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/**
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* Problem statement and explanation: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
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*
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*
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* This algorithm plays an important role for modular arithmetic, and by extension for cyptography algorithms
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*
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*
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* This implementation uses an iterative approach to calculate
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*/
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/**
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*
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*
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* @param {Number} arg1 first argument
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* @param {Number} arg2 second argument
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* @returns Array with GCD and first and second Bézout coefficients
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*/
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const extendedEuclideanGCD = (arg1, arg2) => {
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if(typeof arg1 != 'number' || typeof arg2 != 'number') throw new TypeError('Not a Number');
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if(arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers');
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if (typeof arg1 !== 'number' || typeof arg2 !== 'number') throw new TypeError('Not a Number')
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if (arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers')
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// Make the order of coefficients correct, as the algorithm assumes r0 > r1
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if (arg1 < arg2) {
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const res = extendedEuclideanGCD(arg2,arg1)
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const temp = res[1]
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res[1] = res[2]
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res[2] = temp
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return res;
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}
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// Make the order of coefficients correct, as the algorithm assumes r0 > r1
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if (arg1 < arg2) {
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const res = extendedEuclideanGCD(arg2, arg1)
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const temp = res[1]
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res[1] = res[2]
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res[2] = temp
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return res
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}
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// At this point arg1 > arg2
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// At this point arg1 > arg2
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// Remainder values
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let r0 = arg1
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let r1 = arg2
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// Remainder values
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let r0 = arg1
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let r1 = arg2
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// Coefficient1 values
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let s0 = 1
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let s1 = 0
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// Coefficient1 values
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let s0 = 1
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let s1 = 0
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// Coefficient 2 values
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let t0 = 0
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let t1 = 1
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while(r1 != 0) {
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const q = Math.floor(r0 / r1);
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// Coefficient 2 values
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let t0 = 0
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let t1 = 1
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const r2 = r0 - r1*q;
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const s2 = s0 - s1*q;
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const t2 = t0 - t1*q;
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r0 = r1
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r1 = r2
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s0 = s1
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s1 = s2
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t0 = t1
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t1 = t2
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}
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return [r0,s0,t0];
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while (r1 != 0) {
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const q = Math.floor(r0 / r1)
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const r2 = r0 - r1 * q
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const s2 = s0 - s1 * q
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const t2 = t0 - t1 * q
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r0 = r1
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r1 = r2
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s0 = s1
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s1 = s2
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t0 = t1
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t1 = t2
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}
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return [r0, s0, t0]
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}
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export { extendedEuclideanGCD };
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export { extendedEuclideanGCD }
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// ex
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