Note
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How to optimize convolution using TensorCores¶
Author: Siyuan Feng
In this tutorial, we will demonstrate how to write a high performance convolution schedule using TensorCores in TVM. In this example, we assume the input to convolution has a large batch. We strongly recommend covering the How to optimize convolution on GPU tutorial first.
TensorCore Introduction¶
Each Tensor Core provides a 4x4x4 matrix processing array that operates
D = A * B + C, where A, B, C and D are 4x4 matrices as Figure shows.
The matrix multiplication inputs A and B are FP16 matrices, while the accumulation
matrices C and D may be FP16 or FP32 matrices.
However, CUDA programmers can only use warp-level primitive
wmma::mma_sync(acc_frag, a_frag, b_frag, acc_frag) to perform
16x16x16 half-precision matrix multiplication on tensor cores. Before invoking
the matrix multiplication, programmers must load data from memory into registers
with primitive wmma::load_matrix_sync, explicitly. The NVCC compiler translates
that primitive into multiple memory load instructions. At run time, every thread loads
16 elements from matrix A and 16 elements from B.
Preparation and Algorithm¶
We use the fixed size for input tensors with 256 channels and 14 x 14 dimensions. The batch size is 256. Convolution filters contain 512 filters of size 3 x 3. We use stride size 1 and padding size 1 for the convolution. In the example, we use NHWCnc memory layout.The following code defines the convolution algorithm in TVM.
import tvm
from tvm import te
import numpy as np
from tvm.contrib import nvcc
# The sizes of inputs and filters
batch_size = 256
height = 14
width = 14
in_channels = 256
out_channels = 512
kernel_h = 3
kernel_w = 3
pad_h = 1
pad_w = 1
stride_h = 1
stride_w = 1
# TensorCore shape
block_size = 16
assert batch_size % block_size == 0
assert in_channels % block_size == 0
assert out_channels % block_size == 0
# Input feature map: (N, H, W, IC, n, ic)
data_shape = (
batch_size // block_size,
height,
width,
in_channels // block_size,
block_size,
block_size,
)
# Kernel: (H, W, IC, OC, ic, oc)
kernel_shape = (
kernel_h,
kernel_w,
in_channels // block_size,
out_channels // block_size,
block_size,
block_size,
)
# Output feature map: (N, H, W, OC, n, oc)
output_shape = (
batch_size // block_size,
height,
width,
out_channels // block_size,
block_size,
block_size,
)
# Reduction axes
kh = te.reduce_axis((0, kernel_h), name="kh")
kw = te.reduce_axis((0, kernel_w), name="kw")
ic = te.reduce_axis((0, in_channels // block_size), name="ic")
ii = te.reduce_axis((0, block_size), name="ii")
# Algorithm
A = te.placeholder(data_shape, name="A", dtype="float16")
W = te.placeholder(kernel_shape, name="W", dtype="float16")
Apad = te.compute(
(
batch_size // block_size,
height + 2 * pad_h,
width + 2 * pad_w,
in_channels // block_size,
block_size,
block_size,
),
lambda n, h, w, i, nn, ii: tvm.tir.if_then_else(
tvm.tir.all(h >= pad_h, h - pad_h < height, w >= pad_w, w - pad_w < width),
A[n, h - pad_h, w - pad_w, i, nn, ii],
tvm.tir.const(0.0, "float16"),
),
name="Apad",
)
Conv = te.compute(
output_shape,
lambda n, h, w, o, nn, oo: te.sum(
Apad[n, h * stride_h + kh, w * stride_w + kw, ic, nn, ii].astype("float32")
* W[kh, kw, ic, o, ii, oo].astype("float32"),
axis=[ic, kh, kw, ii],
),
name="Conv",
)
s = te.create_schedule(Conv.op)
s[Apad].compute_inline()
Memory Scope¶
In traditional GPU schedule, we have global, shared and local memory scope.
To support TensorCores, we add another three special memory scope: wmma.matrix_a,
wmma.matrix_b and wmma.accumulator. On hardware, all fragments scope
stores at the on-chip registers level, the same place with local memory.
