python3使用除法和地板除法产生两种不同的结果

Question

When using the normal division

9999999999999999 / 2

returned value: 5000000000000000.0

and when using the floor division

9999999999999999 // 2

returned value: 4999999999999999

I am using python 3.8.1 can anyone explain this? Thanks in advance

Answer 1

The / operator on int operands uses float arithmetic. Assuming an IEEE 754 compatible system, a float has 53 bits of precision. Thus, it cannot exactly represent 9999999999999999, which is a 54-bit number. So this value gets rounded up to 1e+16, and half of this is 5000000000000000.0.

The // operator on int operands uses int arithmetic. The Python 3 int type has unlimited range, so can represent 9999999999999999 exactly. Halving this number gives 4999999999999999 (with a discarded remainder of 1).