2022-01-17 10:04:55 +00:00
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function abs(a) {
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return (a >= 0) ? a : -a;
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}
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function bitLength(a) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (a === 1n) {
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return 1;
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}
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let bits = 1;
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do {
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bits++;
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} while ((a >>= 1n) > 1n);
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return bits;
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}
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function eGcd(a, b) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof b === 'number')
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b = BigInt(b);
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if (a <= 0n || b <= 0n)
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2023-04-11 08:43:47 +00:00
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throw new RangeError('a and b MUST be > 0');
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2022-01-17 10:04:55 +00:00
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let x = 0n;
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let y = 1n;
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let u = 1n;
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let v = 0n;
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while (a !== 0n) {
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const q = b / a;
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const r = b % a;
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const m = x - (u * q);
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const n = y - (v * q);
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b = a;
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a = r;
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x = u;
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y = v;
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u = m;
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v = n;
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}
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return {
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g: b,
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2023-04-11 08:43:47 +00:00
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x,
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y
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2022-01-17 10:04:55 +00:00
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};
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}
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function gcd(a, b) {
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let aAbs = (typeof a === 'number') ? BigInt(abs(a)) : abs(a);
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let bAbs = (typeof b === 'number') ? BigInt(abs(b)) : abs(b);
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if (aAbs === 0n) {
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return bAbs;
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}
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else if (bAbs === 0n) {
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return aAbs;
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}
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let shift = 0n;
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while (((aAbs | bAbs) & 1n) === 0n) {
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aAbs >>= 1n;
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bAbs >>= 1n;
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shift++;
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}
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while ((aAbs & 1n) === 0n)
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aAbs >>= 1n;
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do {
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while ((bAbs & 1n) === 0n)
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bAbs >>= 1n;
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if (aAbs > bAbs) {
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const x = aAbs;
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aAbs = bAbs;
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bAbs = x;
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}
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bAbs -= aAbs;
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} while (bAbs !== 0n);
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return aAbs << shift;
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}
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function lcm(a, b) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof b === 'number')
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b = BigInt(b);
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if (a === 0n && b === 0n)
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return BigInt(0);
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return abs((a / gcd(a, b)) * b);
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}
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function max(a, b) {
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return (a >= b) ? a : b;
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}
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function min(a, b) {
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return (a >= b) ? b : a;
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}
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function toZn(a, n) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof n === 'number')
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n = BigInt(n);
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if (n <= 0n) {
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throw new RangeError('n must be > 0');
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}
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const aZn = a % n;
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return (aZn < 0n) ? aZn + n : aZn;
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}
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function modInv(a, n) {
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const egcd = eGcd(toZn(a, n), n);
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if (egcd.g !== 1n) {
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2023-04-11 08:43:47 +00:00
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throw new RangeError(`${a.toString()} does not have inverse modulo ${n.toString()}`);
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2022-01-17 10:04:55 +00:00
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}
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else {
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return toZn(egcd.x, n);
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}
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}
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function modPow(b, e, n) {
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if (typeof b === 'number')
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b = BigInt(b);
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if (typeof e === 'number')
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e = BigInt(e);
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if (typeof n === 'number')
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n = BigInt(n);
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if (n <= 0n) {
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throw new RangeError('n must be > 0');
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}
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else if (n === 1n) {
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return 0n;
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}
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b = toZn(b, n);
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if (e < 0n) {
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return modInv(modPow(b, abs(e), n), n);
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}
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let r = 1n;
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while (e > 0) {
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if ((e % 2n) === 1n) {
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r = r * b % n;
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}
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e = e / 2n;
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b = b ** 2n % n;
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}
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return r;
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}
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export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn };
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