// gcc -O3 -o xor16 xor16.c  -msse4.2
#include <stdint.h>
#include <stdio.h>
#include <stddef.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stdbool.h>
#include "benchmark.h"
#include <x86intrin.h>

int32_t xor_uint16(const uint16_t *array_1, int32_t card_1,
                   const uint16_t *array_2, int32_t card_2, uint16_t *out) {
  int32_t pos1 = 0, pos2 = 0, pos_out = 0;
  while (pos1 < card_1 && pos2 < card_2) {
    const uint16_t v1 = array_1[pos1];
    const uint16_t v2 = array_2[pos2];
    if (v1 == v2) {
      ++pos1;
      ++pos2;
      continue;
    }
    if (v1 < v2) {
      out[pos_out++] = v1;
      ++pos1;
    } else {
      out[pos_out++] = v2;
      ++pos2;
    }
  }
  if (pos1 < card_1) {
      const size_t n_elems = card_1 - pos1;
      memcpy(out + pos_out, array_1 + pos1, n_elems * sizeof(uint16_t));
      pos_out += n_elems;
  } else if (pos2 < card_2) {
      const size_t n_elems = card_2 - pos2;
      memcpy(out + pos_out, array_2 + pos2, n_elems * sizeof(uint16_t));
      pos_out += n_elems;
  }

  return pos_out;
}

// Assuming that vInput1 and vInput2 are sorted, produces a sorted output going
// from vecMin all the way to vecMax
// developed originally for merge sort using SIMD instructions.
// Standard merge. See, e.g., Inoue and Taura, SIMD- and Cache-Friendly
// Algorithm for Sorting an Array of Structures
static inline void sse_merge(const __m128i *vInput1,
                             const __m128i *vInput2,             // input 1 & 2
                             __m128i *vecMin, __m128i *vecMax) { // output
  __m128i vecTmp;
  vecTmp = _mm_min_epu16(*vInput1, *vInput2);
  *vecMax = _mm_max_epu16(*vInput1, *vInput2);
  vecTmp = _mm_alignr_epi8(vecTmp, vecTmp, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  vecTmp = _mm_alignr_epi8(*vecMin, *vecMin, 2);
  *vecMin = _mm_min_epu16(vecTmp, *vecMax);
  *vecMax = _mm_max_epu16(vecTmp, *vecMax);
  *vecMin = _mm_alignr_epi8(*vecMin, *vecMin, 2);
}

static uint8_t uniqshuf[] = {
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,
    0xc,  0xd,  0xe,  0xf,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xa,  0xb,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0xa,  0xb,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xa,  0xb,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xa,  0xb,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,
    0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,
    0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x8,  0x9,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x8,  0x9,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0xc,  0xd,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0xc,  0xd,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xc,  0xd,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,
    0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x8,  0x9,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x8,  0x9,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x8,  0x9,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,  0xa,  0xb,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x6,  0x7,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0xa,  0xb,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0xa,  0xb,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xa,  0xb,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x8,  0x9,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0xe,  0xf,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xe,  0xf,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xe,  0xf,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x8,  0x9,
    0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x8,  0x9,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0xa,  0xb,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0xa,  0xb,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xa,  0xb,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,
    0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,  0x8,  0x9,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0x8,  0x9,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x8,  0x9,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x8,  0x9,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x8,  0x9,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x6,  0x7,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,  0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x6,  0x7,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0xc,  0xd,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0xc,  0xd,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xc,  0xd,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xa,  0xb,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x8,  0x9,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xa,  0xb,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0xa,  0xb,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xa,  0xb,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xa,  0xb,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0x6,  0x7,  0x8,  0x9,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x6,  0x7,
    0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,  0x8,  0x9,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x6,  0x7,
    0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x6,  0x7,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x8,  0x9,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,
    0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x4,  0x5,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x8,  0x9,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x8,  0x9,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x4,  0x5,  0x6,  0x7,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,
    0x6,  0x7,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x4,  0x5,  0x6,  0x7,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,  0x6,  0x7,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0x6,  0x7,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x6,  0x7,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x6,  0x7,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x2,  0x3,
    0x4,  0x5,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x2,  0x3,  0x4,  0x5,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0x4,  0x5,  0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x4,  0x5,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0x0,  0x1,  0x2,  0x3,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x2,  0x3,  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0,  0x1,  0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF};

