chore: import upstream snapshot with attribution

math/extended_euclid_algorithm.cpp

@@ -0,0 +1,97 @@
+/**
+ * @file
+ * @brief GCD using [extended Euclid's algorithm]
+ * (https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm)
+ *
+ * Finding coefficients of a and b ie x and y in  Bézout's identity
+ * \f[\text{gcd}(a, b) = a \times x + b \times y \f]
+ * This is also used in finding Modular
+ * multiplicative inverse of a number. (A * B)%M == 1 Here B is the MMI of A for
+ * given M, so extendedEuclid (A, M) gives B.
+ */
+#include <algorithm>  // for swap function
+#include <iostream>
+#include <cstdint>
+
+/**
+ * function to update the coefficients per iteration
+ * \f[r_0,\,r = r,\, r_0 - \text{quotient}\times r\f]
+ *
+ * @param[in,out] r signed or unsigned
+ * @param[in,out] r0 signed or unsigned
+ * @param[in] quotient  unsigned
+ */
+template <typename T, typename T2>
+inline void update_step(T *r, T *r0, const T2 quotient) {
+    T temp = *r;
+    *r = *r0 - (quotient * temp);
+    *r0 = temp;
+}
+
+/**
+ * Implementation using iterative algorithm from
+ * [Wikipedia](https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Pseudocode)
+ *
+ * @param[in] A unsigned
+ * @param[in] B unsigned
+ * @param[out] GCD unsigned
+ * @param[out] x signed
+ * @param[out] y signed
+ */
+template <typename T1, typename T2>
+void extendedEuclid_1(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y) {
+    if (B > A)
+        std::swap(A, B);  // Ensure that A >= B
+
+    T2 s = 0, s0 = 1;
+    T2 t = 1, t0 = 0;
+    T1 r = B, r0 = A;
+
+    while (r != 0) {
+        T1 quotient = r0 / r;
+        update_step(&r, &r0, quotient);
+        update_step(&s, &s0, quotient);
+        update_step(&t, &t0, quotient);
+    }
+    *GCD = r0;
+    *x = s0;
+    *y = t0;
+}
+
+/**
+ * Implementation using recursive algorithm
+ *
+ * @param[in] A unsigned
+ * @param[in] B unsigned
+ * @param[out] GCD unsigned
+ * @param[in,out] x signed
+ * @param[in,out] y signed
+ */
+template <typename T, typename T2>
+void extendedEuclid(T A, T B, T *GCD, T2 *x, T2 *y) {
+    if (B > A)
+        std::swap(A, B);  // Ensure that A >= B
+
+    if (B == 0) {
+        *GCD = A;
+        *x = 1;
+        *y = 0;
+    } else {
+        extendedEuclid(B, A % B, GCD, x, y);
+        T2 temp = *x;
+        *x = *y;
+        *y = temp - (A / B) * (*y);
+    }
+}
+
+/// Main function
+int main() {
+    uint32_t a, b, gcd;
+    int32_t x, y;
+    std::cin >> a >> b;
+    extendedEuclid(a, b, &gcd, &x, &y);
+    std::cout << gcd << " " << x << " " << y << std::endl;
+    extendedEuclid_1(a, b, &gcd, &x, &y);
+    std::cout << gcd << " " << x << " " << y << std::endl;
+    return 0;
+}