在解释语言上使用非常大的整数时出现意外结果 [英] Unexpected results when working with very big integers on interpreted languages

问题描述

我正在尝试获取1 + 2 + ... + 1000000000的总和，但是我在PHP和

I am trying to get the sum of 1 + 2 + ... + 1000000000, but I'm getting funny results in PHP and Node.js.

PHP

$sum = 0;
for($i = 0; $i <= 1000000000 ; $i++) {
    $sum += $i;
}
printf("%s", number_format($sum, 0, "", ""));   // 500000000067108992

Node.js

var sum = 0;
for (i = 0; i <= 1000000000; i++) {
    sum += i ;
}
console.log(sum); // 500000000067109000

可以使用以下方法计算出正确答案

The correct answer can be calculated using

1 + 2 + ... + n = n(n+1)/2

正确答案= 500000000500000000 ，所以我决定尝试另一种语言.

Correct answer = 500000000500000000, so I decided to try another language.

GO

var sum , i int64
for i = 0 ; i <= 1000000000; i++ {
    sum += i
}
fmt.Println(sum) // 500000000500000000

但是效果很好！那么我的PHP和Node.js代码有什么问题呢?

But it works fine! So what is wrong with my PHP and Node.js code?

也许这是解释语言的问题，这就是为什么它可以在像Go这样的编译语言下工作的原因?如果是这样，其他解释语言(例如Python和Perl)是否会遇到相同的问题?

Perhaps this a problem of interpreted languages, and that's why it works in a compiled language like Go? If so, would other interpreted languages such as Python and Perl have the same problem?

推荐答案

Python可以工作:

Python works:

>>> sum(x for x in xrange(1000000000 + 1))
500000000500000000

或者:

>>> sum(xrange(1000000000+1))
500000000500000000

Python的int自动提升为支持任意精度的Python long.它将在32或64位平台上产生正确的答案.

Python's int auto promotes to a Python long which supports arbitrary precision. It will produce the correct answer on 32 or 64 bit platforms.

这可以通过将2提高到远大于平台的位宽的幂来看到:

This can be seen by raising 2 to a power far greater than the bit width of the platform:

>>> 2**99
633825300114114700748351602688L

您可以(使用Python)证明您在PHP中获得的错误值是因为当值大于2 ** 32-1时，PHP会升为浮点数:

You can demonstrate (with Python) that the erroneous values you are getting in PHP is because PHP is promoting to a float when the values are greater than 2**32-1:

>>> int(sum(float(x) for x in xrange(1000000000+1)))
500000000067108992

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