# Designate the memory hierarchy
AS = s.cache_read(Apad, "shared", [Conv])
WS = s.cache_read(W, "shared", [Conv])
AF = s.cache_read(AS, "wmma.matrix_a", [Conv])
WF = s.cache_read(WS, "wmma.matrix_b", [Conv])
ConvF = s.cache_write(Conv, "wmma.accumulator")
Define Tensor Intrinsic¶
In fact, TensorCore is a special hardware operation. So, we can just use tensorize to replace a unit of computation with the TensorCore instruction. The first thing is that we need to define tensor intrinsic.
There are four basic operation in TensorCore: fill_fragment, load_matrix,
mma_sync and store_matrix. Since fill_fragment and mma_sync
are both used in matrix multiplication, so we can just write following three intrinsics.
def intrin_wmma_load_matrix(scope):
n = 16
A = te.placeholder((n, n), name="A", dtype="float16")
BA = tvm.tir.decl_buffer(A.shape, A.dtype, scope="shared", data_alignment=32, offset_factor=256)
C = te.compute((n, n), lambda i, j: A[i, j], name="C")
BC = tvm.tir.decl_buffer(C.shape, C.dtype, scope=scope, data_alignment=32, offset_factor=256)
def intrin_func(ins, outs):
ib = tvm.tir.ir_builder.create()
BA = ins[0]
BC = outs[0]
ib.emit(
tvm.tir.call_intrin(
"handle",
"tir.tvm_load_matrix_sync",
BC.data,
n,
n,
n,
BC.elem_offset // 256,
BA.access_ptr("r"),
n,
"row_major",
)
)
return ib.get()
return te.decl_tensor_intrin(C.op, intrin_func, binds={A: BA, C: BC})
def intrin_wmma_gemm():
n = 16
A = te.placeholder((n, n), name="A", dtype="float16")
B = te.placeholder((n, n), name="B", dtype="float16")
k = te.reduce_axis((0, n), name="k")
C = te.compute(
(n, n),
lambda ii, jj: te.sum(A[ii, k].astype("float") * B[k, jj].astype("float"), axis=k),
name="C",
)
BA = tvm.tir.decl_buffer(
A.shape, A.dtype, name="BA", scope="wmma.matrix_a", data_alignment=32, offset_factor=256
)
BB = tvm.tir.decl_buffer(
B.shape, B.dtype, name="BB", scope="wmma.matrix_b", data_alignment=32, offset_factor=256
)
BC = tvm.tir.decl_buffer(
C.shape, C.dtype, name="BC", scope="wmma.accumulator", data_alignment=32, offset_factor=256
)
def intrin_func(ins, outs):
BA, BB = ins
(BC,) = outs
def init():
ib = tvm.tir.ir_builder.create()
ib.emit(
tvm.tir.call_intrin(
"handle", "tir.tvm_fill_fragment", BC.data, n, n, n, BC.elem_offset // 256, 0.0
)
)
return ib.get()
def update():
ib = tvm.tir.ir_builder.create()
ib.emit(
tvm.tir.call_intrin(
"handle",
"tir.tvm_mma_sync",
BC.data,
BC.elem_offset // 256,
BA.data,
BA.elem_offset // 256,
BB.data,
BB.elem_offset // 256,
BC.data,
BC.elem_offset // 256,
)
)
return ib.get()
return update(), init(), update()
return te.decl_tensor_intrin(C.op, intrin_func, binds={A: BA, B: BB, C: BC})
def intrin_wmma_store_matrix():
n = 16
A = te.placeholder((n, n), name="A", dtype="float32")
BA = tvm.tir.decl_buffer(
A.shape, A.dtype, scope="wmma.accumulator", data_alignment=32, offset_factor=256
)
C = te.compute((n, n), lambda i, j: A[i, j], name="C")
BC = tvm.tir.decl_buffer(C.shape, C.dtype, scope="global", data_alignment=32, offset_factor=256)
def intrin_func(ins, outs):
ib = tvm.tir.ir_builder.create()
BA = ins[0]
BC = outs[0]
ib.emit(
tvm.tir.call_intrin(
"handle",
"tir.tvm_store_matrix_sync",
BA.data,
n,
n,
n,
BA.elem_offset // 256,
BC.access_ptr("w"),
n,
"row_major",
)
)
return ib.get()
return te.decl_tensor_intrin(C.op, intrin_func, binds={A: BA, C: BC})
Scheduling the Computation¶
To use TensorCores in TVM, we must schedule the computation into specific structure to match the tensor intrinsic. The same as traditional GPU programs, we can also use shared memory to boost the speed. If you have any questions about blocking and shared memory, please refer How to optimize convolution on GPU.
