使用Auto TensorCore CodeGen优化Matmul
本文将演示如何使用TVM Auto TensorCore CodeGen在Volta / Turing GPU上编写高性能matmul调度。这是一个生成tensorcore内核的解决方案，其中大多数转换都是通过ir传递完成的。用户还可以编写带有张量的调度，生成TensorCore代码。两种解决方案都使用相同的tensorcore内部函数。有关更多详细信息，请参阅如何使用TensorCores优化卷积。
准备和算法
支持两种输入数据类型：float16和int8。对于float16，累加器为float32。对于int8，累加器为int32。对于数据布局，“ N”表示无转置，而“ T”表示转置。
import logging
import sys

import numpy as np
import tvm
from tvm import te

from tvm import autotvm
from tvm.contrib import nvcc

def matmul_nn(A, B, L, dtype=“float16”, layout=“NN”):
k = te.reduce_axis((0, L), name=“k”)
if dtype == “float16”:
out_type = “float”
elif dtype == “int8”:
out_type = “int”
elif dtype == “int4” or dtype == “int1”:
out_type = “int”
if layout == “NN”:
return te.compute(
(N, M), lambda i, j: te.sum(A[i, k].astype(out_type) * B[k, j].astype(out_type), axis=k)
)
if layout == “NT”:
return te.compute(
(N, M), lambda i, j: te.sum(A[k, i].astype(out_type) * B[k, j].astype(out_type), axis=k)
)
if layout == “TN”:
return te.compute(
(N, M), lambda i, j: te.sum(A[i, k].astype(out_type) * B[j, k].astype(out_type), axis=k)
)
if layout == “TT”:
return te.compute(
(N, M), lambda i, j: te.sum(A[k, i].astype(out_type) * B[j, k].astype(out_type), axis=k)
)
调度计算
此调度与GPU上的非张量内核Matmul调度没有什么不同。请参阅如何优化CPU上的GEMM文档，以了解优化调度的基础。设置“ tensor_core”编译指示时，“为tensorcore重写” ir传递pass，将自动转换tensorcore代码生成调度，否则将生成性能较低但功能相同的普通CUDA代码。
TesnsorCore的要求
请注意，在以下两种情况下，即使设置了“ tensor_core”编译指示，TVM仍将退回到正常的CUDA代码源：（1）输入矩阵的m，n或k并非16的倍数；（2）在CUDA9上，warp块大小不是16x16x16，或者在CUDA版本> = 10.0上不是{16x16x16、32x8x16、8x32x16}之一。
在此调度中，storage_align用于减少共享内存的存储区冲突。请参考此文档以了解storage_align原语的用法。需要为某些共享内存缓冲区添加偏移量以减少存储区冲突。根据wmma doc，load_matrix_sync的步幅必须是16字节的倍数，选择8作为float16的偏移量，选择16作为int8的偏移量。
使用AutoTVM在此时间表中搜索最佳配置。
@autotvm.template(“tutorial/auto_tensorcore/test_gemm”)
def test_gemm(N, L, M, dtype, layout):
if layout == “NN”:
shape_a = (N, L)
shape_b = (L, M)
elif layout == “NT”:
shape_a = (L, N)
shape_b = (L, M)
elif layout == “TN”:
shape_a = (N, L)
shape_b = (M, L)
elif layout == “TT”:
shape_a = (L, N)
shape_b = (M, L)
else:
print(“Unsupported layout:”, layout)
sys.exit(1)
A = te.placeholder(shape_a, name=“A”, dtype=dtype)
B = te.placeholder(shape_b, name=“B”, dtype=dtype)
C = matmul_nn(A, B, L, dtype, layout)

