即使对于巨型矩阵，NUMBA CUDA 也比并行 CPU 慢

Question

网上只有几个关于使用 cuda 进行 numba 的示例，我发现它们都比并行 CPU 方法慢。 使用 CUDA 目标和模板进行矢量化甚至更糟，所以我尝试创建自定义 kernel。 您到处都能找到的一篇博文是https://gist.github.com/mrocklin/9272bf84a8faffdbbe2cd44b4bc4ce3c 。 这个例子是一个简单的模糊过滤器：

import numpy as np
import time
from numba import njit, prange,cuda
import timeit
import numba.cuda


@numba.cuda.jit
def smooth_gpu(x, out):
    i, j = cuda.grid(2)
    n, m = x.shape

    if 1 <= i < n - 1 and 1 <= j < m - 1:
        out[i, j] = (x[i - 1, j - 1] + x[i - 1, j] + x[i - 1, j + 1] +
                    x[i    , j - 1] + x[i    , j] + x[i    , j + 1] +
                    x[i + 1, j - 1] + x[i + 1, j] + x[i + 1, j + 1]) / 9

x_gpu = np.ones((10000, 10000), dtype='float32')
out_gpu = np.zeros((10000, 10000), dtype='float32')

threadsperblock = (16, 16)
blockspergrid_x = math.ceil(x_gpu.shape[0] / threadsperblock[0])
blockspergrid_y = math.ceil(x_gpu.shape[1] / threadsperblock[1])
blockspergrid = (blockspergrid_x, blockspergrid_y)

# run on gpu
smooth_gpu[blockspergrid, threadsperblock](x_gpu, out_gpu) # compile before measuring time
start_time = time.time()
smooth_gpu[blockspergrid, threadsperblock](x_gpu, out_gpu)
print("GPU Time: {0:1.6f}s ".format(time.time() - start_time))

和 CPU 版本：

x_cpu = np.ones((10000, 10000), dtype='float32')
out_cpu = np.zeros((10000, 10000), dtype='float32')


@njit(nopython=True,parallel=True)
def smooth_cpu(x, out_cpu):

    for i in prange(1,np.shape(x)[0]-1):
        for j in range(1,np.shape(x)[1]-1):
            out_cpu[i, j] =  (x[i - 1, j - 1] + x[i - 1, j] + x[i - 1, j + 1] + x[i    , j - 1] + x[i    , j] + x[i    , j + 1] +x[i + 1, j - 1] + x[i + 1, j] + x[i + 1, j + 1]) / 9

# run on cpu
smooth_cpu(x_cpu, out_cpu) # compile before measuring time
start_time = time.time()
smooth_cpu(x_cpu, out_cpu)
print("CPU Time: {0:1.6f}s ".format(time.time() - start_time))

GPU 版本大约为 500 毫秒，CPU 版本为 50 毫秒。 到底是怎么回事？

Answer 1

我要指出两点：

1. 您在 GPU 版本的时序中包括将输入数组从主机传输到设备所需的时间，以及从设备到主机的结果。 如果这是您比较的目的，那就这样吧； 结论是 GPU 不适合这项任务（以一种有趣的方式）。

2. GPU 代码虽然给出了正确的结果，但并不是为了获得良好的性能而组织起来的。 问题出在这里：

    i, j = cuda.grid(2)

   再加上这些索引用于访问数据的顺序：

    out[i, j] = (x[i - 1, j - 1]...

   这会导致 GPU 的访问效率低下。 我们可以通过颠倒上面描述的两个顺序之一来解决这个问题。

考虑到上述两个问题，以下是您的代码稍作调整：

$ cat t29a.py
import numpy as np
import time
from numba import njit, prange,cuda
import timeit
import numba.cuda


x_cpu = np.ones((10000, 10000), dtype='float32')
out_cpu = np.zeros((10000, 10000), dtype='float32')


@njit(parallel=True)
def smooth_cpu(x, out_cpu):

    for i in prange(1,x.shape[0]-1):
        for j in range(1,x.shape[1]-1):
            out_cpu[i, j] =  (x[i - 1, j - 1] + x[i - 1, j] + x[i - 1, j + 1] + x[i    , j - 1] + x[i    , j] + x[i    , j + 1] +x[i + 1, j - 1] + x[i + 1, j] + x[i + 1, j + 1]) / 9

# run on cpu
smooth_cpu(x_cpu, out_cpu) # compile before measuring time
start_time = time.time()
smooth_cpu(x_cpu, out_cpu)
print("CPU Time: {0:1.6f}s ".format(time.time() - start_time))
$ python t29a.py
CPU Time: 0.161944s

$ cat t29.py
import numpy as np
import time
from numba import njit, prange,cuda
import timeit
import numba.cuda
import math

