Python中不准确的对数

问题描述

我每天都在公司使用 Python 2.4.我使用了标准数学库中的通用对数函数log"，当我输入 log(2**31, 2) 时，它返回 31.000000000000004，这让我觉得有点奇怪.

I work daily with Python 2.4 at my company. I used the versatile logarithm function 'log' from the standard math library, and when I entered log(2**31, 2) it returned 31.000000000000004, which struck me as a bit odd.

我对 2 的其他幂也做了同样的事情，而且效果很好.我跑了 'log10(2**31)/log10(2)' 得到了 31.0 轮

I did the same thing with other powers of 2, and it worked perfectly. I ran 'log10(2**31) / log10(2)' and I got a round 31.0

我尝试在 Python 3.0.1 中运行相同的原始函数，假设它已在更高级的版本中得到修复.

I tried running the same original function in Python 3.0.1, assuming that it was fixed in a more advanced version.

为什么会这样?Python中的数学函数是否可能存在一些不准确之处?

Why does this happen? Is it possible that there are some inaccuracies in mathematical functions in Python?

推荐答案

这对于计算机算术来说是意料之中的.它遵循特定规则，例如 IEEE 754，可能与您所学的数学不符在学校.

This is to be expected with computer arithmetic. It is following particular rules, such as IEEE 754, that probably don't match the math you learned in school.

如果这确实很重要，请使用 Python 的 十进制类型.

If this actually matters, use Python's decimal type.

例子:

from decimal import Decimal, Context
ctx = Context(prec=20)
two = Decimal(2)
ctx.divide(ctx.power(two, Decimal(31)).ln(ctx), two.ln(ctx))

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