#include "reduce.h"
#include "params.h"

static const uint32_t qinv = 7679; // -inverse_mod(q,2^18)
static const uint32_t rlog = 18;

/*************************************************
 * Name:        montgomery_reduce
 *
 * Description: Montgomery reduction; given a 32-bit integer a, computes
 *              16-bit integer congruent to a * R^-1 mod q,
 *              where R=2^18 (see value of rlog)
 *
 * Arguments:   - uint32_t a: input unsigned integer to be reduced; has to be in
 *{0,...,2281446912}
 *
 * Returns:     unsigned integer in {0,...,2^13-1} congruent to a * R^-1 modulo
 *q.
 **************************************************/
uint16_t PQCLEAN_KYBER768_montgomery_reduce(uint32_t a) {
    uint32_t u;

    u = (a * qinv);
    u &= ((1 << rlog) - 1);
    u *= KYBER_Q;
    a = a + u;
    return (uint16_t)(a >> rlog);
}

/*************************************************
 * Name:        barrett_reduce
 *
 * Description: Barrett reduction; given a 16-bit integer a, computes
 *              16-bit integer congruent to a mod q in {0,...,11768}
 *
 * Arguments:   - uint16_t a: input unsigned integer to be reduced
 *
 * Returns:     unsigned integer in {0,...,11768} congruent to a modulo q.
 **************************************************/
uint16_t PQCLEAN_KYBER768_barrett_reduce(uint16_t a) {
    uint16_t u;

    u = a >> 13; //((uint32_t) a * sinv) >> 16;
    u *= KYBER_Q;
    a -= u;
    return a;
}

/*************************************************
 * Name:        freeze
 *
 * Description: Full reduction; given a 16-bit integer a, computes
 *              unsigned integer a mod q.
 *
 * Arguments:   - uint16_t x: input unsigned integer to be reduced
 *
 * Returns:     unsigned integer in {0,...,q-1} congruent to a modulo q.
 **************************************************/
uint16_t PQCLEAN_KYBER768_freeze(uint16_t x) {
    uint16_t m, r;
    int16_t c;
    r = PQCLEAN_KYBER768_barrett_reduce(x);

    m = r - KYBER_Q;
    c = m;
    c >>= 15;
    r = m ^ ((r ^ m) & c);

    return r;
}