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Check number of stages for pipelined kernel #173

Merged
merged 1 commit into from
Nov 14, 2023
Merged

Check number of stages for pipelined kernel #173

merged 1 commit into from
Nov 14, 2023

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thomasfaingnaert
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@thomasfaingnaert
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@maleadt How do you prefer we handle this case? Using a ConfigError as I do now? If so, we might want to also change the "Requested too much shared memory" error above to throw a ConfigError.

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maleadt commented Nov 14, 2023

If so, we might want to also change the "Requested too much shared memory" error above to throw a ConfigError.

That sounds right.

@thomasfaingnaert thomasfaingnaert force-pushed the tf/check-pipelined-iterations branch from da6d101 to 7e9645b Compare November 14, 2023 21:54
@thomasfaingnaert thomasfaingnaert merged commit 912fa05 into master Nov 14, 2023
@thomasfaingnaert thomasfaingnaert deleted the tf/check-pipelined-iterations branch November 14, 2023 22:29
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maleadt commented Nov 14, 2023

Benchmark results for commit 7e9645b (comparing to 433aa68):

test master PR Δmin
FPU GEMM Int32*Int32=Int32 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 7.39 μs ± 1.63% (7.15 … 7.87 μs) 8.36 μs ± 2.08% (8.11 … 8.58 μs) +13.3% ❌
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.16 μs ± 1.73% (8.82 … 9.3 μs) 8.08 μs ± 2.16% (7.87 … 8.34 μs) -10.8% ✅
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (TT) OP (8, 16, 2), base shape (4, 8, 1) 132.0 μs ± 0.858% (129.0 … 134.0 μs) 148.0 μs ± 0.366% (146.0 … 149.0 μs) +12.7% ❌
FPU GEMM Int64*Int64=Int64 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 21.4 μs ± 0.721% (21.2 … 21.7 μs) 24.3 μs ± 0.398% (23.8 … 24.8 μs) +12.4% ❌
FPU GEMM Float32*Float32=Float64 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 156.0 μs ± 0.689% (155.0 … 159.0 μs) 178.0 μs ± 0.715% (177.0 … 180.0 μs) +14.1% ❌
Tropical GEMM Float32*Float32=Float32 (128×256) · (256×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 124.0 μs ± 0.157% (124.0 … 124.0 μs) 123.0 μs ± 2.29% (108.0 … 124.0 μs) -12.2% ✅
WMMA GEMM Float16*Float16+Float16=Float16 (2048×2048) · (2048×2048) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 231.0 μs ± 1.09% (224.0 … 238.0 μs) 230.0 μs ± 1.39% (208.0 … 237.0 μs) -7.1% ✅
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 148.0 μs ± 0.158% (147.0 … 149.0 μs) 143.0 μs ± 5.42% (129.0 … 149.0 μs) -12.0% ✅
WMMA GEMM+bias Float16*Float16+Float32=Float32 (128×128) · (128×128) (TN) OP (16, 16, 16) 8.91 μs ± 1.82% (8.58 … 9.3 μs) 10.1 μs ± 1.36% (9.78 … 10.3 μs) +13.9% ❌
FPU GEMM Float32*Float32=Float64 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 156.0 μs ± 0.474% (154.0 … 159.0 μs) 177.0 μs ± 0.395% (175.0 … 180.0 μs) +14.1% ❌
