Let’s talk about the computational accuracy of js

We all know that using js to do calculations will definitely encounter calculation accuracy problems (or rounding errors), but how to avoid these pitfalls, here is the plan I compiled from the Internet , welcome to discuss.

Reason for loss of accuracy

The binary implementation of the computer and the number of digits limitations some numbers cannot be represented finitely. Just like some irrational numbers cannot be represented finitely, such as pi 3.1415926…, 1.3333… etc. JavaScript uses 64 bits to store numeric types, so any excess is discarded. The omitted part is the part where accuracy is lost.

The following is the binary representation corresponding to the decimal number

0.1 >> 0.0001 1001 1001 1001…（1001无限循环）
0.2 >> 0.0011 0011 0011 0011…（0011无限循环）

Solution

If you need a more complex calculation library, you can consider math.js, etc. Well-known class library

Floating point number (decimal)

For decimals, there are still many chances of problems on the front end, especially in some e-commerce websites involving amounts and other data. Solution: Put the decimal into an integer (multiply the multiple), and then reduce it back to the original multiple (divide the multiple). The operation result after converting to an integer cannot exceed Math.pow(2,53)

// 0.1 + 0.2
(0.1*10 + 0.2*10) / 10 == 0.3 // true

float Point precision operation

/**
 * floatObj 包含加减乘除四个方法，能确保浮点数运算不丢失精度
 *
 * ** method **
 *  add / subtract / multiply /divide
 *
 * ** explame **
 *  0.1 + 0.2 == 0.30000000000000004 （多了 0.00000000000004）
 *  0.2 + 0.4 == 0.6000000000000001  （多了 0.0000000000001）
 *  19.9 * 100 == 1989.9999999999998 （少了 0.0000000000002）
 *
 * floatObj.add(0.1, 0.2) >> 0.3
 * floatObj.multiply(19.9, 100) >> 1990
 *
 */
var floatObj = function() {
    /*
     * 判断obj是否为一个整数
     */
    function isInteger(obj) {
        return Math.floor(obj) === obj
    }
    /*
     * 将一个浮点数转成整数，返回整数和倍数。如 3.14 >> 314，倍数是 100
     * @param floatNum {number} 小数
     * @return {object}
     *   {times:100, num: 314}
     */
    function toInteger(floatNum) {
        var ret = {times: 1, num: 0}
        if (isInteger(floatNum)) {
            ret.num = floatNum
            return ret
        }
        var strfi  = floatNum + ''
        var dotPos = strfi.indexOf('.')
        var len    = strfi.substr(dotPos+1).length
        var times  = Math.pow(10, len)
        var intNum = parseInt(floatNum * times + 0.5, 10)
        ret.times  = times
        ret.num    = intNum
        return ret
    }
    /*
     * 核心方法，实现加减乘除运算，确保不丢失精度
     * 思路：把小数放大为整数（乘），进行算术运算，再缩小为小数（除）
     *
     * @param a {number} 运算数1
     * @param b {number} 运算数2
     * @param digits {number} 精度，保留的小数点数，比如 2, 即保留为两位小数
     * @param op {string} 运算类型，有加减乘除（add/subtract/multiply/divide）
     *
     */
    function operation(a, b, digits, op) {
        var o1 = toInteger(a)
        var o2 = toInteger(b)
        var n1 = o1.num
        var n2 = o2.num
        var t1 = o1.times
        var t2 = o2.times
        var max = t1 > t2 ? t1 : t2
        var result = null
        switch (op) {
            case 'add':
                if (t1 === t2) { // 两个小数位数相同
                    result = n1 + n2
                } else if (t1 > t2) { // o1 小数位 大于 o2
                    result = n1 + n2 * (t1 / t2)
                } else { // o1 小数位 小于 o2
                    result = n1 * (t2 / t1) + n2
                }
                return result / max
            case 'subtract':
                if (t1 === t2) {
                    result = n1 - n2
                } else if (t1 > t2) {
                    result = n1 - n2 * (t1 / t2)
                } else {
                    result = n1 * (t2 / t1) - n2
                }
                return result / max
            case 'multiply':
                result = (n1 * n2) / (t1 * t2)
                return result
            case 'divide':
                result = (n1 / n2) * (t2 / t1)
                return result
        }
    }
    // 加减乘除的四个接口
    function add(a, b, digits) {
        return operation(a, b, digits, 'add')
    }
    function subtract(a, b, digits) {
        return operation(a, b, digits, 'subtract')
    }
    function multiply(a, b, digits) {
        return operation(a, b, digits, 'multiply')
    }
    function divide(a, b, digits) {
        return operation(a, b, digits, 'divide')
    }
    // exports
    return {
        add: add,
        subtract: subtract,
        multiply: multiply,
        divide: divide
    }
}();

Usage method:

floatTool.add(a,b);//相加
floatTool.subtract(a,b);//相减
floatTool.multiply(a,b);//相乘
floatTool.divide(a,b);//相除

Super large integer

Although the operation result does not exceed Math.pow(2,53) The above method can also be used for integers (9007199254740992), but if there are more than one, in the actual scenario there may be some batch number, number segment and other requirements. Here I also found a solution, directly enter the code .

