quant_common.c 981 KB
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/*
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 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
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 *
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 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
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 */

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#include "av1/common/common.h"
#include "av1/common/onyxc_int.h"
#include "av1/common/entropy.h"
#include "av1/common/quant_common.h"
#include "av1/common/seg_common.h"
#include "av1/common/blockd.h"
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#if CONFIG_NEW_QUANT
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// Zero-bin widths expressed as a fraction over 128 of the quant stepsize.
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// So a value x indicates the bin is actually factor x/128 of the
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// nominal quantization step. The width is only
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// for one side of zero, so the actual width is twice that.
//
// Functions with nuq correspond to "non uniform quantization"
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// TODO(sarahparker, debargha): Optimize these tables

typedef struct {
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  uint8_t zbin;  // zero-bin width
  uint8_t doff;  // dequantization offset
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} qprofile_type;

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static const qprofile_type nuq[QUANT_PROFILES][2] = {
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  {
      // lossless
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      { 64, 0 },  // dc
      { 64, 0 },  // ac
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  },
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  // dq_type = 1
  {
      // Y/intra, dq_type 1, low quality
      { 66, 12 },  // dc
      { 66, 12 },  // ac
  },
  {
      // Y/intra, dq_type 1, high quality
      { 66, 6 },  // dc
      { 66, 6 },  // ac
  },
  {
      // UV/intra, dq_type 1, low quality
      { 66, 12 },  // dc
      { 66, 12 },  // ac
  },
  {
      // UV/intra, dq_type 1, high quality
      { 66, 6 },  // dc
      { 66, 6 },  // ac
  },
  {
      // Y/inter, dq_type 1, low quality
      { 66, 12 },  // dc
      { 66, 12 },  // ac
  },
  {
      // Y/inter, dq_type 1, high quality
      { 66, 6 },  // dc
      { 66, 6 },  // ac
  },
  {
      // UV/inter, dq_type 1, low quality
      { 66, 12 },  // dc
      { 66, 12 },  // ac
  },
  {
      // UV/inter, dq_type 1, high quality
      { 66, 6 },  // dc
      { 66, 6 },  // ac
  },

  // dq_type = 2
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  {
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      // Y/intra, dq_type 2, low quality
      { 72, 12 },  // dc
      { 72, 12 },  // ac
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  },
  {
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      // Y/intra, dq_type 2, high quality
      { 72, 6 },  // dc
      { 72, 6 },  // ac
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  },
  {
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      // UV/intra, dq_type 2, low quality
      { 72, 12 },  // dc
      { 72, 12 },  // ac
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  },
  {
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      // UV/intra, dq_type 2, high quality
      { 72, 6 },  // dc
      { 72, 6 },  // ac
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  },
  {
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      // Y/inter, dq_type 2, low quality
      { 72, 12 },  // dc
      { 72, 12 },  // ac
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  },
  {
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      // Y/inter, dq_type 2, high quality
      { 72, 6 },  // dc
      { 72, 6 },  // ac
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  },
  {
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      // UV/inter, dq_type 2, low quality
      { 72, 12 },  // dc
      { 72, 12 },  // ac
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  },
  {
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      // UV/inter, dq_type 2, high quality
      { 72, 6 },  // dc
      { 72, 6 },  // ac
  },

  // dq_type = 3
  {
      // Y/intra, dq_type 3, low quality
      { 80, 12 },  // dc
      { 80, 12 },  // ac
  },
  {
      // Y/intra, dq_type 3, high quality
      { 82, 6 },  // dc
      { 82, 6 },  // ac
  },
  {
      // UV/intra, dq_type 3, low quality
      { 80, 12 },  // dc
      { 80, 12 },  // ac
  },
  {
      // UV/intra, dq_type 3, high quality
      { 82, 6 },  // dc
      { 82, 6 },  // ac
  },
  {
      // Y/inter, dq_type 3, low quality
      { 80, 12 },  // dc
      { 80, 12 },  // ac
  },
  {
      // Y/inter, dq_type 3, high quality
      { 82, 6 },  // dc
      { 82, 6 },  // ac
  },
  {
      // UV/inter, dq_type 3, low quality
      { 80, 12 },  // dc
      { 80, 12 },  // ac
  },
  {
      // UV/inter, dq_type 3, high quality
      { 82, 6 },  // dc
      { 82, 6 },  // ac
  },
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};

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static INLINE uint8_t get_nuq_zbin(int is_ac_coeff, int q_profile) {
  return nuq[q_profile][is_ac_coeff].zbin;
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}
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static INLINE uint8_t quant_to_doff_fixed(int is_ac_coeff, int q_profile) {
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  return nuq[q_profile][is_ac_coeff].doff;
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}

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// get zero bin width
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static INLINE void get_cuml_bins_nuq(int q, int is_ac_coeff,
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                                     tran_low_t *zbin_width, int q_profile) {
  const uint8_t zbin = get_nuq_zbin(is_ac_coeff, q_profile);
  zbin_width[0] = ROUND_POWER_OF_TWO(zbin * q, 7);
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}

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void av1_get_dequant_val_nuq(int q, int is_ac_coeff, tran_low_t *dq,
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                             tran_low_t *cuml_bins, int q_profile) {
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  tran_low_t cuml_bins_[NUQ_KNOTS], *cuml_bins_ptr;
  tran_low_t doff;
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  // Get the quantization boundary for the zero bin
  const uint8_t zbin = get_nuq_zbin(is_ac_coeff, q_profile);
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  cuml_bins_ptr = (cuml_bins ? cuml_bins : cuml_bins_);
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  get_cuml_bins_nuq(q, is_ac_coeff, cuml_bins_ptr, q_profile);
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  // Get the dequantization offset that will be applied to all non-zero bins.
  // This is computed as: ((x0 - 64 - d) / 128) * Q
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  doff = quant_to_doff_fixed(is_ac_coeff, q_profile);
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  dq[0] = ROUND_POWER_OF_TWO((zbin - 64 - doff) * q, 7);
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  dq[1] = ROUND_POWER_OF_TWO((zbin - 64 - doff) * q, 8);
  dq[2] = ROUND_POWER_OF_TWO((zbin - 64 - doff) * q, 9);
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}

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tran_low_t av1_dequant_abscoeff_nuq(int v, int q, const tran_low_t *dq,
                                    int shift) {
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  if (v == 0) return 0;
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  return ((q * v) >> shift) + dq[shift];
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}

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tran_low_t av1_dequant_coeff_nuq(int v, int q, const tran_low_t *dq,
                                 int shift) {
  tran_low_t dqmag = av1_dequant_abscoeff_nuq(abs(v), q, dq, shift);
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  return (v < 0 ? -dqmag : dqmag);
}
#endif  // CONFIG_NEW_QUANT

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static const int16_t dc_qlookup_Q3[QINDEX_RANGE] = {
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  4,    8,    8,    9,    10,  11,  12,  12,  13,  14,  15,   16,   17,   18,
  19,   19,   20,   21,   22,  23,  24,  25,  26,  26,  27,   28,   29,   30,
  31,   32,   32,   33,   34,  35,  36,  37,  38,  38,  39,   40,   41,   42,
  43,   43,   44,   45,   46,  47,  48,  48,  49,  50,  51,   52,   53,   53,
  54,   55,   56,   57,   57,  58,  59,  60,  61,  62,  62,   63,   64,   65,
  66,   66,   67,   68,   69,  70,  70,  71,  72,  73,  74,   74,   75,   76,
  77,   78,   78,   79,   80,  81,  81,  82,  83,  84,  85,   85,   87,   88,
  90,   92,   93,   95,   96,  98,  99,  101, 102, 104, 105,  107,  108,  110,
  111,  113,  114,  116,  117, 118, 120, 121, 123, 125, 127,  129,  131,  134,
  136,  138,  140,  142,  144, 146, 148, 150, 152, 154, 156,  158,  161,  164,
  166,  169,  172,  174,  177, 180, 182, 185, 187, 190, 192,  195,  199,  202,
  205,  208,  211,  214,  217, 220, 223, 226, 230, 233, 237,  240,  243,  247,
  250,  253,  257,  261,  265, 269, 272, 276, 280, 284, 288,  292,  296,  300,
  304,  309,  313,  317,  322, 326, 330, 335, 340, 344, 349,  354,  359,  364,
  369,  374,  379,  384,  389, 395, 400, 406, 411, 417, 423,  429,  435,  441,
  447,  454,  461,  467,  475, 482, 489, 497, 505, 513, 522,  530,  539,  549,
  559,  569,  579,  590,  602, 614, 626, 640, 654, 668, 684,  700,  717,  736,
  755,  775,  796,  819,  843, 869, 896, 925, 955, 988, 1022, 1058, 1098, 1139,
  1184, 1232, 1282, 1336,
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};