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.1 μs ± 1.89% (8.82 … 9.54 μs) 8.02 μs ± 2.0% (7.87 … 8.34 μs) -10.8% ✅
WMMA diagonal GEMM diag(Float16)*Float16=Float32 (128×128) · (128×128) (NN) OP (16, 16, 16) 9.93 μs ± 1.38% (9.54 … 10.3 μs) 11.2 μs ± 1.16% (11.0 … 11.7 μs) +15.0% ❌
WMMA GEMM+bias Float16*Float16+Float32=Float32 (128×128) · (128×128) (NT) OP (16, 16, 16) 9.05 μs ± 1.89% (8.82 … 9.3 μs) 10.3 μs ± 1.15% (9.78 … 10.7 μs) +10.8% ❌
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 134.0 μs ± 3.06% (129.0 … 140.0 μs) 145.0 μs ± 4.78% (139.0 … 331.0 μs) +7.6% ❌
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.43 μs ± 1.69% (8.11 … 8.82 μs) 7.43 μs ± 1.51% (7.15 … 7.87 μs) -11.8% ✅
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.97 μs ± 1.68% (8.58 … 9.3 μs) 7.95 μs ± 1.69% (7.63 … 8.34 μs) -11.1% ✅
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.07 μs ± 1.85% (8.82 … 9.54 μs) 8.02 μs ± 1.98% (7.87 … 8.34 μs) -10.8% ✅
Tropical GEMM Float32*Float32=Float32 (256×256) · (256×256) (NT) OP (8, 16, 2), base shape (4, 8, 1) 127.0 μs ± 0.136% (127.0 … 128.0 μs) 112.0 μs ± 0.146% (111.0 … 112.0 μs) -12.2% ✅
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 145.0 μs ± 4.89% (130.0 … 150.0 μs) 148.0 μs ± 4.69% (147.0 … 307.0 μs) +13.0% ❌
Tropical GEMM Float32*Float32=Float32 (128×256) · (256×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 125.0 μs ± 0.122% (124.0 … 125.0 μs) 123.0 μs ± 4.58% (109.0 … 126.0 μs) -12.1% ✅
FPU GEMM Int32*Int32=Int32 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 9.41 μs ± 1.62% (9.06 … 9.78 μs) 10.7 μs ± 1.21% (10.5 … 11.0 μs) +15.8% ❌
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.47 μs ± 1.85% (8.11 … 8.82 μs) 7.46 μs ± 1.74% (7.15 … 7.87 μs) -11.8% ✅
FPU GEMM Float32*Float32=Float64 (128×128) · (128×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 180.0 μs ± 0.22% (178.0 … 182.0 μs) 180.0 μs ± 1.22% (158.0 … 181.0 μs) -11.3% ✅

Comparison with baseline

test GemmKernels Baseline %
FPU GEMM Float32*Float32=Float32 (256×256) · (256×256) (TT) OP (8, 16, 2), base shape (4, 8, 1) 15.0 μs ± 1.1% (14.8 … 15.3 μs) 7.22 μs ± 1.73% (6.68 … 7.63 μs) 45.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (4, 32, 1), base shape (1, 32, 1) 16.1 μs ± 0.992% (15.7 … 16.5 μs) 4.18 μs ± 3.7% (4.05 … 4.53 μs) 25.8
WMMA GEMM Float16*Float16+Float16=Float16 (2048×2048) · (2048×2048) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 230.0 μs ± 0.735% (225.0 … 235.0 μs) 191.0 μs ± 1.92% (180.0 … 195.0 μs) 80.3
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 7.95 μs ± 1.69% (7.63 … 8.34 μs) 2.35 μs ± 6.61% (2.15 … 2.62 μs) 28.1
WMMA GEMM Float16*Float16+Float16=Float16 (2048×2048) · (2048×2048) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 217.0 μs ± 3.96% (204.0 … 229.0 μs) 186.0 μs ± 2.54% (172.0 … 193.0 μs) 84.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (16, 16, 1), base shape (8, 4, 1) 14.5 μs ± 1.05% (14.3 … 14.8 μs) 4.04 μs ± 3.49% (3.81 … 4.29 μs) 26.7
FPU GEMM Float32*Float32=Float32 (2048×2048) · (2048×2048) (NN) OP (8, 16, 2), base shape (4, 8, 1) 1.84 ms ± 2.73% (1.81 … 2.02 ms) 1.01 ms ± 1.19% (0.937 … 1.02 ms) 51.8