In this example, each block contains 2x4 warps, and each warp calls 4x2 TensorCore instructions. Thus, the output shape of each warp is 64x32 and each block outputs 128x128 titles. Due to the limit of shared memory space, we only load 2 blocks (2x128x128 tiles) one time.
Note
Warp-level Operation
Note that all TensorCore instructions are warp-level instructions, which means all 32 threads in a warp should do this instruction simultaneously. Making threadIdx.x extent=32 is one of the easiest way to solve this. Then We can bind threadIdx.x to any loops except those contain TensorCore intrinsics directly or indirectly. Also note that it is not the unique solution. The only thing we should do is to make sure all threads in a warp can call TensorCore at the same time.
# Define tiling sizes
block_row_warps = 4
block_col_warps = 2
warp_row_tiles = 2
warp_col_tiles = 4
warp_size = 32
chunk = 2
block_x = te.thread_axis("blockIdx.x")
block_y = te.thread_axis("blockIdx.y")
block_z = te.thread_axis("blockIdx.z")
thread_x = te.thread_axis("threadIdx.x")
thread_y = te.thread_axis("threadIdx.y")
thread_z = te.thread_axis("threadIdx.z")
nc, hc, wc, oc, nnc, ooc = Conv.op.axis
block_k = s[Conv].fuse(hc, wc)
s[Conv].bind(block_k, block_z)
nc, nci = s[Conv].split(nc, factor=warp_row_tiles)
block_i, nc = s[Conv].split(nc, factor=block_row_warps)
oc, oci = s[Conv].split(oc, factor=warp_col_tiles)
block_j, oc = s[Conv].split(oc, factor=block_col_warps)
s[Conv].reorder(block_k, block_i, block_j, nc, oc, nci, oci, nnc, ooc)
s[Conv].bind(block_i, block_x)
s[Conv].bind(block_j, block_y)
s[Conv].bind(nc, thread_y)
s[Conv].bind(oc, thread_z)
# Schedule local computation
s[ConvF].compute_at(s[Conv], oc)
n, h, w, o, nnf, oof = ConvF.op.axis
ko, ki = s[ConvF].split(ic, factor=chunk)
s[ConvF].reorder(ko, kh, ki, kw, n, o, nnf, oof, ii)
# Move intermediate computation into each output compute tile
s[AF].compute_at(s[ConvF], kw)
s[WF].compute_at(s[ConvF], kw)
# Schedule for A's share memory
s[AS].compute_at(s[ConvF], kh)
n, h, w, i, nn, ii = AS.op.axis
tx, xo = s[AS].split(n, nparts=block_row_warps)
ty, yo = s[AS].split(xo, nparts=block_col_warps)
t = s[AS].fuse(nn, ii)
to, ti = s[AS].split(t, factor=warp_size)
s[AS].bind(tx, thread_y)
s[AS].bind(ty, thread_z)
s[AS].bind(ti, thread_x)
# Schedule for W's share memory
s[WS].compute_at(s[ConvF], kh)
kh, kw, ic, o, ii, oo = WS.op.axis
tx, xo = s[WS].split(o, nparts=block_row_warps)
ty, yo = s[WS].split(xo, nparts=block_col_warps)
t = s[WS].fuse(ii, oo)
to, ti = s[WS].split(t, nparts=warp_size)
s[WS].bind(tx, thread_y)
s[WS].bind(ty, thread_z)
s[WS].bind(to, thread_x)
s[WS].vectorize(ti)
print(tvm.lower(s, [A, W, Conv], simple_mode=True))
# from tvm.script import ir as I
# from tvm.script import tir as T
@I.ir_module
class Module:
@T.prim_func
def main(A: T.Buffer((16, 14, 14, 16, 16, 16), "float16"), W: T.Buffer((3, 3, 16, 32, 16, 16), "float16"), Conv: T.Buffer((16, 14, 14, 32, 16, 16), "float32")):
