如何在GPU上优化卷积
本文将演示如何在TVM中编写高性能的卷积实现。以平方大小的输入张量和滤波器为例，并假设卷积的输入量很大。使用不同的布局来存储数据，以实现更好的数据局部性。缓冲区布局为HWCN，代表高度，宽度，通道，批次。
准备和算法
将固定大小用于256通道和14 x 14尺寸的输入张量。批处理大小为256。卷积过滤器包含512个大小为3 x 3的过滤器。对于卷积，使用步幅大小1和填充大小1。以下代码定义了TVM中的卷积算法。
import numpy as np
import tvm
from tvm import te
# The sizes of inputs and filters
batch = 256
in_channel = 256
out_channel = 512
in_size = 14
kernel = 3
pad = 1
stride = 1
# Algorithm
A = te.placeholder((in_size, in_size, in_channel, batch), name="A")
W = te.placeholder((kernel, kernel, in_channel, out_channel), name="W")
out_size = (in_size - kernel + 2 * pad) // stride + 1
# Pad input
Apad = te.compute(
(in_size + 2 * pad, in_size + 2 * pad, in_channel, batch),
lambda yy, xx, cc, nn: tvm.tir.if_then_else(
tvm.tir.all(yy >= pad, yy - pad < in_size, xx >= pad, xx - pad < in_size),
A[yy - pad, xx - pad, cc, nn],
tvm.tir.const(0.0, "float32"),
),
name="Apad",
)
# Create reduction variables
rc = te.reduce_axis((0, in_channel), name="rc")
ry = te.reduce_axis((0, kernel), name="ry")
rx = te.reduce_axis((0, kernel), name="rx")
# Compute the convolution
B = te.compute(
(out_size, out_size, out_channel, batch),
lambda yy, xx, ff, nn: te.sum(
Apad[yy * stride + ry, xx * stride + rx, rc, nn] * W[ry, rx, rc, ff], axis=[ry, rx, rc]
),
name="B",
)
存储层级
首先指定缓冲区的内存层次结构。下图显示了GPU内存层次结构。与CPU内存层次结构的一个重要区别是，GPU提供了一个称为共享内存的缓存缓冲区，该缓冲区由程序员管理。如何最大化共享内存中的数据重用，对于在GPU内核中实现高性能至关重要。
将Apad和W都加载到缓冲区AA和WW中，将它们存储在共享内存中。这些缓冲区稍后将由同一线程块内的所有线程共享，以计算卷积。然后，每个线程将自己的部分从共享缓冲区加载到其本地寄存器AL和WL中。BL是输出B的本地缓存，它也存储在线程本地寄存器中。
# Designate the memory hierarchy
s = te.create_schedule(B.op)
s[Apad].compute_inline() # compute Apad inline
AA = s.cache_read(Apad, "shared", [B])
WW = s.cache_read(W, "shared", [B])
AL = s.cache_read(AA, "local", [B])
WL = s.cache_read(WW, "local", [B])
BL = s.cache_write(B, "local")
阻塞Blocking
以下代码将工作负载分为线程块和单个线程。在矩阵乘法中遵循阻塞方案。如下图所示，给定像素坐标（y，x），线程块负责为输出通道和批处理计算block_factor x block_factor（64 x 64）的区域。由于共享内存空间的限制，每次仅将Apad和B中的step x block_factor（8 x 64）数据加载到共享内存中的缓冲区中。
# tile consts
tile = 8
num_thread = 8
block_factor = tile * num_thread
step = 8
vthread = 2
# Get the GPU thread indices
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((0, num_thread), "threadIdx.x")
thread_y = te.thread_axis((0, num_thread), "threadIdx.y")
thread_xz = te.thread_axis((0, vthread), "vthread", name="vx")
thread_yz = te.thread_axis((0, vthread), "vthread", name="vy")
# Split the workloads
hi, wi, fi, ni = s[B].op.axis
bz = s[B].fuse(hi, wi)
by, fi = s[B].split(fi, factor=block_factor)
