#include <stdint.h>
#include "params.h"
#include "reduce.h"

/*************************************************
* 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=2^16
*
* Arguments:   - int32_t a: input integer to be reduced; has to be in {-q2^15,...,q2^15-1}
*
* Returns:     integer in {-q+1,...,q-1} congruent to a * R^-1 modulo q.
**************************************************/
int16_t montgomery_reduce(int32_t a)
{
  int32_t t;
  int16_t u;

  u = a * QINV;
  t = (int32_t)u * KYBER_Q;
  t = a - t;
  t >>= 16;
  return t;
}

/*************************************************
* Name:        barrett_reduce
*
* Description: Barrett reduction; given a 16-bit integer a, computes
*              16-bit integer congruent to a mod q in {0,...,q}
*
* Arguments:   - int16_t a: input integer to be reduced
*
* Returns:     integer in {0,...,q} congruent to a modulo q.
**************************************************/
int16_t barrett_reduce(int16_t a) {
  int32_t t;
  const int32_t v = (1U << 26)/KYBER_Q + 1;

  t = v*a;
  t >>= 26;
  t *= KYBER_Q;
  return a - t;
}