Why does Python's hash of infinity have the digits of π? Why does Python's hash of infinity have the digits of π? python python

Why does Python's hash of infinity have the digits of π?

Summary: It's not a coincidence; _PyHASH_INF is hardcoded as 314159 in the default CPython implementation of Python, and was picked as an arbitrary value (obviously from the digits of π) by Tim Peters in 2000.

The value of hash(float('inf')) is one of the system-dependent parameters of the built-in hash function for numeric types, and is also available as sys.hash_info.inf in Python 3:

>>> import sys>>> sys.hash_infosys.hash_info(width=64, modulus=2305843009213693951, inf=314159, nan=0, imag=1000003, algorithm='siphash24', hash_bits=64, seed_bits=128, cutoff=0)>>> sys.hash_info.inf314159

(Same results with PyPy too.)

In terms of code, hash is a built-in function. Calling it on a Python float object invokes the function whose pointer is given by the tp_hash attribute of the built-in float type (PyTypeObject PyFloat_Type), which is the float_hash function, defined as return _Py_HashDouble(v->ob_fval), which in turn has

    if (Py_IS_INFINITY(v))        return v > 0 ? _PyHASH_INF : -_PyHASH_INF;

where _PyHASH_INF is defined as 314159:

#define _PyHASH_INF 314159

In terms of history, the first mention of 314159 in this context in the Python code (you can find this with git bisect or git log -S 314159 -p) was added by Tim Peters in August 2000, in what is now commit 39dce293 in the cpython git repository.

The commit message says:

Fix for http://sourceforge.net/bugs/?func=detailbug&bug_id=111866&group_id=5470. This was a misleading bug -- the true "bug" was that hash(x) gave an error return when x is an infinity. Fixed that. Added new Py_IS_INFINITY macro to pyport.h. Rearranged code to reduce growing duplication in hashing of float and complex numbers, pushing Trent's earlier stab at that to a logical conclusion. Fixed exceedingly rare bug where hashing of floats could return -1 even if there wasn't an error (didn't waste time trying to construct a test case, it was simply obvious from the code that it could happen). Improved complex hash so that hash(complex(x, y)) doesn't systematically equal hash(complex(y, x)) anymore.

In particular, in this commit he ripped out the code of static long float_hash(PyFloatObject *v) in Objects/floatobject.c and made it just return _Py_HashDouble(v->ob_fval);, and in the definition of long _Py_HashDouble(double v) in Objects/object.c he added the lines:

        if (Py_IS_INFINITY(intpart))            /* can't convert to long int -- arbitrary */            v = v < 0 ? -271828.0 : 314159.0;

So as mentioned, it was an arbitrary choice. Note that 271828 is formed from the first few decimal digits of e.

Related later commits:

_PyHASH_INF is defined as a constant equal to 314159.

I can't find any discussion about this, or comments giving a reason. I think it was chosen more or less arbitrarily. I imagine that as long as they don't use the same meaningful value for other hashes, it shouldn't matter.



returns 314159. The value is not generated, it's built into the source code.In fact,


returns -271828, or approximately -e, in python 2 (it's -314159 now).

The fact that the two most famous irrational numbers of all time are used as the hash values makes it very unlikely to be a coincidence.