#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)
{
	int16_t t;
	
	t = (int16_t)a*QINV;
	t = (a - (int32_t)t*NTRUPLUS_Q) >> 16;
	return t;
}

/*************************************************
* Name:        barrett_reduce
*
* Description: Barrett reduction; given a 16-bit integer a, computes
*              centered representative congruent to a mod q in {-(q-1)/2,...,(q-1)/2}
*
* Arguments:   - int16_t a: input integer to be reduced
*
* Returns:     integer in {-(q-1)/2,...,(q-1)/2} congruent to a modulo q.
**************************************************/
int16_t barrett_reduce(int16_t a)
{
	int16_t t;
	const int16_t v = ((1<<26) + NTRUPLUS_Q/2)/NTRUPLUS_Q;
	
	t  = ((int32_t)v*a + (1<<25)) >> 26;
	t *= NTRUPLUS_Q;
	return a - t;
}