s = te.create_schedule(C.op)
y, x = s[C].op.axis
k = s[C].op.reduce_axis[0]# storage_align params
factor = 16
offset = 8
if dtype == "int8":factor = 32offset = 16
elif dtype == "int4":factor = 64offset = 32
elif dtype == "int1":factor = 256offset = 128# create cache stages
AA = s.cache_read(A, "shared", [C])
if layout == "NN" or layout == "TN":s[AA].storage_align(AA.op.axis[0], factor, offset)
AL = s.cache_read(AA, "local", [C])
BB = s.cache_read(B, "shared", [C])
if layout == "TT" or layout == "NT":s[BB].storage_align(BB.op.axis[0], factor, offset)
BL = s.cache_read(BB, "local", [C])
CL = s.cache_write(C, "local")# autotvm search space definition
cfg = autotvm.get_config()cfg.define_knob("bx", [2, 4, 8])
cfg.define_knob("by", [8, 16, 32, 64])
cfg.define_knob("step_k", [1, 2, 4, 8, 16, 32])
cfg.define_knob("v", [4, 8, 16, 32])
by = cfg["by"].val
bx = cfg["bx"].val
step_k = cfg["step_k"].val
v = cfg["v"].val# thread tile
TX = 8
TY = 1
if dtype == "int4" or dtype == "int1":TX = 2
# warp tile
warp_tile_m = 16  # it could also be 8 or 32 on CUDA version >= 10.0
warp_tile_k = 16  # it must be 16 for fp16/int8 data type
if dtype == "int4":warp_tile_m = 8warp_tile_k = 32
elif dtype == "int1":warp_tile_m = 8warp_tile_k = 128
# block tile
tile_x = bx * TX
tile_y = by * TYyo, ty = s[C].split(y, tile_y)
ty, yi = s[C].split(ty, TY)# schedule for C stage
xo, xi = s[C].split(x, tile_x)
WX = min(warp_tile_m, tile_x)
tz, xi = s[C].split(xi, WX)
tx, xi = s[C].split(xi, TX)
s[C].reorder(yo, xo, tz, ty, tx, yi, xi)
s[C].bind(yo, te.thread_axis("blockIdx.y"))
s[C].bind(xo, te.thread_axis("blockIdx.x"))
s[C].bind(ty, te.thread_axis("threadIdx.y"))
s[C].bind(tz, te.thread_axis("threadIdx.z"))
s[C].bind(tx, te.thread_axis("threadIdx.x"))# schedule for CL stage
ko, ki = s[CL].split(k, step_k * warp_tile_k)
kl, ki = s[CL].split(ki, warp_tile_k)
s[CL].compute_at(s[C], tx)
yo, xo = CL.op.axis
s[CL].reorder(ko, kl, ki, yo, xo)# schedule for AA stage
s[AA].compute_at(s[CL], ko)
xo, xi = s[AA].split(s[AA].op.axis[1], factor=bx * v)
tz, tx = s[AA].split(xi, factor=(WX // TX) * v)
tx, vec = s[AA].split(tx, factor=v)
fused = s[AA].fuse(s[AA].op.axis[0], xo)
_, ty = s[AA].split(fused, factor=by)
s[AA].bind(ty, te.thread_axis("threadIdx.y"))
s[AA].bind(tz, te.thread_axis("threadIdx.z"))
s[AA].bind(tx, te.thread_axis("threadIdx.x"))
# vectorization is very important for float16/int8 inputs
s[AA].vectorize(vec)# schedule for BB stage
s[BB].compute_at(s[CL], ko)
xo, xi = s[BB].split(s[BB].op.axis[1], factor=bx * v)
tz, tx = s[BB].split(xi, factor=(WX // TX) * v)
tx, vec = s[BB].split(tx, factor=v)
fused = s[BB].fuse(s[BB].op.axis[0], xo)
_, ty = s[BB].split(fused, factor=by)
s[BB].bind(ty, te.thread_axis("threadIdx.y"))
s[BB].bind(tz, te.thread_axis("threadIdx.z"))
s[BB].bind(tx, te.thread_axis("threadIdx.x"))
s[BB].vectorize(vec)s[AL].compute_at(s[CL], kl)
s[BL].compute_at(s[CL], kl)# set the 'tensor_core' pragma for tensorcore codegen
s[CL].pragma(ko, "tensor_core")return s, [A, B, C]

