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

int16_t zetas[128] = {
  2285, 2571, 2970, 1812, 1493, 1422, 287, 202, 3158, 622, 1577, 182, 962, 2127, 1855, 1468, 
  573, 2004, 264, 383, 2500, 1458, 1727, 3199, 2648, 1017, 732, 608, 1787, 411, 3124, 1758, 
  1223, 652, 2777, 1015, 2036, 1491, 3047, 1785, 516, 3321, 3009, 2663, 1711, 2167, 126, 1469, 
  2476, 3239, 3058, 830, 107, 1908, 3082, 2378, 2931, 961, 1821, 2604, 448, 2264, 677, 2054, 
  2226, 430, 555, 843, 2078, 871, 1550, 105, 422, 587, 177, 3094, 3038, 2869, 1574, 1653, 
  3083, 778, 1159, 3182, 2552, 1483, 2727, 1119, 1739, 644, 2457, 349, 418, 329, 3173, 3254, 
  817, 1097, 603, 610, 1322, 2044, 1864, 384, 2114, 3193, 1218, 1994, 2455, 220, 2142, 1670, 
  2144, 1799, 2051, 794, 1819, 2475, 2459, 478, 3221, 3021, 996, 991, 958, 1869, 1522, 1628};

/*************************************************
* Name:        fqmul
*
* Description: Multiplication followed by Montgomery reduction
*
* Arguments:   - int16_t a: first factor
*              - int16_t b: second factor
*
* Returns 16-bit integer congruent to a*b*R^{-1} mod q
**************************************************/
static int16_t fqmul(int16_t a, int16_t b) {
  return montgomery_reduce((int32_t)a*b);
}

/*************************************************
* Name:        ntt
*
* Description: Inplace number-theoretic transform (NTT) in Rq
*              input is in standard order, output is in bitreversed order
*
* Arguments:   - int16_t r[256]: pointer to input/output vector of elements of Zq
**************************************************/
void ntt(int16_t r[256]) {
  unsigned int len, start, j, k;
  int16_t t, zeta;

  k = 1;
  for(len = 128; len >= 2; len >>= 1) {
    for(start = 0; start < 256; start = j + len) {
      zeta = zetas[k++];
      for(j = start; j < start + len; ++j) {
        t = fqmul(zeta, r[j + len]);

        r[j + len] = r[j] - t;
        r[j] = r[j] + t;
      }
    }
  }
}