// write vector new, while omitting repeated values assuming that previously
// written vector was "old"
static inline int store_unique_xor(__m128i old, __m128i newval,
                                   uint16_t *output) {
  __m128i vecTmp1 = _mm_alignr_epi8(newval, old, 16 - 4);
  __m128i vecTmp2 = _mm_alignr_epi8(newval, old, 16 - 2);
  __m128i equalleft = _mm_cmpeq_epi16(vecTmp2, vecTmp1);
  __m128i equalright = _mm_cmpeq_epi16(vecTmp2, newval);
  __m128i equalleftoright = _mm_or_si128(equalleft, equalright);
  int M =
      _mm_movemask_epi8(_mm_packs_epi16(equalleftoright, _mm_setzero_si128()));
  int numberofnewvalues = 8 - _mm_popcnt_u32(M);
  __m128i key = _mm_lddqu_si128((const __m128i *)uniqshuf + M);
  __m128i val = _mm_shuffle_epi8(vecTmp2, key);
  _mm_storeu_si128((__m128i *)output, val);
  return numberofnewvalues;
}

// working in-place, this function overwrites the repeated values
// could be avoided? Warning: assumes len > 0
static inline uint32_t unique_xor(uint16_t *out, uint32_t len) {
  uint32_t pos = 1;
  for (uint32_t i = 1; i < len; ++i) {
    if (out[i] != out[i - 1]) {
      out[pos++] = out[i];
    } else
      pos--; // if it is identical to previous, delete it
  }
  return pos;
}

// use with qsort, could be avoided
static int uint16_compare(const void *a, const void *b) {
  return (*(uint16_t *)a - *(uint16_t *)b);
}

// a one-pass SSE xor algorithm
uint32_t xor_vector16(const uint16_t *__restrict__ array1, uint32_t length1,
                      const uint16_t *__restrict__ array2, uint32_t length2,
                      uint16_t *__restrict__ output) {
  if ((length1 < 8) || (length2 < 8)) {
    return xor_uint16(array1, length1, array2, length2, output);
  }
  __m128i vA, vB, V, vecMin, vecMax;
  __m128i laststore;
  uint16_t *initoutput = output;
  uint32_t len1 = length1 / 8;
  uint32_t len2 = length2 / 8;
  uint32_t pos1 = 0;
  uint32_t pos2 = 0;
  // we start the machine
  vA = _mm_lddqu_si128((const __m128i *)array1 + pos1);
  pos1++;
  vB = _mm_lddqu_si128((const __m128i *)array2 + pos2);
  pos2++;
  sse_merge(&vA, &vB, &vecMin, &vecMax);
  laststore = _mm_set1_epi16(-1);
  uint16_t buffer[17];
  output += store_unique_xor(laststore, vecMin, output);

  laststore = vecMin;
  if ((pos1 < len1) && (pos2 < len2)) {
    uint16_t curA, curB;
    curA = array1[8 * pos1];
    curB = array2[8 * pos2];
    while (true) {
      if (curA <= curB) {
        V = _mm_lddqu_si128((const __m128i *)array1 + pos1);
        pos1++;
        if (pos1 < len1) {
          curA = array1[8 * pos1];
        } else {
          break;
        }
      } else {
        V = _mm_lddqu_si128((const __m128i *)array2 + pos2);
        pos2++;
        if (pos2 < len2) {
          curB = array2[8 * pos2];
        } else {
          break;
        }
      }
      sse_merge(&V, &vecMax, &vecMin, &vecMax);
      // conditionally stores the last value of laststore as well as all but the
      // last value of vecMin
      output += store_unique_xor(laststore, vecMin, output);
      laststore = vecMin;
    }
    sse_merge(&V, &vecMax, &vecMin, &vecMax);
    // conditionally stores the last value of laststore as well as all but the
    // last value of vecMin
    output += store_unique_xor(laststore, vecMin, output);
    laststore = vecMin;
  }
  uint32_t len = (uint32_t)(output - initoutput);

