Add explicit multiply-reduce GEMM kernel

python/perf-kernels/README.md

@@ -61,3 +61,20 @@ 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 $16$:
+
+**MI300 Results for FP16:**
+
+| trans   |   M |     N |     K |         Dot GiBps |   Multiply-Reduce GiBps |   Speedup |
+|:--------|----:|------:|------:|------------------:|------------------------:|----------:|
+| TN      |   1 |  8192 | 28672 |           3491.33 |                 2869.87 |      0.82 |
+| TN      |   1 |  6144 |  6144 |           3858.22 |                 2673.33 |      0.69 |
+| TN      |   1 |  4096 |  4096 |           2352.54 |                 1680.93 |      0.71 |
+| TN      |   2 | 16384 | 16384 |           3412.17 |                 3318.44 |      0.97 |

python/perf-kernels/multreduce_matmul_kernel.py

@@ -0,0 +1,73 @@
+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, SPLIT_K: tl.constexpr, GROUP_SIZE_M: tl.constexpr,
+                             BIAS: tl.constexpr, EVEN_K: tl.constexpr):
+    pid = tl.program_id(axis=0)
+    pid_z = tl.program_id(1)
+    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
+    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
+    if GROUP_SIZE_M == 1:
+        pid_m = pid // num_pid_n
+        pid_n = pid % num_pid_n
+    else:
+        num_pid_in_group = GROUP_SIZE_M * num_pid_n
+        group_id = pid // num_pid_in_group
+        first_pid_m = group_id * GROUP_SIZE_M
+        group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)
+        pid_m = first_pid_m + (pid % group_size_m)
+        pid_n = (pid % num_pid_in_group) // group_size_m
+    if SPLIT_K == 1:
+        offs_k = tl.arange(0, BLOCK_SIZE_K)
+    else:
+        offs_k = pid_z * BLOCK_SIZE_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 * SPLIT_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)
+        # TODO: `min_dot_size` isn't always (16, 16, 16), it's in fact architecture
+        #       dependent and data type dependent. Please check this source file:
+        #       `${TRITON_ROOT}/third_party/amd/backend/compiler.py`
+        #       (look for `min_dot_size` function).
+        #       Q: How can we implement this `if` statement more precisely?
+        #       A: Maybe we can use an approach similar to `EVEN_K`, in which the kernel caller
+        #          inspect all relevant information and provides a Boolean flag for the kernel.
+        if (BLOCK_SIZE_M < 16 or BLOCK_SIZE_N < 16) or BLOCK_SIZE_K < 16:
+            # Explicit multiply-reduce for small block sizes.
+            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)
+        else:
+            # Triton dot product for other block sizes.
+            accumulator += tl.dot(a, b)
+        a_ptrs += BLOCK_SIZE_K * SPLIT_K * stride_ak
+        b_ptrs += BLOCK_SIZE_K * SPLIT_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)
+    if SPLIT_K == 1:
+        tl.store(c_ptrs, c, mask=c_mask)
+    else:
+        tl.atomic_add(c_ptrs, c, mask=c_mask)