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

static const uint32_t qinv = 12287; // -inverse_mod(p,2^18)
static const uint32_t rlog = 18;

/*************************************************
* Name:        verify
*
* 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,...,1073491968}
*
* Returns:     unsigned integer in {0,...,2^14-1} congruent to a * R^-1 modulo q.
**************************************************/
uint16_t PQCLEAN_NEWHOPE512CPA_CLEAN_montgomery_reduce(uint32_t a) {
    uint32_t u;

    u = (a * qinv);
    u &= ((1 << rlog) - 1);
    u *= NEWHOPE_Q;
    a = a + u;
    return a >> 18;
}