一、原因
js的Number在内存中存储使用的是一种64位双精度浮点数存储方法。其中,1位用来表示符号,0为正,1为负;11位用来表示指数;52位用来表示尾数。他的表示格式为:s * m * ( 2 ^ e ) (s为符号位,m为尾数,e为指数)
将十进制的小数转换为二进制的小数,采用“乘二取整法”,即小数部分乘以2,取整数部分,剩下的小数部分继续乘以二,取整数部分,直到取到小数部分为0为止。在线进制转换请戳这里
举例:0.1 + 0.2 = 0.30000000000000004
0.1(10) 可转换成二进制:0.0001100110011001100110011001100110011001100110011001101(2) 即:
e = -4; m = 1.1001100110011001100110011001100110011001100110011010
0.2(10) 可转换成二进制:0.001100110011001100110011001100110011001100110011001101(2) 即:
e = -3; m = 1.1001100110011001100110011001100110011001100110011010
二者相加:
e = -3; m = 0.1100110011001100110011001100110011001100110011001101(52位) +
e = -3; m = 1.1001100110011001100110011001100110011001100110011010(52位) 结果是:
e = -3; m = 10.0110011001100110011001100110011001100110011001100111(52位) 即
e = -2; m = 1.00110011001100110011001100110011001100110011001100111(53位) 根据round to nearest, tie to even(有近取近,无近取偶)的方法取到近似值:
e = -2; m = 1.0011001100110011001100110011001100110011001100110100(52位) 可转换成十进制:0.30000000000000004
二、解决方法
加法:
add(arg1, arg2) { var r1, r2, m; try { r1 = arg1.toString().split(".")[1].length; } catch (e) { r1 = 0; } try { r2 = arg2.toString().split(".")[1].length; } catch (e) { r2 = 0; } m = Math.pow(10, Math.max(r1, r2)); return (arg1 * m + arg2 * m) / m; // 有问题。例如2.3 * 100 = 229.99999999999997 // return (Math.round(arg1 * m) + Math.round(arg2 * m)) / m; // 方法一:四舍五入的方式 // return (this.mul(arg1, m) + this.mul(arg2, m)) / m; // 方法二:乘法自己封装了一层 },
减法:
sub(arg1, arg2) { var r1, r2, m, n; try { r1 = arg1.toString.split(".")[1].length; } catch (e) { r1 = 0; } try { r2 = arg2.toString().split(".")[1].length; } catch (e) { r2 = 0; } m = Math.pow(10, Math.max(r1, r2)); n = (r1 >= r2) ? r1 : r2; return ((arg1 * m - arg2 * m) / m).toFixed(n); },
乘法:
mul(arg1, arg2) { var m = 0, s1 = arg1.toString(), s2 = arg2.toString(); try { m += s1.split(".")[1].length; } catch (e) { } try { m += s2.split(".")[1].length; } catch (e) { } return Number(s1.replace(".", "")) * Number(s2.replace(".", "")) / Math.pow(10, m); },
除法:
div(arg1, arg2) { var t1 = 0, t2 = 0, r1, r2; try { t1 = arg1.toString().split(".")[1].length; } catch (e) { } try { t2 = arg2.toString().split(".")[1].length; } catch (e) { } r1 = Number(arg1.toString().replace(".", "")); r2 = Number(arg2.toString().replace(".", "")); return (r1 / r2) * Math.pow(10, t2 - t1); },
大整数比较大小:
value.toString().length