A method of rounding decimals in JavaScript that is aimed to correct inaccurate calculations

readme.md

Rounding decimal numbers in JavaScript

Problem

Calculations in JavaScript are performed in accordance with IEEE 754 standard. According to this standard, numbers are stored in binary form, which can give unexpected results when working with decimals. Examples:

0.1 + 0.2 == 0.30000000000000004; // = 0.3
Math.round(1.025 * 100) == 102; // 102.5 ≈ 103
(0.101 + 0.704).toFixed(2) == '0.80'; // 0.805 ≈ 0.81
Math.round(-0.5) == 0; // -0.5 ≈ -1 (commercial rounding or "away from zero" strategy)

Solution

Knowing that values contain a fixed number of decimal places (e.g. two for cents) can greatly improve the accuracy of calculations. When possible, a reasonably fast method with a temporary conversion of a number to an integer is used. In other cases the number is converted to a string, this acts similar to Excel's "Set precision as displayed" option. In this way surprises like "extra cent" can be avoided.

License

This project is licensed under the MIT License - see the license.txt for details.

decimal-rounding.ts

// Copyright (c) Artem Avramenko. All rights reserved.
// Licensed under the MIT license. See license.txt for details.

/** 
 * Returns an integer power of ten with maximum accuracy and performance
 */
const pow10 = (() => {
    const precalc = [] as number[];
    for (let i = -323; i < 309; i++) {
        precalc.push(+('1e' + i));
    }
    return (intPow: number) => {
        intPow = +intPow;
        if (Number.isNaN(intPow)) {
            return NaN;
        }
        if (intPow <= -324) {
            return 0;
        }
        if (intPow >= 309) {
            return Infinity;
        }
        return precalc[(intPow|0) + 323];    
    }
})();

/** 
 * A more accurate version of decimal rounding.
 * In certain cases can be hundreds of times slower than normal rounding.
 */
function roundDecimal(value: number, digits = 0, fromDigits = -1) {
    let newValue = +value;
    if (newValue === 0) {
        return newValue;
    }    
    const isNegative = newValue < 0;
    if (isNegative) {
        newValue = -newValue;
    }

    digits |= 0;
    if (digits === 0 && fromDigits < 0) {
        newValue = Math.round(newValue);
    } else if (digits >= 0 && digits <= fromDigits && fromDigits < 309) {
        // knowing that the value already contains decimal, faster corrections can be used
        const fromPow = pow10(fromDigits);
        const toPow = pow10(fromDigits - digits);
        newValue = Math.round(newValue * fromPow);
        const rem = newValue % toPow;
        if (rem >= toPow / 2) {
             newValue += toPow - rem;
         } else {
             newValue -= rem;
         }
         newValue /= fromPow;
    } else if (newValue >= 1e-6 && newValue < 1e21) {
        // slow mode for numbers without exponent
        const s = newValue.toString() + 'e' + digits;
        newValue = Math.round(+s);
        newValue = digits >= 0 ? newValue / pow10(digits) : newValue * pow10(-digits);
    } else {
        // slowest mode (https://developer.mozilla.org/ru/docs/Web/JavaScript/Reference/Global_Objects/Math/round)
        let [valS, powS] = newValue.toString().split('e');
        let pow = +(powS || 0) + digits;
        newValue = Math.round(+(valS + 'e' + pow));
        [valS, powS] = newValue.toString().split('e');
        pow = +(powS || 0) - digits;
        newValue = +(valS + 'e' + pow);
    }

    if (!Number.isFinite(newValue)) {
        return +value;
    }

    return isNegative ? -newValue : newValue;
}

/** 
 * Corrects decimal amounts.
 * Suitable for addition/subtraction operations only.
 */
function normalizeDecimal(value: number, digits: number) {
    return roundDecimal(value, digits, digits);
}

/**
 * Corrects money amounts.
 * Suitable for addition/subtraction operations only.
 */
function normalizeMoney(value: number) {
    return roundDecimal(value, 4, 4);
}

/**
 * Rounds decimal amount.
 * Suitable only for values already containing normalized money.
 */
function roundMoney(money: number, digits = 2) {
    return roundDecimal(money, digits, 4);
}

const expect = (actual: any) => ({
    toBe: (expected: any) => {
        if (actual !== expected) {
            console.error(actual + ' should be ' + expected)
        }
    }
});

expect(normalizeMoney(0.1 + 0.2)).toBe(0.3);
expect(roundMoney(1.0250, 2)).toBe(1.03);
expect(normalizeMoney(0.101 + 0.704)).toBe(0.805);
expect(normalizeDecimal(0.101 + 0.704, 3)).toBe(0.805);
expect(normalizeMoney(0.101 + 0.904)).toBe(1.005);
expect(roundDecimal(0.101 + 0.904, 4)).toBe(1.005);
expect(normalizeMoney(262143.521 + 0.704)).toBe(262144.225);
expect(roundDecimal(1025, -1)).toBe(1030);
expect(roundDecimal(Infinity)).toBe(Infinity);
expect(roundDecimal(-Infinity, 2, 4)).toBe(-Infinity);
expect(roundDecimal(NaN).toString()).toBe('NaN');
expect(roundDecimal(NaN, 2, 4).toString()).toBe('NaN');
expect(1 / roundDecimal(-0, 2)).toBe(-Infinity);
expect(roundDecimal(1.2345678901234565, 15, 15)).toBe(1.234567890123457);
expect(roundDecimal(1.2345678901234562, 15, 15)).toBe(1.234567890123456);
expect(roundDecimal(0.1122334455667752, 15, 15)).toBe(0.112233445566775);
expect(roundDecimal(0.11223344556677449, 15, 15)).toBe(0.112233445566774);
expect(roundDecimal(1.495, 0, 3)).toBe(1);
expect(roundDecimal(1.495, 0, 2)).toBe(2);
expect(roundDecimal(1.495, 0, 1)).toBe(2);
expect(roundDecimal(1.005, 2)).toBe(1.01);
expect(roundDecimal(123450000, -5)).toBe(123500000);
expect(roundDecimal(1.2344e-305, 307, 308)).toBe(1.23e-305);
expect(roundDecimal(1.2345e-305, 307, 308)).toBe(1.24e-305);
expect(roundDecimal(1.234e-320, 322)).toBe(1.23e-320);
expect(roundDecimal(0.00123, 320)).toBe(0.00123);
expect(roundDecimal(0.00123, 307, 308)).toBe(0.00123);
expect(roundDecimal(1.23e308, 307, 308)).toBe(1.23e308);
expect(roundDecimal(1.23e308, -307)).toBe(1.2e308);
expect(roundDecimal(1.23e308, -308)).toBe(1e308);
expect(roundDecimal(1.23e308, -309)).toBe(0);

console.log('Tests finished');

license.txt

The MIT License (MIT)

Copyright (c) 2024 Artem Avramenko

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.