Core: Solve whole TRSM diagonal blocks with the shared packet kernel

Rasmus Munk Larsenrequested to merge
rmlarsen1/eigen-new:perf/trsm-shared-kernel-2 into master

This makes the blocked left triangular solve pass each whole diagonal block to the shared packet TRSM kernel from !3119 (merged), and sizes that kernel's right-hand-side tile from the register file. Across the 276 shapes of benchmarks/Core/bench_trsm_packet.cpp the median change is +17.5% on Apple M4 (NEON) and +0.6% on AVX2, with AVX2 gains of +5% to +11% at n = 192–256; on neither machine is any shape more than 3% slower in both a default and a 64-byte-aligned build.

Why

On AVX2 the trailing gebp updates already run at the GEMM rate. The loss was on the diagonal: its blocks carry k_c/n of the flops (30% for double at n = 256, k_c = 88), and they were solved as max(mr, nr)-row panels (12 for double, 24 for float), each followed by a gebp update of that depth. At n = 256 the packet kernel ran at 37% (double) and 54% (float) of the gebp rate on such panels, and the depth-12/24 updates at 80% and 89% (rdtsc-instrumented copy of the solver, i7-13700HX).

Changes

  1. Whole diagonal blocks. When the packet kernel is enabled and the right-hand side is at least two packets wide, each k_c \times k_c diagonal block is solved in one kernel call, split evenly when k_c exceeds the kernel's 128-row workspace. Column chunks are sized so a chunk of k_c rows stays in L2 between the solve and the pack (k_c \cdot \text{cols} \cdot \texttt{sizeof(Scalar)} \le L_2/2) and are packet-aligned. Narrower right-hand sides keep the old panels, including the compile-time width bound GCC uses to shorten the scalar kernel's loops.
  2. Register-budget tile. Accumulators take half the register file: RhsPackets = min((R - 2) / 5, R / 8), i.e. 1, 2, 4 packets for R = 8, 16, 32 registers. 32-register targets (NEON, SVE, RVV, LSX, AltiVec, ZVector, MSA, HVX; AVX-512 only with EIGEN_USE_AVX512_TRSM_KERNELS=0) go from 2 to 4 packets, with a 2-packet pass for the columns left over; SSE and AVX2 keep 2. A single-packet tile solves 8 rows per step where the registers allow, as a pass ahead of the 4-row loop, so on 16-register targets 2-packet tiles compile to the same instructions as before (AVX2 double solve<2>: 0 of 823 lines differ in a disassembly diff with only addresses stripped). On 32-register targets 2-packet tiles also solve 8 rows per step.
  3. Row-major tails. For a row-major triangle, the last cols % PacketSize columns are solved as one zero-padded packet in a stack copy (out of line) instead of one scalar dot product per coefficient: right-side row-major ×17 shapes (n ≤ 128) run 45–113% faster, n = 512 3–12%. A column-major triangle keeps the scalar tail, a contiguous axpy that compilers vectorize; padding measured 10–17% slower there on AVX2 for a single leftover column.

Unchanged: AVX-512 builds using the specialized TRSM kernels (the default), complex and custom scalars, and the right-side solver for column-major operands.

Performance

x = b; a.triangularView<Mode>().solveInPlace<Side>(x) from benchmarks/Core/bench_trsm_packet.cpp (dynamic Matrix<float|double>; name = triangle/operand layout and side, n = triangle order, nrhs = right-hand sides), CPU time. Each arm ran twice, alternating before/after, each run 3 repetitions of ≥ 0.1 s; the tables give the mean of the two run medians and the change in throughput, t_\text{before}/t_\text{after} - 1.

  • AVX2: 13th Gen Intel(R) Core(TM) i7-13700HX under WSL2, GCC 13.3.0, -O3 -DNDEBUG -mavx2 -mfma, pinned to one core; the 1-min load average was sampled every 5 s and stayed ≤ 1.3 (the benchmark itself is 1.0).
  • NEON: Apple M4 (Mac mini, macOS 27.0), Apple clang 21.0.0, -O3 -DNDEBUG, not pinned, with an idle CI virtual machine running.
  • Google Benchmark 1.9.5 on both. The aligned builds add -falign-functions=64 -falign-loops=64 to both arms.
Shape name/n/nrhs AVX2 before (µs) AVX2 after (µs) AVX2 change AVX2 change, aligned build M4 before (µs) M4 after (µs) M4 change
float/16/16 0.073 0.072 +0.9% -0.6% 0.108 0.095 +13.4%
float/64/64 2.35 2.35 +0.1% -0.9% 4.07 3.16 +28.8%
float/128/128 18.1 17.6 +2.7% +0.4% 30.0 22.1 +35.6%
float/192/192 63.6 60.0 +5.9% +6.2% 89.8 75.1 +19.6%
float/256/256 142.0 135.1 +5.1% +4.4% 214.3 169.2 +26.7%
float/512/512 1,087 1,061 +2.5% +0.3% 1,381 1,232 +12.1%
float/1024/1024 8,207 8,184 +0.3% +0.8% 10,632 9,356 +13.6%
float/2048/2048 64,496 64,213 +0.4% +0.2% 81,128 73,414 +10.5%
double/16/16 0.122 0.120 +1.0% -1.3% 0.211 0.178 +19.0%
double/64/64 4.92 5.09 -3.4% -0.8% 8.11 6.29 +28.9%
double/128/128 35.0 36.0 -2.7% +1.0% 61.9 44.6 +38.8%
double/192/192 132.6 119.7 +10.8% +10.2% 179.0 149.0 +20.1%
double/256/256 314.5 287.3 +9.4% +7.7% 424.0 338.1 +25.4%
double/512/512 2,326 2,241 +3.8% +2.8% 2,848 2,496 +14.1%
double/1024/1024 17,020 17,097 -0.4% +0.1% 21,362 18,928 +12.9%
double/2048/2048 132,494 129,681 +2.2% +2.1% 171,010 147,596 +15.9%
float/1024/128 1,067 1,056 +1.1% +0.4% 1,369 1,219 +12.3%
double/1024/128 2,191 2,192 -0.1% +1.6% 2,775 2,461 +12.8%
float_RightRow/128/17 6.71 3.59 +86.8% +95.3% 8.45 3.97 +112.9%
double_RightRow/512/64 311.9 292.2 +6.7% +6.0% 388.4 328.3 +18.3%
Machine, build Median change 5th percentile Best Shapes > 3% slower under every pairing
i7-13700HX AVX2, default +0.6% -3.2% +101.1% 4
i7-13700HX AVX2, 64-byte aligned +0.8% -2.5% +101.3% 2
Apple M4 NEON, default +17.5% -0.4% +112.9% 0
Apple M4 NEON, 64-byte aligned +17.9% -0.5% +116.9% 0