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static const int16_t dc_qlookup_10_Q3[QINDEX_RANGE] = {
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  4,    9,    10,   13,   15,   17,   20,   22,   25,   28,   31,   34,   37,
  40,   43,   47,   50,   53,   57,   60,   64,   68,   71,   75,   78,   82,
  86,   90,   93,   97,   101,  105,  109,  113,  116,  120,  124,  128,  132,
  136,  140,  143,  147,  151,  155,  159,  163,  166,  170,  174,  178,  182,
  185,  189,  193,  197,  200,  204,  208,  212,  215,  219,  223,  226,  230,
  233,  237,  241,  244,  248,  251,  255,  259,  262,  266,  269,  273,  276,
  280,  283,  287,  290,  293,  297,  300,  304,  307,  310,  314,  317,  321,
  324,  327,  331,  334,  337,  343,  350,  356,  362,  369,  375,  381,  387,
  394,  400,  406,  412,  418,  424,  430,  436,  442,  448,  454,  460,  466,
  472,  478,  484,  490,  499,  507,  516,  525,  533,  542,  550,  559,  567,
  576,  584,  592,  601,  609,  617,  625,  634,  644,  655,  666,  676,  687,
  698,  708,  718,  729,  739,  749,  759,  770,  782,  795,  807,  819,  831,
  844,  856,  868,  880,  891,  906,  920,  933,  947,  961,  975,  988,  1001,
  1015, 1030, 1045, 1061, 1076, 1090, 1105, 1120, 1137, 1153, 1170, 1186, 1202,
  1218, 1236, 1253, 1271, 1288, 1306, 1323, 1342, 1361, 1379, 1398, 1416, 1436,
  1456, 1476, 1496, 1516, 1537, 1559, 1580, 1601, 1624, 1647, 1670, 1692, 1717,
  1741, 1766, 1791, 1817, 1844, 1871, 1900, 1929, 1958, 1990, 2021, 2054, 2088,
  2123, 2159, 2197, 2236, 2276, 2319, 2363, 2410, 2458, 2508, 2561, 2616, 2675,
  2737, 2802, 2871, 2944, 3020, 3102, 3188, 3280, 3375, 3478, 3586, 3702, 3823,
  3953, 4089, 4236, 4394, 4559, 4737, 4929, 5130, 5347,
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};

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static const int16_t dc_qlookup_12_Q3[QINDEX_RANGE] = {
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  4,     12,    18,    25,    33,    41,    50,    60,    70,    80,    91,
  103,   115,   127,   140,   153,   166,   180,   194,   208,   222,   237,
  251,   266,   281,   296,   312,   327,   343,   358,   374,   390,   405,
  421,   437,   453,   469,   484,   500,   516,   532,   548,   564,   580,
  596,   611,   627,   643,   659,   674,   690,   706,   721,   737,   752,
  768,   783,   798,   814,   829,   844,   859,   874,   889,   904,   919,
  934,   949,   964,   978,   993,   1008,  1022,  1037,  1051,  1065,  1080,
  1094,  1108,  1122,  1136,  1151,  1165,  1179,  1192,  1206,  1220,  1234,
  1248,  1261,  1275,  1288,  1302,  1315,  1329,  1342,  1368,  1393,  1419,
  1444,  1469,  1494,  1519,  1544,  1569,  1594,  1618,  1643,  1668,  1692,
  1717,  1741,  1765,  1789,  1814,  1838,  1862,  1885,  1909,  1933,  1957,
  1992,  2027,  2061,  2096,  2130,  2165,  2199,  2233,  2267,  2300,  2334,
  2367,  2400,  2434,  2467,  2499,  2532,  2575,  2618,  2661,  2704,  2746,
  2788,  2830,  2872,  2913,  2954,  2995,  3036,  3076,  3127,  3177,  3226,
  3275,  3324,  3373,  3421,  3469,  3517,  3565,  3621,  3677,  3733,  3788,
  3843,  3897,  3951,  4005,  4058,  4119,  4181,  4241,  4301,  4361,  4420,
  4479,  4546,  4612,  4677,  4742,  4807,  4871,  4942,  5013,  5083,  5153,
  5222,  5291,  5367,  5442,  5517,  5591,  5665,  5745,  5825,  5905,  5984,
  6063,  6149,  6234,  6319,  6404,  6495,  6587,  6678,  6769,  6867,  6966,
  7064,  7163,  7269,  7376,  7483,  7599,  7715,  7832,  7958,  8085,  8214,
  8352,  8492,  8635,  8788,  8945,  9104,  9275,  9450,  9639,  9832,  10031,
  10245, 10465, 10702, 10946, 11210, 11482, 11776, 12081, 12409, 12750, 13118,
  13501, 13913, 14343, 14807, 15290, 15812, 16356, 16943, 17575, 18237, 18949,
  19718, 20521, 21387,
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};

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static const int16_t ac_qlookup_Q3[QINDEX_RANGE] = {
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  20,   21,   22,   23,   24,   25,   26,   27,   28,   29,   30,   31,   32,
  33,   34,   35,   36,   37,   38,   39,   40,   41,   42,   43,   44,   45,
  46,   47,   48,   49,   50,   51,   52,   53,   54,   55,   56,   57,   58,
  59,   60,   61,   62,   63,   64,   65,   66,   67,   68,   69,   70,   71,
  72,   73,   74,   75,   76,   77,   78,   79,   80,   81,   82,   83,   84,
  85,   86,   87,   88,   89,   90,   91,   92,   93,   94,   95,   96,   97,
  98,   99,   100,  101,  102,  104,  106,  108,  110,  112,  114,  116,  118,
  120,  122,  124,  126,  128,  130,  132,  134,  136,  138,  140,  142,  144,
  146,  148,  150,  152,  155,  158,  161,  164,  167,  170,  173,  176,  179,
  182,  185,  188,  191,  194,  197,  200,  203,  207,  211,  215,  219,  223,
  227,  231,  235,  239,  243,  247,  251,  255,  260,  265,  270,  275,  280,
  285,  290,  295,  300,  305,  311,  317,  323,  329,  335,  341,  347,  353,
  359,  366,  373,  380,  387,  394,  401,  408,  416,  424,  432,  440,  448,
  456,  465,  474,  483,  492,  501,  510,  520,  530,  540,  550,  560,  571,
  582,  593,  604,  615,  627,  639,  651,  663,  676,  689,  702,  715,  729,
  743,  757,  771,  786,  801,  816,  832,  848,  864,  881,  898,  915,  933,
  951,  969,  988,  1007, 1026, 1046, 1066, 1087, 1108, 1129, 1151, 1173, 1196,
  1219, 1243, 1267, 1292, 1317, 1343, 1369, 1396, 1423, 1451, 1479, 1508, 1537,
  1567, 1597, 1628, 1660, 1692, 1725, 1759, 1793, 1828,
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};

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static const int16_t ac_qlookup_10_Q3[QINDEX_RANGE] = {
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  4,    9,    11,   13,   16,   18,   21,   24,   27,   30,   33,   37,   40,
  44,   48,   51,   55,   59,   63,   67,   71,   75,   79,   83,   88,   92,
  96,   100,  105,  109,  114,  118,  122,  127,  131,  136,  140,  145,  149,
  154,  158,  163,  168,  172,  177,  181,  186,  190,  195,  199,  204,  208,
  213,  217,  222,  226,  231,  235,  240,  244,  249,  253,  258,  262,  267,
  271,  275,  280,  284,  289,  293,  297,  302,  306,  311,  315,  319,  324,
  328,  332,  337,  341,  345,  349,  354,  358,  362,  367,  371,  375,  379,
  384,  388,  392,  396,  401,  409,  417,  425,  433,  441,  449,  458,  466,
  474,  482,  490,  498,  506,  514,  523,  531,  539,  547,  555,  563,  571,
  579,  588,  596,  604,  616,  628,  640,  652,  664,  676,  688,  700,  713,
  725,  737,  749,  761,  773,  785,  797,  809,  825,  841,  857,  873,  889,
  905,  922,  938,  954,  970,  986,  1002, 1018, 1038, 1058, 1078, 1098, 1118,
  1138, 1158, 1178, 1198, 1218, 1242, 1266, 1290, 1314, 1338, 1362, 1386, 1411,
  1435, 1463, 1491, 1519, 1547, 1575, 1603, 1631, 1663, 1695, 1727, 1759, 1791,
  1823, 1859, 1895, 1931, 1967, 2003, 2039, 2079, 2119, 2159, 2199, 2239, 2283,
  2327, 2371, 2415, 2459, 2507, 2555, 2603, 2651, 2703, 2755, 2807, 2859, 2915,
  2971, 3027, 3083, 3143, 3203, 3263, 3327, 3391, 3455, 3523, 3591, 3659, 3731,
  3803, 3876, 3952, 4028, 4104, 4184, 4264, 4348, 4432, 4516, 4604, 4692, 4784,
  4876, 4972, 5068, 5168, 5268, 5372, 5476, 5584, 5692, 5804, 5916, 6032, 6148,
  6268, 6388, 6512, 6640, 6768, 6900, 7036, 7172, 7312,
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};

