const _ZERO = BigInt(0);
const _ONE = BigInt(1);
const _TWO = BigInt(2);

/**
 * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
 *  
 * @param {number|bigint} a 
 * 
 * @returns {bigint} the absolute value of a
 */
function abs(a) {
    a = BigInt(a);
    return (a >= _ZERO) ? a : -a;
}

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

/**
 * @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
 * @property {bigint} g
 * @property {bigint} x 
 * @property {bigint} y
 */
/**
 * 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 {number|bigint} a 
 * @param {number|bigint} b 
 * 
 * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
 */
function eGcd(a, b) {
    a = BigInt(a);
    b = BigInt(b);
    if (a <= _ZERO | b <= _ZERO)
        return NaN; // a and b MUST be positive

    let x = _ZERO;
    let y = _ONE;
    let u = _ONE;
    let v = _ZERO;

    while (a !== _ZERO) {
        let q = b / a;
        let r = b % a;
        let m = x - (u * q);
        let n = y - (v * q);
        b = a;
        a = r;
        x = u;
        y = v;
        u = m;
        v = n;
    }
    return {
        b: b,
        x: x,
        y: y
    };
}

/**
 * Greatest-common divisor of two integers based on the iterative binary algorithm.
 * 
 * @param {number|bigint} a 
 * @param {number|bigint} b 
 * 
 * @returns {bigint} The greatest common divisor of a and b
 */
function gcd(a, b) {
    a = abs(a);
    b = abs(b);
    if (a === _ZERO)
        return b;
    else if (b === _ZERO)
        return a;

    let shift = _ZERO;
    while (!((a | b) & _ONE)) {
        a >>= _ONE;
        b >>= _ONE;
        shift++;
    }
    while (!(a & _ONE)) a >>= _ONE;
    do {
        while (!(b & _ONE)) b >>= _ONE;
        if (a > b) {
            let x = a;
            a = b;
            b = x;
        }
        b -= a;
    } while (b);

    // rescale
    return a << shift;
}

/**
 * The test first tries if any of the first 250 small primes are a factor of the input number and then passes several 
 * iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
 * 
 * @param {number|bigint} w An integer to be tested for primality
 * @param {number} iterations The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
 * 
 * @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
 */
async function isProbablyPrime(w, iterations = 16) {
    if (typeof w === 'number') {
        w = BigInt(w);
    }
    { // browser
        return new Promise((resolve, reject) => {
            const worker = new Worker(_isProbablyPrimeWorkerUrl());

            worker.onmessage = (event) => {
                worker.terminate();
                resolve(event.data.isPrime);
            };

            worker.onmessageerror = (event) => {
                reject(event);
            };

            worker.postMessage({
                'rnd': w,
                'iterations': iterations,
                'id': 0
            });
        });
    }
}

/**
 * The least common multiple computed as abs(a*b)/gcd(a,b)
 * @param {number|bigint} a 
 * @param {number|bigint} b 
 * 
 * @returns {bigint} The least common multiple of a and b
 */
function lcm(a, b) {
    a = BigInt(a);
    b = BigInt(b);
    if (a === _ZERO && b === _ZERO)
        return _ZERO;
    return abs(a * b) / gcd(a, b);
}

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

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

/**
 * Modular inverse.
 * 
 * @param {number|bigint} a The number to find an inverse for
 * @param {number|bigint} n The modulo
 * 
 * @returns {bigint} the inverse modulo n or NaN if it does not exist
 */
function modInv(a, n) {
    if (a == _ZERO | n <= _ZERO)
        return NaN;

    let egcd = eGcd(toZn(a, n), n);
    if (egcd.b !== _ONE) {
        return NaN; // modular inverse does not exist
    } else {
        return toZn(egcd.x, n);
    }
}

/**
 * Modular exponentiation b**e mod n. Currently using the right-to-left binary method
 * 
 * @param {number|bigint} b base
 * @param {number|bigint} e exponent
 * @param {number|bigint} n modulo
 * 
 * @returns {bigint} b**e mod n
 */
function modPow(b, e, n) {
    n = BigInt(n);
    if (n === _ZERO)
        return NaN;
    else if (n === _ONE)
        return _ZERO;

    b = toZn(b, n);

    e = BigInt(e);
    if (e < _ZERO) {
        return modInv(modPow(b, abs(e), n), n);
    }

    let r = _ONE;
    while (e > 0) {
        if ((e % _TWO) === _ONE) {
            r = (r * b) % n;
        }
        e = e / _TWO;
        b = b ** _TWO % n;
    }
    return r;
}