"Slower under every pairing" means the new code's faster run is still > 3% slower than master's slower run. On AVX2 the flagged shapes differ between the two builds, and each is within 3% in the other one. double_Right/64/4096 runs the right-side solver, which this MR does not change, so code placement alone moved it by 5.5%:

Machine, build Shape Change Same shape, other build
AVX2 default double_Right/64/4096 -5.5% +1.2%
AVX2 default double/128/8 -4.9% -0.6%
AVX2 default double/64/8 -4.8% -0.9%
AVX2 default float/64/4 -3.9% +1.5%
AVX2 aligned float_RowTri/64/4 -6.0% -2.8%
AVX2 aligned float_RowTri/128/4 -4.6% -0.3%

Validation

  • trsm_packet, trsm_packet_cancellation, trsm_packet_cancellation_fastmath, product_trsolve, triangular, triangular_in_place (46 executables), EIGEN_REPEAT=3 EIGEN_SEED=42, all passing in four configurations: GCC 13.3 AVX2+FMA (C++14); Apple clang 21 NEON; GCC 13.3 AVX-512F/DQ/VL/BW on AMD RYZEN AI MAX+ 395 w/ Radeon 8060S (WSL2), with the default AVX-512 TRSM kernels and with EIGEN_USE_AVX512_TRSM_KERNELS=0 (4-packet tiles on x86).
  • The existing tests reach each new path. On NEON, each mutation below makes trsm_packet_1 and trsm_packet_2 fail; the first two also fail product_trsolve_18:
    • skipping the pack after a whole-block panel;
    • solving one packet in the 2-packet leftover pass (NEON);
    • dropping the padded tail's copy-back.
  • C++14 builds with GCC 13.3 and clang 18; clang-format-17, scripts/check_style.py and scripts/clang_tidy_hook.py on the diff are clean.