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static const int16_t ac_qlookup_12_Q3[QINDEX_RANGE] = {
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  4,     13,    19,    27,    35,    44,    54,    64,    75,    87,    99,
  112,   126,   139,   154,   168,   183,   199,   214,   230,   247,   263,
  280,   297,   314,   331,   349,   366,   384,   402,   420,   438,   456,
  475,   493,   511,   530,   548,   567,   586,   604,   623,   642,   660,
  679,   698,   716,   735,   753,   772,   791,   809,   828,   846,   865,
  884,   902,   920,   939,   957,   976,   994,   1012,  1030,  1049,  1067,
  1085,  1103,  1121,  1139,  1157,  1175,  1193,  1211,  1229,  1246,  1264,
  1282,  1299,  1317,  1335,  1352,  1370,  1387,  1405,  1422,  1440,  1457,
  1474,  1491,  1509,  1526,  1543,  1560,  1577,  1595,  1627,  1660,  1693,
  1725,  1758,  1791,  1824,  1856,  1889,  1922,  1954,  1987,  2020,  2052,
  2085,  2118,  2150,  2183,  2216,  2248,  2281,  2313,  2346,  2378,  2411,
  2459,  2508,  2556,  2605,  2653,  2701,  2750,  2798,  2847,  2895,  2943,
  2992,  3040,  3088,  3137,  3185,  3234,  3298,  3362,  3426,  3491,  3555,
  3619,  3684,  3748,  3812,  3876,  3941,  4005,  4069,  4149,  4230,  4310,
  4390,  4470,  4550,  4631,  4711,  4791,  4871,  4967,  5064,  5160,  5256,
  5352,  5448,  5544,  5641,  5737,  5849,  5961,  6073,  6185,  6297,  6410,
  6522,  6650,  6778,  6906,  7034,  7162,  7290,  7435,  7579,  7723,  7867,
  8011,  8155,  8315,  8475,  8635,  8795,  8956,  9132,  9308,  9484,  9660,
  9836,  10028, 10220, 10412, 10604, 10812, 11020, 11228, 11437, 11661, 11885,
  12109, 12333, 12573, 12813, 13053, 13309, 13565, 13821, 14093, 14365, 14637,
  14925, 15213, 15502, 15806, 16110, 16414, 16734, 17054, 17390, 17726, 18062,
  18414, 18766, 19134, 19502, 19886, 20270, 20670, 21070, 21486, 21902, 22334,
  22766, 23214, 23662, 24126, 24590, 25070, 25551, 26047, 26559, 27071, 27599,
  28143, 28687, 29247,
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};

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#if !CONFIG_DAALA_TX

// Coefficient scaling and quantization with AV1 TX are tailored to
// the AV1 TX transforms.  Regardless of the bit-depth of the input,
// the transform stages scale the coefficient values up by a factor of
// 8 (3 bits) over the scale of the pixel values.  Thus, for 8-bit
// input, the coefficients have effectively 11 bits of scale depth
// (8+3), 10-bit input pixels result in 13-bit coefficient depth
// (10+3) and 12-bit pixels yield 15-bit (12+3) coefficient depth.
// All quantizers are built using this invariant of x8, 3-bit scaling,
// thus the Q3 suffix.

// A partial exception to this rule is large transforms; to avoid
// overflow, TX blocks with > 256 pels (>16x16) are scaled only
// 4-times unity (2 bits) over the pixel depth, and TX blocks with
// over 1024 pixels (>32x32) are scaled up only 2x unity (1 bit).
// This descaling is found via av1_tx_get_scale().  Thus, 16x32, 32x16
// and 32x32 transforms actually return Q2 coefficients, and 32x64,
// 64x32 and 64x64 transforms return Q1 coefficients.  However, the
// quantizers are de-scaled down on-the-fly by the same amount
// (av1_tx_get_scale()) during quantization, and as such the
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// dequantized/decoded coefficients, even for large TX blocks, are always
// effectively Q3. Meanwhile, quantized/coded coefficients are Q0
// because Qn quantizers are applied to Qn tx coefficients.
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// Note that encoder decision making (which uses the quantizer to
// generate several bespoke lamdas for RDO and other heuristics)
// expects quantizers to be larger for higher-bitdepth input.  In
// addition, the minimum allowable quantizer is 4; smaller values will
// underflow to 0 in the actual quantization routines.

int16_t av1_dc_quant_Q3(int qindex, int delta, aom_bit_depth_t bit_depth) {
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  switch (bit_depth) {
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    case AOM_BITS_8: return dc_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)];
    case AOM_BITS_10: return dc_qlookup_10_Q3[clamp(qindex + delta, 0, MAXQ)];
    case AOM_BITS_12: return dc_qlookup_12_Q3[clamp(qindex + delta, 0, MAXQ)];
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    default:
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      assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
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      return -1;
  }
}

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int16_t av1_ac_quant_Q3(int qindex, int delta, aom_bit_depth_t bit_depth) {
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  switch (bit_depth) {
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    case AOM_BITS_8: return ac_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)];
    case AOM_BITS_10: return ac_qlookup_10_Q3[clamp(qindex + delta, 0, MAXQ)];
    case AOM_BITS_12: return ac_qlookup_12_Q3[clamp(qindex + delta, 0, MAXQ)];
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    default:
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      assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
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      return -1;
  }
}

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// In AV1 TX, the coefficients are always scaled up a factor of 8 (3
// bits), so QTX == Q3.

int16_t av1_dc_quant_QTX(int qindex, int delta, aom_bit_depth_t bit_depth) {
  return av1_dc_quant_Q3(qindex, delta, bit_depth);
}

int16_t av1_ac_quant_QTX(int qindex, int delta, aom_bit_depth_t bit_depth) {
  return av1_ac_quant_Q3(qindex, delta, bit_depth);
}

int16_t av1_qindex_from_ac_Q3(int ac_Q3, aom_bit_depth_t bit_depth) {
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  int i;
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  const int16_t *tab = ac_qlookup_Q3;
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  switch (bit_depth) {
    case AOM_BITS_10: {
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      tab = ac_qlookup_10_Q3;
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      break;
    }
    case AOM_BITS_12: {
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      tab = ac_qlookup_12_Q3;
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      break;
    }
    default:
      assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
      return -1;
  }
  (void)bit_depth;
  for (i = 0; i < QINDEX_RANGE; i++) {
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    if (ac_Q3 <= tab[i]) return i;
  }
  return QINDEX_RANGE - 1;
}

#else   // CONFIG_DAALA_TX

// Daala TX uses a constant effective coefficient depth
// (TX_COEFF_DEPTH) regardless of input pixel bitdepth or transform
// size. This means that coefficient scale and range is identical
// regardless of the bit depth of the pixel input.  However, the
// existing encoder heuristics and RDO loop were built expecting a
// quantizer that scales with bitdepth, treating it more as a
// proto-lambda than a quantizer.  The assumption that quantizer scale
// increases with bitdepth is spread throughout the encoder.

// For this reason, we need to be able to find an old-style 'Q3'
// quantizer that scales with pixel depth (to be used in encoder
// decision making) as well as the literal quantizer that is used in
// actual quantization/dequantization.  That is centralized here.

// Right now, the existing quantization code and setup are not
// particularly well suited to Daala TX.  The scale range used by, eg,
// the 12 bit lookups is intentionally larger in order to provide more
// fine control at the top end of the quality range, as 12-bit input
// would be assumed to offer a lower noise floor than an 8-bit input.
// However, the 12-bit lookups assume an effective 15-bit TX depth,
// while we intend to run Daala TX somewhere between 12 and 14.  We
// can't simply scale it down, because this would violate the minimum
// allowable quantizer in the current code (4).