/**
 * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. 
 * The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI 
 * main process, and it can be much faster (if several cores or cpu are available). 
 * The node version can also use worker_threads if they are available (enabled by default with Node 11 and 
 * and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
 * 
 * @param {number} bitLength The required bit length for the generated prime
 * @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
 * @param {boolean} sync NOT RECOMMENDED. Invoke the function synchronously. It won't use workers so it'll be slower and may freeze thw window in browser's javascript.
 * 
 * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
 */
function prime(bitLength, iterations = 16) {
    if (bitLength < 1)
        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
    return new Promise((resolve) => {
        let workerList = [];
        const _onmessage = (msg, newWorker) => {
            if (msg.isPrime) {
                // if a prime number has been found, stop all the workers, and return it
                for (let j = 0; j < workerList.length; j++) {
                    workerList[j].terminate();
                }
                while (workerList.length) {
                    workerList.pop();
                }
                resolve(msg.value);
            } else { // if a composite is found, make the worker test another random number
                let buf = randBits(bitLength, true);
                let rnd = fromBuffer(buf);
                try {
                    newWorker.postMessage({
                        'rnd': rnd,
                        'iterations': iterations,
                        'id': msg.id
                    });
                } catch (error) {
                    // The worker has already terminated. There is nothing to handle here
                }
            }
        };
        { //browser
            let workerURL = _isProbablyPrimeWorkerUrl();
            for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
                let newWorker = new Worker(workerURL);
                newWorker.onmessage = (event) => _onmessage(event.data, newWorker);
                workerList.push(newWorker);
            }
        }
        for (let i = 0; i < workerList.length; i++) {
            let buf = randBits(bitLength, true);
            let rnd = fromBuffer(buf);
            workerList[i].postMessage({
                'rnd': rnd,
                'iterations': iterations,
                'id': i
            });
        }
    });
}

/**
 * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. 
 * The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
 * 
 * @param {number} bitLength The required bit length for the generated prime
 * @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
 * 
 * @returns {bigint} A bigint probable prime of bitLength bits.
 */
function primeSync(bitLength, iterations = 16) {
    if (bitLength < 1)
        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
    let rnd = _ZERO;
    do {
        rnd = fromBuffer(randBytesSync(bitLength / 8, true));
    } while (!_isProbablyPrime(rnd, iterations));
    return rnd;
}

/**
 * Returns a cryptographically secure random integer between [min,max]
 * @param {bigint} max Returned value will be <= max
 * @param {bigint} min Returned value will be >= min
 * 
 * @returns {bigint} A cryptographically secure random bigint between [min,max]
 */
function randBetween(max, min = _ONE) {
    if (max <= min) throw new Error('max must be > min');
    const interval = max - min;
    let bitLen = bitLength(interval);
    let rnd;
    do {
        let buf = randBits(bitLen);
        rnd = fromBuffer(buf);
    } while (rnd > interval);
    return rnd + min;
}

/**
 * Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 * 
 * @param {number} bitLength The desired number of random bits
 * @param {boolean} forceLength If we want to force the output to have a specific bit length. It basically forces the msb to be 1
 * 
 * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
 */
function randBits(bitLength, forceLength = false) {
    if (bitLength < 1)
        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);

    const byteLength = Math.ceil(bitLength / 8);
    let rndBytes = randBytesSync(byteLength, false);
    // Fill with 0's the extra bits
    rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1);
    if (forceLength) {
        let mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128;
        rndBytes[0] = rndBytes[0] | mask;
    }
    return rndBytes;
}

/**
 * Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 * 
 * @param {number} byteLength The desired number of random bytes
 * @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
 * 
 * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
 */
function randBytes(byteLength, forceLength = false) {
    if (byteLength < 1)
        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);

    let buf;
    { // browser
        return new Promise(function (resolve) {
            buf = new Uint8Array(byteLength);
            self.crypto.getRandomValues(buf);
            // If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
            if (forceLength)
                buf[0] = buf[0] | 128;
            resolve(buf);
        });
    }
}

/**
 * Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 * 
 * @param {number} byteLength The desired number of random bytes
 * @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
 * 
 * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
 */
function randBytesSync(byteLength, forceLength = false) {
    if (byteLength < 1)
        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);

    let buf;
    { // browser
        buf = new Uint8Array(byteLength);
        self.crypto.getRandomValues(buf);
    }
    // If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
    if (forceLength)
        buf[0] = buf[0] | 128;
    return buf;
}

/**
 * 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 {bigint} The smallest positive representation of a in modulo n
 */
function toZn(a, n) {
    n = BigInt(n);
    if (n <= 0)
        return NaN;

    a = BigInt(a) % n;
    return (a < 0) ? a + n : a;
}



/* HELPER FUNCTIONS */

function fromBuffer(buf) {
    let ret = _ZERO;
    for (let i of buf.values()) {
        let bi = BigInt(i);
        ret = (ret << BigInt(8)) + bi;
    }
    return ret;
}

function _isProbablyPrimeWorkerUrl() {
    // Let's us first add all the required functions
    let workerCode = `'use strict';const _ZERO = BigInt(0);const _ONE = BigInt(1);const _TWO = BigInt(2);const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBits = ${randBits.toString()};const randBytesSync = ${randBytesSync.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`;

    const onmessage = async function (event) { // Let's start once we are called
        // event.data = {rnd: <bigint>, iterations: <number>}
        const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations);
        postMessage({
            'isPrime': isPrime,
            'value': event.data.rnd,
            'id': event.data.id
        });
    };

    workerCode += `onmessage = ${onmessage.toString()};`;

    return _workerUrl(workerCode);
}

function _workerUrl(workerCode) {
    workerCode = `(() => {${workerCode}})()`; // encapsulate IIFE
    const _blob = new Blob([workerCode], { type: 'text/javascript' });
    return window.URL.createObjectURL(_blob);
}

function _isProbablyPrime(w, iterations = 16) {
    /*
	PREFILTERING. Even values but 2 are not primes, so don't test. 
	1 is not a prime and the M-R algorithm needs w>1.
	*/
    if (w === _TWO)
        return true;
    else if ((w & _ONE) === _ZERO || w === _ONE)
        return false;

