From 855695c0bd4d902ed5cbc48f38e519525c82fda5 Mon Sep 17 00:00:00 2001 From: Bruno Mazzotti Date: Tue, 30 Jul 2024 19:18:04 +0000 Subject: [PATCH] Add explicit multiply-reduce GEMM kernel --- python/perf-kernels/README.md | 17 +++++ .../perf-kernels/multreduce_matmul_kernel.py | 73 +++++++++++++++++++ 2 files changed, 90 insertions(+) create mode 100644 python/perf-kernels/multreduce_matmul_kernel.py diff --git a/python/perf-kernels/README.md b/python/perf-kernels/README.md index 5bcedbf49cdd..1bb5ec91ce89 100644 --- a/python/perf-kernels/README.md +++ b/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 | diff --git a/python/perf-kernels/multreduce_matmul_kernel.py b/python/perf-kernels/multreduce_matmul_kernel.py new file mode 100644 index 000000000000..7c234f920910 --- /dev/null +++ b/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)