// As such, we do the simplest thing for the time being: Always use
// the 8-bit scale range for all inputs and scale the QTX and Q3
// returns accordingly, which will always be no-ops or upshifts.  This
// might well work well enough; if not, we'll need to patch quantizer
// scaling to extend the high-bitdepth quality range upward at some
// later date.

int16_t av1_dc_quant_Q3(int qindex, int delta, aom_bit_depth_t bit_depth) {
  assert(bit_depth >= 8);
  return qindex == 0 ? dc_qlookup_Q3[0]
                     :  // Do not scale lossless
             dc_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)] *
                 (1 << (bit_depth - 8));
}

int16_t av1_ac_quant_Q3(int qindex, int delta, aom_bit_depth_t bit_depth) {
  assert(bit_depth >= 8);
  return qindex == 0 ? ac_qlookup_Q3[0]
                     :  // Do not scale lossless
             ac_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)] *
                 (1 << (bit_depth - 8));
}

int16_t av1_dc_quant_QTX(int qindex, int delta, aom_bit_depth_t bit_depth) {
  (void)bit_depth;
  return qindex == 0 ? dc_qlookup_Q3[0]
                     :  // Do not scale lossless
             dc_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)] *
                 (1 << (TX_COEFF_DEPTH - 11));
}

int16_t av1_ac_quant_QTX(int qindex, int delta, aom_bit_depth_t bit_depth) {
  (void)bit_depth;
  return qindex == 0 ? ac_qlookup_Q3[0]
                     :  // Do not scale lossless
             ac_qlookup_Q3[clamp(qindex + delta, 0, MAXQ)] *
                 (1 << (TX_COEFF_DEPTH - 11));
}

int16_t av1_qindex_from_ac_Q3(int ac_QTX, aom_bit_depth_t bit_depth) {
  int i;
  const int16_t *tab = ac_qlookup_Q3;
  int scale = (1 << (TX_COEFF_DEPTH - 11));
  (void)bit_depth;
  for (i = 0; i < QINDEX_RANGE; i++) {
    if (ac_QTX <= tab[i] * scale) return i;
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  }
  return QINDEX_RANGE - 1;
}
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#endif  // !CONFIG_DAALA_TX
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int av1_get_qindex(const struct segmentation *seg, int segment_id,
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                   int base_qindex) {
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  if (segfeature_active(seg, segment_id, SEG_LVL_ALT_Q)) {
    const int data = get_segdata(seg, segment_id, SEG_LVL_ALT_Q);
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    const int seg_qindex = base_qindex + data;
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    return clamp(seg_qindex, 0, MAXQ);
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  } else {
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    return base_qindex;
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  }
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}
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#if CONFIG_AOM_QM
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const qm_val_t *aom_iqmatrix(AV1_COMMON *cm, int qmlevel, int plane,
                             TX_SIZE tx_size) {
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  return &cm->giqmatrix[qmlevel][plane][tx_size][0];
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}
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const qm_val_t *aom_qmatrix(AV1_COMMON *cm, int qmlevel, int plane,
                            TX_SIZE tx_size) {
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  return &cm->gqmatrix[qmlevel][plane][tx_size][0];
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}

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#define QM_TOTAL_SIZE 3344
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static const uint16_t wt_matrix_ref[NUM_QM_LEVELS][2][QM_TOTAL_SIZE];
static const uint16_t iwt_matrix_ref[NUM_QM_LEVELS][2][QM_TOTAL_SIZE];
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void aom_qm_init(AV1_COMMON *cm) {
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  int q, c, t;
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  int current;
  for (q = 0; q < NUM_QM_LEVELS; ++q) {
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    for (c = 0; c < av1_num_planes(cm); ++c) {
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      current = 0;
      for (t = 0; t < TX_SIZES_ALL; ++t) {
        const int size = tx_size_2d[t];
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        const int qm_tx_size = av1_get_adjusted_tx_size(t);
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        if (q == NUM_QM_LEVELS - 1) {
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          cm->gqmatrix[q][c][t] = NULL;
          cm->giqmatrix[q][c][t] = NULL;
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        } else if (t != qm_tx_size) {  // Reuse matrices for 'qm_tx_size'
          cm->gqmatrix[q][c][t] = cm->gqmatrix[q][c][qm_tx_size];
          cm->giqmatrix[q][c][t] = cm->giqmatrix[q][c][qm_tx_size];
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        } else {
          assert(current + size <= QM_TOTAL_SIZE);
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          cm->gqmatrix[q][c][t] = &wt_matrix_ref[q][c >= 1][current];
          cm->giqmatrix[q][c][t] = &iwt_matrix_ref[q][c >= 1][current];
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          current += size;
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        }
      }
    }
  }
}

