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?
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bemax ( b − ½b1-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无限与此同时,你的 Math.pow(100,1000)
~ 26643.9 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
?
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 bemax ( b − ½ b1-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
Meanwhile, your Math.pow(100,1000)
~ 26643.9 is well beyond 21024 - 2970. It is already infinity.
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