添加到 Number.MAX_VALUE [英] Adding to Number.MAX_VALUE

问题描述

这个问题的答案可能非常明显，但我无法通过粗略搜索在 Mozilla 文档或 Google 上找到它.

如果你有这样的代码

Number.MAX_VALUE + 1;//无穷大，对吧?Number.MIN_VALUE - 1;//-无穷大，对吧?

然后我希望将 anything 添加到 Number.MAX_VALUE 会将其推送到 Infinity.结果只是Number.MAX_VALUE 直接向我吐口水.

然而，在 Chrome JS 控制台中玩弄时，我注意到它实际上并没有变成 Infinity，直到我添加/减去足够多:

Number.MAX_VALUE + Math.pow(100,1000);//现在我们击中了 InfinityNumber.MIN_VALUE - Math.pow(100,1000);//- 最后是无穷大

Number.MAX_VALUE 和 Infinity 之间的这个缓冲区"的解释是什么?

解决方案

标准...

在 ECMAScript 中，两个非零有限数的加法实现为 _{^{(ECMA-262 §11.6.3 Applying the Additive Operators to Numbers")}}:<块引用>

使用IEEE 754 舍入到最近模式计算和舍入到最接近的可表示值.如果幅度太大而无法表示，则运算会溢出，结果是适当符号的无穷大.

IEEE-754 的舍入到最近模式指定 _{^{(IEEE-754 2008 §4.3.1 Rounding-direction attributes to Nearest")}}

<块引用>

在以下两个舍入方向属性中，无限精确的结果大小至少b^emax ( b − ½b^1-p ) 应四舍五入到∞，符号不变；这里的 emax 和 p 由目标格式决定(见 3.3).与:

• roundTiesToEven，应传递最接近无限精确结果的浮点数；如果括号中不可表示的无限精确结果的两个最接近的浮点数相等，则应传递具有偶数最低有效位的那个
• roundTiesToAway，传递最接近无限精确结果的浮点数；如果括号中无法表示的无限精确结果的两个最接近的浮点数相等，则应交付数量级较大的浮点数.

ECMAScript 没有指定哪一个舍入到最近，但这里没有关系，因为两者给出了相同的结果.ECMAScript 中的数字是double"，其中

• b = 2
• emax = 1023
• p = 53,

所以结果必须至少为 2¹⁰²⁴ - 2⁹⁷⁰ ~ 1.7976931348623158 × 10³⁰⁸为了四舍五入到无穷大.否则它只会四舍五入到 MAX_VALUE，因为 比 Infinity 更接近.

注意MAX_VALUE = 2¹⁰²⁴ - 2⁹⁷¹，所以你至少需要加上2⁹⁷¹ - 2⁹⁷⁰ = 2⁹⁷⁰ ~ 9.979202 × 10²⁹¹ 以获得无穷大.我们可以检查:

<预><代码>>>>Number.MAX_VALUE + 9.979201e2911.7976931348623157e+308>>>Number.MAX_VALUE + 9.979202e291无限

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与此同时，你的 Math.pow(100,1000) ~ 2^6643.9 远远超过 2¹⁰²⁴ - 2⁹⁷⁰.它是已经是无穷大了.

The answer to this question may be painfully obvious but I can't find it in the Mozilla docs nor on Google from a cursory search.

If you have some code like this

Number.MAX_VALUE + 1; // Infinity, right?
Number.MIN_VALUE - 1; // -Infinity, right?

Then I would expect adding anything to Number.MAX_VALUE would push it over to Infinity. The result is just Number.MAX_VALUE spat right back at me.

However, when playing around in the Chrome JS console, I noticed that it didn't actually become Infinity until I added/subtracted enough:

Number.MAX_VALUE + Math.pow(100,1000); // now we hit Infinity
Number.MIN_VALUE - Math.pow(100,1000); // -Infinity at last

What is the explanation for this "buffer" between Number.MAX_VALUE and Infinity?

解决方案

Standardwise...

In ECMAScript, addition of two nonzero finite numbers is implemented as _{^{(ECMA-262 §11.6.3 "Applying the Additive Operators to Numbers")}}:

the sum is computed and rounded to the nearest representable value using IEEE 754 round-to-nearest mode. If the magnitude is too large to represent, the operation overflows and the result is then an infinity of appropriate sign.

IEEE-754's round-to-nearest mode specifies that _{^{(IEEE-754 2008 §4.3.1 "Rounding-direction attributes to nearest")}}

In the following two rounding-direction attributes, an infinitely precise result with magnitude at least b^emax ( b − ½ b^1-p ) shall round to ∞ with no change in sign; here emax and p are determined by the destination format (see 3.3). With:

• roundTiesToEven, the floating-point number nearest to the infinitely precise result shall be delivered; if the two nearest floating-point numbers bracketing an unrepresentable infinitely precise result are equally near, the one with an even least significant digit shall be delivered
• roundTiesToAway, the floating-point number nearest to the infinitely precise result shall be delivered; if the two nearest floating-point numbers bracketing an unrepresentable infinitely precise result are equally near, the one with larger magnitude shall be delivered.

ECMAScript does not specify which of the round-to-nearest, but it doesn't matter here because both gives the same result. The number in ECMAScript is "double", in which

• b = 2
• emax = 1023
• p = 53,

so the result must be at least 2¹⁰²⁴ - 2⁹⁷⁰ ~ 1.7976931348623158 × 10³⁰⁸ in order to round to infinity. Otherwise it will just round to MAX_VALUE, because that is the closer than Infinity.

Notice that MAX_VALUE = 2¹⁰²⁴ - 2⁹⁷¹, so you need to add at least 2⁹⁷¹ - 2⁹⁷⁰ = 2⁹⁷⁰ ~ 9.979202 × 10²⁹¹ in order to get infinity. We could check:

>>> Number.MAX_VALUE + 9.979201e291
1.7976931348623157e+308
>>> Number.MAX_VALUE + 9.979202e291
Infinity

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Meanwhile, your Math.pow(100,1000) ~ 2^6643.9 is well beyond 2¹⁰²⁴ - 2⁹⁷⁰. It is already infinity.

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