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