聊聊js的運算精度問題

0.1 >> 0.0001 1001 1001 1001…（1001無限循環）
0.2 >> 0.0011 0011 0011 0011…（0011無限循環）

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

/**
 * floatObj 包含加減乘除四個方法，能確保浮點數運算不丟失精度
 *
 * ** 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() {
 /*
 * 判斷obj是否為一個整數
 */
 function isInteger(obj) {
 return Math.floor(obj) === obj
 }
 /*
 * 將一個浮點數轉成整數，返回整數和倍數。如 3.14 >> 314，倍數是 100
 * @param floatNum {number} 小數
 * @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，實現加減乘除運算，確保不丟失精度
 * 思路：把小數放大為整數（乘），進行算術運算，再縮小為小數（除）
 *
 * @param a {number} 運算數1
 * @param b {number} 運算數2
 * @param digits {number} 精度，保留的小數點數，比如 2, 即保留為兩位小數
 * @param op {string} 運算類型，有加減乘除（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) { // 兩個小數位數相同
 result = n1 + n2
 } else if (t1 > t2) { // o1 小數位 大于 o2
 result = n1 + n2 * (t1 / t2)
 } else { // o1 小數位 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
 }
 }
 // 加減乘除的四個接口
 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
 }
}();

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

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 += '0';
 }
 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] === '0') {
 Adb = Adb.substr(1);
 }
 if (Adb.length === lb) {
 max = Math.ceil((parseInt(Adb.charAt(0)) + 1) / b0); // 不可能取到這個最大值,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 + '');
 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('0');
 }
 result.splice(result.length - point, 0, '.');
 if (!result[0] && result[1] !== '.') {
 result.shift();
 }
 point = false;
 let position = result.indexOf('.');
 for (let i = position + 1; i < result.length; i++) {
 if (result[i]) {
 point = true;
 break;
 }
 }
 if (!point) {
 result.splice(position);
 }
 result = result.join('');
 return result;
}
function multiply(A, B) {
 let result = [];
 (A += ''), (B += '');
 const l = -4; // 以支持百萬位精確運算，但速度減半
 let r1 = [],
 r2 = [];
 while (A !== '') {
 r1.unshift(parseInt(A.substr(l)));
 A = A.slice(0, l);
 }
 while (B !== '') {
 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] += '';
 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] = '0' + result[i];
 }
 }
 if (result[0]) {
 result = result.join('');
 } else {
 result = '0';
 }
 return result;
}
function add(A, B) {
 let result = [];
 (A += ''), (B += '');
 const l = -15;
 while (A !== '' && B !== '') {
 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] += '';
 if (result[i].length > -l) {
 result[i - 1] += 1;
 result[i] = result[i].substr(1);
 } else {
 while (result[i].length < -l) {
 result[i] = '0' + result[i];
 }
 }
 }
 while (A && (result[0] + '').length > -l) {
 result[0] = (result[0] + '').substr(1);
 result.unshift(parseInt(A.substr(l)) + 1);
 A = A.slice(0, l);
 }
 if (A) {
 while ((result[0] + '').length < -l) {
 result[0] = '0' + result[0];
 }
 result.unshift(A);
 }
 if (result[0]) {
 result = result.join('');
 } else {
 result = '0';
 }
 return result;
}
function reduce(A, B) {
 let result = [];
 (A += ''), (B += '');
 while (A[0] === '0') {
 A = A.substr(1);
 }
 while (B[0] === '0') {
 B = B.substr(1);
 }
 const l = -15;
 let N = '1';
 for (let i = 0; i < -l; i++) {
 N += '0';
 }
 N = parseInt(N);
 while (A !== '' && B !== '') {
 result.unshift(parseInt(A.substr(l)) - parseInt(B.substr(l)));
 A = A.slice(0, l);
 B = B.slice(0, l);
 }
 if (A !== '' || B !== '') {
 let s = B === '' ? 1 : -1;
 A += B;
 while (A !== '') {
 result.unshift(s * parseInt(A.substr(l)));
 A = A.slice(0, l);
 }
 }
 while (result.length !== 0 && result[0] === 0) {
 result.shift();
 }
 let s = '';
 if (result.length === 0) {
 result = 0;
 } else if (result[0] < 0) {
 s = '-';
 for (let i = result.length - 1; i > 0; i--) {
 if (result[i] > 0) {
 result[i] -= N;
 result[i - 1]++;
 }
 result[i] *= -1;
 result[i] += '';
 while (result[i].length < -l) {
 result[i] = '0' + 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] += '';
 while (result[i].length < -l) {
 result[i] = '0' + result[i];
 }
 }
 }
 if (result) {
 while ((result[0] = parseInt(result[0])) === 0) {
 result.shift();
 }
 result = s + result.join('');
 }
 return result;
}

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

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

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