自动调谐和测试AutoTune and Test
使用调谐器来调整调度，使用最佳配置生成代码，运行内核与numpy进行比较，以检查结果是否正确。

check whether the gpu has tensorcore

if not tvm.gpu(0).exist or not tvm.runtime.enabled(“cuda”):
raise Exception(“skip building this tutorial because cuda is not enabled…”)

ctx = tvm.gpu()
if not nvcc.have_tensorcore(ctx.compute_version):
raise Exception(“the gpu has no tensorcore, skipping…”)

M, N, L = 512, 32, 512
dtype = “float16”
layout = “NN”
if len(sys.argv) >= 4:
M, N, L = int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])
if len(sys.argv) >= 5:
dtype = sys.argv[4]
if len(sys.argv) >= 6:
layout = sys.argv[5]

check whether current gpu arch support support current dtype’s wmma codegen

cuda_compute_capability = tvm.runtime._ffi_api.GetDeviceAttr(2, 0, 4)
major, minor = nvcc.parse_compute_version(cuda_compute_capability)
if dtype == “int8”:
assert major == 7 and minor >= 2
elif dtype == “int4” or dtype == “int1”:
# int4/int1 only support layout TN
assert major == 7 and minor == 5 and layout == “TN”

def tune_and_evaluate(M, N, L, dtype, layout):
task = autotvm.task.create(
“tutorial/auto_tensorcore/test_gemm”, args=(N, L, M, dtype, layout), target=“cuda”
)
print(task.config_space)