Online calculation: https://www.shen.ee/math.html

function compare(p, q) {
  while (p[0] === '0') {
    p = p.substr(1);
  }
  while (q[0] === '0') {
    q = q.substr(1);
  }
  if (p.length > q.length) {
    return 1;
  } else if (p.length < q.length) {
    return -1;
  } else {
    let i = 0;
    let a, b;
    while (1) {
      a = parseInt(p.charAt(i));
      b = parseInt(q.charAt(i));
      if (a > b) {
        return 1;
      } else if (a < b) {
        return -1;
      } else if (i === p.length - 1) {
        return 0;
      }
      i++;
    }
  }
}
function divide(A, B) {
  let result = [];
  let max = 9;
  let point = 5;
  let fill = 0;
  if (B.length - A.length > 0) {
    point += fill = B.length - A.length;
  }
  for (let i = 0; i < point; i++) {
    A += &#39;0&#39;;
  }
  let la = A.length;
  let lb = B.length;
  let b0 = parseInt(B.charAt(0));
  let Adb = A.substr(0, lb);
  A = A.substr(lb);
  let temp, r;
  for (let j = 0; j < la - lb + 1; j++) {
    while (Adb[0] === &#39;0&#39;) {
      Adb = Adb.substr(1);
    }
    if (Adb.length === lb) {
      max = Math.ceil((parseInt(Adb.charAt(0)) + 1) / b0); // 不可能取到这个最大值,1<= max <= 10
    } else if (Adb.length > lb) {
      max = Math.ceil((parseInt(Adb.substr(0, 2)) + 1) / b0);
    } else {
      result.push(0);
      Adb += A[0];
      A = A.substr(1);
      continue;
    }
    for (let i = max - 1; i >= 0; i--) {
      if (i === 0) {
        result.push(0);
        Adb += A[0];
        A = A.substr(1);
        break;
      } else {
        temp = temp || multiply(B, i + &#39;&#39;);
        r = compare(temp, Adb);
        if (r === 0 || r === -1) {
          result.push(i);
          if (r) {
            Adb = reduce(Adb, temp);
            Adb += A[0];
          } else {
            Adb = A[0];
          }
          A = A.substr(1);
          break;
        } else {
          temp = reduce(temp, B);
        }
      }
    }
    temp = 0;
  }
  for (let i = 0; i < fill; i++) {
    result.unshift(&#39;0&#39;);
  }
  result.splice(result.length - point, 0, &#39;.&#39;);
  if (!result[0] && result[1] !== &#39;.&#39;) {
    result.shift();
  }
  point = false;
  let position = result.indexOf(&#39;.&#39;);
  for (let i = position + 1; i < result.length; i++) {
    if (result[i]) {
      point = true;
      break;
    }
  }
  if (!point) {
    result.splice(position);
  }
  result = result.join(&#39;&#39;);
  return result;
}
function multiply(A, B) {
  let result = [];
  (A += &#39;&#39;), (B += &#39;&#39;);
  const l = -4; // 以支持百万位精确运算，但速度减半
  let r1 = [],
    r2 = [];
  while (A !== &#39;&#39;) {
    r1.unshift(parseInt(A.substr(l)));
    A = A.slice(0, l);
  }
  while (B !== &#39;&#39;) {
    r2.unshift(parseInt(B.substr(l)));
    B = B.slice(0, l);
  }
  let index, value;
  for (let i = 0; i < r1.length; i++) {
    for (let j = 0; j < r2.length; j++) {
      value = 0;
      if (r1[i] && r2[j]) {
        value = r1[i] * r2[j];
      }
      index = i + j;
      if (result[index]) {
        result[index] += value;
      } else {
        result[index] = value;
      }
    }
  }
  for (let i = result.length - 1; i > 0; i--) {
    result[i] += &#39;&#39;;
    if (result[i].length > -l) {
      result[i - 1] += parseInt(result[i].slice(0, l));
      result[i] = result[i].substr(l);
    }
    while (result[i].length < -l) {
      result[i] = &#39;0&#39; + result[i];
    }
  }
  if (result[0]) {
    result = result.join(&#39;&#39;);
  } else {
    result = &#39;0&#39;;