Not done

  • Not measured on AMD Zen 5 or against a vendor BLAS. The AVX2 comparison page (libeigen.gitlab.io, Zen 5) measured master 15f227178, before !3119 (merged).
  • The right-side solver for column-major operands is untouched.
Appendix A: all 276 shapes, AVX2 (i7-13700HX)
Shape Before (µs) After (µs) Change Max run-to-run spread Change, aligned build
float/8/8 0.025 0.023 +7.0% 2.2% +4.6%
float/12/12 0.153 0.157 -2.5% 1.2% +0.7%
float/16/16 0.073 0.072 +0.9% 4.2% -0.6%
float/24/24 0.188 0.182 +3.5% 0.5% +3.3%
float/31/31 0.949 0.973 -2.4% 0.9% -2.0%
float/32/32 0.358 0.360 -0.7% 1.4% -0.1%
float/33/33 0.565 0.563 +0.3% 0.8% +0.3%
float/48/48 1.07 1.07 -0.1% 1.1% -1.3%
float/63/63 3.98 3.86 +3.1% 3.4% -0.1%
float/64/64 2.35 2.35 +0.1% 0.6% -0.9%
float/65/65 2.92 2.93 -0.5% 1.5% -1.6%
float/95/95 11.0 10.7 +2.7% 1.2% +3.6%
float/96/96 7.88 7.82 +0.8% 0.2% +0.0%
float/97/97 9.22 9.24 -0.1% 0.7% +0.8%
float/100/100 10.4 10.3 +1.2% 1.0% +0.5%
float/127/127 23.8 23.2 +2.7% 1.0% +0.3%
float/128/128 18.1 17.6 +2.7% 2.5% +0.4%
float/129/129 22.7 21.2 +7.0% 4.3% +5.8%
float/192/192 63.6 60.0 +5.9% 0.2% +6.2%
float/256/256 142.0 135.1 +5.1% 0.4% +4.4%
float/257/257 151.4 145.7 +4.0% 1.5% +4.5%
float/512/512 1,087 1,061 +2.5% 0.5% +0.3%
float/1024/1024 8,207 8,184 +0.3% 1.3% +0.8%
float/2048/2048 64,496 64,213 +0.4% 0.8% +0.2%
float/4096/4096 512,795 499,709 +2.6% 0.9% -0.0%
float/64/1 0.425 0.416 +2.0% 3.7% +0.2%
float/64/4 0.777 0.808 -3.9% 0.8% +1.5%
float/64/8 0.406 0.332 +22.3% 0.8% +21.7%
float/64/16 0.603 0.605 -0.3% 1.3% -0.9%
float/64/17 0.938 0.941 -0.3% 0.7% -0.3%
float/64/4096 183.6 181.3 +1.3% 4.1% -0.4%
float/128/4 2.04 2.07 -1.9% 0.2% -0.1%
float/128/8 1.64 1.23 +33.4% 3.9% +33.0%
float/128/17 3.14 3.05 +2.8% 1.3% -0.3%
float/1024/8 119.5 119.6 -0.2% 7.0% -1.9%
float/1024/32 311.9 298.8 +4.4% 4.2% +4.6%
float/1024/128 1,067 1,056 +1.1% 3.3% +0.4%
float/4096/32 5,671 5,727 -1.0% 8.2% +1.5%
double/8/8 0.035 0.035 +0.0% 2.7% -0.6%
double/12/12 0.074 0.075 -1.2% 4.4% -0.4%
double/16/16 0.122 0.120 +1.0% 1.9% -1.3%
double/24/24 0.312 0.312 +0.0% 1.6% -0.7%
double/31/31 0.946 1.04 -8.6% 16.1% -0.1%
double/32/32 0.669 0.680 -1.6% 1.5% -0.1%
double/33/33 0.925 0.933 -0.9% 0.8% +0.1%
double/48/48 2.07 2.13 -2.9% 0.9% -1.0%
double/63/63 6.06 6.01 +0.8% 4.8% +1.8%
double/64/64 4.92 5.09 -3.4% 1.1% -0.8%
double/65/65 5.86 5.94 -1.3% 2.7% -1.0%
double/95/95 19.6 19.0 +3.2% 1.1% -1.2%
double/96/96 15.7 16.0 -1.9% 0.7% -1.3%
double/97/97 18.6 18.9 -1.9% 2.8% +1.5%
double/100/100 18.4 18.5 -0.6% 2.5% +0.9%
double/127/127 43.0 42.5 +1.3% 3.2% +1.7%
double/128/128 35.0 36.0 -2.7% 1.3% +1.0%
double/129/129 46.9 43.1 +8.8% 3.0% +6.7%
double/192/192 132.6 119.7 +10.8% 1.9% +10.2%
double/256/256 314.5 287.3 +9.4% 1.3% +7.7%
double/257/257 330.5 305.5 +8.2% 2.4% +6.0%
double/512/512 2,326 2,241 +3.8% 3.4% +2.8%
double/1024/1024 17,020 17,097 -0.4% 3.2% +0.1%
double/2048/2048 132,494 129,681 +2.2% 1.0% +2.1%
double/4096/4096 1,021,231 1,013,150 +0.8% 0.8% +0.3%
double/64/1 0.567 0.575 -1.5% 0.9% -1.5%
double/64/4 0.411 0.329 +25.0% 0.6% +24.7%
double/64/8 0.569 0.598 -4.8% 2.8% -0.9%
double/64/16 1.14 1.17 -2.3% 1.1% -0.9%
double/64/17 1.57 1.57 -0.3% 0.9% -0.0%
double/64/4096 372.2 379.1 -1.8% 0.7% -0.2%
double/128/4 1.71 1.35 +26.8% 1.2% +28.3%
double/128/8 2.12 2.23 -4.9% 0.4% -0.6%
double/128/17 5.83 5.94 -1.8% 2.4% +0.3%
double/1024/8 253.5 262.1 -3.3% 9.3% +4.5%
double/1024/32 623.4 631.2 -1.2% 3.0% +0.4%
double/1024/128 2,191 2,192 -0.1% 1.1% +1.6%
double/4096/32 11,831 11,817 +0.1% 0.6% -0.1%
float_RowTri/8/8 0.027 0.025 +7.9% 0.5% +5.7%
float_RowTri/12/12 0.137 0.104 +32.1% 3.3% +26.9%
float_RowTri/16/16 0.082 0.084 -2.6% 8.2% +0.2%
float_RowTri/24/24 0.205 0.200 +2.1% 2.9% +1.1%
float_RowTri/31/31 1.10 0.545 +101.1% 2.4% +98.1%
float_RowTri/32/32 0.386 0.389 -0.7% 2.5% +0.7%
float_RowTri/33/33 0.590 0.587 +0.6% 4.3% +4.2%
float_RowTri/48/48 1.13 1.13 -0.5% 1.0% +0.8%
float_RowTri/63/63 5.45 2.96 +84.3% 0.4% +83.1%
float_RowTri/64/64 2.47 2.49 -0.8% 1.7% -0.6%
float_RowTri/65/65 3.26 3.16 +3.2% 2.5% +2.4%
float_RowTri/95/95 15.8 9.76 +62.2% 1.0% +61.1%
float_RowTri/96/96 8.44 8.34 +1.1% 1.1% +1.0%
float_RowTri/97/97 10.4 10.1 +3.0% 1.0% +3.6%
float_RowTri/100/100 13.6 10.2 +33.0% 2.5% +29.8%
float_RowTri/127/127 33.5 22.0 +52.1% 1.1% +50.9%
float_RowTri/128/128 18.9 19.0 -0.5% 0.9% +1.4%
float_RowTri/129/129 23.2 22.3 +4.1% 4.2% +3.4%
float_RowTri/192/192 65.7 62.1 +5.9% 0.5% +6.8%
