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clang-format and clang-tidy fixes for 2ad5420a

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94
math/modular_division.cpp
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@ -1,11 +1,12 @@
/** /**
* @file * @file
* @brief An algorithm to divide two numbers under modulo p [Modular * @brief An algorithm to divide two numbers under modulo p [Modular
* Division](https://www.geeksforgeeks.org/modular-division) * Division](https://www.geeksforgeeks.org/modular-division)
* @details To calculate division of two numbers under modulo p * @details To calculate division of two numbers under modulo p
* Modulo operator is not distributive under division, therefore * Modulo operator is not distributive under division, therefore
* we first have to calculate the inverse of divisor using * we first have to calculate the inverse of divisor using
* [Fermat's little theorem](https://en.wikipedia.org/wiki/Fermat%27s_little_theorem) * [Fermat's little
theorem](https://en.wikipedia.org/wiki/Fermat%27s_little_theorem)
* Now, we can multiply the dividend with the inverse of divisor * Now, we can multiply the dividend with the inverse of divisor
* and modulo is distributive over multiplication operation. * and modulo is distributive over multiplication operation.
* Let, * Let,
@ -31,51 +32,52 @@
* @brief Mathematical algorithms * @brief Mathematical algorithms
*/ */
namespace math { namespace math {
/** /**
* @namespace modular_division * @namespace modular_division
* @brief Functions for Modular Division implementation * @brief Functions for Modular Division implementation
*/ */
namespace modular_division { namespace modular_division {
/** /**
* @brief This function calculates a raised to exponent b under modulo c using * @brief This function calculates a raised to exponent b under modulo c using
* modular exponentiation. * modular exponentiation.
* @param a integer base * @param a integer base
* @param b unsigned integer exponent * @param b unsigned integer exponent
* @param c integer modulo * @param c integer modulo
* @return a raised to power b modulo c * @return a raised to power b modulo c
*/ */
uint64_t power(uint64_t a, uint64_t b, uint64_t c) { uint64_t power(uint64_t a, uint64_t b, uint64_t c) {
uint64_t ans = 1; /// Initialize the answer to be returned uint64_t ans = 1; /// Initialize the answer to be returned
a = a % c; /// Update a if it is more than or equal to c a = a % c; /// Update a if it is more than or equal to c
if (a == 0) { if (a == 0) {
return 0; /// In case a is divisible by c; return 0; /// In case a is divisible by c;
}
while (b > 0) {
/// If b is odd, multiply a with answer
if (b & 1) {
ans = ((ans % c) * (a % c)) % c;
}
/// b must be even now
b = b >> 1; /// b = b/2
a = ((a % c) * (a % c)) % c;
}
return ans;
} }
while (b > 0) {
/// If b is odd, multiply a with answer
if (b & 1) {
ans = ((ans % c) * (a % c)) % c;
}
/// b must be even now
b = b >> 1; /// b = b/2
a = ((a % c) * (a % c)) % c;
}
return ans;
}
/** /**
* @brief This function calculates modular division * @brief This function calculates modular division
* @param a integer dividend * @param a integer dividend
* @param b integer divisor * @param b integer divisor
* @param p integer modulo * @param p integer modulo
* @return a/b modulo c * @return a/b modulo c
*/ */
uint64_t mod_division(uint64_t a, uint64_t b, uint64_t p) { uint64_t mod_division(uint64_t a, uint64_t b, uint64_t p) {
uint64_t inverse = power(b, p-2, p)%p; /// Calculate the inverse of b uint64_t inverse = power(b, p - 2, p) % p; /// Calculate the inverse of b
uint64_t result = ((a%p)*(inverse%p))%p; /// Calculate the final result uint64_t result =
return result; ((a % p) * (inverse % p)) % p; /// Calculate the final result
} return result;
} // namespace modular_division }
} // namespace math } // namespace modular_division
} // namespace math
/** /**
* Function for testing power function. * Function for testing power function.
@ -107,6 +109,6 @@ static void test() {
* @returns 0 on exit * @returns 0 on exit
*/ */
int main(int argc, char *argv[]) { int main(int argc, char *argv[]) {
test(); // execute the tests test(); // execute the tests
return 0; return 0;
} }