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (32, 4, 1), base shape (32, 1, 1) 13.1 μs ± 0.933% (12.6 … 13.4 μs) 4.03 μs ± 3.31% (3.81 … 4.29 μs) 30.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (32, 4, 1), base shape (16, 2, 1) 19.1 μs ± 0.897% (18.8 … 19.3 μs) 4.08 μs ± 2.68% (3.81 … 4.29 μs) 20.3
FPU GEMM Float16*Float16=Float32 (2048×2048) · (2048×2048) (TT) OP (8, 16, 2), base shape (4, 8, 1) 1.84 ms ± 2.29% (1.8 … 2.02 ms) 292.0 μs ± 0.32% (290.0 … 293.0 μs) 16.1
FPU GEMM Float64*Float64=Float64 (2048×2048) · (2048×2048) (TN) OP (8, 16, 2), base shape (4, 8, 1) 46.1 ms ± 0.884% (46.0 … 52.4 ms) 40.9 ms ± 0.405% (40.8 … 44.0 ms) 88.7
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (32, 4, 1), base shape (16, 2, 1) 19.1 μs ± 0.905% (18.8 … 19.3 μs) 4.28 μs ± 3.36% (4.05 … 4.53 μs) 21.5
FPU GEMM Float64*Float64=Float64 (256×256) · (256×256) (TN) OP (8, 16, 2), base shape (4, 8, 1) 275.0 μs ± 30.6% (255.0 … 2550.0 μs) 109.0 μs ± 5.64% (109.0 … 249.0 μs) 42.7
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.49 μs ± 1.9% (8.11 … 8.82 μs) 3.82 μs ± 2.97% (3.58 … 4.29 μs) 44.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 15.3 μs ± 1.12% (15.0 … 15.7 μs) 4.07 μs ± 2.82% (3.81 … 4.29 μs) 25.4
WMMA GEMM Float16*Float16+Float16=Float16 (512×256) · (256×512) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.74 μs ± 1.88% (8.34 … 9.06 μs) 5.17 μs ± 3.01% (4.77 … 5.48 μs) 57.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (4, 8, 1), base shape (4, 8, 1) 15.2 μs ± 1.1% (15.0 … 15.5 μs) 4.3 μs ± 3.35% (4.05 … 4.53 μs) 27.0
FPU GEMM Float32*Float32=Float32 (2048×2048) · (2048×2048) (TT) OP (8, 16, 2), base shape (4, 8, 1) 1.88 ms ± 2.9% (1.84 … 2.05 ms) 1.1 ms ± 2.52% (1.03 … 1.34 ms) 56.2
FPU GEMM Float64*Float64=Float64 (256×256) · (256×256) (NN) OP (8, 16, 2), base shape (4, 8, 1) 279.0 μs ± 6.03% (256.0 … 292.0 μs) 109.0 μs ± 0.157% (109.0 … 109.0 μs) 42.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (4, 8, 1), base shape (4, 8, 1) 15.2 μs ± 1.07% (15.0 … 15.5 μs) 4.04 μs ± 3.48% (3.81 … 4.29 μs) 25.4
WMMA GEMM Float16*Float16+Float32=Float32 (2048×2048) · (2048×2048) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 365.0 μs ± 5.12% (343.0 … 390.0 μs) 291.0 μs ± 0.154% (290.0 … 293.0 μs) 84.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (16, 16, 1), base shape (4, 8, 1) 15.3 μs ± 0.915% (15.0 … 15.7 μs) 4.08 μs ± 2.63% (3.81 … 4.29 μs) 25.4
FPU GEMM Float32*Float32=Float32 (2048×2048) · (2048×2048) (TN) OP (8, 16, 2), base shape (4, 8, 1) 1.45 ms ± 2.25% (1.43 … 1.53 ms) 1.11 ms ± 1.41% (1.04 … 1.14 ms) 72.4
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.08 μs ± 2.16% (7.87 … 8.34 μs) 2.22 μs ± 7.57% (1.91 … 2.38 μs) 24.2
FPU GEMM Float16*Float16=Float32 (2048×2048) · (2048×2048) (NN) OP (8, 16, 2), base shape (4, 8, 1) 1.86 ms ± 2.93% (1.82 … 2.03 ms) 293.0 μs ± 0.141% (292.0 … 294.0 μs) 16.1
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (TT) OP (8, 16, 2), base shape (4, 8, 1) 148.0 μs ± 0.366% (146.0 … 149.0 μs) 28.7 μs ± 0.453% (28.4 … 29.1 μs) 19.4