float_RowTri/256/256 143.4 140.6 +2.0% 2.1% +1.1%
float_RowTri/257/257 154.4 149.6 +3.2% 1.4% +3.0%
float_RowTri/512/512 1,113 1,081 +3.0% 2.4% +3.7%
float_RowTri/1024/1024 8,322 8,282 +0.5% 1.6% -1.1%
float_RowTri/2048/2048 64,792 64,415 +0.6% 0.9% +1.0%
float_RowTri/4096/4096 510,065 499,823 +2.0% 1.0% +1.8%
float_RowTri/64/1 0.436 0.442 -1.3% 0.6% -2.3%
float_RowTri/64/4 0.883 0.908 -2.8% 0.6% -6.0%
float_RowTri/64/8 0.417 0.337 +23.9% 1.2% +20.0%
float_RowTri/64/16 0.632 0.642 -1.6% 0.6% +1.0%
float_RowTri/64/17 1.10 0.981 +11.9% 1.1% +12.7%
float_RowTri/64/4096 190.3 189.1 +0.6% 2.7% +1.1%
float_RowTri/128/4 2.36 2.37 -0.3% 2.0% -4.6%
float_RowTri/128/8 1.65 1.20 +36.8% 0.6% +32.6%
float_RowTri/128/17 4.25 3.53 +20.3% 1.2% +18.1%
float_RowTri/1024/8 162.2 159.2 +1.8% 16.5% -2.5%
float_RowTri/1024/32 348.5 335.1 +4.0% 7.1% +0.0%
float_RowTri/1024/128 1,124 1,103 +1.9% 3.3% +3.0%
float_RowTri/4096/32 6,618 6,663 -0.7% 2.2% +1.3%
double_RowTri/8/8 0.038 0.042 -10.4% 23.2% -0.5%
double_RowTri/12/12 0.078 0.083 -5.6% 11.7% -0.5%
double_RowTri/16/16 0.127 0.134 -5.3% 13.8% -0.7%
double_RowTri/24/24 0.329 0.338 -2.8% 5.8% -0.4%
double_RowTri/31/31 1.01 0.830 +22.1% 3.6% +27.2%
double_RowTri/32/32 0.705 0.717 -1.8% 4.4% +0.0%
double_RowTri/33/33 0.972 0.933 +4.2% 6.2% +5.5%
double_RowTri/48/48 2.27 2.32 -2.5% 3.2% -0.6%
double_RowTri/63/63 6.83 5.80 +17.7% 2.0% +15.2%
double_RowTri/64/64 5.40 5.42 -0.4% 1.2% +0.4%
double_RowTri/65/65 6.55 6.29 +4.2% 3.3% +3.3%
double_RowTri/95/95 21.8 18.9 +15.3% 5.2% +7.5%
double_RowTri/96/96 17.0 17.3 -1.4% 0.1% -1.4%
double_RowTri/97/97 19.9 19.7 +1.1% 5.5% +1.2%
double_RowTri/100/100 20.0 19.7 +1.5% 4.7% +0.5%
double_RowTri/127/127 47.5 43.0 +10.5% 1.0% +10.4%
double_RowTri/128/128 37.9 38.3 -1.0% 1.7% -0.4%
double_RowTri/129/129 48.6 45.0 +8.0% 0.0% +5.1%
double_RowTri/192/192 131.8 124.3 +6.0% 2.1% +8.6%
double_RowTri/256/256 316.3 294.7 +7.3% 2.9% +5.6%
double_RowTri/257/257 339.7 317.1 +7.1% 3.6% +7.0%
double_RowTri/512/512 2,295 2,269 +1.1% 3.6% +1.8%
double_RowTri/1024/1024 17,444 17,312 +0.8% 3.7% +2.2%
double_RowTri/2048/2048 132,502 130,260 +1.7% 2.2% +0.4%
double_RowTri/4096/4096 1,024,703 1,027,362 -0.3% 2.7% +0.7%
double_RowTri/64/1 0.645 0.660 -2.2% 2.5% -1.1%
double_RowTri/64/4 0.409 0.338 +21.1% 1.1% +20.4%
double_RowTri/64/8 0.618 0.622 -0.7% 2.5% -0.2%
double_RowTri/64/16 1.25 1.24 +0.3% 1.9% -0.6%
double_RowTri/64/17 1.76 1.61 +9.5% 1.1% +11.4%
double_RowTri/64/4096 395.6 403.6 -2.0% 2.4% +0.3%
double_RowTri/128/4 1.67 1.26 +32.3% 1.0% +33.8%
double_RowTri/128/8 2.32 2.34 -0.8% 1.6% -0.4%
double_RowTri/128/17 6.67 6.00 +11.1% 1.4% +13.0%
double_RowTri/1024/8 289.3 298.9 -3.2% 10.3% +10.7%
double_RowTri/1024/32 678.3 686.0 -1.1% 2.4% -2.3%
double_RowTri/1024/128 2,254 2,248 +0.3% 0.6% +2.5%
double_RowTri/4096/32 13,677 13,923 -1.8% 6.1% -3.9%
float_Right/8/8 0.077 0.076 +1.3% 0.8% +0.7%
float_Right/12/12 0.164 0.162 +1.2% 0.7% +0.4%
float_Right/16/16 0.217 0.218 -0.5% 0.7% -0.9%
float_Right/24/24 0.448 0.447 +0.2% 0.6% +0.3%
float_Right/31/31 1.14 1.11 +3.4% 3.3% -4.1%
float_Right/32/32 0.702 0.700 +0.4% 4.2% -8.6%
float_Right/33/33 0.893 0.868 +2.8% 9.8% -7.0%
float_Right/48/48 1.47 1.52 -3.0% 6.1% +0.7%
float_Right/63/63 5.11 5.09 +0.4% 1.0% -0.2%
float_Right/64/64 3.99 3.96 +0.9% 1.0% -2.0%
float_Right/65/65 4.65 4.56 +2.0% 1.9% -3.2%
float_Right/95/95 11.4 11.3 +0.6% 4.7% -0.0%
float_Right/96/96 9.34 9.29 +0.6% 3.9% +2.9%
float_Right/97/97 10.7 10.7 +0.2% 2.1% +2.9%
float_Right/100/100 11.7 11.7 +0.4% 3.8% -0.6%
float_Right/127/127 22.9 23.2 -0.9% 1.4% -0.0%
float_Right/128/128 20.2 20.3 -0.6% 1.6% +2.2%
float_Right/129/129 22.5 22.3 +0.7% 3.8% -0.4%
float_Right/192/192 61.5 60.8 +1.2% 1.5% +0.8%
float_Right/256/256 139.3 138.2 +0.8% 2.2% +1.2%
float_Right/257/257 146.7 145.7 +0.7% 1.1% +0.1%
float_Right/512/512 1,062 1,054 +0.7% 1.3% -0.3%
float_Right/1024/1024 8,004 7,923 +1.0% 0.5% -0.2%
float_Right/2048/2048 62,769 62,425 +0.6% 2.0% +1.3%
float_Right/4096/4096 498,398 496,644 +0.4% 1.3% +0.4%
float_Right/64/1 0.879 0.887 -0.9% 1.6% +0.3%
float_Right/64/4 1.29 1.33 -2.6% 1.9% +1.0%
float_Right/64/8 1.31 1.32 -0.8% 3.2% +2.4%
float_Right/64/16 1.49 1.56 -4.6% 8.8% +0.9%
float_Right/64/17 1.63 1.72 -5.3% 8.7% +1.2%
float_Right/64/4096 226.7 224.5 +1.0% 1.8% +0.9%
float_Right/128/4 3.49 3.49 -0.1% 2.3% -0.3%
float_Right/128/8 3.67 3.61 +1.7% 3.6% +1.0%
float_Right/128/17 4.93 4.83 +2.0% 2.7% +1.5%