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/* Provide 16 sets of quantization matrices for chroma and luma
   and each TX size. Matrices for different TX sizes are in fact
   sub-sampled from the 32x32 and 16x16 sizes, but explicitly
   defined here for convenience. Intra and inter matrix sets are the
   same but changing DEFAULT_QM_INTER_OFFSET from zero allows
   for different matrices for inter and intra blocks in the same
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   frame.
   Matrices for different QM levels have been rescaled in the
   frequency domain according to different nominal viewing
   distances.
 */
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static const uint16_t iwt_matrix_ref[NUM_QM_LEVELS][2][QM_TOTAL_SIZE] = {
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  {
      { /* Luma */
        /* Size 4x4 */
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        32, 43, 73, 97, 43, 67, 94, 110, 73, 94, 137, 150, 97, 110, 150, 200,
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        /* Size 8x8 */
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        32, 32, 38, 51, 68, 84, 95, 109, 32, 35, 40, 49, 63, 76, 89, 102, 38,
        40, 54, 65, 78, 91, 98, 106, 51, 49, 65, 82, 97, 111, 113, 121, 68, 63,
        78, 97, 117, 134, 138, 142, 84, 76, 91, 111, 134, 152, 159, 168, 95, 89,
        98, 113, 138, 159, 183, 199, 109, 102, 106, 121, 142, 168, 199, 220,
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        /* Size 16x16 */
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        32, 31, 31, 34, 36, 44, 48, 59, 65, 80, 83, 91, 97, 104, 111, 119, 31,
        32, 32, 33, 34, 41, 44, 54, 59, 72, 75, 83, 90, 97, 104, 112, 31, 32,
        33, 35, 36, 42, 45, 54, 59, 71, 74, 81, 86, 93, 100, 107, 34, 33, 35,
        39, 42, 47, 51, 58, 63, 74, 76, 81, 84, 90, 97, 105, 36, 34, 36, 42, 48,
        54, 57, 64, 68, 79, 81, 88, 91, 96, 102, 105, 44, 41, 42, 47, 54, 63,
        67, 75, 79, 90, 92, 95, 100, 102, 109, 112, 48, 44, 45, 51, 57, 67, 71,
        80, 85, 96, 99, 107, 108, 111, 117, 120, 59, 54, 54, 58, 64, 75, 80, 92,
        98, 110, 113, 115, 116, 122, 125, 130, 65, 59, 59, 63, 68, 79, 85, 98,
        105, 118, 121, 127, 130, 134, 135, 140, 80, 72, 71, 74, 79, 90, 96, 110,
        118, 134, 137, 140, 143, 144, 146, 152, 83, 75, 74, 76, 81, 92, 99, 113,
        121, 137, 140, 151, 152, 155, 158, 165, 91, 83, 81, 81, 88, 95, 107,
        115, 127, 140, 151, 159, 166, 169, 173, 179, 97, 90, 86, 84, 91, 100,
        108, 116, 130, 143, 152, 166, 174, 182, 189, 193, 104, 97, 93, 90, 96,
        102, 111, 122, 134, 144, 155, 169, 182, 191, 200, 210, 111, 104, 100,
        97, 102, 109, 117, 125, 135, 146, 158, 173, 189, 200, 210, 220, 119,
        112, 107, 105, 105, 112, 120, 130, 140, 152, 165, 179, 193, 210, 220,
        231,
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        /* Size 32x32 */
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        32, 31, 31, 31, 31, 32, 34, 35, 36, 39, 44, 46, 48, 54, 59, 62, 65, 71,
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        80, 81, 83, 88, 91, 94, 97, 101, 104, 107, 111, 115, 119, 123, 31, 32,
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        32, 32, 32, 32, 34, 34, 35, 38, 42, 44, 46, 51, 56, 59, 62, 68, 76, 77,
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        78, 84, 86, 89, 92, 95, 99, 102, 105, 109, 113, 116, 31, 32, 32, 32, 32,
        32, 33, 34, 34, 37, 41, 42, 44, 49, 54, 56, 59, 65, 72, 73, 75, 80, 83,
        86, 90, 93, 97, 101, 104, 108, 112, 116, 31, 32, 32, 32, 33, 33, 34, 35,
        35, 38, 41, 43, 45, 49, 54, 56, 59, 64, 72, 73, 74, 79, 82, 85, 88, 91,
        94, 97, 101, 104, 107, 111, 31, 32, 32, 33, 33, 34, 35, 36, 36, 39, 42,
        44, 45, 50, 54, 56, 59, 64, 71, 72, 74, 78, 81, 84, 86, 89, 93, 96, 100,
        104, 107, 111, 32, 32, 32, 33, 34, 35, 37, 37, 38, 40, 42, 44, 46, 49,
        53, 55, 58, 63, 69, 70, 72, 76, 79, 82, 85, 89, 93, 96, 99, 102, 106,
        109, 34, 34, 33, 34, 35, 37, 39, 41, 42, 45, 47, 49, 51, 54, 58, 60, 63,
        68, 74, 75, 76, 80, 81, 82, 84, 87, 90, 93, 97, 101, 105, 110, 35, 34,
        34, 35, 36, 37, 41, 43, 45, 47, 50, 52, 53, 57, 61, 63, 65, 70, 76, 77,
        79, 82, 84, 86, 89, 91, 92, 93, 96, 100, 103, 107, 36, 35, 34, 35, 36,
        38, 42, 45, 48, 50, 54, 55, 57, 60, 64, 66, 68, 73, 79, 80, 81, 85, 88,
        90, 91, 93, 96, 99, 102, 103, 105, 107, 39, 38, 37, 38, 39, 40, 45, 47,
        50, 54, 58, 59, 61, 65, 69, 71, 73, 78, 84, 85, 86, 91, 92, 92, 95, 98,
        100, 101, 103, 106, 110, 114, 44, 42, 41, 41, 42, 42, 47, 50, 54, 58,
        63, 65, 67, 71, 75, 77, 79, 84, 90, 91, 92, 95, 95, 97, 100, 101, 102,
        105, 109, 111, 112, 114, 46, 44, 42, 43, 44, 44, 49, 52, 55, 59, 65, 67,
        69, 74, 78, 80, 82, 87, 93, 94, 95, 98, 100, 103, 102, 105, 108, 110,
        111, 113, 117, 121, 48, 46, 44, 45, 45, 46, 51, 53, 57, 61, 67, 69, 71,
        76, 80, 83, 85, 90, 96, 97, 99, 103, 107, 105, 108, 111, 111, 113, 117,
        119, 120, 122, 54, 51, 49, 49, 50, 49, 54, 57, 60, 65, 71, 74, 76, 82,
        87, 89, 92, 97, 104, 105, 106, 111, 110, 111, 114, 113, 116, 120, 120,
        121, 125, 130, 59, 56, 54, 54, 54, 53, 58, 61, 64, 69, 75, 78, 80, 87,
        92, 95, 98, 103, 110, 111, 113, 115, 115, 119, 116, 120, 122, 122, 125,
        129, 130, 130, 62, 59, 56, 56, 56, 55, 60, 63, 66, 71, 77, 80, 83, 89,
        95, 98, 101, 107, 114, 115, 117, 119, 123, 121, 125, 126, 125, 129, 131,
        131, 135, 140, 65, 62, 59, 59, 59, 58, 63, 65, 68, 73, 79, 82, 85, 92,
        98, 101, 105, 111, 118, 119, 121, 126, 127, 128, 130, 130, 134, 133,
        135, 140, 140, 140, 71, 68, 65, 64, 64, 63, 68, 70, 73, 78, 84, 87, 90,
        97, 103, 107, 111, 117, 125, 126, 128, 134, 132, 136, 133, 138, 137,
        140, 143, 142, 145, 150, 80, 76, 72, 72, 71, 69, 74, 76, 79, 84, 90, 93,
        96, 104, 110, 114, 118, 125, 134, 135, 137, 139, 140, 139, 143, 142,
        144, 146, 146, 151, 152, 151, 81, 77, 73, 73, 72, 70, 75, 77, 80, 85,
        91, 94, 97, 105, 111, 115, 119, 126, 135, 137, 138, 144, 147, 146, 148,
        149, 151, 150, 156, 155, 157, 163, 83, 78, 75, 74, 74, 72, 76, 79, 81,
        86, 92, 95, 99, 106, 113, 117, 121, 128, 137, 138, 140, 147, 151, 156,
        152, 157, 155, 161, 158, 162, 165, 164, 88, 84, 80, 79, 78, 76, 80, 82,