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.02 μs ± 1.98% (7.87 … 8.34 μs) 2.46 μs ± 6.7% (2.15 … 2.62 μs) 27.3
FPU GEMM Float64*Float64=Float64 (2048×2048) · (2048×2048) (TT) OP (8, 16, 2), base shape (4, 8, 1) 46.1 ms ± 0.745% (46.0 … 52.4 ms) 40.8 ms ± 0.00522% (40.8 … 40.8 ms) 88.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (32, 4, 1), base shape (32, 1, 1) 12.6 μs ± 1.31% (12.4 … 12.9 μs) 4.19 μs ± 3.69% (4.05 … 4.53 μs) 32.7
WMMA GEMM Float16*Float16+Float32=Float32 (2048×2048) · (2048×2048) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 370.0 μs ± 5.26% (348.0 … 397.0 μs) 291.0 μs ± 0.16% (289.0 … 293.0 μs) 83.2
FPU GEMM Float16*Float16=Float32 (256×256) · (256×256) (TN) OP (8, 16, 2), base shape (4, 8, 1) 13.0 μs ± 1.16% (12.6 … 13.1 μs) 3.79 μs ± 3.24% (3.58 … 4.29 μs) 28.3
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.42 μs ± 1.87% (8.11 … 8.82 μs) 3.71 μs ± 3.69% (3.58 … 4.05 μs) 44.1
WMMA GEMM Float16*Float16+Float32=Float32 (2048×2048) · (2048×2048) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 367.0 μs ± 5.2% (342.0 … 389.0 μs) 293.0 μs ± 4.42% (290.0 … 515.0 μs) 84.9
FPU GEMM Float16*Float16=Float32 (2048×2048) · (2048×2048) (NT) OP (8, 16, 2), base shape (4, 8, 1) 2.31 ms ± 3.47% (2.27 … 2.56 ms) 291.0 μs ± 0.213% (289.0 … 293.0 μs) 12.8
FPU GEMM Float16*Float16=Float32 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 6.91 μs ± 0.818% (6.44 … 7.15 μs) 2.33 μs ± 5.96% (2.15 … 2.62 μs) 33.3
WMMA GEMM Float16*Float16+Float32=Float32 (256×128) · (128×256) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.06 μs ± 1.92% (8.82 … 9.3 μs) 2.88 μs ± 4.82% (2.62 … 3.1 μs) 29.7
WMMA GEMM Float16*Float16+Float32=Float32 (128×256) · (256×128) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.3 μs ± 1.19% (12.2 … 12.6 μs) 2.92 μs ± 5.11% (2.62 … 3.1 μs) 21.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (4, 8, 2), base shape (4, 8, 1) 16.0 μs ± 1.03% (15.7 … 16.5 μs) 4.17 μs ± 3.61% (4.05 … 4.53 μs) 25.8
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 16.4 μs ± 1.0% (16.0 … 16.7 μs) 4.18 μs ± 3.66% (4.05 … 4.53 μs) 25.4
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (32, 4, 1), base shape (32, 1, 1) 31.6 μs ± 0.467% (31.5 … 31.9 μs) 4.08 μs ± 2.75% (3.81 … 4.29 μs) 12.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (8, 16, 2), base shape (4, 8, 1) 13.5 μs ± 1.0% (13.1 … 13.8 μs) 4.04 μs ± 3.39% (3.81 … 4.29 μs) 29.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (4, 32, 1), base shape (1, 32, 1) 15.7 μs ± 1.08% (15.5 … 16.0 μs) 4.08 μs ± 2.78% (3.81 … 4.29 μs) 24.6
FPU GEMM Float16*Float16=Float32 (256×256) · (256×256) (NT) OP (8, 16, 2), base shape (4, 8, 1) 18.1 μs ± 0.873% (17.9 … 18.4 μs) 3.91 μs ± 3.62% (3.58 … 4.29 μs) 20.0
WMMA GEMM Float16*Float16+Float16=Float16 (2048×2048) · (2048×2048) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 225.0 μs ± 0.735% (221.0 … 229.0 μs) 187.0 μs ± 1.96% (178.0 … 193.0 μs) 80.7