float_Right/1024/8 158.4 162.2 -2.4% 0.3% -4.8%
float_Right/1024/32 327.8 330.6 -0.9% 4.6% +1.0%
float_Right/1024/128 1,064 1,065 -0.1% 3.7% -0.5%
float_Right/4096/32 7,157 7,137 +0.3% 4.6% +3.9%
double_Right/8/8 0.081 0.079 +1.7% 2.2% +0.9%
double_Right/12/12 0.151 0.145 +3.7% 1.4% -0.3%
double_Right/16/16 0.273 0.270 +1.1% 4.1% +0.1%
double_Right/24/24 0.501 0.486 +3.3% 6.5% -5.0%
double_Right/31/31 1.17 1.21 -3.2% 4.8% +1.1%
double_Right/32/32 0.983 0.972 +1.2% 4.8% +3.1%
double_Right/33/33 1.18 1.18 +0.5% 7.8% +1.6%
double_Right/48/48 2.95 3.01 -1.9% 4.3% -3.6%
double_Right/63/63 6.70 6.80 -1.5% 3.6% -1.3%
double_Right/64/64 6.43 6.29 +2.2% 0.5% +2.0%
double_Right/65/65 6.91 6.75 +2.4% 2.4% -0.7%
double_Right/95/95 20.1 19.8 +1.6% 1.9% +0.4%
double_Right/96/96 18.5 18.6 -0.3% 5.4% +2.8%
double_Right/97/97 19.6 19.8 -1.2% 1.9% +0.5%
double_Right/100/100 20.9 20.3 +2.9% 4.3% -0.1%
double_Right/127/127 42.4 43.7 -3.1% 4.2% -0.9%
double_Right/128/128 40.2 41.0 -1.7% 3.2% +2.4%
double_Right/129/129 42.5 42.5 -0.1% 2.4% -0.7%
double_Right/192/192 126.8 123.9 +2.4% 6.9% +1.0%
double_Right/256/256 288.5 286.1 +0.8% 1.0% -0.6%
double_Right/257/257 298.9 306.7 -2.5% 3.9% -0.6%
double_Right/512/512 2,169 2,128 +1.9% 1.7% +1.5%
double_Right/1024/1024 16,223 16,141 +0.5% 1.5% +1.5%
double_Right/2048/2048 127,588 128,558 -0.8% 2.1% +0.0%
double_Right/4096/4096 998,629 1,011,635 -1.3% 0.6% +0.1%
double_Right/64/1 0.870 0.863 +0.8% 0.9% +0.0%
double_Right/64/4 1.15 1.17 -1.2% 1.9% -1.1%
double_Right/64/8 1.42 1.40 +1.5% 1.2% -2.7%
double_Right/64/16 2.61 2.60 +0.5% 2.0% +0.1%
double_Right/64/17 2.82 2.79 +1.3% 1.8% +0.5%
double_Right/64/4096 421.7 446.3 -5.5% 3.3% +1.2%
double_Right/128/4 4.03 4.08 -1.3% 0.5% -4.8%
double_Right/128/8 5.28 5.15 +2.4% 8.2% +0.5%
double_Right/128/17 7.70 7.94 -3.1% 4.4% +1.8%
double_Right/1024/8 329.9 333.5 -1.1% 3.1% -2.7%
double_Right/1024/32 688.4 694.6 -0.9% 3.7% +5.5%
double_Right/1024/128 2,153 2,161 -0.4% 2.0% -1.3%
double_Right/4096/32 13,239 13,657 -3.1% 1.7% +1.3%
float_Upper/24/17 0.212 0.212 -0.2% 1.5% +1.6%
float_Upper/64/17 0.875 0.872 +0.3% 0.4% +0.1%
float_Upper/128/17 2.94 2.92 +0.9% 0.8% +1.9%
float_Upper/512/17 50.5 48.7 +3.7% 2.8% +4.1%
float_Upper/24/64 0.461 0.464 -0.7% 1.0% +1.3%
float_Upper/64/64 2.38 2.38 +0.4% 1.7% +1.4%
float_Upper/128/64 8.86 9.13 -3.0% 2.0% -0.1%
float_Upper/512/64 143.3 138.1 +3.7% 2.2% +5.6%
float_Upper/24/512 4.34 4.38 -0.9% 4.4% -1.4%
float_Upper/64/512 20.3 20.3 +0.1% 0.8% -0.1%
float_Upper/128/512 71.6 72.6 -1.3% 3.2% +0.4%
float_Upper/512/512 1,079 1,049 +2.9% 1.4% +4.0%
double_Upper/24/17 0.316 0.325 -2.6% 1.7% -0.2%
double_Upper/64/17 1.59 1.58 +0.6% 2.1% +0.5%
double_Upper/128/17 5.49 5.59 -1.8% 1.5% -0.3%
double_Upper/512/17 105.5 102.8 +2.7% 8.5% +4.3%
double_Upper/24/64 0.855 0.859 -0.5% 2.0% +0.5%
double_Upper/64/64 5.06 5.03 +0.6% 1.9% +1.0%
double_Upper/128/64 17.8 17.8 -0.2% 2.2% +0.8%
double_Upper/512/64 297.1 284.8 +4.3% 1.7% +4.5%
double_Upper/24/512 7.99 8.12 -1.6% 2.4% +1.1%
double_Upper/64/512 40.4 40.2 +0.4% 1.7% -0.2%
double_Upper/128/512 143.9 143.8 +0.0% 1.8% +2.5%
double_Upper/512/512 2,304 2,285 +0.9% 2.1% +2.5%
float_RightRow/24/17 0.400 0.225 +78.2% 3.3% +80.5%
float_RightRow/64/17 1.90 0.969 +96.1% 0.7% +101.3%
float_RightRow/128/17 6.71 3.59 +86.8% 8.0% +95.3%
float_RightRow/512/17 57.5 52.3 +9.9% 2.6% +8.3%
float_RightRow/24/64 0.498 0.501 -0.7% 0.8% +1.7%
float_RightRow/64/64 2.47 2.43 +1.8% 0.8% +1.2%
float_RightRow/128/64 9.34 9.46 -1.3% 9.9% +1.4%
float_RightRow/512/64 146.6 140.0 +4.7% 1.3% +5.7%
float_RightRow/24/512 4.62 4.69 -1.5% 1.8% -2.1%
float_RightRow/64/512 20.8 20.6 +1.4% 0.7% -0.0%
float_RightRow/128/512 74.6 75.8 -1.6% 13.5% +1.1%
float_RightRow/512/512 1,096 1,045 +4.9% 1.1% +3.5%
double_RightRow/24/17 0.512 0.323 +58.3% 3.2% +60.2%
double_RightRow/64/17 2.51 1.63 +54.5% 1.2% +58.5%
double_RightRow/128/17 8.93 6.16 +45.1% 5.0% +50.5%
double_RightRow/512/17 109.6 106.6 +2.8% 2.7% +4.3%
double_RightRow/24/64 0.900 0.904 -0.5% 2.2% -1.0%
double_RightRow/64/64 5.32 5.24 +1.6% 2.4% +1.3%
double_RightRow/128/64 19.5 19.8 -1.7% 6.1% +0.8%
double_RightRow/512/64 311.9 292.2 +6.7% 1.8% +6.0%
double_RightRow/24/512 8.47 8.50 -0.3% 1.1% +0.9%
double_RightRow/64/512 42.2 42.6 -0.9% 2.7% +0.8%
double_RightRow/128/512 156.2 160.0 -2.4% 4.7% +2.2%
double_RightRow/512/512 2,317 2,287 +1.3% 1.3% +3.6%
Appendix B: all 276 shapes, NEON (Apple M4)
