bigint-mod-arith/dist/esm/index.browser.js

/**
 * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
 *
 * @param a
 *
 * @returns The absolute value of a
 */
function abs(a) {
    return (a >= 0) ? a : -a;
}

/**
 * Returns the bitlength of a number
 *
 * @param a
 * @returns The bit length
 */
function bitLength(a) {
    a = BigInt(a);
    if (a === 1n) {
        return 1;
    }
    let bits = 1;
    do {
        bits++;
    } while ((a >>= 1n) > 1n);
    return bits;
}

/**
 * An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
 * Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
 *
 * @param a
 * @param b
 *
 * @returns A triple (g, x, y), such that ax + by = g = gcd(a, b).
 */
function eGcd(a, b) {
    let aBigint = BigInt(a);
    let bBigInt = BigInt(b);
    if (aBigint <= 0n || bBigInt <= 0n)
        throw new RangeError('a and b MUST be > 0'); // a and b MUST be positive
    let x = 0n;
    let y = 1n;
    let u = 1n;
    let v = 0n;
    while (aBigint !== 0n) {
        const q = bBigInt / aBigint;
        const r = bBigInt % aBigint;
        const m = x - (u * q);
        const n = y - (v * q);
        bBigInt = aBigint;
        aBigint = r;
        x = u;
        y = v;
        u = m;
        v = n;
    }
    return {
        g: bBigInt,
        x: x,
        y: y
    };
}

/**
 * Greatest-common divisor of two integers based on the iterative binary algorithm.
 *
 * @param a
 * @param b
 *
 * @returns The greatest common divisor of a and b
 */
function gcd(a, b) {
    let aAbs = BigInt(abs(a));
    let bAbs = BigInt(abs(b));
    if (aAbs === 0n) {
        return bAbs;
    }
    else if (bAbs === 0n) {
        return aAbs;
    }
    let shift = 0n;
    while (((aAbs | bAbs) & 1n) === 0n) {
        aAbs >>= 1n;
        bAbs >>= 1n;
        shift++;
    }
    while ((aAbs & 1n) === 0n)
        aAbs >>= 1n;
    do {
        while ((bAbs & 1n) === 0n)
            bAbs >>= 1n;
        if (aAbs > bAbs) {
            const x = aAbs;
            aAbs = bAbs;
            bAbs = x;
        }
        bAbs -= aAbs;
    } while (bAbs !== 0n);
    // rescale
    return aAbs << shift;
}

/**
 * The least common multiple computed as abs(a*b)/gcd(a,b)
 * @param a
 * @param b
 *
 * @returns The least common multiple of a and b
 */
function lcm(a, b) {
    const aBigInt = BigInt(a);
    const bBigInt = BigInt(b);
    if (aBigInt === 0n && bBigInt === 0n)
        return BigInt(0);
    return abs(aBigInt * bBigInt) / gcd(aBigInt, bBigInt);
}

/**
 * Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
 *
 * @param a
 * @param b
 *
 * @returns Maximum of numbers a and b
 */
function max(a, b) {
    return (a >= b) ? a : b;
}

/**
 * Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
 *
 * @param a
 * @param b
 *
 * @returns Minimum of numbers a and b
 */
function min(a, b) {
    return (a >= b) ? b : a;
}

/**
 * Finds the smallest positive element that is congruent to a in modulo n
 * @param {number|bigint} a An integer
 * @param {number|bigint} n The modulo
 *
 * @returns The smallest positive representation of a in modulo n or number NaN if n < 0
 */
function toZn(a, n) {
    const nBigInt = BigInt(n);
    if (n <= 0) {
        return NaN;
    }
    const aZn = BigInt(a) % nBigInt;
    return (aZn < 0n) ? aZn + nBigInt : aZn;
}

/**
 * Modular inverse.
 *
 * @param a The number to find an inverse for
 * @param n The modulo
 *
 * @returns The inverse modulo n or number NaN if it does not exist
 */
function modInv(a, n) {
    try {
        const egcd = eGcd(toZn(a, n), n);
        if (egcd.g !== 1n) {
            return NaN; // modular inverse does not exist
        }
        else {
            return toZn(egcd.x, n);
        }
    }
    catch (error) {
        return NaN;
    }
}

/**
 * Modular exponentiation b**e mod n. Currently using the right-to-left binary method
 *
 * @param b base
 * @param e exponent
 * @param n modulo
 *
 * @returns b**e mod n or number NaN if n <= 0
 */
function modPow(b, e, n) {
    const nBigInt = BigInt(n);
    if (nBigInt <= 0n) {
        return NaN;
    }
    else if (nBigInt === 1n) {
        return BigInt(0);
    }
    let bZn = toZn(b, nBigInt);
    e = BigInt(e);
    if (e < 0n) {
        return modInv(modPow(bZn, abs(e), nBigInt), nBigInt);
    }
    let r = 1n;
    while (e > 0) {
        if ((e % 2n) === 1n) {
            r = (r * bZn) % nBigInt;
        }
        e = e / 2n;
        bZn = bZn ** 2n % nBigInt;
    }
    return r;
}

export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn };
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