@numba.cuda.jit
def smooth_gpu(x, out):
    j, i = cuda.grid(2)
    m, n = x.shape

    if 1 <= i < n - 1 and 1 <= j < m - 1:
        out[i, j] = (x[i - 1, j - 1] + x[i - 1, j] + x[i - 1, j + 1] +
                    x[i    , j - 1] + x[i    , j] + x[i    , j + 1] +
                    x[i + 1, j - 1] + x[i + 1, j] + x[i + 1, j + 1]) / 9

x = np.ones((10000, 10000), dtype='float32')
out = np.zeros((10000, 10000), dtype='float32')
x_gpu = cuda.to_device(x)
out_gpu = cuda.device_array_like(out)
threadsperblock = (16, 16)
blockspergrid_x = math.ceil(x_gpu.shape[0] / threadsperblock[0])
blockspergrid_y = math.ceil(x_gpu.shape[1] / threadsperblock[1])
blockspergrid = (blockspergrid_x, blockspergrid_y)

# run on gpu
smooth_gpu[blockspergrid, threadsperblock](x_gpu, out_gpu) # compile before measuring time
cuda.synchronize()
start_time = time.time()
smooth_gpu[blockspergrid, threadsperblock](x_gpu, out_gpu)
cuda.synchronize()
print("GPU Time: {0:1.6f}s ".format(time.time() - start_time))
$ python t29.py
GPU Time: 0.021776s
$

所以我们看看如果我们针对两个问题进行调整，GPU（在我的例子中是 GTX 960）比 CPU 快大约 8 倍。 这样的测量在某种程度上取决于用于比较的 CPU 和 GPU ——你不应该假设我的测量与你的测量相当——最好运行这些修改后的代码进行比较。 但是，数据传输时间肯定比 GPU 的计算时间要大很多，而且在我的情况下也超过了 CPU 的计算时间。 这意味着（至少在我的情况下，在任何方面都不是特别快的系统）即使我们将 GPU 计算时间减少到零，传输数据的成本仍然会超过 CPU 计算时间成本。

因此，当你遇到这种情况时，是不可能获胜的。 那时可以给出的唯一建议是“不要那样做”，即找到一个更有趣、更复杂的问题让 GPU 解决。 如果我们在计算上使问题变得非常简单，比如这个问题，或者向量加法，这是你唯一想在 GPU 上做的事情，与在 CPU 上做的比较几乎从来都不是一个有趣的比较。 希望您能看到让矩阵变大在这里并没有太大帮助，因为它也会影响数据传输时间/成本。

如果我们考虑到数据传输成本（并且不要在我们的 GPU 代码中犯下严重的性能错误），根据我的测试，GPU 比 CPU 快。 如果我们包括数据传输成本，对于这个非常简单的问题，很可能 GPU 不可能比 CPU 更快（即使 GPU 计算时间减少到零）。

毫无疑问，GPU 外壳可以做更多的改进（例如改变方块形状，使用共享 memory 等），但我个人不希望花时间打磨无趣的东西。

您可以在此处获得 Numba GPU memory 管理的更多描述。

与索引排序相关的 memory 效率问题的一般描述在这里

Answer 2

我发现这个比较很有趣，并想研究重用编译内核、cuda 流和随机数据的影响，以确保没有花哨的编译器优化扭曲我们所看到的。

我修改了 Robert Crovella 发布的代码示例，并在学校的一个适度的 ML 装备上运行了脚本：

代码

import numpy as np
from time import perf_counter
from numba import njit, prange,cuda

# cpuinfo is a third party package from here:
#   https://github.com/workhorsy/py-cpuinfo
# or you can just install it using pip with:
#   python -m pip install -U py-cpuinfo
from cpuinfo import get_cpu_info

print("Some diagnostic info for the system running this script:")
# prints information about the cuda GPU
cuda.detect()
print()
# Prints a json string describing the cpu
s = get_cpu_info()
print("Cpu info")
for k,v in s.items():
    print(f"\t{k}: {v}")
print()

cpu_s1 = "CPU execution time:"
cpu_s2 = "CPU full setup/execution time:"
gpu_s1 = "GPU kernel execution time:"
gpu_s2 = "GPU full kernel setup/execution time:"
l = len(gpu_s2) + 1
# using randomized floats to ensure there isn't some compiler optimization that
# recognizes that all values of the x array are constant 1's and does something
# goofy under the hood. Each timing scenario will then use a copy of this array.
common_x = np.random.random((10000, 10000)).astype(np.float32)

def time_njit(n_loops=2):
    start_time_full_function = perf_counter()

