
  • examples/debug_dct.rs: Test harness comparing scalar vs AVX2 outputs
  • examples/debug_data26.rs: Step-by-step data2_6 computation tracing
  • examples/debug_full_dct.rs: Full DCT with intermediate value dumps
  • examples/trace_transpose.rs: Transpose verification
  • examples/profile_dct.rs: Profiling runner for perf analysis

Next Steps

  1. Consider merging to main branch - Implementation is complete and tested

  2. Entropy encoding optimization - DCT is now fast (~12µs/1000 blocks)

    • Entropy encoding may be the new bottleneck
    • Consider Huffman table lookups optimization

  3. Profile full encoder - Measure DCT impact on end-to-end encoding time

Benchmark Command

cd ~/work/mozjpeg-rs-simd-speedup
RUSTFLAGS="-C target-cpu=native" cargo bench --bench dct -- --noplot