    /*
    Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
    */
    const firstPrimes = [
        3,
        5,
        7,
        11,
        13,
        17,
        19,
        23,
        29,
        31,
        37,
        41,
        43,
        47,
        53,
        59,
        61,
        67,
        71,
        73,
        79,
        83,
        89,
        97,
        101,
        103,
        107,
        109,
        113,
        127,
        131,
        137,
        139,
        149,
        151,
        157,
        163,
        167,
        173,
        179,
        181,
        191,
        193,
        197,
        199,
        211,
        223,
        227,
        229,
        233,
        239,
        241,
        251,
        257,
        263,
        269,
        271,
        277,
        281,
        283,
        293,
        307,
        311,
        313,
        317,
        331,
        337,
        347,
        349,
        353,
        359,
        367,
        373,
        379,
        383,
        389,
        397,
        401,
        409,
        419,
        421,
        431,
        433,
        439,
        443,
        449,
        457,
        461,
        463,
        467,
        479,
        487,
        491,
        499,
        503,
        509,
        521,
        523,
        541,
        547,
        557,
        563,
        569,
        571,
        577,
        587,
        593,
        599,
        601,
        607,
        613,
        617,
        619,
        631,
        641,
        643,
        647,
        653,
        659,
        661,
        673,
        677,
        683,
        691,
        701,
        709,
        719,
        727,
        733,
        739,
        743,
        751,
        757,
        761,
        769,
        773,
        787,
        797,
        809,
        811,
        821,
        823,
        827,
        829,
        839,
        853,
        857,
        859,
        863,
        877,
        881,
        883,
        887,
        907,
        911,
        919,
        929,
        937,
        941,
        947,
        953,
        967,
        971,
        977,
        983,
        991,
        997,
        1009,
        1013,
        1019,
        1021,
        1031,
        1033,
        1039,
        1049,
        1051,
        1061,
        1063,
        1069,
        1087,
        1091,
        1093,
        1097,
        1103,
        1109,
        1117,
        1123,
        1129,
        1151,
        1153,
        1163,
        1171,
        1181,
        1187,
        1193,
        1201,
        1213,
        1217,
        1223,
        1229,
        1231,
        1237,
        1249,
        1259,
        1277,
        1279,
        1283,
        1289,
        1291,
        1297,
        1301,
        1303,
        1307,
        1319,
        1321,
        1327,
        1361,
        1367,
        1373,
        1381,
        1399,
        1409,
        1423,
        1427,
        1429,
        1433,
        1439,
        1447,
        1451,
        1453,
        1459,
        1471,
        1481,
        1483,
        1487,
        1489,
        1493,
        1499,
        1511,
        1523,
        1531,
        1543,
        1549,
        1553,
        1559,
        1567,
        1571,
        1579,
        1583,
        1597,
    ];
    for (let i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) {
        const p = BigInt(firstPrimes[i]);
        if (w === p)
            return true;
        else if (w % p === _ZERO)
            return false;
    }

    /*
    1. Let a be the largest integer such that 2**a divides w−1.
    2. m = (w−1) / 2**a.
    3. wlen = len (w).
    4. For i = 1 to iterations do
        4.1 Obtain a string b of wlen bits from an RBG.
        Comment: Ensure that 1 < b < w−1.
        4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
        4.3 z = b**m mod w.
        4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
        4.5 For j = 1 to a − 1 do.
        4.5.1 z = z**2 mod w.
        4.5.2 If (z = w−1), then go to step 4.7.
        4.5.3 If (z = 1), then go to step 4.6.
        4.6 Return COMPOSITE.
        4.7 Continue.
        Comment: Increment i for the do-loop in step 4.
    5. Return PROBABLY PRIME.
    */
    let a = _ZERO, d = w - _ONE;
    while (d % _TWO === _ZERO) {
        d /= _TWO;
        ++a;
    }

    let m = (w - _ONE) / (_TWO ** a);

    loop: do {
        let b = randBetween(w - _ONE, _TWO);
        let z = modPow(b, m, w);
        if (z === _ONE || z === w - _ONE)
            continue;

        for (let j = 1; j < a; j++) {
            z = modPow(z, _TWO, w);
            if (z === w - _ONE)
                continue loop;
            if (z === _ONE)
                break;
        }
        return false;
    } while (--iterations);

    return true;
}

export { abs, bitLength, eGcd, gcd, isProbablyPrime, lcm, max, min, modInv, modPow, prime, primeSync, randBetween, randBits, randBytes, randBytesSync, toZn };