在Python中准确地乘以非常大的数字

问题描述

我试图在Python中将很大的浮点数乘以很大的整数，并注意到很小的不准确性.例如:

I am trying to multiply very large floats by very large integers in Python and am noticing small inaccuracies.For example:

a = 45310630.0
b = 1023473145

c = int(a * b)
print(c)

我得到的答案是46374212988031352，但我知道答案应该是46374212988031350.当我将变量"a"更改为整数时，可以正确执行乘法.但是，由于"a"来自除法(可能不是整数)，所以我不能简单地将其转换为整数.

The answer I am getting is 46374212988031352 but I know the answer should be 46374212988031350. When I change variable "a" to an integer, the multiplication is performed correctly. However, since "a" comes from a division (and might not be a whole number), I can't simply convert it to an integer.

推荐答案

如果使用 fractions.Fraction ，您可以准确地处理较大的数字，但需要付出一定的效率:

If you use fractions.Fraction you can handle larger numbers accurately, at the cost of some efficiency:

from fractions import Fraction
a = Fraction(45310630.0)
b = Fraction(1023473145)

c = int(a * b)
print(c)

输出:

46374212988031350

一些时间:

In [2]: a = Fraction(45310630.0)
   ...: b = Fraction(1023473145)
   ...:

In [3]: %timeit int(a * b)
3.92 µs ± 21.9 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

In [4]: a = 45310630.0
   ...: b = 1023473145
   ...:

In [5]: %timeit int(a * b)
479 ns ± 13.9 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

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