Shape Before (µs) After (µs) Change Max run-to-run spread Change, aligned build
float/8/8 0.030 0.029 +5.5% 0.9% +6.2%
float/12/12 0.068 0.066 +3.0% 1.7% +4.6%
float/16/16 0.108 0.095 +13.4% 1.2% +14.5%
float/24/24 0.304 0.252 +20.4% 1.8% +23.3%
float/31/31 0.823 0.733 +12.3% 3.4% +9.5%
float/32/32 0.613 0.507 +20.7% 3.5% +23.5%
float/33/33 0.820 0.720 +13.9% 1.8% +14.9%
float/48/48 1.86 1.46 +27.1% 4.1% +30.2%
float/63/63 4.90 3.99 +23.0% 3.5% +22.8%
float/64/64 4.07 3.16 +28.8% 2.6% +31.3%
float/65/65 4.85 3.83 +26.8% 2.3% +29.0%
float/95/95 14.9 11.5 +29.6% 4.0% +31.1%
float/96/96 12.8 9.68 +32.6% 2.8% +33.2%
float/97/97 14.5 11.0 +31.6% 3.7% +32.0%
float/100/100 14.8 11.1 +33.0% 3.6% +33.1%
float/127/127 34.2 25.5 +33.9% 2.4% +34.6%
float/128/128 30.0 22.1 +35.6% 3.6% +37.0%
float/129/129 31.7 27.0 +17.5% 0.9% +18.4%
float/192/192 89.8 75.1 +19.6% 2.5% +20.7%
float/256/256 214.3 169.2 +26.7% 2.4% +28.0%
float/257/257 220.6 180.9 +22.0% 2.4% +23.3%
float/512/512 1,381 1,232 +12.1% 2.1% +12.7%
float/1024/1024 10,632 9,356 +13.6% 0.9% +14.1%
float/2048/2048 81,128 73,414 +10.5% 2.1% +11.5%
float/4096/4096 625,321 574,468 +8.9% 1.7% +9.7%
float/64/1 0.515 0.523 -1.5% 0.7% -0.7%
float/64/4 0.370 0.292 +26.9% 2.7% +27.1%
float/64/8 0.528 0.443 +19.3% 3.0% +19.9%
float/64/16 1.05 0.808 +30.2% 2.2% +30.5%
float/64/17 1.34 1.12 +19.9% 2.2% +19.8%
float/64/4096 260.5 207.6 +25.5% 2.9% +25.7%
float/128/4 1.50 1.03 +45.3% 4.2% +46.0%
float/128/8 1.88 1.44 +30.4% 2.1% +34.2%
float/128/17 4.47 3.47 +28.8% 2.1% +30.1%
float/1024/8 133.8 130.9 +2.2% 2.5% +2.4%
float/1024/32 381.1 346.4 +10.0% 2.3% +12.0%
float/1024/128 1,369 1,219 +12.3% 2.0% +13.4%
float/4096/32 6,580 6,295 +4.5% 2.8% +5.7%
double/8/8 0.047 0.039 +19.4% 0.3% +19.6%
double/12/12 0.105 0.091 +15.2% 0.1% +13.7%
double/16/16 0.211 0.178 +19.0% 2.5% +16.2%
double/24/24 0.614 0.478 +28.5% 2.2% +30.2%
double/31/31 1.39 1.18 +18.4% 1.7% +19.2%
double/32/32 1.21 0.997 +21.0% 2.4% +23.6%
double/33/33 1.59 1.27 +25.0% 1.6% +21.9%
double/48/48 3.60 2.89 +24.5% 2.4% +31.0%
double/63/63 9.08 7.13 +27.3% 1.3% +29.7%
double/64/64 8.11 6.29 +28.9% 2.1% +32.7%
double/65/65 9.35 7.29 +28.3% 1.8% +31.5%
double/95/95 29.1 22.2 +31.1% 2.6% +31.9%
double/96/96 26.1 19.9 +30.9% 1.3% +30.8%
double/97/97 29.1 22.2 +31.0% 1.3% +31.2%
double/100/100 29.2 22.6 +29.5% 2.0% +31.0%
double/127/127 66.7 48.6 +37.2% 3.1% +37.3%
double/128/128 61.9 44.6 +38.8% 1.2% +38.0%
double/129/129 61.7 55.2 +11.8% 1.2% +11.2%
double/192/192 179.0 149.0 +20.1% 0.4% +19.4%
double/256/256 424.0 338.1 +25.4% 0.4% +25.4%
double/257/257 436.9 357.5 +22.2% 1.2% +22.1%
double/512/512 2,848 2,496 +14.1% 0.3% +14.4%
double/1024/1024 21,362 18,928 +12.9% 0.5% +13.0%
double/2048/2048 171,010 147,596 +15.9% 0.8% +16.3%
double/4096/4096 1,260,041 1,150,375 +9.5% 0.4% +9.6%
double/64/1 0.687 0.708 -3.0% 1.2% -0.7%
double/64/4 0.532 0.443 +20.1% 2.6% +21.7%
double/64/8 1.05 0.806 +30.1% 0.5% +32.5%
double/64/16 2.05 1.60 +28.1% 1.1% +32.0%
double/64/17 2.43 1.97 +23.4% 2.4% +25.7%
double/64/4096 519.9 414.1 +25.5% 0.7% +27.4%
double/128/4 1.93 1.46 +32.0% 1.8% +32.7%
double/128/8 3.85 2.75 +40.0% 1.3% +40.7%
double/128/17 8.87 6.67 +33.0% 1.2% +31.1%
double/1024/8 281.9 266.6 +5.7% 2.6% +4.5%
double/1024/32 784.4 708.2 +10.8% 0.7% +11.1%
double/1024/128 2,775 2,461 +12.8% 0.3% +12.2%
double/4096/32 12,672 12,065 +5.0% 0.4% +5.8%
float_RowTri/8/8 0.032 0.030 +5.0% 0.1% +3.2%
float_RowTri/12/12 0.068 0.066 +2.8% 0.1% +2.3%
float_RowTri/16/16 0.116 0.097 +19.0% 0.8% +20.9%
float_RowTri/24/24 0.311 0.258 +20.6% 0.3% +21.1%
float_RowTri/31/31 0.833 0.708 +17.5% 1.1% +18.4%
float_RowTri/32/32 0.625 0.505 +23.9% 1.6% +24.2%
float_RowTri/33/33 0.867 0.708 +22.6% 2.7% +22.3%
float_RowTri/48/48 1.91 1.46 +30.2% 1.2% +27.6%
float_RowTri/63/63 5.28 3.88 +35.9% 1.6% +35.2%
float_RowTri/64/64 4.13 3.21 +28.7% 1.6% +27.1%
float_RowTri/65/65 5.08 3.89 +30.7% 1.5% +31.1%
float_RowTri/95/95 16.4 11.4 +44.2% 1.6% +44.5%
float_RowTri/96/96 12.9 9.78 +32.1% 0.2% +31.2%
float_RowTri/97/97 15.0 11.3 +33.5% 1.8% +33.7%
float_RowTri/100/100 15.0 11.2 +33.9% 0.4% +32.1%
float_RowTri/127/127 37.1 25.3 +46.8% 2.0% +47.1%
float_RowTri/128/128 30.9 22.6 +36.9% 0.7% +37.1%
float_RowTri/129/129 32.5 27.2 +19.4% 0.3% +19.4%
float_RowTri/192/192 92.8 76.0 +22.1% 0.4% +22.2%
float_RowTri/256/256 219.2 170.2 +28.8% 1.2% +29.5%
float_RowTri/257/257 226.3 181.9 +24.4% 0.7% +25.3%
float_RowTri/512/512 1,399 1,236 +13.2% 0.5% +13.3%