    @njit(parallel=True,nogil=True)
    def smooth_cpu(x, out):
        h,w = x.shape
        for i in prange(1,h-1):
            for j in range(1,w-1):
                out[i, j] =  (x[i - 1, j - 1] + x[i - 1, j] +
                                  x[i - 1, j + 1] + x[i    , j - 1] +
                                  x[i    , j]     + x[i    , j + 1] +
                                  x[i + 1, j - 1] + x[i + 1, j] +
                                  x[i + 1, j + 1]) / 9


    pre_x = np.ones((10,10),dtype=common_x.dtype)
    pre_out = np.ones((10,10),dtype=common_x.dtype)
    _x = common_x.copy()
    _out = np.zeros_like(_x)
    # run on cpu
    smooth_cpu(pre_x, pre_out) # compile before measuring time
    start_time = perf_counter()
    for _ in range(n_loops):
        # realistically, we wouldn't typically run just a single blurring pass
        smooth_cpu(_x, _out)
        smooth_cpu(_out,_x)
    end_time = perf_counter()
    end_time_full_function = perf_counter()
    print(f"{cpu_s1:<{l}} {end_time - start_time:1.6f}s running {n_loops} loops"
          f"\n{cpu_s2:<{l}} {end_time_full_function - start_time_full_function:1.6f}s")
    return _x



def time_cuda(n_loops=2):
    """There is room for optimization in how we use cuda.shared.array memory on the GPU
    -- where I'm not aware of any analogues tricks for the cpu function -- that would
    allow us to minimize the number of times each thread-block needs to access data in
    the GPU's global memory. But such an implementation would take us deeper into the
    weeds than this toy problem calls for.

    Maybe if I need to take a break from my other work later I'll come back to this
    and flesh out an example of what I mean.
    """
    start_time_full_function = perf_counter()
    @cuda.jit
    def smooth_gpu(x, out):
        """slight change to the cuda kernel. This version uses **striding** to reduce
        processor overhead spent allocating and deallocating a lot of thread blocks
        that ultimately have each thread compute a single calculation before being
        disposed of.

        This way we offset some of the overhead cost spent on block allocation by
         making each block do a bit more work.

        Note: For this to work right, we have to allocate fewer blocks with
              our `blockspergrid_j` and `blockspergrid_i` variables.
        """
        jstart, istart = cuda.grid(2)
        jstep, istep = cuda.gridsize(2)
        rows,cols = x.shape
        # note that for strided kernels, thread indices
        # are completely independent of the data size/shape
        for i in range(istart+1,rows-1,istep):
            for j in range(jstart+1,cols-1,jstep):
                # Because we created x and out using column-major memory ordering,
                # we want to make sure the most frequently changing index (j)
                # is iterating through the last dimension of the array.
                out[i,j] = (x[i - 1, j - 1] + x[i - 1, j] + x[i - 1, j + 1] +
                            x[i    , j - 1] + x[i    , j] + x[i    , j + 1] +
                            x[i + 1, j - 1] + x[i + 1, j] + x[i + 1, j + 1]) / 9

    _x = common_x.copy()
    _out = np.zeros_like(_x)
    stream = cuda.stream()
    x_gpu = cuda.to_device(_x,stream)
    out_gpu = cuda.to_device(_out,stream)
    tpbj = 16
    tpbi = 16
    threadsperblock = tpbj,tpbi
    blockspergrid_j = (_x.shape[0]+tpbj-1) // tpbj
    blockspergrid_i = (_x.shape[1]+tpbi-1) // tpbi
    # reduce the number of blocks in each axis
    # by a quarter to give room for striding
    blockspergrid = (blockspergrid_j//4, blockspergrid_i//4)
    # run on gpu
    compiled = smooth_gpu[blockspergrid, threadsperblock, stream] # compile before measuring time

    start_time = perf_counter()
    for _ in range(n_loops):
        # realistically, we wouldn't typically run just a single blurring pass
        compiled(x_gpu, out_gpu)
        compiled(out_gpu,x_gpu)
    x_gpu.copy_to_host(_out,stream)
    stream.synchronize()
    end_time = perf_counter()
    end_time_full_function = perf_counter()
    print(f"{gpu_s1:<{l}} {end_time-start_time:1.6f}s running {n_loops} loops"
          f"\n{gpu_s2:<{l}} {end_time_full_function-start_time_full_function:1.6f}s")
    return _out

if __name__ == '__main__':
    a = time_njit(1)
    b = time_cuda(1)
    assert np.allclose(a,b),"The two functions didn't actually compute the same results"
    print(f"{'    '*4}Outputs are equivalent")
    a = time_njit(5)
    b = time_cuda(5)
    assert np.allclose(a,b),"The two functions didn't actually compute the same results"
    print(f"{'    '*4}Results are equivalent")
    a = time_njit(10)
    b = time_cuda(10)
    assert np.allclose(a,b),"The two functions didn't actually compute the same results"
    print(f"{'    '*4}Results are equivalent")
    a = time_njit(20)
    b = time_cuda(20)
    assert np.allclose(a,b),"The two functions didn't actually compute the same results"
    print(f"{'    '*4}Results are equivalent")

