浮点数运算

operation.js

/**
 * operation 浮点数运算
 * https://github.com/nefe/number-precision
 * @desc 解决浮动运算问题，避免小数点后产生多位数和计算精度损失。
 * 问题示例：2.3 + 2.4 = 4.699999999999999，1.0 - 0.9 = 0.09999999999999998
 */

/**
 * 精确加法
 */
function add(num1, num2) {
    const others = []
    for (let _i = 2; _i < arguments.length; _i++) {
        others[_i - 2] = arguments[_i]
    }
    if (others.length > 0) {
        return add.apply(void 0, [add(num1, num2), others[0]].concat(others.slice(1)))
    }
    const baseNum = Math.pow(10, Math.max(digitLength(num1), digitLength(num2)))
    return (multiply(num1, baseNum) + multiply(num2, baseNum)) / baseNum
}

/**
 * 精确减法
 */
function subtract(num1, num2) {
    const others = []
    for (let _i = 2; _i < arguments.length; _i++) {
        others[_i - 2] = arguments[_i]
    }
    if (others.length > 0) {
        return subtract.apply(void 0, [subtract(num1, num2), others[0]].concat(others.slice(1)))
    }
    const baseNum = Math.pow(10, Math.max(digitLength(num1), digitLength(num2)))
    return (multiply(num1, baseNum) - multiply(num2, baseNum)) / baseNum
}

/**
 * 精确乘法
 */
function multiply(num1, num2) {
    const others = []
    for (let _i = 2; _i < arguments.length; _i++) {
        others[_i - 2] = arguments[_i]
    }
    if (others.length > 0) {
        return multiply.apply(void 0, [multiply(num1, num2), others[0]].concat(others.slice(1)))
    }
    const num1Changed = float2Fixed(num1)
    const num2Changed = float2Fixed(num2)
    const baseNum = digitLength(num1) + digitLength(num2)
    const leftValue = num1Changed * num2Changed
    checkBoundary(leftValue)
    return leftValue / Math.pow(10, baseNum)
}

/**
 * 精确除法
 */
function divide(num1, num2) {
    const others = []
    for (let _i = 2; _i < arguments.length; _i++) {
        others[_i - 2] = arguments[_i]
    }
    if (others.length > 0) {
        return divide.apply(void 0, [divide(num1, num2), others[0]].concat(others.slice(1)))
    }
    const num1Changed = float2Fixed(num1)
    const num2Changed = float2Fixed(num2)
    checkBoundary(num1Changed)
    checkBoundary(num2Changed)
    // fix: 类似 10 ** -4 为 0.00009999999999999999，strip 修正
    return multiply((num1Changed / num2Changed), strip(Math.pow(10, digitLength(num2) - digitLength(num1))))
}

/**
 * 把错误的数据转正
 * strip(0.09999999999999998)=0.1
 */
function strip(num, precision) {
    if (!num) return num
    if (precision === void 0) { precision = 12 }
    return +parseFloat(num.toPrecision(precision))
}

/**
 * Return digits length of a number
 * @param {*number} num Input number
 */
function digitLength(num) {
    if (!num) return num
    // Get digit length of e
    const eSplit = num.toString().split(/[eE]/)
    const len = (eSplit[0].split('.')[1] || '').length - (+(eSplit[1] || 0))
    return len > 0 ? len : 0
}

/**
 * 把小数转成整数，支持科学计数法。如果是小数则放大成整数
 * @param {*number} num 输入数
 */
function float2Fixed(num) {
    if (!num) return num
    if (num.toString().indexOf('e') === -1) {
        return Number(num.toString().replace('.', ''))
    }
    const dLen = digitLength(num)
    return dLen > 0 ? strip(num * Math.pow(10, dLen)) : num
}

/**
 * 检测数字是否越界，如果越界给出提示
 * @param {*number} num 输入数
 */
function checkBoundary(num) {
    if (!num) return num
    if (_boundaryCheckingState) {
        if (num > Number.MAX_SAFE_INTEGER || num < Number.MIN_SAFE_INTEGER) {
            global.console.warn(num + " is beyond boundary when transfer to integer, the results may not be accurate")
        }
    }
}

/**
 * 四舍五入
 */
function round(num, ratio) {
    const base = Math.pow(10, ratio)
    return divide(Math.round(multiply(num, base)), base)
}

/**
 * 是否进行边界检查，默认开启
 * @param flag 标记开关，true 为开启，false 为关闭，默认为 true
 */
let _boundaryCheckingState = true
function enableBoundaryChecking(flag) {
    if (flag === void 0) { flag = true }
    _boundaryCheckingState = flag
}

export default {
    add,
    subtract,
    multiply,
    divide,
    strip,
    round,
    digitLength,
    float2Fixed,
    enableBoundaryChecking,
}

// case
console.log(operation.add(0.1, 0.2), 0.1 + 0.2) // 0.3 0.30000000000000004
console.log(operation.subtract(300.73, 70), 300.73 - 70) // 230.73 230.73000000000002
console.log(operation.subtract(2, 0.14), 2 - 0.14) // 1.86 1.8599999999999999
console.log(operation.subtract(1.05, 1), 1.05 - 1) // 0.05 0.050000000000000044
console.log(operation.subtract(300.73, 300), 300.73 - 300) // 0.73 0.7300000000000182
console.log(operation.multiply(1073.4, 100), 1073.4 * 100) // 107340 107340.00000000001
console.log(operation.multiply(7.11, 10), 7.11 * 10) // 71.1 71.10000000000001
console.log(operation.divide(7.11, 10), 7.11 / 10) // 0.711 0.7110000000000001


// 以下乘除不准确
/* operation 浮点数运算
*  add / subtract / multiply /divide
* operation.add(0.1, 0.2) >> 0.3
* operation.multiply(19.9, 100) >> 1990
*
*/
import _ from 'lodash'

/*
 * 判断obj是否为一个整数
 */
function isInteger(obj) {
    return _.isInteger(_.toNumber(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) {
    if (!floatNum) {
        return {
            times: 1,
            num: floatNum,
        }
    }

    const ret = { times: 1, num: 0 }
    if (isInteger(floatNum)) {
        ret.num = floatNum
        return ret
    }
    const strfi = floatNum + ''
    const dotPos = strfi.indexOf('.')
    const len = strfi.substr(dotPos + 1).length
    const times = Math.pow(10, len)
    const intNum = Number(floatNum.toString().replace('.', ''))
    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, op) {
    const o1 = toInteger(a)
    const o2 = toInteger(b)
    const n1 = o1.num
    const n2 = o2.num
    const t1 = o1.times
    const t2 = o2.times
    const max = t1 > t2 ? t1 : t2
    let 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
    }
}

export default {
    add() {
        return operation(...arguments, 'add')
    },

    subtract() {
        return operation(...arguments, 'subtract')
    },

    multiply() {
        return operation(...arguments, 'multiply')
    },

    divide() {
        return operation(...arguments, 'divide')
    },
}