logging.getLogger("autotvm").setLevel(logging.DEBUG)
logging.getLogger("autotvm").addHandler(logging.StreamHandler(sys.stdout))measure_option = autotvm.measure_option(builder="local", runner=autotvm.LocalRunner(number=5))tuner = autotvm.tuner.XGBTuner(task)
tuner.tune(n_trial=1000,measure_option=measure_option,callbacks=[autotvm.callback.log_to_file("matmul.log")],
)dispatch_context = autotvm.apply_history_best("matmul.log")
best_config = dispatch_context.query(task.target, task.workload)
print("\nBest config:")
print(best_config)
with autotvm.apply_history_best("matmul.log"):with tvm.target.Target("cuda"):s, arg_bufs = test_gemm(N, L, M, dtype, layout)print(tvm.lower(s, arg_bufs, simple_mode=True))func = tvm.build(s, arg_bufs)
dev_module = func.imported_modules[0]
print(dev_module.get_source())# check correctness
if layout == "NN":shape_a = (N, L)shape_b = (L, M)
elif layout == "NT":shape_a = (L, N)shape_b = (L, M)
elif layout == "TN":shape_a = (N, L)shape_b = (M, L)
elif layout == "TT":shape_a = (L, N)shape_b = (M, L)a_np = None
b_np = None
c_np = None
c_np_type = None
if dtype == "float16":c_np_type = np.float32a_np = np.random.uniform(size=shape_a).astype(np.float16)b_np = np.random.uniform(size=shape_b).astype(np.float16)if layout == "NN":c_np = np.dot(a_np, b_np)elif layout == "NT":c_np = np.dot(a_np.T, b_np)elif layout == "TN":c_np = np.dot(a_np, b_np.T)elif layout == "TT":c_np = np.dot(a_np.T, b_np.T)
elif dtype == "int8":c_np_type = np.int32a_np = np.random.randint(low=-128, high=127, size=shape_a).astype(np.int8)b_np = np.random.randint(low=-128, high=127, size=shape_b).astype(np.int8)if layout == "NN":c_np = np.dot(a_np.astype(np.int32), b_np.astype(np.int32))elif layout == "NT":c_np = np.dot(a_np.astype(np.int32).T, b_np.astype(np.int32))elif layout == "TN":c_np = np.dot(a_np.astype(np.int32), b_np.astype(np.int32).T)elif layout == "TT":c_np = np.dot(a_np.astype(np.int32).T, b_np.astype(np.int32).T)
elif dtype == "int4":c_np_type = np.int32a_np_int = np.random.randint(low=-8, high=7, size=shape_a).astype(np.int32)b_np_int = np.random.randint(low=-8, high=7, size=shape_b).astype(np.int32)# "TN"c_np = np.dot(a_np_int.astype(np.int32), b_np_int.astype(np.int32).T)a_np = np.zeros(shape=(N, int(L / 8)), dtype=np.int32)b_np = np.zeros(shape=(M, int(L / 8)), dtype=np.int32)# a_np --> col_majorfor i in range(N):for j in range(int(L / 8)):for k in range(8):a_np[i, j] = a_np[i, j] | ((a_np_int[i, j * 8 + k] & 0xF) << ((7 - k) * 4))# b_np --> row_majorfor i in range(M):for j in range(int(L / 8)):for k in range(8):b_np[i, j] = b_np[i, j] | ((b_np_int[i, j * 8 + k] & 0xF) << ((7 - k) * 4))
elif dtype == "int1":c_np_type = np.int32a_np_int = np.random.randint(low=0, high=1, size=shape_a).astype(np.int32)b_np_int = np.random.randint(low=0, high=1, size=shape_b).astype(np.int32)# "TN"c_np = np.dot(a_np_int.astype(np.int32), b_np_int.astype(np.int32).T)a_np = np.zeros(shape=(N, int(L / 32)), dtype=np.int32)b_np = np.zeros(shape=(M, int(L / 32)), dtype=np.int32)for i in range(N):for j in range(int(L / 32)):for k in range(32):a_np[i, j] = a_np[i, j] | ((a_np_int[i, j * 32 + k] & 0xF) << (31 - k))for i in range(M):for j in range(int(L / 32)):for k in range(32):b_np[i, j] = b_np[i, j] | ((b_np_int[i, j * 32 + k] & 0xF) << (31 - k))c_tvm = tvm.nd.array(np.zeros(c_np.shape, dtype=c_np_type), ctx=ctx)
a_tvm = tvm.nd.array(a_np, ctx=ctx)
b_tvm = tvm.nd.array(b_np, ctx=ctx)
func(a_tvm, b_tvm, c_tvm)tvm.testing.assert_allclose(c_np, c_tvm.asnumpy(), rtol=1e-3)evaluator = func.time_evaluator(func.entry_name, ctx, number=100)
print("Time cost of this operator: %f" % evaluator(a_tvm, b_tvm, c_tvm).mean)

We do not run the tuning in our webpage server since it takes some time.

Uncomment the following line to run it by yourself.

tune_and_evaluate(M, N, L, dtype, layout)

