static void extendedGCD(uint64_t a, uint64_t b, int64_t *x, int64_t *y) {
if (b == 0) {
*x = 1;
*y = 0;
return;
}
int64_t d = a / b, xp, yp;
extendedGCD(b, a % b, &xp, &yp);
*x = yp;
*y = xp - (d * yp);
}
/**
* \brief Extended Euclidean algorithm
*
* Computes 'x' and 'y' that satisfy gcd(a, b) = ax + by,
* where x and y may be negative.
*/
void extendedGCD(uint64_t a, uint64_t b, int64_t &x, int64_t &y) {
if (b == 0) {
x = 1; y = 0;
return;
}
int64_t d = a / b, x_, y_;
extendedGCD(b, a % b, x_, y_);
x = y_;
y = x_ - (int64_t) (d * y_);
}
static uint64_t multiplicativeInverse(int64_t a, int64_t n) {
int64_t x, y;
extendedGCD(a, n, &x, &y);
return Mod(x, n);
}
/**
* \brief Compute the multiplicative inverse of a math::modulo n,
* where a and n a re relative prime. The result is in the
* range 1, ..., n - 1.
*/
uint64_t multiplicativeInverse(int64_t a, int64_t n) {
int64_t x, y;
extendedGCD(a, n, x, y);
return math::modulo(x, n);
}
