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@HDCharles
Created September 19, 2023 23:56
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not using block pointers
@triton.jit
def matmul_kernel_with_block_pointers(
# Pointers to matrices
a_ptr, b_ptr, c_ptr, s1_ptr, s2_ptr,
# Matrix dimensions
M, N, K,
# The stride variables represent how much to increase the ptr by when moving by 1
# element in a particular dimension. E.g. `stride_am` is how much to increase `a_ptr`
# by to get the element one row down (A has M rows).
stride_am, stride_ak,
stride_bk, stride_bn,
stride_cm, stride_cn,
stride_s1m, stride_s1n,
stride_s2m, stride_s2n,
# Meta-parameters
BLOCK_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr,
BLOCK_SIZE_K: tl.constexpr,
GROUP_SIZE_M: tl.constexpr
):
"""Kernel for computing the matmul C = A x B.
A has shape (M, K), B has shape (K, N) and C has shape (M, N)
"""
# -----------------------------------------------------------
# Map program ids `pid` to the block of C it should compute.
# This is done in a grouped ordering to promote L2 data reuse.
# See above `L2 Cache Optimizations` section for details.
pid = tl.program_id(axis=0)
num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
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
# ----------------------------------------------------------
# Create pointers for the first blocks of A and B.
# We will advance this pointer as we move in the K direction
# and accumulate
# `a_ptrs` is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers
# `b_ptrs` is a block of [BLOCK_SIZE_K, BLOCK_SIZE_N] pointers
# See above `Pointer Arithmetics` section for details
offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M
offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N
offs_k = tl.arange(0, BLOCK_SIZE_K)
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)
# -----------------------------------------------------------
# Iterate to compute a block of the C matrix.
# We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block
# of fp32 values for higher accuracy.
# `accumulator` will be converted back to fp16 after the loop.
accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
# Load the next block of A and B, generate a mask by checking the K dimension.
# If it is out of bounds, set it to 0.
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)
# We accumulate along the K dimension.
accumulator += tl.dot(a, b)
# Advance the ptrs to the next K block.
a_ptrs += BLOCK_SIZE_K * stride_ak
b_ptrs += BLOCK_SIZE_K * stride_bk
c = accumulator
offs_m = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
offs_n = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
s1_ptrs = s1_ptr + offs_m[:, None] * stride_s1m + offs_n[None, :] * stride_s1n
s2_ptrs = s2_ptr + offs_m[:, None] * stride_s2m + offs_n[None, :] * stride_s2n
s1 = tl.load(s1_ptrs)
s2 = tl.load(s2_ptrs)
c = c * s1 * s2
c = c.to(tl.float16)
# -----------------------------------------------------------
# Write back the block of the output matrix C with masks.
c_ptrs = c_ptr + stride_cm * offs_m[:, None] + stride_cn * offs_n[None, :]
c_mask = (offs_m[:, None] < M) & (offs_n[None, :] < N)
# Epilogue
tl.store(c_ptrs, c, mask=c_mask)
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