text: #include "poly_mul.h"
  #include <stdint.h>
  #include <string.h>
  
  #define SCHB_N 16
  
  #define N_RES (SABER_N << 1)
  #define N_SB (SABER_N >> 2)
  #define N_SB_RES (2*N_SB-1)
  
  #define OVERFLOWING_MUL(X, Y) ((uint16_t)((uint32_t)(X) * (uint32_t)(Y)))
  
  #define KARATSUBA_N 64
  static void karatsuba_simple(const uint16_t *a_1, const uint16_t *b_1, uint16_t *result_final) {
      uint16_t d01[KARATSUBA_N / 2 - 1];
      uint16_t d0123[KARATSUBA_N / 2 - 1];
      uint16_t d23[KARATSUBA_N / 2 - 1];
      uint16_t result_d01[KARATSUBA_N - 1];
  
      int32_t i, j;
  
      memset(result_d01, 0, (KARATSUBA_N - 1)*sizeof(uint16_t));
      memset(d01, 0, (KARATSUBA_N / 2 - 1)*sizeof(uint16_t));
      memset(d0123, 0, (KARATSUBA_N / 2 - 1)*sizeof(uint16_t));
      memset(d23, 0, (KARATSUBA_N / 2 - 1)*sizeof(uint16_t));
      memset(result_final, 0, (2 * KARATSUBA_N - 1)*sizeof(uint16_t));
  
      uint16_t acc1, acc2, acc3, acc4, acc5, acc6, acc7, acc8, acc9, acc10;
  
  
      for (i = 0; i < KARATSUBA_N / 4; i++) {
          acc1 = a_1[i]; //a0
          acc2 = a_1[i + KARATSUBA_N / 4]; //a1
          acc3 = a_1[i + 2 * KARATSUBA_N / 4]; //a2
          acc4 = a_1[i + 3 * KARATSUBA_N / 4]; //a3
          for (j = 0; j < KARATSUBA_N / 4; j++) {
  
              acc5 = b_1[j]; //b0
              acc6 = b_1[j + KARATSUBA_N / 4]; //b1
  
              result_final[i + j + 0 * KARATSUBA_N / 4] =
                  result_final[i + j + 0 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc1, acc5);
              result_final[i + j + 2 * KARATSUBA_N / 4] =
                  result_final[i + j + 2 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc2, acc6);
  
              acc7 = acc5 + acc6; //b01
              acc8 = acc1 + acc2; //a01
              d01[i + j] = d01[i + j] + acc7 * acc8;
              //--------------------------------------------------------
  
              acc7 = b_1[j + 2 * KARATSUBA_N / 4]; //b2
              acc8 = b_1[j + 3 * KARATSUBA_N / 4]; //b3
              result_final[i + j + 4 * KARATSUBA_N / 4] =
                  result_final[i + j + 4 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc7, acc3);
  
              result_final[i + j + 6 * KARATSUBA_N / 4] =
                  result_final[i + j + 6 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc8, acc4);
  
              acc9 = acc3 + acc4;
              acc10 = acc7 + acc8;
              d23[i + j] = d23[i + j] + OVERFLOWING_MUL(acc9, acc10);
              //--------------------------------------------------------
  
              acc5 = acc5 + acc7; //b02
              acc7 = acc1 + acc3; //a02
              result_d01[i + j + 0 * KARATSUBA_N / 4] =
                  result_d01[i + j + 0 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc5, acc7);
  
              acc6 = acc6 + acc8; //b13
              acc8 = acc2 + acc4;
              result_d01[i + j + 2 * KARATSUBA_N / 4] =
                  result_d01[i + j + 2 * KARATSUBA_N / 4] +
                  OVERFLOWING_MUL(acc6, acc8);
  
              acc5 = acc5 + acc6;
              acc7 = acc7 + acc8;
              d0123[i + j] = d0123[i + j] + OVERFLOWING_MUL(acc5, acc7);
          }
      }
  
      // 2nd last stage
  
      for (i = 0; i < KARATSUBA_N / 2 - 1; i++) {
          d0123[i] = d0123[i] - result_d01[i + 0 * KARATSUBA_N / 4] - result_d01[i + 2 * KARATSUBA_N / 4];
          d01[i] = d01[i] - result_final[i + 0 * KARATSUBA_N / 4] - result_final[i + 2 * KARATSUBA_N / 4];
          d23[i] = d23[i] - result_final[i + 4 * KARATSUBA_N / 4] - result_final[i + 6 * KARATSUBA_N / 4];
      }
  
      for (i = 0; i < KARATSUBA_N / 2 - 1; i++) {
          result_d01[i + 1 * KARATSUBA_N / 4] = result_d01[i + 1 * KARATSUBA_N / 4] + d0123[i];
          result_final[i + 1 * KARATSUBA_N / 4] = result_final[i + 1 * KARATSUBA_N / 4] + d01[i];
          result_final[i + 5 * KARATSUBA_N / 4] = result_final[i + 5 * KARATSUBA_N / 4] + d23[i];
      }
  
      // Last stage
      for (i = 0; i < KARATSUBA_N - 1; i++) {
          result_d01[i] = result_d01[i] - result_final[i] - result_final[i + KARATSUBA_N];
      }
  
      for (i = 0; i < KARATSUBA_N - 1; i++) {
          result_final[i + 1 * KARATSUBA_N / 2] = result_final[i + 1 * KARATSUBA_N / 2] + result_d01[i];
      }
  