WMMA GEMM Float16*Float16+Float16=Float16 (2048×2048) · (2048×2048) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 230.0 μs ± 1.39% (208.0 … 237.0 μs) 185.0 μs ± 2.18% (175.0 … 189.0 μs) 84.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (4, 32, 1), base shape (2, 16, 1) 21.9 μs ± 0.773% (21.7 … 22.2 μs) 4.29 μs ± 3.51% (4.05 … 4.53 μs) 18.7
WMMA GEMM Float16*Float16+Float32=Float32 (128×256) · (256×128) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.2 μs ± 1.39% (11.9 … 12.4 μs) 3.1 μs ± 3.61% (2.86 … 3.34 μs) 24.0
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 148.0 μs ± 4.69% (147.0 … 307.0 μs) 28.6 μs ± 0.525% (28.4 … 28.8 μs) 19.3
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (16, 16, 1), base shape (8, 4, 1) 14.5 μs ± 1.07% (14.3 … 14.8 μs) 4.08 μs ± 2.73% (3.81 … 4.29 μs) 26.7
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (4, 8, 2), base shape (4, 8, 1) 12.4 μs ± 1.38% (12.2 … 12.6 μs) 4.03 μs ± 3.69% (3.81 … 4.29 μs) 31.4
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (16, 16, 1), base shape (4, 8, 1) 15.4 μs ± 1.07% (15.3 … 15.7 μs) 4.04 μs ± 3.42% (3.81 … 4.29 μs) 25.0
WMMA GEMM Float16*Float16+Float16=Float16 (256×512) · (512×256) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.0 μs ± 1.37% (11.7 … 12.4 μs) 5.22 μs ± 3.32% (5.01 … 5.72 μs) 42.9
WMMA GEMM Float16*Float16+Float16=Float16 (512×512) · (512×512) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.4 μs ± 1.5% (11.9 … 12.6 μs) 7.25 μs ± 1.91% (6.91 … 7.63 μs) 58.0
WMMA GEMM Float16*Float16+Float16=Float16 (512×256) · (256×512) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.69 μs ± 2.11% (8.34 … 9.06 μs) 4.98 μs ± 3.5% (4.77 … 5.25 μs) 57.1
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 143.0 μs ± 5.42% (129.0 … 149.0 μs) 28.7 μs ± 0.476% (28.4 … 29.1 μs) 21.9
WMMA GEMM Float16*Float16+Float32=Float32 (256×256) · (256×256) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.4 μs ± 1.38% (12.2 … 12.6 μs) 3.81 μs ± 3.17% (3.58 … 4.29 μs) 29.4
WMMA GEMM Float16*Float16+Float32=Float32 (256×256) · (256×256) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.2 μs ± 1.36% (11.9 … 12.4 μs) 3.97 μs ± 4.02% (3.58 … 4.53 μs) 30.0
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (4, 32, 1), base shape (2, 16, 1) 21.9 μs ± 0.754% (21.7 … 22.2 μs) 4.04 μs ± 3.43% (3.81 … 4.53 μs) 17.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (32, 4, 1), base shape (16, 2, 1) 19.1 μs ± 0.88% (18.8 … 19.3 μs) 4.03 μs ± 3.46% (3.81 … 4.29 μs) 20.3
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (4, 8, 2), base shape (4, 8, 1) 11.8 μs ± 1.36% (11.7 … 12.2 μs) 4.29 μs ± 3.44% (4.05 … 4.53 μs) 34.7
WMMA GEMM Float16*Float16+Float16=Float16 (256×512) · (512×256) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.2 μs ± 1.45% (11.9 … 12.4 μs) 5.2 μs ± 3.31% (5.01 … 5.48 μs) 42.0
WMMA GEMM Float16*Float16+Float16=Float16 (512×256) · (256×512) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.71 μs ± 2.01% (8.34 … 9.06 μs) 5.13 μs ± 2.89% (4.77 … 5.48 μs) 57.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (4, 16, 1), base shape (4, 8, 1) 15.2 μs ± 1.13% (15.0 … 15.5 μs) 4.29 μs ± 3.43% (4.05 … 4.53 μs) 27.0