        85, 91, 95, 98, 103, 111, 115, 119, 126, 134, 139, 144, 147, 152, 154,
        158, 163, 159, 165, 163, 168, 168, 169, 176, 91, 86, 83, 82, 81, 79, 81,
        84, 88, 92, 95, 100, 107, 110, 115, 123, 127, 132, 140, 147, 151, 154,
        159, 161, 166, 171, 169, 173, 173, 176, 179, 177, 94, 89, 86, 85, 84,
        82, 82, 86, 90, 92, 97, 103, 105, 111, 119, 121, 128, 136, 139, 146,
        156, 158, 161, 166, 168, 174, 179, 178, 180, 183, 183, 190, 97, 92, 90,
        88, 86, 85, 84, 89, 91, 95, 100, 102, 108, 114, 116, 125, 130, 133, 143,
        148, 152, 163, 166, 168, 174, 176, 182, 187, 189, 188, 193, 191, 101,
        95, 93, 91, 89, 89, 87, 91, 93, 98, 101, 105, 111, 113, 120, 126, 130,
        138, 142, 149, 157, 159, 171, 174, 176, 183, 184, 191, 195, 199, 197,
        204, 104, 99, 97, 94, 93, 93, 90, 92, 96, 100, 102, 108, 111, 116, 122,
        125, 134, 137, 144, 151, 155, 165, 169, 179, 182, 184, 191, 193, 200,
        204, 210, 206, 107, 102, 101, 97, 96, 96, 93, 93, 99, 101, 105, 110,
        113, 120, 122, 129, 133, 140, 146, 150, 161, 163, 173, 178, 187, 191,
        193, 200, 202, 210, 214, 222, 111, 105, 104, 101, 100, 99, 97, 96, 102,
        103, 109, 111, 117, 120, 125, 131, 135, 143, 146, 156, 158, 168, 173,
        180, 189, 195, 200, 202, 210, 212, 220, 224, 115, 109, 108, 104, 104,
        102, 101, 100, 103, 106, 111, 113, 119, 121, 129, 131, 140, 142, 151,
        155, 162, 168, 176, 183, 188, 199, 204, 210, 212, 220, 222, 230, 119,
        113, 112, 107, 107, 106, 105, 103, 105, 110, 112, 117, 120, 125, 130,
        135, 140, 145, 152, 157, 165, 169, 179, 183, 193, 197, 210, 214, 220,
        222, 231, 232, 123, 116, 116, 111, 111, 109, 110, 107, 107, 114, 114,
        121, 122, 130, 130, 140, 140, 150, 151, 163, 164, 176, 177, 190, 191,
        204, 206, 222, 224, 230, 232, 242,
677
        /* Size 4x8 */
678
679
        32, 42, 75, 91, 33, 42, 69, 86, 37, 58, 84, 91, 49, 71, 103, 110, 65,
        84, 125, 128, 80, 97, 142, 152, 91, 100, 145, 178, 104, 112, 146, 190,
680
        /* Size 8x4 */
681
682
        32, 33, 37, 49, 65, 80, 91, 104, 42, 42, 58, 71, 84, 97, 100, 112, 75,
        69, 84, 103, 125, 142, 145, 146, 91, 86, 91, 110, 128, 152, 178, 190,
683
        /* Size 8x16 */
684
685
686
687
688
689
690
691
        32, 32, 36, 53, 65, 87, 93, 99, 31, 33, 34, 49, 59, 78, 86, 93, 32, 34,
        36, 50, 59, 77, 82, 89, 34, 37, 42, 54, 63, 79, 80, 88, 36, 38, 48, 60,
        68, 84, 86, 90, 44, 43, 53, 71, 79, 95, 94, 97, 48, 46, 56, 76, 85, 102,
        105, 105, 58, 54, 63, 87, 98, 116, 112, 115, 65, 58, 68, 92, 105, 124,
        122, 124, 79, 70, 79, 104, 118, 141, 135, 135, 82, 72, 81, 106, 121,
        144, 149, 146, 91, 80, 88, 106, 130, 148, 162, 159, 97, 86, 94, 107,
        128, 157, 167, 171, 103, 93, 98, 114, 131, 150, 174, 186, 110, 100, 101,
        117, 138, 161, 183, 193, 118, 107, 105, 118, 136, 157, 182, 203,
692
        /* Size 16x8 */
693
694
695
696
697
698
699
700
        32, 31, 32, 34, 36, 44, 48, 58, 65, 79, 82, 91, 97, 103, 110, 118, 32,
        33, 34, 37, 38, 43, 46, 54, 58, 70, 72, 80, 86, 93, 100, 107, 36, 34,
        36, 42, 48, 53, 56, 63, 68, 79, 81, 88, 94, 98, 101, 105, 53, 49, 50,
        54, 60, 71, 76, 87, 92, 104, 106, 106, 107, 114, 117, 118, 65, 59, 59,
        63, 68, 79, 85, 98, 105, 118, 121, 130, 128, 131, 138, 136, 87, 78, 77,
        79, 84, 95, 102, 116, 124, 141, 144, 148, 157, 150, 161, 157, 93, 86,
        82, 80, 86, 94, 105, 112, 122, 135, 149, 162, 167, 174, 183, 182, 99,
        93, 89, 88, 90, 97, 105, 115, 124, 135, 146, 159, 171, 186, 193, 203,
701
        /* Size 16x32 */
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
        32, 31, 32, 34, 36, 44, 53, 59, 65, 79, 87, 90, 93, 96, 99, 102, 31, 32,
        32, 34, 35, 42, 51, 56, 62, 75, 82, 85, 88, 91, 94, 97, 31, 32, 33, 33,
        34, 41, 49, 54, 59, 72, 78, 82, 86, 90, 93, 97, 31, 32, 33, 34, 35, 41,
        49, 54, 59, 71, 78, 81, 84, 87, 90, 93, 32, 32, 34, 35, 36, 42, 50, 54,
        59, 71, 77, 80, 82, 86, 89, 93, 32, 33, 35, 37, 38, 42, 49, 53, 58, 69,
        75, 78, 82, 86, 89, 92, 34, 34, 37, 39, 42, 48, 54, 58, 63, 73, 79, 78,
        80, 83, 88, 92, 35, 34, 37, 41, 45, 50, 57, 61, 65, 76, 82, 83, 84, 84,
        87, 90, 36, 34, 38, 43, 48, 54, 60, 64, 68, 78, 84, 87, 86, 89, 90, 90,
        39, 37, 40, 45, 50, 58, 65, 69, 73, 84, 89, 89, 91, 91, 93, 96, 44, 41,
        43, 48, 53, 63, 71, 75, 79, 90, 95, 93, 94, 95, 97, 97, 46, 43, 44, 49,
        55, 65, 73, 78, 82, 93, 98, 100, 98, 100, 99, 103, 48, 45, 46, 51, 56,
        67, 76, 80, 85, 96, 102, 102, 105, 102, 105, 104, 53, 49, 50, 54, 60,
        71, 82, 87, 92, 103, 109, 107, 107, 110, 107, 111, 58, 54, 54, 58, 63,
        75, 87, 92, 98, 110, 116, 115, 112, 111, 115, 112, 61, 57, 56, 60, 66,
        77, 89, 95, 101, 114, 120, 118, 119, 118, 116, 120, 65, 60, 58, 63, 68,
        79, 92, 98, 105, 118, 124, 123, 122, 123, 124, 121, 71, 65, 63, 68, 73,
        84, 97, 103, 111, 125, 132, 132, 130, 128, 127, 130, 79, 72, 70, 74, 79,
        90, 104, 110, 118, 133, 141, 136, 135, 135, 135, 131, 81, 74, 71, 75,
        80, 91, 105, 112, 119, 135, 142, 140, 140, 138, 139, 142, 82, 75, 72,
        76, 81, 92, 106, 113, 121, 136, 144, 151, 149, 149, 146, 143, 88, 80,
        77, 80, 85, 97, 108, 115, 126, 142, 149, 153, 153, 152, 152, 154, 91,
        83, 80, 81, 88, 100, 106, 114, 130, 142, 148, 155, 162, 160, 159, 155,
        94, 85, 83, 82, 91, 100, 105, 118, 131, 137, 153, 160, 165, 167, 166,
        168, 97, 88, 86, 85, 94, 100, 107, 123, 128, 140, 157, 161, 167, 173,
        171, 169, 100, 91, 89, 87, 97, 100, 111, 121, 127, 145, 152, 164, 173,
        178, 182, 181, 103, 94, 93, 90, 98, 101, 114, 120, 131, 144, 150, 170,
        174, 180, 186, 183, 107, 97, 96, 93, 100, 104, 117, 119, 136, 142, 155,
        168, 177, 187, 191, 198, 110, 101, 100, 97, 101, 108, 117, 123, 138,
        141, 161, 165, 183, 188, 193, 200, 114, 104, 104, 100, 103, 112, 117,
        127, 137, 146, 159, 167, 185, 190, 201, 206, 118, 108, 107, 103, 105,
        115, 118, 131, 136, 151, 157, 172, 182, 197, 203, 208, 122, 111, 111,
        107, 107, 119, 119, 136, 136, 156, 156, 178, 179, 203, 204, 217,
734
        /* Size 32x16 */
735
        32, 31, 31, 31, 32, 32, 34, 35, 36, 39, 44, 46, 48, 53, 58, 61, 65, 71,
736
        79, 81, 82, 88, 91, 94, 97, 100, 103, 107, 110, 114, 118, 122, 31, 32,