  // we finish the rest off using a scalar algorithm
  // could be improved?
  // conditionally stores the last value of laststore as well as all but the
  // last value of vecMax,
  // we store to "buffer"
  int leftoversize = store_unique_xor(laststore, vecMax, buffer);
  uint16_t vec7 = _mm_extract_epi16(vecMax, 7);
  uint16_t vec6 = _mm_extract_epi16(vecMax, 6);
  if (vec7 != vec6)
    buffer[leftoversize++] = vec7;
  if (pos1 == len1) {

    memcpy(buffer + leftoversize, array1 + 8 * pos1,
           (length1 - 8 * len1) * sizeof(uint16_t));
    leftoversize += length1 - 8 * len1;
    if (leftoversize == 0) { // trivial case
      memcpy(output, array2 + 8 * pos2,
             (length2 - 8 * pos2) * sizeof(uint16_t));
      len += (length2 - 8 * pos2);
    } else {

      qsort(buffer, leftoversize, sizeof(uint16_t), uint16_compare);
      leftoversize = unique_xor(buffer, leftoversize);
      len += xor_uint16(buffer, leftoversize, array2 + 8 * pos2,
                        length2 - 8 * pos2, output);
    }
  } else {
    memcpy(buffer + leftoversize, array2 + 8 * pos2,
           (length2 - 8 * len2) * sizeof(uint16_t));
    leftoversize += length2 - 8 * len2;
    if (leftoversize == 0) { // trivial case
      memcpy(output, array1 + 8 * pos1,
             (length1 - 8 * pos1) * sizeof(uint16_t));
      len += (length1 - 8 * pos1);
    } else {
      qsort(buffer, leftoversize, sizeof(uint16_t), uint16_compare);
      leftoversize = unique_xor(buffer, leftoversize);
      len += xor_uint16(buffer, leftoversize, array1 + 8 * pos1,
                        length1 - 8 * pos1, output);
    }
  }
  return len;
}

void randomtest() {
  const int repeat = 50;
  int lenA = (rand() % 4096);
  int lenB = (rand() % 4096);
  uint16_t *A = (uint16_t *)malloc(lenA * sizeof(uint16_t));
  uint16_t *B = (uint16_t *)malloc(lenB * sizeof(uint16_t));
  if (lenA > 0) {
    A[0] = rand() % 10;
    for (int i = 1; i < lenA; i++)
      A[i] = A[i - 1] + 1 + (rand() % (50000 / lenA));
  }
  if (lenB > 0) {
    B[0] = rand() % 10;
    for (int i = 1; i < lenB; i++)
      B[i] = B[i - 1] + 1 + (rand() % (50000 / lenB));
  }
  uint16_t *buffer1 = (uint16_t *)malloc((lenB + lenA) * sizeof(uint16_t));
  uint16_t *buffer2 = (uint16_t *)malloc((lenB + lenA) * sizeof(uint16_t));

  // first side
  int f1 = xor_uint16(A, lenA, B, lenB, buffer1);

  int g1 = xor_vector16(A, lenA, B, lenB, buffer2);
  if (f1 != g1) {
    printf("A:");
    for (int k = 0; k < lenA; ++k)
      printf(" %d ", A[k]);
    printf("\n");
    printf("B:");
    for (int k = 0; k < lenB; ++k)
      printf(" %d ", B[k]);
    printf("\n");

    printf("xor:");
    for (int k = 0; k < f1; ++k)
      printf(" %d ", buffer1[k]);
    printf("\n");
    printf("simd xor:");
    for (int k = 0; k < g1; ++k)
      printf(" %d ", buffer2[k]);
    printf("\n");
  }

  assert(f1 == g1);
  for (int k = 0; k < g1; ++k)
    assert(buffer1[k] == buffer2[k]);
  BEST_TIME(xor_uint16(A, lenA, B, lenB, buffer1), f1, , repeat, lenA + lenB,
            true);
  BEST_TIME(xor_vector16(A, lenA, B, lenB, buffer2), f1, , repeat, lenA + lenB,
            true);

  // second side
  int f2 = xor_uint16(B, lenB, A, lenA, buffer1);
  int g2 = xor_vector16(B, lenB, A, lenA, buffer2);
  assert(f2 == g2);
  for (int k = 0; k < g2; ++k)
    assert(buffer1[k] == buffer2[k]);
  BEST_TIME(xor_uint16(B, lenB, A, lenA, buffer1), f2, , repeat, lenA + lenB,
            true);
  BEST_TIME(xor_vector16(B, lenB, A, lenA, buffer2), f2, , repeat, lenA + lenB,
            true);

  // cleaning
  free(A);
  free(B);
  free(buffer1);
  free(buffer2);
}

int main() {
  for (int k = 0; k < 100000; ++k) {
    printf("\n\n\n");
    randomtest();
  }
}