WMMA GEMM Float16*Float16+Float32=Float32 (256×256) · (256×256) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.2 μs ± 1.25% (11.9 … 12.4 μs) 3.96 μs ± 3.84% (3.81 … 4.29 μs) 32.0
FPU GEMM Float64*Float64=Float64 (2048×2048) · (2048×2048) (NT) OP (8, 16, 2), base shape (4, 8, 1) 46.5 ms ± 1.02% (46.4 … 52.8 ms) 40.9 ms ± 1.19% (40.8 … 47.4 ms) 88.0
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (8, 8, 1), base shape (4, 8, 1) 15.4 μs ± 0.831% (15.3 … 15.7 μs) 4.08 μs ± 2.63% (3.81 … 4.29 μs) 25.0
WMMA GEMM Float16*Float16+Float16=Float16 (512×256) · (256×512) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.79 μs ± 2.03% (8.34 … 9.06 μs) 4.94 μs ± 3.36% (4.77 … 5.25 μs) 57.1
WMMA GEMM Float16*Float16+Float16=Float16 (512×512) · (512×512) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.4 μs ± 1.42% (12.2 … 12.9 μs) 7.4 μs ± 1.52% (7.15 … 7.87 μs) 58.8
WMMA GEMM Float16*Float16+Float32=Float32 (2048×2048) · (2048×2048) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 373.0 μs ± 34.5% (350.0 … 2660.0 μs) 298.0 μs ± 35.4% (290.0 … 2590.0 μs) 82.8
WMMA GEMM Float16*Float16+Float16=Float16 (512×512) · (512×512) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.3 μs ± 1.4% (11.9 … 12.6 μs) 7.32 μs ± 2.04% (7.15 … 7.63 μs) 60.0
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (4, 8, 1), base shape (4, 8, 1) 15.2 μs ± 1.13% (15.0 … 15.5 μs) 4.08 μs ± 2.61% (3.81 … 4.29 μs) 25.4
FPU GEMM Float16*Float16=Float32 (128×128) · (128×128) (NT) OP (8, 16, 2), base shape (4, 8, 1) 9.23 μs ± 1.64% (8.82 … 9.54 μs) 2.3 μs ± 5.23% (1.91 … 2.62 μs) 21.6
WMMA GEMM Float16*Float16+Float32=Float32 (256×128) · (128×256) (NN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.29 μs ± 1.74% (9.06 … 9.54 μs) 2.92 μs ± 5.15% (2.62 … 3.1 μs) 28.9
WMMA GEMM Float16*Float16+Float32=Float32 (128×128) · (128×128) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 8.02 μs ± 2.0% (7.87 … 8.34 μs) 2.31 μs ± 5.21% (1.91 … 2.62 μs) 24.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (16, 16, 1), base shape (8, 4, 1) 14.6 μs ± 0.863% (14.3 … 15.0 μs) 4.19 μs ± 3.71% (4.05 … 4.53 μs) 28.3
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (4, 32, 1), base shape (1, 32, 1) 33.0 μs ± 0.406% (32.7 … 33.1 μs) 4.03 μs ± 3.53% (3.81 … 4.29 μs) 11.7
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (4, 16, 1), base shape (4, 8, 1) 15.2 μs ± 1.13% (15.0 … 15.5 μs) 4.02 μs ± 3.32% (3.81 … 4.29 μs) 25.4
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (32, 4, 1), base shape (16, 2, 1) 19.2 μs ± 0.801% (18.8 … 19.3 μs) 4.18 μs ± 3.7% (4.05 … 4.53 μs) 21.5
FPU GEMM Float32*Float32=Float32 (2048×2048) · (2048×2048) (NT) OP (8, 16, 2), base shape (4, 8, 1) 2.36 ms ± 2.75% (2.33 … 2.63 ms) 867.0 μs ± 0.843% (823.0 … 873.0 μs) 35.3
FPU GEMM Float64*Float64=Float64 (256×256) · (256×256) (TT) OP (8, 16, 2), base shape (4, 8, 1) 287.0 μs ± 29.3% (256.0 … 2550.0 μs) 109.0 μs ± 0.146% (109.0 … 110.0 μs) 42.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TT) OP (8, 8, 1), base shape (4, 8, 1) 15.3 μs ± 1.03% (15.0 … 15.5 μs) 4.04 μs ± 3.61% (3.81 … 4.53 μs) 25.4