bx, ni = s[B].split(ni, factor=block_factor)
# Bind the iteration variables to GPU thread indices
s[B].bind(bz, block_z)
s[B].bind(by, block_y)
s[B].bind(bx, block_x)
虚拟线程分割Virtual Thread Split
将工作负载从线程块划分到各个线程。为避免内存库冲突，使用虚拟线程将区域划分为4个部分，然后平铺为8x8网格。如下图所示，每个线程计算4个网格，每个网格的大小为4 x 4。
tyz, fi = s[B].split(fi, nparts=vthread) # virtual thread split
txz, ni = s[B].split(ni, nparts=vthread) # virtual thread split
ty, fi = s[B].split(fi, nparts=num_thread)
tx, ni = s[B].split(ni, nparts=num_thread)
s[B].reorder(bz, by, bx, tyz, txz, ty, tx, fi, ni)
s[B].bind(tyz, thread_yz)
s[B].bind(txz, thread_xz)
s[B].bind(ty, thread_y)
s[B].bind(tx, thread_x)
协作获取Cooperative Fetching
每个时间步骤都需要将步骤x block_factor数据从GPU全局内存传输到共享内存。为了减少每个线程的内存传输，以下代码使同一线程块中的线程，可以协作地从全局内存中获取相关数据。
# Schedule BL local write
s[BL].compute_at(s[B], tx)
yi, xi, fi, ni = s[BL].op.axis
ry, rx, rc = s[BL].op.reduce_axis
rco, rci = s[BL].split(rc, factor=step)
s[BL].reorder(rco, ry, rx, rci, fi, ni)
# Attach computation to iteration variables
s[AA].compute_at(s[BL], rx)
s[WW].compute_at(s[BL], rx)
s[AL].compute_at(s[BL], rci)
s[WL].compute_at(s[BL], rci)
# Schedule for A's shared memory load
yi, xi, ci, ni = s[AA].op.axis
ty, ci = s[AA].split(ci, nparts=num_thread)
tx, ni = s[AA].split(ni, nparts=num_thread)
_, ni = s[AA].split(ni, factor=4)
s[AA].reorder(ty, tx, yi, xi, ci, ni)
s[AA].bind(ty, thread_y)
s[AA].bind(tx, thread_x)
s[AA].vectorize(ni) # vectorize memory load
# Schedule for W's shared memory load
yi, xi, ci, fi = s[WW].op.axis
ty, ci = s[WW].split(ci, nparts=num_thread)
tx, fi = s[WW].split(fi, nparts=num_thread)
_, fi = s[WW].split(fi, factor=4)
s[WW].reorder(ty, tx, yi, xi, ci, fi)
s[WW].bind(ty, thread_y)
s[WW].bind(tx, thread_x)
s[WW].vectorize(fi) # vectorize memory load
生成CUDA内核
最后，使用TVM生成和编译CUDA内核，并评估卷积的延迟。
func = tvm.build(s, [A, W, B], "cuda")
ctx = tvm.gpu(0)
a_np = np.random.uniform(size=(in_size, in_size, in_channel, batch)).astype(A.dtype)
w_np = np.random.uniform(size=(kernel, kernel, in_channel, out_channel)).astype(W.dtype)
a = tvm.nd.array(a_np, ctx)
w = tvm.nd.array(w_np, ctx)
b = tvm.nd.array(np.zeros((out_size, out_size, out_channel, batch), dtype=B.dtype), ctx)
func(a, w, b)
evaluator = func.time_evaluator(func.entry_name, ctx, number=1)
print("Convolution: %f ms" % (evaluator(a, w, b).mean * 1e3))
出：
Convolution: 53.197723 ms
https://tvm.apache.org/docs/tutorials/optimize/opt_conv_cuda.html#sphx-glr-tutorials-optimize-opt-conv-cuda-py