737
        32, 32, 32, 33, 34, 34, 34, 37, 41, 43, 45, 49, 54, 57, 60, 65, 72, 74,
738
        75, 80, 83, 85, 88, 91, 94, 97, 101, 104, 108, 111, 32, 32, 33, 33, 34,
739
        35, 37, 37, 38, 40, 43, 44, 46, 50, 54, 56, 58, 63, 70, 71, 72, 77, 80,
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
        83, 86, 89, 93, 96, 100, 104, 107, 111, 34, 34, 33, 34, 35, 37, 39, 41,
        43, 45, 48, 49, 51, 54, 58, 60, 63, 68, 74, 75, 76, 80, 81, 82, 85, 87,
        90, 93, 97, 100, 103, 107, 36, 35, 34, 35, 36, 38, 42, 45, 48, 50, 53,
        55, 56, 60, 63, 66, 68, 73, 79, 80, 81, 85, 88, 91, 94, 97, 98, 100,
        101, 103, 105, 107, 44, 42, 41, 41, 42, 42, 48, 50, 54, 58, 63, 65, 67,
        71, 75, 77, 79, 84, 90, 91, 92, 97, 100, 100, 100, 100, 101, 104, 108,
        112, 115, 119, 53, 51, 49, 49, 50, 49, 54, 57, 60, 65, 71, 73, 76, 82,
        87, 89, 92, 97, 104, 105, 106, 108, 106, 105, 107, 111, 114, 117, 117,
        117, 118, 119, 59, 56, 54, 54, 54, 53, 58, 61, 64, 69, 75, 78, 80, 87,
        92, 95, 98, 103, 110, 112, 113, 115, 114, 118, 123, 121, 120, 119, 123,
        127, 131, 136, 65, 62, 59, 59, 59, 58, 63, 65, 68, 73, 79, 82, 85, 92,
        98, 101, 105, 111, 118, 119, 121, 126, 130, 131, 128, 127, 131, 136,
        138, 137, 136, 136, 79, 75, 72, 71, 71, 69, 73, 76, 78, 84, 90, 93, 96,
        103, 110, 114, 118, 125, 133, 135, 136, 142, 142, 137, 140, 145, 144,
        142, 141, 146, 151, 156, 87, 82, 78, 78, 77, 75, 79, 82, 84, 89, 95, 98,
        102, 109, 116, 120, 124, 132, 141, 142, 144, 149, 148, 153, 157, 152,
        150, 155, 161, 159, 157, 156, 90, 85, 82, 81, 80, 78, 78, 83, 87, 89,
        93, 100, 102, 107, 115, 118, 123, 132, 136, 140, 151, 153, 155, 160,
        161, 164, 170, 168, 165, 167, 172, 178, 93, 88, 86, 84, 82, 82, 80, 84,
        86, 91, 94, 98, 105, 107, 112, 119, 122, 130, 135, 140, 149, 153, 162,
        165, 167, 173, 174, 177, 183, 185, 182, 179, 96, 91, 90, 87, 86, 86, 83,
        84, 89, 91, 95, 100, 102, 110, 111, 118, 123, 128, 135, 138, 149, 152,
        160, 167, 173, 178, 180, 187, 188, 190, 197, 203, 99, 94, 93, 90, 89,
        89, 88, 87, 90, 93, 97, 99, 105, 107, 115, 116, 124, 127, 135, 139, 146,
        152, 159, 166, 171, 182, 186, 191, 193, 201, 203, 204, 102, 97, 97, 93,
        93, 92, 92, 90, 90, 96, 97, 103, 104, 111, 112, 120, 121, 130, 131, 142,
        143, 154, 155, 168, 169, 181, 183, 198, 200, 206, 208, 217,
767
        /* Size 4x16 */
768
769
770
771
        31, 44, 79, 96, 32, 41, 72, 90, 32, 42, 71, 86, 34, 48, 73, 83, 34, 54,
        78, 89, 41, 63, 90, 95, 45, 67, 96, 102, 54, 75, 110, 111, 60, 79, 118,
        123, 72, 90, 133, 135, 75, 92, 136, 149, 83, 100, 142, 160, 88, 100,
        140, 173, 94, 101, 144, 180, 101, 108, 141, 188, 108, 115, 151, 197,
772
        /* Size 16x4 */
773
774
775
776
        31, 32, 32, 34, 34, 41, 45, 54, 60, 72, 75, 83, 88, 94, 101, 108, 44,
        41, 42, 48, 54, 63, 67, 75, 79, 90, 92, 100, 100, 101, 108, 115, 79, 72,
        71, 73, 78, 90, 96, 110, 118, 133, 136, 142, 140, 144, 141, 151, 96, 90,
        86, 83, 89, 95, 102, 111, 123, 135, 149, 160, 173, 180, 188, 197,
777
        /* Size 8x32 */
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
        32, 32, 36, 53, 65, 87, 93, 99, 31, 32, 35, 51, 62, 82, 88, 94, 31, 33,
        34, 49, 59, 78, 86, 93, 31, 33, 35, 49, 59, 78, 84, 90, 32, 34, 36, 50,
        59, 77, 82, 89, 32, 35, 38, 49, 58, 75, 82, 89, 34, 37, 42, 54, 63, 79,
        80, 88, 35, 37, 45, 57, 65, 82, 84, 87, 36, 38, 48, 60, 68, 84, 86, 90,
        39, 40, 50, 65, 73, 89, 91, 93, 44, 43, 53, 71, 79, 95, 94, 97, 46, 44,
        55, 73, 82, 98, 98, 99, 48, 46, 56, 76, 85, 102, 105, 105, 53, 50, 60,
        82, 92, 109, 107, 107, 58, 54, 63, 87, 98, 116, 112, 115, 61, 56, 66,
        89, 101, 120, 119, 116, 65, 58, 68, 92, 105, 124, 122, 124, 71, 63, 73,
        97, 111, 132, 130, 127, 79, 70, 79, 104, 118, 141, 135, 135, 81, 71, 80,
        105, 119, 142, 140, 139, 82, 72, 81, 106, 121, 144, 149, 146, 88, 77,
        85, 108, 126, 149, 153, 152, 91, 80, 88, 106, 130, 148, 162, 159, 94,
        83, 91, 105, 131, 153, 165, 166, 97, 86, 94, 107, 128, 157, 167, 171,
        100, 89, 97, 111, 127, 152, 173, 182, 103, 93, 98, 114, 131, 150, 174,
        186, 107, 96, 100, 117, 136, 155, 177, 191, 110, 100, 101, 117, 138,
        161, 183, 193, 114, 104, 103, 117, 137, 159, 185, 201, 118, 107, 105,
        118, 136, 157, 182, 203, 122, 111, 107, 119, 136, 156, 179, 204,
794
        /* Size 32x8 */
795
        32, 31, 31, 31, 32, 32, 34, 35, 36, 39, 44, 46, 48, 53, 58, 61, 65, 71,
796
        79, 81, 82, 88, 91, 94, 97, 100, 103, 107, 110, 114, 118, 122, 32, 32,
797
        33, 33, 34, 35, 37, 37, 38, 40, 43, 44, 46, 50, 54, 56, 58, 63, 70, 71,
798
        72, 77, 80, 83, 86, 89, 93, 96, 100, 104, 107, 111, 36, 35, 34, 35, 36,
799
        38, 42, 45, 48, 50, 53, 55, 56, 60, 63, 66, 68, 73, 79, 80, 81, 85, 88,
800
801
802
803
804
805
806
807
808
809
810
        91, 94, 97, 98, 100, 101, 103, 105, 107, 53, 51, 49, 49, 50, 49, 54, 57,
        60, 65, 71, 73, 76, 82, 87, 89, 92, 97, 104, 105, 106, 108, 106, 105,
        107, 111, 114, 117, 117, 117, 118, 119, 65, 62, 59, 59, 59, 58, 63, 65,
        68, 73, 79, 82, 85, 92, 98, 101, 105, 111, 118, 119, 121, 126, 130, 131,
        128, 127, 131, 136, 138, 137, 136, 136, 87, 82, 78, 78, 77, 75, 79, 82,
        84, 89, 95, 98, 102, 109, 116, 120, 124, 132, 141, 142, 144, 149, 148,
        153, 157, 152, 150, 155, 161, 159, 157, 156, 93, 88, 86, 84, 82, 82, 80,
        84, 86, 91, 94, 98, 105, 107, 112, 119, 122, 130, 135, 140, 149, 153,
        162, 165, 167, 173, 174, 177, 183, 185, 182, 179, 99, 94, 93, 90, 89,
        89, 88, 87, 90, 93, 97, 99, 105, 107, 115, 116, 124, 127, 135, 139, 146,
        152, 159, 166, 171, 182, 186, 191, 193, 201, 203, 204 },
811
812
      { /* Chroma */
        /* Size 4x4 */
813
        35, 46, 57, 66, 46, 60, 69, 71, 57, 69, 90, 90, 66, 71, 90, 109,
814
        /* Size 8x8 */
815
816
817
818
        31, 38, 47, 50, 57, 63, 67, 71, 38, 47, 46, 47, 52, 57, 62, 67, 47, 46,
        54, 57, 61, 66, 67, 68, 50, 47, 57, 66, 72, 77, 75, 75, 57, 52, 61, 72,
        82, 88, 86, 84, 63, 57, 66, 77, 88, 96, 95, 95, 67, 62, 67, 75, 86, 95,
        104, 107, 71, 67, 68, 75, 84, 95, 107, 113,
819
        /* Size 16x16 */
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
