为什么Number.MAX_SAFE_INTEGER 9,007,199,254,740,991而不是9,007,199,254,740,992？ [英] Why is Number.MAX_SAFE_INTEGER 9,007,199,254,740,991 and not 9,007,199,254,740,992?

问题描述

ECMAScript 6的 Number.MAX_SAFE_INTEGER 应该表示JavaScript在浮点精度出现问题之前可以存储的最大数值。但是，要求添加到此值的数字1也必须表示为数字。

ECMAScript 6's Number.MAX_SAFE_INTEGER supposedly represents the maximum numerical value JavaScript can store before issues arise with floating point precision. However it's a requirement that the number 1 added to this value must also be representable as a Number.

Number.MAX_SAFE_INTEGER

注意 Number的值.MAX_SAFE_INTEGER 是最大的整数 n ，这样 n 和 n + 1 都可以完全表示为 Number 值。

Number.MAX_SAFE_INTEGER

NOTE The value of Number.MAX_SAFE_INTEGER is the largest integer n such that n and n + 1 are both exactly representable as a Number value.

Number.MAX_SAFE_INTEGER 的值为 9007199254740991（2 ^ 53-1）。

- ECMAScript语言规范

Chrome，Firefox，Opera和IE11的JavaScript控制台都可以安全地执行9,007,199,254,740,992的计算。一些测试：

The JavaScript consoles of Chrome, Firefox, Opera and IE11 can all safely perform calculations with the number 9,007,199,254,740,992. Some tests:

// Valid
Math.pow(2, 53)                         // 9007199254740992
9007199254740991 + 1                    // 9007199254740992
9007199254740992 - 1                    // 9007199254740991
9007199254740992 / 2                    // 4503599627370496
4503599627370496 * 2                    // 9007199254740992
parseInt('20000000000000', 16)          // 9007199254740992
parseInt('80000000000', 32)             // 9007199254740992
9007199254740992 - 9007199254740992     // 0
9007199254740992 == 9007199254740991    // false
9007199254740992 == 9007199254740992    // true

// Erroneous
9007199254740992 + 1                    // 9007199254740992
9007199254740993 + ""                   // "9007199254740992"
9007199254740992 == 9007199254740993    // true

为什么要求 n + 1 必须也可以表示为数字？为什么失败会使值不安全？

Why is it a requirement that n + 1 must also be representable as a Number? Why does failing this make the value unsafe?

推荐答案

我会说它因为 Math.pow（2,53）是最大的可直接表示的整数，它的不安全，因为它也是表示的第一个值也是另一个值的近似值：

I would say its because while Math.pow(2, 53) is the largest directly representable integer, its unsafe in that its also the first value who's representation is also an approximation of another value:

9007199254740992 == 9007199254740993 // true

与相比，Math.pow（2,53） - 1

9007199254740991 == 9007199254740993 // false

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