float_RowTri/1024/1024 10,704 9,327 +14.8% 1.1% +15.3%
float_RowTri/2048/2048 81,685 73,265 +11.5% 0.8% +12.0%
float_RowTri/4096/4096 631,277 572,514 +10.3% 0.6% +10.3%
float_RowTri/64/1 0.596 0.602 -1.0% 0.7% -2.4%
float_RowTri/64/4 0.376 0.317 +18.7% 1.3% +20.6%
float_RowTri/64/8 0.544 0.463 +17.5% 1.2% +12.4%
float_RowTri/64/16 1.07 0.822 +30.6% 0.7% +29.4%
float_RowTri/64/17 1.47 1.16 +26.8% 1.4% +26.3%
float_RowTri/64/4096 265.0 211.2 +25.5% 1.7% +23.5%
float_RowTri/128/4 1.57 1.12 +40.1% 0.6% +37.5%
float_RowTri/128/8 1.91 1.47 +29.7% 1.2% +29.6%
float_RowTri/128/17 5.40 3.92 +37.9% 1.5% +38.3%
float_RowTri/1024/8 134.6 114.0 +18.1% 0.7% +18.5%
float_RowTri/1024/32 381.9 331.0 +15.4% 0.9% +15.6%
float_RowTri/1024/128 1,377 1,201 +14.7% 0.6% +14.9%
float_RowTri/4096/32 6,370 5,926 +7.5% 0.7% +8.1%
double_RowTri/8/8 0.050 0.042 +18.2% 0.2% +20.9%
double_RowTri/12/12 0.115 0.100 +15.1% 0.2% +17.1%
double_RowTri/16/16 0.223 0.182 +22.8% 1.7% +25.9%
double_RowTri/24/24 0.648 0.485 +33.5% 1.9% +34.7%
double_RowTri/31/31 1.48 1.22 +20.6% 2.3% +23.2%
double_RowTri/32/32 1.26 1.01 +24.5% 1.6% +24.6%
double_RowTri/33/33 1.66 1.27 +30.9% 0.3% +24.5%
double_RowTri/48/48 3.79 2.92 +29.9% 1.1% +31.5%
double_RowTri/63/63 9.33 7.21 +29.4% 0.1% +29.3%
double_RowTri/64/64 8.37 6.38 +31.3% 0.5% +31.5%
double_RowTri/65/65 9.56 7.28 +31.3% 3.4% +29.2%
double_RowTri/95/95 29.7 22.3 +33.1% 0.5% +33.1%
double_RowTri/96/96 26.6 20.3 +31.0% 0.6% +31.3%
double_RowTri/97/97 29.7 22.3 +33.3% 0.8% +32.6%
double_RowTri/100/100 29.7 22.4 +32.6% 0.7% +32.6%
double_RowTri/127/127 68.1 49.1 +38.7% 1.1% +38.8%
double_RowTri/128/128 62.8 45.8 +37.2% 0.4% +36.6%
double_RowTri/129/129 63.6 56.6 +12.3% 0.3% +14.4%
double_RowTri/192/192 181.8 155.7 +16.8% 0.2% +20.5%
double_RowTri/256/256 427.7 349.3 +22.4% 0.5% +26.0%
double_RowTri/257/257 442.8 368.2 +20.3% 0.1% +23.4%
double_RowTri/512/512 2,869 2,516 +14.1% 0.1% +15.2%
double_RowTri/1024/1024 21,228 18,968 +11.9% 0.2% +13.2%
double_RowTri/2048/2048 170,382 147,416 +15.6% 0.4% +16.1%
double_RowTri/4096/4096 1,257,440 1,149,852 +9.4% 0.2% +9.7%
double_RowTri/64/1 0.770 0.767 +0.4% 0.3% +0.7%
double_RowTri/64/4 0.546 0.461 +18.6% 1.8% +16.6%
double_RowTri/64/8 1.07 0.818 +31.3% 1.2% +30.9%
double_RowTri/64/16 2.11 1.63 +29.6% 1.5% +31.2%
double_RowTri/64/17 2.53 1.98 +28.0% 2.3% +28.6%
double_RowTri/64/4096 527.2 420.4 +25.4% 0.4% +24.7%
double_RowTri/128/4 1.95 1.48 +31.6% 0.8% +31.7%
double_RowTri/128/8 3.88 2.80 +38.7% 0.1% +38.0%
double_RowTri/128/17 9.66 6.93 +39.3% 0.6% +39.6%
double_RowTri/1024/8 259.4 232.5 +11.6% 0.8% +12.2%
double_RowTri/1024/32 749.1 679.5 +10.3% 0.4% +12.4%
double_RowTri/1024/128 2,732 2,465 +10.8% 0.4% +13.2%
double_RowTri/4096/32 13,102 12,407 +5.6% 0.3% +6.2%
float_Right/8/8 0.106 0.105 +0.3% 0.7% +1.1%
float_Right/12/12 0.216 0.216 -0.0% 1.4% -0.5%
float_Right/16/16 0.330 0.331 -0.0% 1.9% -0.7%
float_Right/24/24 0.616 0.604 +2.1% 1.2% +0.6%
float_Right/31/31 1.13 1.12 +1.3% 1.2% -1.5%
float_Right/32/32 1.04 1.04 -0.3% 1.2% -0.7%
float_Right/33/33 1.21 1.18 +3.2% 2.9% -0.3%
float_Right/48/48 2.58 2.25 +14.6% 2.4% +0.6%
float_Right/63/63 5.59 5.55 +0.8% 1.0% -0.3%
float_Right/64/64 5.56 5.41 +2.9% 1.8% -0.1%
float_Right/65/65 5.96 5.92 +0.7% 2.0% +0.2%
float_Right/95/95 14.6 13.8 +5.7% 1.6% -0.2%
float_Right/96/96 11.9 12.2 -2.8% 1.1% -0.3%
float_Right/97/97 15.1 14.3 +5.1% 0.7% -0.2%
float_Right/100/100 15.9 15.3 +3.9% 1.3% +0.0%
float_Right/127/127 28.9 28.7 +0.9% 1.3% -0.4%
float_Right/128/128 26.0 26.5 -1.9% 0.3% -0.1%
float_Right/129/129 27.9 28.0 -0.4% 0.3% -0.2%
float_Right/192/192 79.3 80.3 -1.2% 0.5% -0.5%
float_Right/256/256 181.8 183.5 -0.9% 0.2% +0.1%
float_Right/257/257 189.3 189.7 -0.2% 0.4% -0.1%
float_Right/512/512 1,263 1,267 -0.3% 0.2% -0.1%
float_Right/1024/1024 9,474 9,481 -0.1% 0.1% +0.0%
float_Right/2048/2048 72,782 72,933 -0.2% 0.3% +0.1%
float_Right/4096/4096 571,938 572,415 -0.1% 0.1% +0.0%
float_Right/64/1 0.974 0.967 +0.7% 0.5% -0.2%
float_Right/64/4 1.10 1.11 -0.2% 1.1% -0.1%
float_Right/64/8 1.37 1.37 -0.4% 0.9% +0.8%
float_Right/64/16 2.92 2.91 +0.6% 0.3% +0.2%
float_Right/64/17 3.06 3.05 +0.5% 2.3% -0.2%
float_Right/64/4096 271.7 272.7 -0.4% 0.5% +0.2%
float_Right/128/4 2.81 2.82 -0.3% 0.9% -0.1%
float_Right/128/8 3.58 3.58 -0.2% 2.2% +0.3%
float_Right/128/17 7.92 7.98 -0.8% 2.2% -0.4%
float_Right/1024/8 130.8 131.6 -0.6% 2.0% -0.2%
float_Right/1024/32 349.2 348.8 +0.1% 0.3% +0.1%