T.func_attr({"from_legacy_te_schedule": T.bool(True), "global_symbol": "main", "tir.noalias": T.bool(True)})
blockIdx_z = T.launch_thread("blockIdx.z", 196)
Conv_wmma_accumulator = T.allocate([2048], "float32", "wmma.accumulator")
Apad_shared = T.allocate([12288], "float16", "shared")
W_shared = T.allocate([12288], "float16", "shared")
Apad_shared_wmma_matrix_a = T.allocate([512], "float16", "wmma.matrix_a")
W_shared_wmma_matrix_b = T.allocate([1024], "float16", "wmma.matrix_b")
blockIdx_x = T.launch_thread("blockIdx.x", 2)
blockIdx_y = T.launch_thread("blockIdx.y", 4)
threadIdx_y = T.launch_thread("threadIdx.y", 4)
threadIdx_z = T.launch_thread("threadIdx.z", 2)
Conv_wmma_accumulator_1 = T.Buffer((2048,), data=Conv_wmma_accumulator, scope="wmma.accumulator")
for n_c_init, o_c_init, nn_c_init, oo_c_init in T.grid(2, 4, 16, 16):
Conv_wmma_accumulator_1[n_c_init * 1024 + o_c_init * 256 + nn_c_init * 16 + oo_c_init] = T.float32(0)
for ic_outer, kh in T.grid(8, 3):
threadIdx_x = T.env_thread("threadIdx.x")
Apad_shared_1 = T.Buffer((12288,), "float16", data=Apad_shared, scope="shared")
for ax2, ax3, ax4_ax5_fused_outer in T.grid(3, 2, 8):
cse_var_2: T.int32 = ax3 * 256
cse_var_1: T.int32 = ax4_ax5_fused_outer * 32
T.launch_thread(threadIdx_x, 32)
A_1 = T.Buffer((12845056,), "float16", data=A.data)
Apad_shared_1[threadIdx_y * 3072 + threadIdx_z * 1536 + ax2 * 512 + cse_var_2 + cse_var_1 + threadIdx_x] = T.if_then_else(1 <= blockIdx_z // 14 + kh and blockIdx_z // 14 + kh < 15 and 1 <= ax2 + blockIdx_z % 14 and ax2 + blockIdx_z % 14 < 15, A_1[blockIdx_x * 6422528 + threadIdx_y * 1605632 + threadIdx_z * 802816 + kh * 57344 + blockIdx_z * 4096 + ax2 * 4096 + ic_outer * 512 + cse_var_2 + cse_var_1 + threadIdx_x - 61440], T.float16(0))
W_shared_1 = T.Buffer((12288,), "float16", data=W_shared, scope="shared")
for ax1, ax2 in T.grid(3, 2):
T.launch_thread(threadIdx_x, 32)
W_1 = T.Buffer((1179648,), "float16", data=W.data)
W_shared_1[ax1 * 4096 + ax2 * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8:ax1 * 4096 + ax2 * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8 + 8] = W_1[kh * 393216 + ax1 * 131072 + ic_outer * 16384 + ax2 * 8192 + blockIdx_y * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8:kh * 393216 + ax1 * 131072 + ic_outer * 16384 + ax2 * 8192 + blockIdx_y * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8 + 8]
for ic_inner, kw in T.grid(2, 3):
Apad_shared_wmma_matrix_a_1 = T.Buffer((512,), "float16", data=Apad_shared_wmma_matrix_a, scope="wmma.matrix_a")
for ax0, ax4, ax5 in T.grid(2, 16, 16):
cse_var_3: T.int32 = ax4 * 16
Apad_shared_wmma_matrix_a_1[ax0 * 256 + cse_var_3 + ax5] = Apad_shared_1[threadIdx_y * 3072 + ax0 * 1536 + kw * 512 + ic_inner * 256 + cse_var_3 + ax5]
W_shared_wmma_matrix_b_1 = T.Buffer((1024,), "float16", data=W_shared_wmma_matrix_b, scope="wmma.matrix_b")