样本输出Sample Output
Best config:
[(‘bx’, 4), (‘by’, 32), (‘step_k’, 16), (‘v’, 8)],None,40
Finish loading 162 records
produce compute {
// attr [iter_var(blockIdx.y, , blockIdx.y)] thread_extent = 1
// attr [compute.local] storage_scope = “wmma.accumulator”
allocate compute.local[float32 * 256]
// attr [A.shared] storage_scope = “shared”
allocate A.shared[float16 * 8448]
// attr [B.shared] storage_scope = “shared”
allocate B.shared[float16 * 8192]
// attr [A.shared.local] storage_scope = “wmma.matrix_b”
allocate A.shared.local[float16 * 256]
// attr [B.shared.local] storage_scope = “wmma.matrix_a”
allocate B.shared.local[float16 * 256]
// attr [iter_var(blockIdx.x, , blockIdx.x)] thread_extent = 16
// attr [iter_var(threadIdx.z, , threadIdx.z)] thread_extent = 2
// attr [iter_var(threadIdx.y, , threadIdx.y)] thread_extent = 32
// attr [iter_var(threadIdx.x, , threadIdx.x)] thread_extent = 2
produce compute.local {
for (j.c.init, 0, 1) {
tvm_fill_fragment(compute.local, 16, 16, 16, 0, 0f)
}
// attr [iter_var(k.outer, )] pragma_tensor_core = 1
for (k.outer, 0, 2) {
produce A.shared {
for (ax0.ax1.outer.fused.outer, 0, 8) {
// attr [iter_var(threadIdx.y, , threadIdx.y)] thread_extent = 32
// attr [iter_var(threadIdx.z, , threadIdx.z)] thread_extent = 2
// attr [iter_var(threadIdx.x, , threadIdx.x)] thread_extent = 2
A.shared[ramp((((((ax0.ax1.outer.fused.outer1056) + (floordiv(threadIdx.y, 8)264)) + (floormod(threadIdx.y, 8)32)) + (threadIdx.z16)) + (threadIdx.x8)), 1, 8)] = A[ramp(((((((ax0.ax1.outer.fused.outer2048) + (floordiv(threadIdx.y, 8)512)) + (k.outer256)) + (floormod(threadIdx.y, 8)32)) + (threadIdx.z16)) + (threadIdx.x8)), 1, 8)]
}
}
produce B.shared {
for (ax0.ax1.outer.fused.outer, 0, 8) {
// attr [iter_var(threadIdx.y, , threadIdx.y)] thread_extent = 32
// attr [iter_var(threadIdx.z, , threadIdx.z)] thread_extent = 2
// attr [iter_var(threadIdx.x, , threadIdx.x)] thread_extent = 2
B.shared[ramp(((((ax0.ax1.outer.fused.outer1024) + (threadIdx.y32)) + (threadIdx.z16)) + (threadIdx.x8)), 1, 8)] = B[ramp(((((((k.outer131072) + (ax0.ax1.outer.fused.outer16384)) + (threadIdx.y512)) + (blockIdx.x32)) + (threadIdx.z16)) + (threadIdx.x8)), 1, 8)]
}
}
for (k.inner.outer, 0, 16) {
produce A.shared.local {
for (ax1, 0, 1) {
tvm_load_matrix_sync(A.shared.local, 16, 16, 16, 0, &(A.shared[(((threadIdx.y/16)4224) + (k.inner.outer16))]), 264, “col_major”)
}
}
produce B.shared.local {
for (ax0, 0, 1) {
for (ax1, 0, 1) {
tvm_load_matrix_sync(B.shared.local, 16, 16, 16, 0, &(B.shared[((k.inner.outer512) + (threadIdx.z16))]), 32, “col_major”)
}
}
}
for (k.inner.inner, 0, 1) {
for (j.c, 0, 1) {
tvm_mma_sync(compute.local, 0, B.shared.local, 0, A.shared.local, 0, compute.local, 0)
}
}
}
}
}
for (j.inner.inner.inner, 0, 1) {
tvm_store_matrix_sync(compute.local, 16, 16, 16, 0, &(compute[((((threadIdx.y/16)8192) + (blockIdx.x32)) + (threadIdx.z16))]), 512, “col_major”)
}
}

