Python3舍入到最接近的偶数 [英] Python3 rounding to nearest even

问题描述

Python3.4会四舍五入到最接近的偶数(在平局的情况下).

Python3.4 rounds to the nearest even (in the tie-breaker case).

>>> round(1.5)
2
>>> round(2.5)
2

但是似乎只有四舍五入为整数时才这样做.

But it only seems to do this when rounding to an integer.

>>> round(2.75, 1)
2.8
>>> round(2.85, 1)
2.9

在上面的最后一个示例中，当四舍五入到最接近的偶数时，我希望答案是2.8.

In the final example above, I would have expected 2.8 as the answer when rounding to the nearest even.

为什么两种行为之间存在差异?

Why is there a discrepancy between the two behaviors?

推荐答案

浮点数仅是近似值； 2.85不能精确地表示为 :

Floating point numbers are only approximations; 2.85 cannot be represented exactly:

>>> format(2.85, '.53f')
'2.85000000000000008881784197001252323389053344726562500'

它略高于 2.85.

0.5和0.75 可以用二进制分数精确表示(分别为1/2和1/2 + 1/4).

0.5 and 0.75 can be represented exactly with binary fractions (1/2 and 1/2 + 1/4, respectively).

round()函数​​对此进行了明确记录:

注意:round()对于浮点的行为可能令人惊讶:例如，round(2.675, 2)给出2.67而不是预期的2.68.这不是错误:这是由于大多数小数部分不能完全表示为浮点数的结果.请参阅 浮点算法:问题和局限性 更多信息.

Note: The behavior of round() for floats can be surprising: for example, round(2.675, 2) gives 2.67 instead of the expected 2.68. This is not a bug: it’s a result of the fact that most decimal fractions can’t be represented exactly as a float. See Floating Point Arithmetic: Issues and Limitations for more information.

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