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对NumPy的SeedSequence内部机制的困惑

2 投票
1 回答
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提问于 2025-04-14 17:47

如果这有帮助的话，我是在一台运行Windows 11 Pro的64位桌面电脑上使用Python 3.11.5和NumPy 1.26.4。

为了更好地理解当我从某个给定的SeedSequence请求np.random.Generator对象时，NumPy在背后到底做了些什么，我决定用纯Python重现一下从给定的熵值初始化SeedSequence时发生的事情。

根据我在这里找到的SeedSequence的源代码，我理解了uint32溢出是如何工作的，并且在我的机器上，np.dtype(np.uint32).itemsize的值是4，也就是说XSHIFT，定义为np.dtype(np.uint32).itemsize * 8 // 2，是16，因此我写了以下代码：

seed = int(input('Please enter a seed: '))
Entropy = seed
Spawn_key = ()
Pool_size = 8
N_children_spawned = 0
Pool = [0 for _ in range(Pool_size)]
Assembled_entropy = []
Ent = Entropy + 0
while Ent > 0:
    Assembled_entropy.append(Ent & 0xffffffff)
    Ent >>= 32
if not Assembled_entropy:
    Assembled_entropy = [0]

hash_const = 0x43b0d7e5
for i in range(Pool_size):
    if i < len(Assembled_entropy):
        Assembled_entropy[i] ^= hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        Assembled_entropy[i] *= hash_const
        Assembled_entropy[i] &= 0xffffffff
        Assembled_entropy[i] ^= Assembled_entropy[i] >> 16
        Pool[i] = Assembled_entropy[i]
    else:
        value = hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        value *= hash_const
        value &= 0xffffffff
        value ^= value >> 16
        Pool[i] = value
for i_src in range(Pool_size):
    for i_dst in range(Pool_size):
        if i_src != i_dst:
            Pool[i_src] ^= hash_const
            hash_const *= 0x931e8875
            hash_const &= 0xffffffff
            Pool[i_src] *= hash_const
            Pool[i_src] &= 0xffffffff
            Pool[i_src] ^= Pool[i_src] >> 16
            x = (0xca01f9dd * Pool[i_dst]) & 0xffffffff
            y = (0x4973f715 * Pool[i_src]) & 0xffffffff
            Pool[i_dst] = x - y
            Pool[i_dst] &= 0xffffffff
            Pool[i_dst] ^= Pool[i_dst] >> 16
for i_src in range(Pool_size, len(Assembled_entropy)):
    for i_dst in range(Pool_size):
        Assembled_entropy[i_src] ^= hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        Assembled_entropy[i_src] *= hash_const
        Assembled_entropy[i_src] &= 0xffffffff
        Assembled_entropy[i_src] ^= Assembled_entropy[i_src] >> 16
        x = (0xca01f9dd * Pool[i_dst]) & 0xffffffff
        y = (0x4973f715 * Assembled_entropy[i_src]) & 0xffffffff
        Pool[i_dst] = x - y
        Pool[i_dst] &= 0xffffffff
        Pool[i_dst] ^= Pool[i_dst] >> 16
print(Pool)

我在下面复制了一些测试运行的输出结果。

Please enter a seed: 0
[595626433, 3558985979, 200295889, 3864401631, 3155212474, 198111058, 4047350828, 373757291]

Please enter a seed: 1
[2396653877, 491222160, 2441066534, 3196981647, 1764919720, 3210735412, 1132315803, 1197535761]

Please enter a seed: 123456789
[2161290507, 266876805, 2694113549, 3306969538, 3218948428, 3543586554, 886289367, 3129292100]

Please enter a seed: 123456789123456789
[2628723507, 610487362, 209721652, 1960674985, 3519121735, 1259052354, 2097159984, 3934338599]

Please enter a seed: 123456789123456789123456789123456789
[2988668238, 798946769, 2484899198, 1005350017, 2633831484, 343737596, 1402961265, 3184558744]

Please enter a seed: 123456789123456789123456789123456789123456789123456789123456789123456789
[431881030, 3789410928, 218849910, 879851040, 1423068736, 85390627, 3721593143, 198649564]

Please enter a seed: 123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
[702225118, 2293461530, 514808704, 2115883586, 3179647446, 3197133803, 3807436730, 1822195906]

from numpy.random import SeedSequence
seed = int(input('Please enter a seed: '))
seedseq = SeedSequence(entropy=seed, spawn_key=[], pool_size=8, n_children_spawned=0)
print([int(value) for value in seedseq.pool])