  }
  
  
  
  static void toom_cook_4way (const uint16_t *a1, const uint16_t *b1, uint16_t *result) {
      uint16_t inv3 = 43691, inv9 = 36409, inv15 = 61167;
  
      uint16_t aw1[N_SB], aw2[N_SB], aw3[N_SB], aw4[N_SB], aw5[N_SB], aw6[N_SB], aw7[N_SB];
      uint16_t bw1[N_SB], bw2[N_SB], bw3[N_SB], bw4[N_SB], bw5[N_SB], bw6[N_SB], bw7[N_SB];
      uint16_t w1[N_SB_RES] = {0}, w2[N_SB_RES] = {0}, w3[N_SB_RES] = {0}, w4[N_SB_RES] = {0},
                              w5[N_SB_RES] = {0}, w6[N_SB_RES] = {0}, w7[N_SB_RES] = {0};
      uint16_t r0, r1, r2, r3, r4, r5, r6, r7;
      uint16_t *A0, *A1, *A2, *A3, *B0, *B1, *B2, *B3;
      A0 = (uint16_t *)a1;
      A1 = (uint16_t *)&a1[N_SB];
      A2 = (uint16_t *)&a1[2 * N_SB];
      A3 = (uint16_t *)&a1[3 * N_SB];
      B0 = (uint16_t *)b1;
      B1 = (uint16_t *)&b1[N_SB];
      B2 = (uint16_t *)&b1[2 * N_SB];
      B3 = (uint16_t *)&b1[3 * N_SB];
  
      uint16_t *C;
      C = result;
  
      int i, j;
  
      // EVALUATION
      for (j = 0; j < N_SB; ++j) {
          r0 = A0[j];
          r1 = A1[j];
          r2 = A2[j];
          r3 = A3[j];
          r4 = r0 + r2;
          r5 = r1 + r3;
          r6 = r4 + r5;
          r7 = r4 - r5;
          aw3[j] = r6;
          aw4[j] = r7;
          r4 = ((r0 << 2) + r2) << 1;
          r5 = (r1 << 2) + r3;
          r6 = r4 + r5;
          r7 = r4 - r5;
          aw5[j] = r6;
          aw6[j] = r7;
          r4 = (r3 << 3) + (r2 << 2) + (r1 << 1) + r0;
          aw2[j] = r4;
          aw7[j] = r0;
          aw1[j] = r3;
      }
      for (j = 0; j < N_SB; ++j) {
          r0 = B0[j];
          r1 = B1[j];
          r2 = B2[j];
          r3 = B3[j];
          r4 = r0 + r2;
          r5 = r1 + r3;
          r6 = r4 + r5;
          r7 = r4 - r5;
          bw3[j] = r6;
          bw4[j] = r7;
          r4 = ((r0 << 2) + r2) << 1;
          r5 = (r1 << 2) + r3;
          r6 = r4 + r5;
          r7 = r4 - r5;
          bw5[j] = r6;
          bw6[j] = r7;
          r4 = (r3 << 3) + (r2 << 2) + (r1 << 1) + r0;
          bw2[j] = r4;
          bw7[j] = r0;
          bw1[j] = r3;
      }
  
      // MULTIPLICATION
  
      karatsuba_simple(aw1, bw1, w1);
      karatsuba_simple(aw2, bw2, w2);
      karatsuba_simple(aw3, bw3, w3);
      karatsuba_simple(aw4, bw4, w4);
      karatsuba_simple(aw5, bw5, w5);
      karatsuba_simple(aw6, bw6, w6);
      karatsuba_simple(aw7, bw7, w7);
  
      // INTERPOLATION
      for (i = 0; i < N_SB_RES; ++i) {
          r0 = w1[i];
          r1 = w2[i];
          r2 = w3[i];
          r3 = w4[i];
          r4 = w5[i];
          r5 = w6[i];
          r6 = w7[i];
  
          r1 = r1 + r4;
          r5 = r5 - r4;
          r3 = ((r3 - r2) >> 1);
          r4 = r4 - r0;
          r4 = r4 - (r6 << 6);
          r4 = (r4 << 1) + r5;
          r2 = r2 + r3;
          r1 = r1 - (r2 << 6) - r2;
          r2 = r2 - r6;
          r2 = r2 - r0;
          r1 = r1 + 45 * r2;
          r4 = (uint16_t)(((r4 - (r2 << 3)) * (uint32_t)inv3) >> 3);
          r5 = r5 + r1;
          r1 = (uint16_t)(((r1 + (r3 << 4)) * (uint32_t)inv9) >> 1);
          r3 = -(r3 + r1);
          r5 = (uint16_t)(((30 * r1 - r5) * (uint32_t)inv15) >> 2);
          r2 = r2 - r4;
          r1 = r1 - r5;
  
          C[i]     += r6;
          C[i + 64]  += r5;
          C[i + 128] += r4;
          C[i + 192] += r3;
          C[i + 256] += r2;
          C[i + 320] += r1;
          C[i + 384] += r0;
      }
  }
  
  void PQCLEAN_LIGHTSABER_CLEAN_pol_mul(uint16_t *a, uint16_t *b, uint16_t *res, uint16_t p, uint32_t n) {
      uint32_t i;
      // normal multiplication
      uint16_t c[512];
  
      for (i = 0; i < 512; i++) {
          c[i] = 0;
      }
  
      toom_cook_4way(a, b, c);
  
      // reduction
      for (i = n; i < 2 * n; i++) {
          res[i - n] = (c[i - n] - c[i]) & (p - 1);
      }
  }
  