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 7.46 μs ± 1.74% (7.15 … 7.87 μs) 3.62 μs ± 2.77% (3.34 … 4.05 μs) 46.7
WMMA GEMM Float16*Float16+Float32=Float32 (128×256) · (256×128) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.2 μs ± 1.41% (11.9 … 12.4 μs) 3.01 μs ± 4.67% (2.62 … 3.1 μs) 22.0
FPU GEMM Float16*Float16=Float32 (128×128) · (128×128) (TT) OP (8, 16, 2), base shape (4, 8, 1) 8.15 μs ± 1.44% (7.87 … 8.58 μs) 2.18 μs ± 7.85% (1.91 … 2.38 μs) 24.2
WMMA GEMM Float16*Float16+Float16=Float16 (512×512) · (512×512) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.5 μs ± 1.4% (12.2 … 12.9 μs) 7.31 μs ± 1.98% (7.15 … 7.63 μs) 58.8
WMMA GEMM Float16*Float16+Float32=Float32 (256×256) · (256×256) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.4 μs ± 1.39% (12.2 … 12.6 μs) 3.9 μs ± 3.67% (3.58 … 4.29 μs) 29.4
FPU GEMM Float32*Float32=Float32 (256×256) · (256×256) (NN) OP (8, 16, 2), base shape (4, 8, 1) 15.3 μs ± 1.15% (15.0 … 15.7 μs) 6.79 μs ± 2.04% (6.44 … 6.91 μs) 42.9
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (8, 8, 1), base shape (4, 8, 1) 15.4 μs ± 1.1% (15.3 … 15.7 μs) 4.17 μs ± 3.65% (4.05 … 4.53 μs) 26.6
FPU GEMM Float64*Float64=Float64 (256×256) · (256×256) (NT) OP (8, 16, 2), base shape (4, 8, 1) 287.0 μs ± 4.33% (256.0 … 293.0 μs) 110.0 μs ± 7.66% (109.0 … 302.0 μs) 42.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (4, 16, 1), base shape (4, 8, 1) 15.3 μs ± 0.961% (15.0 … 15.7 μs) 4.18 μs ± 3.55% (4.05 … 4.53 μs) 27.0
WMMA GEMM Float16*Float16+Float32=Float32 (256×128) · (128×256) (TT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.18 μs ± 1.58% (8.82 … 9.54 μs) 2.91 μs ± 5.07% (2.62 … 3.1 μs) 29.7
FPU GEMM Float16*Float16=Float32 (128×128) · (128×128) (NN) OP (8, 16, 2), base shape (4, 8, 1) 9.22 μs ± 1.31% (8.82 … 9.54 μs) 2.23 μs ± 7.46% (1.91 … 2.38 μs) 21.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (8, 8, 1), base shape (4, 8, 1) 15.2 μs ± 1.12% (15.0 … 15.5 μs) 4.28 μs ± 3.53% (4.05 … 4.77 μs) 27.0
FPU GEMM Float16*Float16=Float32 (256×256) · (256×256) (TT) OP (8, 16, 2), base shape (4, 8, 1) 15.8 μs ± 1.07% (15.5 … 16.0 μs) 3.96 μs ± 3.86% (3.58 … 4.29 μs) 23.1
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (16, 16, 1), base shape (4, 8, 1) 15.3 μs ± 0.951% (15.0 … 15.7 μs) 4.18 μs ± 3.62% (4.05 … 4.53 μs) 27.0
WMMA GEMM Float16*Float16+Float32=Float32 (128×256) · (256×128) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.4 μs ± 1.38% (12.2 … 12.6 μs) 2.74 μs ± 5.52% (2.38 … 2.86 μs) 19.6
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (4, 8, 2), base shape (4, 8, 1) 15.0 μs ± 1.1% (14.5 … 15.3 μs) 4.08 μs ± 2.66% (3.81 … 4.29 μs) 26.2
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (32, 4, 1), base shape (32, 1, 1) 31.6 μs ± 0.459% (31.5 … 31.9 μs) 4.3 μs ± 3.4% (4.05 … 4.53 μs) 12.9
