为什么JavaScript中带小数的最大位数只有16 [英] Why max digits with decimal in JavaScript are only 16
问题描述
前一段时间，当我测试某些HTML表单时遇到了这个问题. JavaScript Number中带有小数点的最大位数仅为16
I came across this issue a while back when I was testing some HTML forms. The Maximum number of digits in JavaScript Number with a decimal point is only 16
我尝试了以下
var x = 12345678912345.6789
x是12345678912345.68-仅16位数字
x is 12345678912345.68 - 16 Digits only
var x = 123456789123.6789
x是123456789123.6789-仅16位数字
x is 123456789123.6789 - 16 Digits only
new Number(12345678912345.6789)
12345678912345.68-仅16位
12345678912345.68 - 16 Digits only
new Number(123456789123.6789)
123456789123.6789-仅16位
123456789123.6789 - 16 Digits only
如果计算总位数，则为16.如果增加小数点前的位数，则将小数点后的位数四舍五入
if you count the total digits, they are 16. If you increase digits before decimal point, the digits after decimal point get rounded
类似地
new Number(.12345678912367890)
是0.1234567891236789-仅16位(注意尾随0缺失)
is 0.1234567891236789 - 16 Digits only (notice trailing 0 is missing)
这让我推断出我的数字中只能有16位数字，其中包含小数.如果我尝试添加更多数字，数字开始四舍五入
Which makes me deduce that I can only have 16 Digits in a number with Decimal in it. If I try to add more digits, the number starts to round
我还观察到，当我在ASP.NET MVC中将带小数的数字序列化为JSoN时，它还会将数字转换为最大16位数字，并四舍五入
I also observed that when I serialize a number with decimal into JSoN in ASP.NET MVC, it also converts the number to Max 16 Digits and rounds the rest
我的问题:为什么?
推荐答案
According to JS/ECMAScript specification, the Number type uses double-precision floating point which has 64-bit format (binary64), consists of a sign bit (determines positive or negative value), 11 exponent bits and 52 fraction bits (each digit represents 4-bits, hence 64-bit has 16 digits):
代表双精度64位格式IEEE的Number类型 IEEE二进制标准中指定的754-2008值 浮点算法.
The Number type representing the double-precision 64-bit format IEEE 754-2008 values as specified in the IEEE Standard for Binary Floating-Point Arithmetic.
可以使用双精度正确表示的最大正数是9007199254740992，可以通过使用Math.pow(2, 53)来实现.如果数字范围在Math.pow(2, 53)和Math.pow(2, 54)之间(或在Math.pow(2, -53)和Math.pow(2, -54)之间)，则只能正确地表示偶数，因为指数位会影响小数位的LSB(最低有效位).
The maximum positive number which can be represented properly using double precision is 9007199254740992, which can be achieved by using Math.pow(2, 53). If the number range is between Math.pow(2, 53) and Math.pow(2, 54) (or between Math.pow(2, -53) and Math.pow(2, -54)), only even numbers can be represented properly because the exponent bits will affect LSB (least-significant bit) on the fraction bits.
让我们回顾大量部分:
var x = 12345678912345.6789
var x = new Number(12345678912345.6789)
该数字包含52个以上的小数位(总共72个位)，因此用于将小数位保持为52的舍入.
This number contains more than 52 fractional bits (72 bits in total), hence the rounding used to keep the fractional bits to 52.
也使用此十进制数字:
var x = new Number(.12345678912367890)
该数字包含68个小数位，因此最后一个零被切掉以保持64位长度.
This number contains 68 fractional bits, hence the last zero is chopped off to keep 64-bit length.
通常，大于9007199254740992或小于1.1102230246251565E-16的数字表示形式将存储为文字字符串而不是Number.如果需要计算非常大的数字，则可以使用某些外部库来执行任意精度算术.
Usually numeric representation larger than 9007199254740992 or smaller than 1.1102230246251565E-16 are stored as literal strings instead of Number. If you need to compute very large numbers, there are certain external libraries available to perform arbitrary precision arithmetic.
进一步阅读:
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