  }
  return result;
}
function add(A, B) {
  let result = [];
  (A += &#39;&#39;), (B += &#39;&#39;);
  const l = -15;
  while (A !== &#39;&#39; && B !== &#39;&#39;) {
    result.unshift(parseInt(A.substr(l)) + parseInt(B.substr(l)));
    A = A.slice(0, l);
    B = B.slice(0, l);
  }
  A += B;
  for (let i = result.length - 1; i > 0; i--) {
    result[i] += &#39;&#39;;
    if (result[i].length > -l) {
      result[i - 1] += 1;
      result[i] = result[i].substr(1);
    } else {
      while (result[i].length < -l) {
        result[i] = &#39;0&#39; + result[i];
      }
    }
  }
  while (A && (result[0] + &#39;&#39;).length > -l) {
    result[0] = (result[0] + &#39;&#39;).substr(1);
    result.unshift(parseInt(A.substr(l)) + 1);
    A = A.slice(0, l);
  }
  if (A) {
    while ((result[0] + &#39;&#39;).length < -l) {
      result[0] = &#39;0&#39; + result[0];
    }
    result.unshift(A);
  }
  if (result[0]) {
    result = result.join(&#39;&#39;);
  } else {
    result = &#39;0&#39;;
  }
  return result;
}
function reduce(A, B) {
  let result = [];
  (A += &#39;&#39;), (B += &#39;&#39;);
  while (A[0] === &#39;0&#39;) {
    A = A.substr(1);
  }
  while (B[0] === &#39;0&#39;) {
    B = B.substr(1);
  }
  const l = -15;
  let N = &#39;1&#39;;
  for (let i = 0; i < -l; i++) {
    N += &#39;0&#39;;
  }
  N = parseInt(N);
  while (A !== &#39;&#39; && B !== &#39;&#39;) {
    result.unshift(parseInt(A.substr(l)) - parseInt(B.substr(l)));
    A = A.slice(0, l);
    B = B.slice(0, l);
  }
  if (A !== &#39;&#39; || B !== &#39;&#39;) {
    let s = B === &#39;&#39; ? 1 : -1;
    A += B;
    while (A !== &#39;&#39;) {
      result.unshift(s * parseInt(A.substr(l)));
      A = A.slice(0, l);
    }
  }
  while (result.length !== 0 && result[0] === 0) {
    result.shift();
  }
  let s = &#39;&#39;;
  if (result.length === 0) {
    result = 0;
  } else if (result[0] < 0) {
    s = &#39;-&#39;;
    for (let i = result.length - 1; i > 0; i--) {
      if (result[i] > 0) {
        result[i] -= N;
        result[i - 1]++;
      }
      result[i] *= -1;
      result[i] += &#39;&#39;;
      while (result[i].length < -l) {
        result[i] = &#39;0&#39; + result[i];
      }
    }
    result[0] *= -1;
  } else {
    for (let i = result.length - 1; i > 0; i--) {
      if (result[i] < 0) {
        result[i] += N;
        result[i - 1]--;
      }
      result[i] += &#39;&#39;;
      while (result[i].length < -l) {
        result[i] = &#39;0&#39; + result[i];
      }
    }
  }
  if (result) {
    while ((result[0] = parseInt(result[0])) === 0) {
      result.shift();
    }
    result = s + result.join(&#39;&#39;);
  }
  return result;
}

Instructions for use: Negative numbers are not allowed, and it is best to use strings for parameters

divide(A,B)    // 除法
multiply(A,B)    //乘法
add(A,B)    //加法
reduce(A,B)    //减法

toFixed's fix

In Firefox/Chrome, toFixed does not round the last digit of 5 as expected.

1.35.toFixed(1) // 1.4 正确
1.335.toFixed(2) // 1.33  错误
1.3335.toFixed(3) // 1.333 错误
1.33335.toFixed(4) // 1.3334 正确
1.333335.toFixed(5)  // 1.33333 错误
1.3333335.toFixed(6) // 1.333333 错误

There is no problem with the implementation of Firefox and Chrome. The root cause is the loss of precision of floating point numbers in the computer.

Repair method:

function toFixed(num, s) {
    var times = Math.pow(10, s)
    var des = num * times + 0.5
    des = parseInt(des, 10) / times
    return des + ''
}

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