然而，将这些相同的值提供给上面版本的程序，直接调用NumPy的SeedSequence，却得到了非常不同的结果：

Please enter a seed: 0
[2043904064, 467759482, 3940449851, 2747621207, 4006820188, 4161973813, 800317807, 2622167125]

Please enter a seed: 1
[476219752, 3923368624, 2653737542, 2876255837, 1861759290, 3300511046, 3253139541, 2224879358]

Please enter a seed: 123456789
[480462800, 1421661229, 2686834002, 3365909768, 3295673516, 1830753151, 1249963727, 3680881655]

Please enter a seed: 123456789123456789
[3112345096, 1618497203, 2864025213, 3262672577, 379697145, 163816190, 1265228116, 2568065655]

Please enter a seed: 123456789123456789123456789123456789
[2197723902, 2868273012, 1547285866, 2772382071, 2016971656, 1130152919, 897020445, 135618137]

Please enter a seed: 123456789123456789123456789123456789123456789123456789123456789123456789
[3230290517, 251217303, 1180998335, 454107561, 4150025399, 1840013050, 1216833737, 89665521]

Please enter a seed: 123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
[902839167, 3446715647, 2106916613, 1578536987, 595141342, 3126308643, 400300642, 3659109886]

这是怎么回事呢？

更新：根据@OskarHoffman的回答，我已经修正了我的代码。这里附上，以防有人感兴趣。

seed = int(input('Please enter a seed: '))
Entropy = seed
Spawn_key = ()
Pool_size = 8
N_children_spawned = 0
Pool = [0 for _ in range(Pool_size)]
Assembled_entropy = []
Ent = Entropy + 0
while Ent > 0:
    Assembled_entropy.append(Ent & 0xffffffff)
    Ent >>= 32
if not Assembled_entropy:
    Assembled_entropy = [0]

hash_const = 0x43b0d7e5
for i in range(Pool_size):
    if i < len(Assembled_entropy):
        temp = Assembled_entropy[i] ^ hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        temp *= hash_const
        temp &= 0xffffffff
        temp ^= temp >> 16
        Pool[i] = temp
    else:
        value = hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        value *= hash_const
        value &= 0xffffffff
        value ^= value >> 16
        Pool[i] = value
for i_src in range(Pool_size):
    for i_dst in range(Pool_size):
        if i_src != i_dst:
            temp = Pool[i_src] ^ hash_const
            hash_const *= 0x931e8875
            hash_const &= 0xffffffff
            temp *= hash_const
            temp &= 0xffffffff
            temp ^= temp >> 16
            x = (0xca01f9dd * Pool[i_dst]) & 0xffffffff
            y = (0x4973f715 * temp) & 0xffffffff
            Pool[i_dst] = x - y
            Pool[i_dst] &= 0xffffffff
            Pool[i_dst] ^= Pool[i_dst] >> 16
for i_src in range(Pool_size, len(Assembled_entropy)):
    for i_dst in range(Pool_size):
        temp = Assembled_entropy[i_src] ^ hash_const
        hash_const *= 0x931e8875
        hash_const &= 0xffffffff
        temp *= hash_const
        temp &= 0xffffffff
        temp ^= temp >> 16
        x = (0xca01f9dd * Pool[i_dst]) & 0xffffffff
        y = (0x4973f715 * temp) & 0xffffffff
        Pool[i_dst] = x - y
        Pool[i_dst] &= 0xffffffff
        Pool[i_dst] ^= Pool[i_dst] >> 16
print(Pool)
numpy 源代码分析 随机数生成 溢出处理 seedsequence 熵值初始化 bit_generator 测试运行输出

1 个回答

1

你们的第二个for循环在实现hashmix()函数时有区别。你在i_src这个位置上修改了Pool列表的值来计算y。而numpy的实现则没有这样做。它只是复制了Pool[i_src]的值（通过把它作为参数传给hashmix函数），然后只修改这个复制的值（最后会丢弃这个复制的值）。

所以把那个for循环改成：

for i_src in range(Pool_size):
    for i_dst in range(Pool_size):
        if i_src != i_dst:
            # work with new variable instead of modifying Pool[i_src]
            temp = Pool[i_src] ^ hash_const
            hash_const *= 0x931e8875
            hash_const &= 0xffffffff
            temp *= hash_const
            temp &= 0xffffffff
            temp ^= temp >> 16
            x = (0xca01f9dd * Pool[i_dst]) & 0xffffffff
            y = (0x4973f715 * temp) & 0xffffffff
            Pool[i_dst] = x - y
            Pool[i_dst] &= 0xffffffff
            Pool[i_dst] ^= Pool[i_dst] >> 16

我得到了和numpy实现一样的结果。

回答于 2025-04-14 由 Python大师
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