float_Right/1024/128 1,224 1,228 -0.3% 0.1% +0.1%
float_Right/4096/32 6,061 6,040 +0.4% 0.8% -0.5%
double_Right/8/8 0.131 0.132 -0.7% 1.1% -0.8%
double_Right/12/12 0.243 0.242 +0.4% 0.8% +0.6%
double_Right/16/16 0.383 0.378 +1.2% 0.4% +2.7%
double_Right/24/24 0.828 0.817 +1.4% 1.3% +0.1%
double_Right/31/31 1.45 1.44 +0.5% 1.1% -0.4%
double_Right/32/32 1.51 1.52 -0.5% 1.1% +1.5%
double_Right/33/33 1.74 1.72 +1.1% 5.3% -4.2%
double_Right/48/48 3.83 3.80 +1.0% 1.6% +0.5%
double_Right/63/63 8.27 8.11 +2.0% 0.3% -0.6%
double_Right/64/64 8.37 8.25 +1.4% 1.6% -0.5%
double_Right/65/65 9.00 8.86 +1.6% 0.8% -0.4%
double_Right/95/95 23.5 22.7 +3.5% 0.6% +0.0%
double_Right/96/96 23.5 22.9 +2.6% 1.1% +0.1%
double_Right/97/97 24.8 24.0 +3.6% 1.0% -0.4%
double_Right/100/100 26.1 25.4 +2.6% 1.1% -0.2%
double_Right/127/127 51.7 49.8 +3.9% 0.6% -0.1%
double_Right/128/128 51.9 49.8 +4.3% 0.6% -0.2%
double_Right/129/129 54.5 52.5 +3.7% 1.7% -0.8%
double_Right/192/192 149.0 146.4 +1.8% 0.1% -1.2%
double_Right/256/256 333.3 330.2 +0.9% 0.2% -0.5%
double_Right/257/257 341.5 338.5 +0.9% 0.2% -0.3%
double_Right/512/512 2,415 2,415 -0.0% 0.0% -0.0%
double_Right/1024/1024 18,397 18,393 +0.0% 0.0% -0.0%
double_Right/2048/2048 144,833 144,816 +0.0% 0.1% -0.0%
double_Right/4096/4096 1,141,169 1,141,497 -0.0% 0.0% +0.0%
double_Right/64/1 0.932 0.922 +1.1% 2.3% -0.1%
double_Right/64/4 1.14 1.15 -0.8% 2.2% -0.6%
double_Right/64/8 2.72 2.66 +2.2% 0.9% -0.1%
double_Right/64/16 3.38 3.32 +1.8% 1.5% +0.3%
double_Right/64/17 3.57 3.59 -0.5% 3.2% +0.3%
double_Right/64/4096 496.2 495.1 +0.2% 0.2% -0.4%
double_Right/128/4 3.72 3.71 +0.4% 1.4% -0.3%
double_Right/128/8 5.81 5.61 +3.5% 0.7% +1.3%
double_Right/128/17 9.45 9.14 +3.4% 0.5% -0.1%
double_Right/1024/8 260.5 259.0 +0.6% 0.5% +0.1%
double_Right/1024/32 687.1 682.2 +0.7% 0.2% +0.0%
double_Right/1024/128 2,396 2,395 +0.0% 0.1% -0.0%
double_Right/4096/32 12,043 12,053 -0.1% 0.7% +0.4%
float_Upper/24/17 0.293 0.255 +14.9% 0.3% +16.4%
float_Upper/64/17 1.29 1.10 +17.3% 0.1% +17.0%
float_Upper/128/17 4.46 3.44 +29.8% 0.1% +29.5%
float_Upper/512/17 64.1 60.3 +6.2% 0.9% +6.1%
float_Upper/24/64 0.818 0.634 +29.0% 0.4% +25.6%
float_Upper/64/64 3.93 3.18 +23.4% 0.4% +22.6%
float_Upper/128/64 15.0 11.0 +36.8% 0.7% +36.6%
float_Upper/512/64 187.1 165.9 +12.8% 0.3% +12.7%
float_Upper/24/512 6.36 4.90 +29.9% 0.1% +31.5%
float_Upper/64/512 32.2 26.6 +21.4% 0.2% +21.5%
float_Upper/128/512 121.3 89.0 +36.3% 0.5% +35.9%
float_Upper/512/512 1,398 1,236 +13.1% 0.2% +12.6%
double_Upper/24/17 0.515 0.416 +23.8% 0.4% +23.9%
double_Upper/64/17 2.34 1.96 +19.2% 0.4% +20.8%
double_Upper/128/17 8.67 6.63 +30.8% 0.6% +30.5%
double_Upper/512/17 131.5 122.0 +7.8% 0.9% +8.1%
double_Upper/24/64 1.65 1.26 +31.2% 0.2% +29.5%
double_Upper/64/64 7.89 6.38 +23.6% 0.1% +24.4%
double_Upper/128/64 30.7 22.5 +36.6% 0.6% +36.5%
double_Upper/512/64 389.7 335.7 +16.1% 0.9% +15.5%
double_Upper/24/512 13.5 10.7 +26.4% 1.3% +26.3%
double_Upper/64/512 63.9 52.6 +21.6% 0.4% +23.0%
double_Upper/128/512 244.2 178.5 +36.8% 0.2% +36.4%
double_Upper/512/512 2,848 2,500 +13.9% 0.2% +14.4%
float_RightRow/24/17 0.446 0.258 +73.1% 1.2% +73.4%
float_RightRow/64/17 2.35 1.17 +100.8% 1.1% +101.8%
float_RightRow/128/17 8.45 3.97 +112.9% 1.7% +116.9%
float_RightRow/512/17 67.5 60.5 +11.6% 0.4% +17.4%
float_RightRow/24/64 0.825 0.650 +26.8% 0.5% +28.2%
float_RightRow/64/64 4.05 3.25 +24.6% 1.6% +23.8%
float_RightRow/128/64 15.2 11.1 +36.2% 0.6% +35.5%
float_RightRow/512/64 188.8 163.2 +15.7% 0.0% +18.5%
float_RightRow/24/512 6.39 4.96 +28.8% 0.2% +30.0%
float_RightRow/64/512 33.0 27.0 +22.4% 0.2% +22.4%
float_RightRow/128/512 122.4 90.4 +35.4% 0.2% +35.0%
float_RightRow/512/512 1,403 1,235 +13.6% 0.2% +13.7%
double_RightRow/24/17 0.678 0.427 +58.6% 0.8% +59.3%
double_RightRow/64/17 3.42 1.99 +72.2% 0.3% +72.1%
double_RightRow/128/17 12.8 6.90 +85.3% 1.6% +83.1%
double_RightRow/512/17 129.0 115.0 +12.2% 0.3% +10.6%
double_RightRow/24/64 1.68 1.28 +31.3% 0.7% +29.4%
double_RightRow/64/64 8.00 6.46 +23.9% 0.6% +23.1%
double_RightRow/128/64 31.1 22.9 +35.7% 0.1% +34.8%
double_RightRow/512/64 388.4 328.3 +18.3% 0.4% +17.0%
double_RightRow/24/512 13.8 10.9 +26.4% 0.9% +24.7%
double_RightRow/64/512 65.3 53.2 +22.8% 0.2% +22.2%
double_RightRow/128/512 248.1 182.9 +35.6% 0.5% +34.5%
double_RightRow/512/512 2,874 2,492 +15.3% 0.5% +15.1%

🤖 Generated with Claude Code

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