WMMA GEMM Float16*Float16+Float32=Float32 (256×128) · (128×256) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 9.15 μs ± 1.7% (8.82 … 9.3 μs) 2.91 μs ± 5.34% (2.62 … 3.1 μs) 29.7
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (4, 32, 1), base shape (2, 16, 1) 21.9 μs ± 0.759% (21.7 … 22.2 μs) 4.18 μs ± 3.67% (4.05 … 4.53 μs) 18.7
FPU GEMM Float16*Float16=Float32 (256×256) · (256×256) (NN) OP (8, 16, 2), base shape (4, 8, 1) 15.7 μs ± 1.14% (15.5 … 16.0 μs) 3.97 μs ± 3.86% (3.81 … 4.29 μs) 24.6
FPU GEMM Float16*Float16=Float32 (2048×2048) · (2048×2048) (TN) OP (8, 16, 2), base shape (4, 8, 1) 1.55 ms ± 3.12% (1.52 … 1.67 ms) 293.0 μs ± 0.289% (290.0 … 296.0 μs) 19.2
FPU GEMM Float64*Float64=Float64 (2048×2048) · (2048×2048) (NN) OP (8, 16, 2), base shape (4, 8, 1) 46.5 ms ± 1.79% (46.3 … 57.9 ms) 40.9 ms ± 0.643% (40.8 … 45.6 ms) 88.2
WMMA GEMM Float16*Float16+Float16=Float16 (256×512) · (512×256) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.1 μs ± 1.38% (11.9 … 12.4 μs) 5.1 μs ± 3.39% (4.77 … 5.72 μs) 40.0
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (4, 32, 1), base shape (2, 16, 1) 22.0 μs ± 0.646% (21.7 … 22.2 μs) 4.07 μs ± 2.88% (3.81 … 4.29 μs) 17.6
WMMA GEMM Float16*Float16+Float16=Float16 (256×512) · (512×256) (NT) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 12.0 μs ± 1.4% (11.7 … 12.4 μs) 4.49 μs ± 3.72% (4.29 … 4.77 μs) 36.7
FPU GEMM Float32*Float32=Float32 (256×256) · (256×256) (NT) OP (8, 16, 2), base shape (4, 8, 1) 18.2 μs ± 0.772% (18.1 … 18.6 μs) 6.77 μs ± 2.12% (6.44 … 6.91 μs) 35.5
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NN) OP (4, 16, 1), base shape (4, 8, 1) 15.2 μs ± 1.15% (15.0 … 15.5 μs) 4.08 μs ± 2.75% (3.81 … 4.53 μs) 25.4
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (NT) OP (4, 8, 1), base shape (4, 8, 1) 15.3 μs ± 1.11% (15.0 … 15.5 μs) 4.18 μs ± 3.72% (4.05 … 4.53 μs) 27.0
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (4, 32, 1), base shape (1, 32, 1) 33.0 μs ± 0.479% (32.7 … 33.1 μs) 4.29 μs ± 3.54% (4.05 … 4.53 μs) 12.4
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 12.1 μs ± 1.2% (11.9 … 12.4 μs) 4.3 μs ± 3.26% (4.05 … 4.77 μs) 34.0
FPU GEMM Float64*Float64=Float64 (128×128) · (128×128) (TN) OP (8, 16, 2), base shape (4, 8, 1) 145.0 μs ± 4.78% (139.0 … 331.0 μs) 30.9 μs ± 0.396% (30.5 … 31.2 μs) 21.9
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (16, 16, 1), base shape (4, 8, 1) 15.2 μs ± 1.13% (15.0 … 15.5 μs) 4.29 μs ± 3.53% (4.05 … 4.53 μs) 27.0
WMMA GEMM Float16*Float16+Float16=Float16 (256×256) · (256×256) (TN) Block (128, 128, 64) Warps (4, 2) OP (16, 16, 16) 7.43 μs ± 1.51% (7.15 … 7.87 μs) 3.58 μs ± 2.8% (3.1 … 4.05 μs) 43.3
FPU GEMM Float32*Float32=Float32 (128×128) · (128×128) (TN) OP (16, 16, 1), base shape (8, 4, 1) 14.5 μs ± 1.07% (14.3 … 14.8 μs) 4.29 μs ± 3.48% (4.05 … 4.53 μs) 28.3
FPU GEMM Float32*Float32=Float32 (256×256) · (256×256) (TN) OP (8, 16, 2), base shape (4, 8, 1) 12.6 μs ± 1.34% (12.4 … 12.9 μs) 7.17 μs ± 1.24% (6.91 … 7.63 μs) 55.8

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2 participants
@thomasfaingnaert @maleadt