Add A^t@B benchmark (#2430)

Based on this feedback
#2408 (review)

Changed GEMM benchmark to include transposed matrices case.

Closes #2424
Relates to
#1795

A@B^t case is important because weight matrix is often stored in [M, K]
format. For example, in
https://pytorch.org/docs/stable/generated/torch.nn.Linear.html
Right now we are about 1.5 times slower on XPU against raw torch for
that case.


A^t@B case is important because it's part of matmul backprop. Right now
we are about 4 times slower on XPU against raw torch for that case.

.github/workflows/triton-benchmarks.yml

@@ -163,13 +163,24 @@ jobs:
         if: ${{ steps.install.outcome == 'success' && !cancelled() }}
         run: |
           cd benchmarks/triton_kernels_benchmark
-          python gemm_bt_benchmark.py --reports $REPORTS
+          TRANSPOSE_B=1 python gemm_benchmark.py --reports $REPORTS
           mv $REPORTS/matmul-performance.csv $REPORTS/matmul-performance-bt.csv
           source ../../scripts/capture-hw-details.sh
 
           TAG=${{ inputs.tag || 'ci' }}
           python ../../scripts/build_report.py $REPORTS/matmul-performance-bt.csv $REPORTS/gemm-bt-triton-report.csv --benchmark gemm-bt --compiler triton --param_cols "B,M,K,N" --tflops_col Triton-TFlops --hbm_col "Triton-GB/s" --tag $TAG
 
+      - name: Run Triton GEMM (A^t@B) kernel benchmark
+        if: ${{ steps.install.outcome == 'success' && !cancelled() }}
+        run: |
+          cd benchmarks/triton_kernels_benchmark
+          TRANSPOSE_A=1 python gemm_benchmark.py --reports $REPORTS
+          mv $REPORTS/matmul-performance.csv $REPORTS/matmul-performance-at.csv
+          source ../../scripts/capture-hw-details.sh
+
+          TAG=${{ inputs.tag || 'ci' }}
+          python ../../scripts/build_report.py $REPORTS/matmul-performance-at.csv $REPORTS/gemm-at-triton-report.csv --benchmark gemm-at --compiler triton --param_cols "B,M,K,N" --tflops_col Triton-TFlops --hbm_col "Triton-GB/s" --tag $TAG
+
       - name: Run Triton GEMM (stream-k) kernel benchmark
         if: ${{ steps.install.outcome == 'success' && !cancelled() }}
         run: |

benchmarks/triton_kernels_benchmark/gemm_benchmark.py

@@ -6,6 +6,7 @@
 To compare the performance to XeTLA kernel.
 
 """
+import os
 
 import torch
 import triton
@@ -17,6 +18,10 @@
 if benchmark_suit.USE_IPEX_OPTION:
     import intel_extension_for_pytorch  # type: ignore # noqa: F401
 
+TRANSPOSE_A = os.getenv('TRANSPOSE_A', '0') == '1'
+TRANSPOSE_B = os.getenv('TRANSPOSE_B', '0') == '1'
+use_xetla = not (TRANSPOSE_A or TRANSPOSE_B)
+
 
 @triton.autotune(
     configs=[
@@ -158,15 +163,22 @@ def matmul_kernel_with_block_pointers_batched(
 
 # We can now create a convenience wrapper function that only takes two input tensors,
 # and (1) checks any shape constraint; (2) launches the above kernel.
-def matmul(a, b, c):
+def matmul(a, b, c, transpose_a=False, transpose_b=False):
+    a_major, a_minor = -2, -1
+    if transpose_a:
+        a_major, a_minor = a_minor, a_major
+    b_minor, b_major = -2, -1
+    if transpose_b:
+        b_major, b_minor = b_minor, b_major
+
+    assert a.shape[a_minor] == b.shape[b_minor], 'Incompatible dimensions'
+    assert a.is_contiguous(), 'Matrix A must be contiguous'
+    assert b.is_contiguous(), 'Matrix B must be contiguous'
+    M, N, K = a.shape[a_major], b.shape[b_major], a.shape[a_minor]
     # Check constraints.
     if len(a.shape) == 3 and len(b.shape) == 3:
         assert a.shape[0] == b.shape[0], 'Incompatible Batch dimension'
-        assert a.shape[2] == b.shape[1], 'Incompatible dimensions'
-        assert a.is_contiguous(), 'Matrix A must be contiguous'
-        assert b.is_contiguous(), 'Matrix B must be contiguous'
-        B, M, K = a.shape
-        B, K, N = b.shape
+        B = a.shape[0]
         # 1D launch kernel where each block gets its own program.
         grid = lambda META: (
             B,
@@ -175,27 +187,37 @@ def matmul(a, b, c):
         matmul_kernel_with_block_pointers_batched[grid](
             a, b, c,  #
             B, M, N, K,  #
-            a.stride(0), a.stride(1), a.stride(2),  #
-            b.stride(0), b.stride(1), b.stride(2),  #
+            a.stride(0), a.stride(a_major), a.stride(a_minor),  #
+            b.stride(0), b.stride(b_minor), b.stride(b_major),  #
             c.stride(0), c.stride(1), c.stride(2))
     elif len(a.shape) == 2 and len(b.shape) == 2:
-        assert a.shape[1] == b.shape[0], 'Incompatible dimensions'
-        assert a.is_contiguous(), 'Matrix A must be contiguous'
-        assert b.is_contiguous(), 'Matrix B must be contiguous'
-        M, K = a.shape
-        K, N = b.shape
         grid = lambda META: (triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']), )
         matmul_kernel_with_block_pointers[grid](
             a, b, c,  #
             M, N, K,  #
-            a.stride(0), a.stride(1),  #
-            b.stride(0), b.stride(1),  #
+            a.stride(a_major), a.stride(a_minor),  #
+            b.stride(b_minor), b.stride(b_major),  #
             c.stride(0), c.stride(1))
     else:
         assert False, 'Input matrixs dimensions mismatch'
     return c
 
