在(看似)无限循环中耗尽浮点精度 [英] Exhausting floating point precision in a (seemingly) infinite loop

问题描述

我有以下Python脚本:

I've got the following Python script:

x = 300000000.0
while (x < x + x):
    x = x + x
    print "exec: " + str(x)
print "terminated" + str(x)

这个看似无限的循环，如果x是一个浮点数，则很快终止.但是，如果我改为将x更改为300000000，它将陷入无限循环(在测试中运行的时间超过一分钟).

This seemingly infinite loop, terminates pretty quickly if x is a floating point number. But if i change x to 300000000 instead, it gets into an infinite loop (runs longer than a minute in my test).

我认为这与以下事实有关:它耗尽了可以在内存中表示的浮点数的精度.有人可以提供更详细的解释吗?

I think this is to do with the fact that it's exhausting the precision of a floating point number that can be represented in memory. Can someone provide a more detailed explanation why this is?

推荐答案

• 将 x 初始化为 300000000 时，整个程序都会使用整数数学.
• 将 x 初始化为 300000000.0 时，将使用浮点数学.
• When you initialize x to 300000000, integer math is used throughout the program.
• When you initialize x to 300000000.0, floating-point math is used instead.

在Python中，整数可以任意增大.(更准确地说，它们受可用内存的限制.)这意味着程序的整数版本需要很长时间才能终止.

In Python, integers can grow arbitrarily large. (More accurately, they're limited by the available memory.) This means that the integer version of your program takes a very long time to terminate.

最大的 float 大约是 1.8e308 .循环的浮点版本大约需要进行1000次迭代才能超过该值，此时 x 被设置为正无穷大，程序终止.

The largest float is about 1.8e308. It takes about 1000 iterations of the floating-point version of the loop to exceed that value, at which point x gets set to positive infinity, and the program terminates.

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