什么时候在Python中hash(n)== n? [英] When is hash(n) == n in Python?

问题描述

我一直在使用Python的哈希函数.对于小整数，始终显示为hash(n) == n.但是，这并不能扩展为大量数字:

I've been playing with Python's hash function. For small integers, it appears hash(n) == n always. However this does not extend to large numbers:

>>> hash(2**100) == 2**100
False

我并不感到惊讶，我知道哈希值取值范围有限.那是什么范围?

I'm not surprised, I understand hash takes a finite range of values. What is that range?

我尝试使用二进制搜索来找到最小的数字hash(n) != n

I tried using binary search to find the smallest number hash(n) != n

>>> import codejamhelpers # pip install codejamhelpers
>>> help(codejamhelpers.binary_search)
Help on function binary_search in module codejamhelpers.binary_search:

binary_search(f, t)
    Given an increasing function :math:`f`, find the greatest non-negative integer :math:`n` such that :math:`f(n) \le t`. If :math:`f(n) > t` for all :math:`n \ge 0`, return None.

>>> f = lambda n: int(hash(n) != n)
>>> n = codejamhelpers.binary_search(f, 0)
>>> hash(n)
2305843009213693950
>>> hash(n+1)
0

2305843009213693951有什么特别之处?我注意到它小于sys.maxsize == 9223372036854775807

What's special about 2305843009213693951? I note it's less than sys.maxsize == 9223372036854775807

我正在使用Python3.我在Python 2上运行了相同的二进制搜索，得到了不同的结果2147483648，我注意到它是sys.maxint+1

I'm using Python 3. I ran the same binary search on Python 2 and got a different result 2147483648, which I note is sys.maxint+1

我还玩过[hash(random.random()) for i in range(10**6)]来估计哈希函数的范围.最大值始终低于上面的n.比较最小值，似乎Python 3的哈希值始终为正值，而Python 2的哈希值可以为负值.

I also played with [hash(random.random()) for i in range(10**6)] to estimate the range of hash function. The max is consistently below n above. Comparing the min, it seems Python 3's hash is always positively valued, whereas Python 2's hash can take negative values.

推荐答案

基于中的python文档pyhash.c 文件:

对于数字类型，数字x的哈希值基于减少量 x以素数P = 2**_PyHASH_BITS - 1取模的形式.它的设计目的是 hash(x) == hash(y)只要x和y在数值上相等，即使 x和y具有不同的类型.

For numeric types, the hash of a number x is based on the reduction of x modulo the prime P = 2**_PyHASH_BITS - 1. It's designed so that hash(x) == hash(y) whenever x and y are numerically equal, even if x and y have different types.

因此对于64/32位计算机，减少量将为2 ^_PyHASH_BITS -1，但是_PyHASH_BITS是什么?

So for a 64/32 bit machine, the reduction would be 2 ^_PyHASH_BITS - 1, but what is _PyHASH_BITS?

您可以在 pyhash.h 头文件中找到它，该文件为64位机器已定义为61(您可以在pyconfig.h文件中阅读更多说明).

You can find it in pyhash.h header file which for a 64 bit machine has been defined as 61 (you can read more explanation in pyconfig.h file).

#if SIZEOF_VOID_P >= 8
#  define _PyHASH_BITS 61
#else
#  define _PyHASH_BITS 31
#endif

因此首先要基于您的平台，例如在我的64位Linux平台上，减少量为2 ⁶¹ -1，即2305843009213693951:

So first off all it's based on your platform for example in my 64bit Linux platform the reduction is 2⁶¹-1, which is 2305843009213693951:

>>> 2**61 - 1
2305843009213693951

还可以使用math.frexp来获取sys.maxint的尾数和指数，对于64位计算机，该值显示max int为2 ⁶³ :

Also You can use math.frexp in order to get the mantissa and exponent of sys.maxint which for a 64 bit machine shows that max int is 2⁶³:

>>> import math
>>> math.frexp(sys.maxint)
(0.5, 64)

您可以通过一个简单的测试来查看差异:

And you can see the difference by a simple test:

>>> hash(2**62) == 2**62
True
>>> hash(2**63) == 2**63
False

阅读有关python哈希算法的完整文档 https://github.com/python/cpython/blob/master/Python/pyhash.c#L34

Read the complete documentation about python hashing algorithm https://github.com/python/cpython/blob/master/Python/pyhash.c#L34

如注释中所述，您可以使用sys.hash_info(在python 3.X中)，这将为您提供用于计算的参数的结构序列 散列.

As mentioned in comment you can use sys.hash_info (in python 3.X) which will give you a struct sequence of parameters used for computing hashes.

>>> sys.hash_info
sys.hash_info(width=64, modulus=2305843009213693951, inf=314159, nan=0, imag=1000003, algorithm='siphash24', hash_bits=64, seed_bits=128, cutoff=0)
>>> 

除了我在前几行中描述的模数之外，还可以得到inf值，如下所示:

Alongside the modulus that I've described in preceding lines, you can also get the inf value as following:

>>> hash(float('inf'))
314159
>>> sys.hash_info.inf
314159

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