for ax3, ax4, ax5 in T.grid(4, 16, 16):
cse_var_5: T.int32 = ax3 * 256
cse_var_4: T.int32 = ax4 * 16
W_shared_wmma_matrix_b_1[cse_var_5 + cse_var_4 + ax5] = W_shared_1[kw * 4096 + ic_inner * 2048 + threadIdx_z * 1024 + cse_var_5 + cse_var_4 + ax5]
for n_c, o_c, nn_c, oo_c, ii in T.grid(2, 4, 16, 16, 16):
cse_var_8: T.int32 = o_c * 256
cse_var_7: T.int32 = nn_c * 16
cse_var_6: T.int32 = n_c * 1024 + cse_var_8 + cse_var_7 + oo_c
Conv_wmma_accumulator_1[cse_var_6] = Conv_wmma_accumulator_1[cse_var_6] + T.Cast("float32", Apad_shared_wmma_matrix_a_1[n_c * 256 + cse_var_7 + ii]) * T.Cast("float32", W_shared_wmma_matrix_b_1[cse_var_8 + ii * 16 + oo_c])
for n_inner, o_inner, nn, oo in T.grid(2, 4, 16, 16):
cse_var_10: T.int32 = o_inner * 256
cse_var_9: T.int32 = nn * 16
Conv_1 = T.Buffer((25690112,), data=Conv.data)
Conv_1[blockIdx_x * 12845056 + threadIdx_y * 3211264 + n_inner * 1605632 + blockIdx_z * 8192 + blockIdx_y * 2048 + threadIdx_z * 1024 + cse_var_10 + cse_var_9 + oo] = Conv_wmma_accumulator_1[n_inner * 1024 + cse_var_10 + cse_var_9 + oo]
Lowering Computation to Intrinsics¶
The last phase is to lower the computation loops down to TensorCore hardware intrinsics by mapping the 2D convolution to tensor intrinsics
# from tvm.script import ir as I
# from tvm.script import tir as T
@I.ir_module
class Module:
@T.prim_func
def main(A: T.Buffer((16, 14, 14, 16, 16, 16), "float16"), W: T.Buffer((3, 3, 16, 32, 16, 16), "float16"), Conv: T.Buffer((16, 14, 14, 32, 16, 16), "float32")):
T.func_attr({"from_legacy_te_schedule": T.bool(True), "global_symbol": "main", "tir.noalias": T.bool(True)})
blockIdx_z = T.launch_thread("blockIdx.z", 196)
Conv_wmma_accumulator = T.allocate([2048], "float32", "wmma.accumulator")
Apad_shared = T.allocate([12288], "float16", "shared")
W_shared = T.allocate([12288], "float16", "shared")
Apad_shared_wmma_matrix_a = T.allocate([512], "float16", "wmma.matrix_a")
W_shared_wmma_matrix_b = T.allocate([1024], "float16", "wmma.matrix_b")
blockIdx_x = T.launch_thread("blockIdx.x", 2)
blockIdx_y = T.launch_thread("blockIdx.y", 4)
threadIdx_y = T.launch_thread("threadIdx.y", 4)
threadIdx_z = T.launch_thread("threadIdx.z", 2)
for n_c_init, o_c_init in T.grid(2, 4):
T.tvm_fill_fragment(Conv_wmma_accumulator, 16, 16, 16, n_c_init * 4 + o_c_init, T.float32(0))
for ic_outer, kh in T.grid(8, 3):
threadIdx_x = T.env_thread("threadIdx.x")
for ax2, ax3, ax4_ax5_fused_outer in T.grid(3, 2, 8):
cse_var_2: T.int32 = ax3 * 256
cse_var_1: T.int32 = ax4_ax5_fused_outer * 32
T.launch_thread(threadIdx_x, 32)
Apad_shared_1 = T.Buffer((12288,), "float16", data=Apad_shared, scope="shared")
A_1 = T.Buffer((12845056,), "float16", data=A.data)