Output：

Some diagnostic info for the system running this script:

Found 1 CUDA devices
id 0    b'GeForce RTX 2080 Ti'                              [SUPPORTED]
                      compute capability: 7.5
                           pci device id: 0
                              pci bus id: 1
Summary:
    1/1 devices are supported

Cpu info:
    python_version: 3.8.8.final.0 (64 bit)
    cpuinfo_version: [7, 0, 0]
    cpuinfo_version_string: 7.0.0
    arch: X86_64
    bits: 64
    count: 8
    arch_string_raw: AMD64
    vendor_id_raw: GenuineIntel
    brand_raw: Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz
    hz_advertised_friendly: 4.0000 GHz
    hz_actual_friendly: 4.0010 GHz
    hz_advertised: [4000000000, 0]
    hz_actual: [4001000000, 0]
    l2_cache_size: 1048576
    stepping: 3
    model: 60
    family: 6
    l3_cache_size: 8388608
    flags: ['3dnow', 'abm', 'acpi', 'aes', 'apic', 'avx', 'avx2', 'bmi1', 'bmi2', 'clflush', 'cmov', 'cx16', 'cx8', 'de', 'dts', 'erms', 'est', 'f16c', 'fma', 'fpu', 'fxsr', 'ht', 'hypervisor', 'ia64', 'invpcid', 'lahf_lm', 'mca', 'mce', 'mmx', 'movbe', 'msr', 'mtrr', 'osxsave', 'pae', 'pat', 'pbe', 'pcid', 'pclmulqdq', 'pdcm', 'pge', 'pni', 'popcnt', 'pse', 'pse36', 'rdrnd', 'sep', 'serial', 'smep', 'ss', 'sse', 'sse2', 'sse4_1', 'sse4_2', 'ssse3', 'tm', 'tm2', 'tsc', 'vme', 'xsave', 'xtpr']
    l2_cache_line_size: 256
    l2_cache_associativity: 6

                Time comparisons for CPU vs GPU implementations:

CPU execution time:                    0.327143s running 1 loops
CPU full setup/execution time:         0.980959s
GPU kernel execution time:             0.088015s running 1 loops
GPU full kernel setup/execution time:  0.868085s
                Outputs are equivalent
CPU execution time:                    1.539007s running 5 loops
CPU full setup/execution time:         2.134781s
GPU kernel execution time:             0.097627s running 5 loops
GPU full kernel setup/execution time:  0.695104s
                Outputs are equivalent
CPU execution time:                    3.463488s running 10 loops
CPU full setup/execution time:         4.310506s
GPU kernel execution time:             0.122363s running 10 loops
GPU full kernel setup/execution time:  0.655500s
                Outputs are equivalent
CPU execution time:                    6.416840s running 20 loops
CPU full setup/execution time:         7.011254s
GPU kernel execution time:             0.158903s running 20 loops
GPU full kernel setup/execution time:  0.723226s
                Outputs are equivalent
CPU execution time:                    9.285086s running 30 loops
CPU full setup/execution time:         9.890282s
GPU kernel execution time:             0.209807s running 30 loops
GPU full kernel setup/execution time:  0.728618s
                Outputs are equivalent
CPU execution time:                    12.610949s running 40 loops
CPU full setup/execution time:         13.177427s
GPU kernel execution time:             0.253696s running 40 loops
GPU full kernel setup/execution time:  0.836536s
                Outputs are equivalent
CPU execution time:                    15.376767s running 50 loops
CPU full setup/execution time:         15.976361s
GPU kernel execution time:             0.289626s running 50 loops
GPU full kernel setup/execution time:  0.841918s
                Outputs are equivalent

Process finished with exit code 0

老实说，这些结果既符合我的期望，也符合我的期望。 我曾预计至少单循环 function 调用会看到 CPU 实现优于 GPU 的实现，但事实并非如此。 :v/ 虽然，随着循环次数的增加，CPU 的时间成本看似线性增加是意料之中的。

至于 GPU 的性能，我真的不知道为什么增加循环次数的时间成本似乎是对数增长（我必须 plot 数据点才能更清楚地看到它）。

无论如何，您看到的结果会因您的机器而异，但我很好奇 cuda 的计算级别 GPU 结果与 CPU 的计算级别相匹配。