#include <cuda_fp16.h>
device half max(const half a, const half b)
{
return __hgt(__half(a), __half(b)) ? a : b;
}
device half min(const half a, const half b)
{
return __hlt(__half(a), __half(b)) ? a : b;
}
device half operator+(const volatile __half &a, const volatile __half &b)
{
return __hadd(a, b);
}
device half operator<=(const volatile __half &a, const volatile __half &b)
{
return __hlt(a, b);
}
device half operator*(const volatile __half &a, const volatile __half &b)
{
return __hmul(a, b);
}
#include <mma.h>
extern “C” global void default_function_kernel0( half* restrict A, half* restrict B, float* restrict compute) {
nvcuda::wmma::fragment<nvcuda::wmma::accumulator, 16, 16, 16, float> compute_local[1];
shared half A_shared[8448];
shared half B_shared[8192];
nvcuda::wmma::fragment<nvcuda::wmma::matrix_b, 16, 16, 16, half, nvcuda::wmma::col_major> A_shared_local[1];
nvcuda::wmma::fragment<nvcuda::wmma::matrix_a, 16, 16, 16, half, nvcuda::wmma::col_major> B_shared_local[1];
for (int j_c_init = 0; j_c_init < 1; ++j_c_init) {
(void)nvcuda::wmma::fill_fragment(compute_local[0], 0.000000e+00f);
}
for (int k_outer = 0; k_outer < 2; ++k_outer) {
__syncthreads();
for (int ax0_ax1_outer_fused_outer = 0; ax0_ax1_outer_fused_outer < 8; ++ax0_ax1_outer_fused_outer) {
((shared float4*)(A_shared + (((((ax0_ax1_outer_fused_outer * 1056) + ((((int)threadIdx.y) >> 3) * 264)) + ((((int)threadIdx.y) & 7) * 32)) + (((int)threadIdx.z) * 16)) + (((int)threadIdx.x) * 8))))[0] = (( float4*)(A + ((((((ax0_ax1_outer_fused_outer * 2048) + ((((int)threadIdx.y) >> 3) * 512)) + (k_outer * 256)) + ((((int)threadIdx.y) & 7) * 32)) + (((int)threadIdx.z) * 16)) + (((int)threadIdx.x) * 8))))[0];
}
for (int ax0_ax1_outer_fused_outer1 = 0; ax0_ax1_outer_fused_outer1 < 8; ++ax0_ax1_outer_fused_outer1) {
((shared float4*)(B_shared + ((((ax0_ax1_outer_fused_outer1 * 1024) + (((int)threadIdx.y) * 32)) + (((int)threadIdx.z) * 16)) + (((int)threadIdx.x) * 8))))[0] = (( float4*)(B + ((((((k_outer * 131072) + (ax0_ax1_outer_fused_outer1 * 16384)) + (((int)threadIdx.y) * 512)) + (((int)blockIdx.x) * 32)) + (((int)threadIdx.z) * 16)) + (((int)threadIdx.x) * 8))))[0];
}
__syncthreads();
for (int k_inner_outer = 0; k_inner_outer < 16; ++k_inner_outer) {
for (int ax1 = 0; ax1 < 1; ++ax1) {
(void)nvcuda::wmma::load_matrix_sync(A_shared_local[0], &(A_shared[(((((int)threadIdx.y) / 16) * 4224) + (k_inner_outer * 16))]), 264);
}
for (int ax0 = 0; ax0 < 1; ++ax0) {
for (int ax11 = 0; ax11 < 1; ++ax11) {
(void)nvcuda::wmma::load_matrix_sync(B_shared_local[0], &(B_shared[((k_inner_outer * 512) + (((int)threadIdx.z) * 16))]), 32);
}
}
for (int k_inner_inner = 0; k_inner_inner < 1; ++k_inner_inner) {
for (int j_c = 0; j_c < 1; ++j_c) {
(void)nvcuda::wmma::mma_sync(compute_local[0], B_shared_local[0], A_shared_local[0], compute_local[0]);
}
}
}
}
for (int j_inner_inner_inner = 0; j_inner_inner_inner < 1; ++j_inner_inner_inner) {
(void)nvcuda::wmma::store_matrix_sync(&(compute[((((((int)threadIdx.y) / 16) * 8192) + (((int)blockIdx.x) * 32)) + (((int)threadIdx.z) * 16))]), compute_local[0], 512, nvcuda::wmma::mem_col_major);
}
}

Time cost of this operator: 0.000008
摘要
本文演示了如何使用TVM的AutoTensorCoreCodeGen生成tensorcore内核。
https://tvm.apache.org/docs/tutorials/optimize/opt_matmul_auto_tensorcore.html#sphx-glr-tutorials-optimize-opt-matmul-auto-tensorcore-py

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