Apad_shared_1[threadIdx_y * 3072 + threadIdx_z * 1536 + ax2 * 512 + cse_var_2 + cse_var_1 + threadIdx_x] = T.if_then_else(1 <= blockIdx_z // 14 + kh and blockIdx_z // 14 + kh < 15 and 1 <= ax2 + blockIdx_z % 14 and ax2 + blockIdx_z % 14 < 15, A_1[blockIdx_x * 6422528 + threadIdx_y * 1605632 + threadIdx_z * 802816 + kh * 57344 + blockIdx_z * 4096 + ax2 * 4096 + ic_outer * 512 + cse_var_2 + cse_var_1 + threadIdx_x - 61440], T.float16(0))
for ax1, ax2 in T.grid(3, 2):
T.launch_thread(threadIdx_x, 32)
W_shared_1 = T.Buffer((12288,), "float16", data=W_shared, scope="shared")
W_1 = T.Buffer((1179648,), "float16", data=W.data)
W_shared_1[ax1 * 4096 + ax2 * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8:ax1 * 4096 + ax2 * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8 + 8] = W_1[kh * 393216 + ax1 * 131072 + ic_outer * 16384 + ax2 * 8192 + blockIdx_y * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8:kh * 393216 + ax1 * 131072 + ic_outer * 16384 + ax2 * 8192 + blockIdx_y * 2048 + threadIdx_y * 512 + threadIdx_z * 256 + threadIdx_x * 8 + 8]
for ic_inner, kw in T.grid(2, 3):
for ax0 in range(2):
T.tvm_load_matrix_sync(Apad_shared_wmma_matrix_a, 16, 16, 16, ax0, T.tvm_access_ptr(T.type_annotation("float16"), Apad_shared, threadIdx_y * 3072 + ax0 * 1536 + kw * 512 + ic_inner * 256, 256, 1), 16, "row_major")
for ax3 in range(4):
T.tvm_load_matrix_sync(W_shared_wmma_matrix_b, 16, 16, 16, ax3, T.tvm_access_ptr(T.type_annotation("float16"), W_shared, kw * 4096 + ic_inner * 2048 + threadIdx_z * 1024 + ax3 * 256, 256, 1), 16, "row_major")
for n_c, o_c in T.grid(2, 4):
cse_var_3: T.int32 = n_c * 4 + o_c
T.tvm_mma_sync(Conv_wmma_accumulator, cse_var_3, Apad_shared_wmma_matrix_a, n_c, W_shared_wmma_matrix_b, o_c, Conv_wmma_accumulator, cse_var_3)
for n_inner, o_inner in T.grid(2, 4):
T.tvm_store_matrix_sync(Conv_wmma_accumulator, 16, 16, 16, n_inner * 4 + o_inner, T.tvm_access_ptr(T.type_annotation("float32"), Conv.data, blockIdx_x * 12845056 + threadIdx_y * 3211264 + n_inner * 1605632 + blockIdx_z * 8192 + blockIdx_y * 2048 + threadIdx_z * 1024 + o_inner * 256, 256, 2), 16, "row_major")
Generate CUDA Kernel¶
Finally we use TVM to generate and compile the CUDA kernel, and evaluate the latency of convolution. Since TensorCores are only supported in NVIDIA GPU with Compute Capability 7.0 or higher, it may not be able to run on our build server
dev = tvm.cuda(0)
if nvcc.have_tensorcore(dev.compute_version):
with tvm.transform.PassContext(config={"tir.UnrollLoop": {"auto_max_step": 16}}):
func = tvm.build(s, [A, W, Conv], "cuda")
a_np = np.random.uniform(size=data_shape).astype(A.dtype)
w_np = np.random.uniform(size=kernel_shape).astype(W.dtype)
a = tvm.nd.array(a_np, dev)
w = tvm.nd.array(w_np, dev)
c = tvm.nd.array(np.zeros(output_shape, dtype=Conv.dtype), dev)
evaluator = func.time_evaluator(func.entry_name, dev, number=10)
print("conv2d with tensor core: %f ms" % (evaluator(a, w, c).mean * 1e3))
conv2d with tensor core: 11.861699 ms
Summary¶
This tutorial demonstrates how TVM scheduling primitives can be used to call TensorCores on specific GPUs.