Add explicit multiply-reduce GEMM kernel

python/perf-kernels/README.md

@@ -61,3 +61,11 @@ fp32, bf16 and f8 (both e5m2 and e4m3) datatypes.
 ## `03-matrix-multiplication-stream-k.py`
 
 This script contains the GEMM kernel that implements [stream-k](https://arxiv.org/abs/2301.03598)
+
+## `multreduce_matmul_kernel.py`
+
+Kernel that implements GEMM with explicit multiply-reduce instructions for small block sizes. Such
+small block sizes aren't natively supported by `tl.dot` operator.
+
+Despite being numerically correct, this kernel performed worse than a corresponding GEMM kernel that
+used `tl.dot` with minimum block size equal to $16$.

python/perf-kernels/multreduce_matmul_kernel.py

@@ -0,0 +1,45 @@
+import triton
+import triton.language as tl
+
+
+# Kernel that implements GEMM with explicit multiply-reduce instructions for small block sizes.
+# Based on **tune_gemm** `matmul_kernel` from commit `cf44637` (see `triton-mlir` branch).
+@triton.jit
+def multreduce_matmul_kernel(a_ptr, b_ptr, c_ptr, bias_ptr, M, N, K, stride_am, stride_ak, stride_bk, stride_bn,
+                             stride_cm, stride_cn, stride_bias, BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr,
+                             BLOCK_SIZE_K: tl.constexpr, BIAS: tl.constexpr, EVEN_K: tl.constexpr):
+    pid = tl.program_id(axis=0)
+    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
+    pid_m = pid // num_pid_n
+    pid_n = pid % num_pid_n
+    offs_k = tl.arange(0, BLOCK_SIZE_K)
+    offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M))
+    offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N))
+    a_ptrs = a_ptr + offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak
+    b_ptrs = b_ptr + offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn
+    if BIAS:
+        bias_ptrs = bias_ptr + offs_am * stride_bias
+        bias = tl.load(bias_ptrs, mask=offs_am < M, other=0.0)
+    acc_dtype = tl.float32 if a_ptr.type.element_ty != tl.int8 else tl.int32
+    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=acc_dtype)
+    for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
+        if EVEN_K:
+            a = tl.load(a_ptrs)
+            b = tl.load(b_ptrs)
+        else:
+            a = tl.load(a_ptrs, mask=offs_k[None, :] < K - k * BLOCK_SIZE_K, other=0.0)
+            b = tl.load(b_ptrs, mask=offs_k[:, None] < K - k * BLOCK_SIZE_K, other=0.0)
+        # Dot product implemented as explicit multiply-reduce:
+        a = tl.reshape(a, (BLOCK_SIZE_M, BLOCK_SIZE_K, 1)).to(acc_dtype)
+        b = tl.reshape(b, (1, BLOCK_SIZE_K, BLOCK_SIZE_N)).to(acc_dtype)
+        accumulator += tl.sum(a * b, axis=1)
+        a_ptrs += BLOCK_SIZE_K * stride_ak
+        b_ptrs += BLOCK_SIZE_K * stride_bk
+    c = accumulator.to(c_ptr.type.element_ty)
+    if BIAS:
+        c += bias[:, None]
+    offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+    offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+    c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :]
+    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
+    tl.store(c_ptrs, c, mask=c_mask)