 
+def get_shapes(B, M, N, K, transpose_a, transpose_b):
+    a_shape = (M, K)
+    if transpose_a:
+        a_shape = (K, M)
+
+    b_shape = (K, N)
+    if transpose_b:
+        b_shape = (N, K)
+
+    if B != 1:
+        a_shape = (B, *a_shape)
+        b_shape = (B, *b_shape)
+    return a_shape, b_shape
+
+
 # Benchmark Performance
 @benchmark_suit.perf_report(
     benchmark_suit.Benchmark(
@@ -228,9 +250,9 @@ def matmul(a, b, c):
         line_arg='provider',
         # argument name whose value corresponds to a different line in the plot
         # possible values for `line_arg``
-        line_vals=['triton', 'xetla'],
+        line_vals=['triton'] + (['xetla'] if use_xetla else []),
         # label name for the lines
-        line_names=['Triton', 'XeTLA'],
+        line_names=['Triton'] + (['XeTLA'] if use_xetla else []),
         # line styles
         styles=[('green', '-'), ('green', '--'), ('blue', '-'), ('blue', '--')],
         ylabel=['GB/s', 'TFlops'],  # label name for the y-axis
@@ -239,27 +261,33 @@ def matmul(a, b, c):
         args={},
     ))
 def benchmark(B, M, N, K, provider):
-    if B == 1:
-        a = torch.rand((M, K), device='xpu', dtype=torch.bfloat16)
-        b = torch.rand((K, N), device='xpu', dtype=torch.bfloat16)
-    else:
-        a = torch.rand((B, M, K), device='xpu', dtype=torch.bfloat16)
-        b = torch.rand((B, K, N), device='xpu', dtype=torch.bfloat16)
+    a_shape, b_shape = get_shapes(B, M, N, K, transpose_a=TRANSPOSE_A, transpose_b=TRANSPOSE_B)
+
+    a = torch.rand(a_shape, device='xpu', dtype=torch.bfloat16)
+    b = torch.rand(b_shape, device='xpu', dtype=torch.bfloat16)
 
     quantiles = [0.5, 0.0, 1.0]
 
+    torch_a = a
+    if TRANSPOSE_A:
+        torch_a = torch.transpose(torch_a, -2, -1)
+
+    torch_b = b
+    if TRANSPOSE_B:
+        torch_b = torch.transpose(torch_b, -2, -1)
+
     if provider == 'onednn':
-        _, min_ms, max_ms, mean_ms, cv = benchmark_suit.do_bench(lambda: torch.matmul(a, b), warmup=10, rep=10,
-                                                                 quantiles=quantiles)
+        _, min_ms, max_ms, mean_ms, cv = benchmark_suit.do_bench(lambda: torch.matmul(torch_a, torch_b), warmup=10,
+                                                                 rep=10, quantiles=quantiles)
     elif provider == 'triton':
         assert len(a.shape) == len(b.shape), 'Incompatible sizes'
         if len(a.shape) == 3:
             c = torch.empty((B, M, N), device='xpu', dtype=torch.float32)
         else:
             assert len(a.shape) == 2, 'Expecting shape of length 2'
             c = torch.empty((M, N), device='xpu', dtype=torch.float32)
-        triton_fn = lambda: matmul(a, b, c)
-        torch_fn = lambda: torch.matmul(a, b).to(torch.float32)
+        triton_fn = lambda: matmul(a, b, c, transpose_a=TRANSPOSE_A, transpose_b=TRANSPOSE_B)
+        torch_fn = lambda: torch.matmul(torch_a, torch_b).to(torch.float32)
         rtol = 1e-2 if a.dtype == torch.bfloat16 else 1e-3
         benchmark_suit.assert_close(triton_fn(), torch_fn(), atol=1e-4, rtol=rtol, err_msg='triton to torch')
         _, min_ms, max_ms, mean_ms, cv = benchmark_suit.do_bench(triton_fn, warmup=10, rep=10, quantiles=quantiles,