        32, 30, 33, 41, 49, 49, 50, 54, 57, 63, 65, 68, 70, 72, 74, 76, 30, 32,
        35, 42, 46, 45, 46, 49, 52, 57, 58, 62, 64, 67, 70, 72, 33, 35, 39, 45,
        47, 45, 46, 49, 51, 56, 57, 60, 62, 64, 66, 69, 41, 42, 45, 48, 50, 49,
        50, 52, 53, 57, 58, 59, 60, 61, 64, 67, 49, 46, 47, 50, 53, 53, 54, 55,
        56, 60, 61, 64, 64, 65, 66, 66, 49, 45, 45, 49, 53, 58, 60, 62, 63, 67,
        68, 67, 69, 68, 70, 70, 50, 46, 46, 50, 54, 60, 61, 65, 67, 71, 71, 74,
        73, 73, 74, 74, 54, 49, 49, 52, 55, 62, 65, 71, 73, 78, 79, 78, 77, 78,
        78, 78, 57, 52, 51, 53, 56, 63, 67, 73, 76, 82, 83, 84, 84, 84, 82, 83,
        63, 57, 56, 57, 60, 67, 71, 78, 82, 89, 90, 90, 89, 88, 87, 88, 65, 58,
        57, 58, 61, 68, 71, 79, 83, 90, 91, 94, 93, 93, 92, 93, 68, 62, 60, 59,
        64, 67, 74, 78, 84, 90, 94, 98, 99, 98, 98, 98, 70, 64, 62, 60, 64, 69,
        73, 77, 84, 89, 93, 99, 102, 103, 104, 104, 72, 67, 64, 61, 65, 68, 73,
        78, 84, 88, 93, 98, 103, 106, 108, 109, 74, 70, 66, 64, 66, 70, 74, 78,
        82, 87, 92, 98, 104, 108, 111, 112, 76, 72, 69, 67, 66, 70, 74, 78, 83,
        88, 93, 98, 104, 109, 112, 116,
835
        /* Size 32x32 */
836
        32, 31, 30, 32, 33, 36, 41, 45, 49, 48, 49, 50, 50, 52, 54, 56, 57, 60,
837
838
839
840
841
842
843
844
        63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 31, 31, 31, 33,
        34, 38, 42, 45, 47, 47, 47, 47, 48, 50, 52, 53, 54, 57, 60, 61, 61, 63,
        64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 30, 31, 32, 33, 35, 40, 42, 44,
        46, 45, 45, 45, 46, 47, 49, 51, 52, 54, 57, 58, 58, 61, 62, 63, 64, 66,
        67, 68, 70, 71, 72, 74, 32, 33, 33, 35, 37, 41, 43, 45, 47, 46, 45, 46,
        46, 47, 49, 50, 51, 54, 57, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68,
        69, 70, 33, 34, 35, 37, 39, 43, 45, 46, 47, 46, 45, 46, 46, 47, 49, 50,
        51, 53, 56, 57, 57, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 36, 38,
845
        40, 41, 43, 47, 47, 47, 48, 46, 45, 46, 46, 47, 48, 49, 50, 52, 54, 55,
846
847
848
849
850
851
        55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 41, 42, 42, 43, 45, 47,
        48, 49, 50, 49, 49, 49, 50, 50, 52, 52, 53, 55, 57, 58, 58, 60, 59, 59,
        60, 61, 61, 63, 64, 66, 67, 69, 45, 45, 44, 45, 46, 47, 49, 50, 51, 51,
        51, 51, 52, 52, 53, 54, 55, 57, 59, 59, 60, 61, 61, 62, 63, 63, 63, 63,
        63, 64, 65, 66, 49, 47, 46, 47, 47, 48, 50, 51, 53, 53, 53, 54, 54, 54,
        55, 56, 56, 58, 60, 61, 61, 63, 64, 64, 64, 64, 65, 66, 66, 66, 66, 66,
852
        48, 47, 45, 46, 46, 46, 49, 51, 53, 54, 55, 56, 56, 57, 58, 59, 60, 61,
853
        63, 64, 64, 66, 66, 65, 66, 67, 67, 67, 67, 68, 69, 70, 49, 47, 45, 45,
854
        45, 45, 49, 51, 53, 55, 58, 59, 60, 61, 62, 63, 63, 65, 67, 67, 68, 69,
855
856
857
858
859
860
        67, 68, 69, 68, 68, 69, 70, 70, 70, 70, 50, 47, 45, 46, 46, 46, 49, 51,
        54, 56, 59, 60, 60, 62, 64, 64, 65, 67, 69, 69, 70, 70, 71, 71, 70, 70,
        71, 71, 71, 71, 72, 74, 50, 48, 46, 46, 46, 46, 50, 52, 54, 56, 60, 60,
        61, 63, 65, 66, 67, 68, 71, 71, 71, 73, 74, 72, 73, 74, 73, 73, 74, 74,
        74, 74, 52, 50, 47, 47, 47, 47, 50, 52, 54, 57, 61, 62, 63, 66, 68, 69,
        70, 72, 75, 75, 75, 77, 75, 75, 76, 75, 75, 76, 75, 75, 76, 77, 54, 52,
861
        49, 49, 49, 48, 52, 53, 55, 58, 62, 64, 65, 68, 71, 72, 73, 75, 78, 78,
862
863
864
865
866
867
        79, 79, 78, 79, 77, 78, 78, 77, 78, 79, 78, 78, 56, 53, 51, 50, 50, 49,
        52, 54, 56, 59, 63, 64, 66, 69, 72, 73, 75, 77, 80, 80, 81, 81, 82, 80,
        81, 81, 79, 81, 80, 79, 81, 82, 57, 54, 52, 51, 51, 50, 53, 55, 56, 60,
        63, 65, 67, 70, 73, 75, 76, 79, 82, 82, 83, 85, 84, 83, 84, 83, 84, 82,
        82, 84, 83, 82, 60, 57, 54, 54, 53, 52, 55, 57, 58, 61, 65, 67, 68, 72,
        75, 77, 79, 82, 85, 85, 86, 88, 86, 87, 85, 86, 85, 85, 86, 84, 85, 86,
868
        63, 60, 57, 57, 56, 54, 57, 59, 60, 63, 67, 69, 71, 75, 78, 80, 82, 85,
869
        89, 89, 90, 90, 90, 89, 89, 88, 88, 88, 87, 88, 88, 87, 64, 61, 58, 57,
870
        57, 55, 58, 59, 61, 64, 67, 69, 71, 75, 78, 80, 82, 85, 89, 90, 91, 92,
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
        93, 92, 92, 91, 91, 90, 91, 90, 90, 92, 65, 61, 58, 58, 57, 55, 58, 60,
        61, 64, 68, 70, 71, 75, 79, 81, 83, 86, 90, 91, 91, 94, 94, 96, 93, 94,
        93, 94, 92, 93, 93, 92, 67, 63, 61, 60, 59, 57, 60, 61, 63, 66, 69, 70,
        73, 77, 79, 81, 85, 88, 90, 92, 94, 96, 96, 97, 98, 95, 97, 95, 96, 95,
        95, 96, 68, 64, 62, 61, 60, 58, 59, 61, 64, 66, 67, 71, 74, 75, 78, 82,
        84, 86, 90, 93, 94, 96, 98, 98, 99, 100, 98, 99, 98, 98, 98, 97, 69, 65,
        63, 62, 61, 59, 59, 62, 64, 65, 68, 71, 72, 75, 79, 80, 83, 87, 89, 92,
        96, 97, 98, 100, 100, 101, 102, 101, 101, 101, 100, 102, 70, 66, 64, 63,
        62, 61, 60, 63, 64, 66, 69, 70, 73, 76, 77, 81, 84, 85, 89, 92, 93, 98,
        99, 100, 102, 102, 103, 104, 104, 103, 104, 102, 71, 67, 66, 64, 63, 62,
        61, 63, 64, 67, 68, 70, 74, 75, 78, 81, 83, 86, 88, 91, 94, 95, 100,
        101, 102, 104, 104, 105, 106, 107, 105, 107, 72, 68, 67, 65, 64, 64, 61,
        63, 65, 67, 68, 71, 73, 75, 78, 79, 84, 85, 88, 91, 93, 97, 98, 102,
        103, 104, 106, 106, 108, 108, 109, 107, 73, 69, 68, 66, 65, 65, 63, 63,
        66, 67, 69, 71, 73, 76, 77, 81, 82, 85, 88, 90, 94, 95, 99, 101, 104,
        105, 106, 109, 108, 110, 111, 112, 74, 70, 70, 67, 66, 66, 64, 63, 66,
        67, 70, 71, 74, 75, 78, 80, 82, 86, 87, 91, 92, 96, 98, 101, 104, 106,
        108, 108, 111, 111, 112, 113, 75, 71, 71, 68, 68, 67, 66, 64, 66, 68,
        70, 71, 74, 75, 79, 79, 84, 84, 88, 90, 93, 95, 98, 101, 103, 107, 108,
        110, 111, 113, 113, 115, 76, 72, 72, 69, 69, 68, 67, 65, 66, 69, 70, 72,
        74, 76, 78, 81, 83, 85, 88, 90, 93, 95, 98, 100, 104, 105, 109, 111,
        112, 113, 116, 115, 78, 74, 74, 70, 70, 69, 69, 66, 66, 70, 70, 74, 74,
        77, 78, 82, 82, 86, 87, 92, 92, 96, 97, 102, 102, 107, 107, 112, 113,
        115, 115, 118,
895
        /* Size 4x8 */
896
897
        31, 47, 60, 66, 40, 45, 54, 61, 46, 56, 64, 64, 48, 61, 75, 73, 54, 65,
        85, 82, 61, 69, 92, 92, 64, 68, 90, 102, 68, 71, 87, 105,
898
        /* Size 8x4 */
899
900
        31, 40, 46, 48, 54, 61, 64, 68, 47, 45, 56, 61, 65, 69, 68, 71, 60, 54,
        64, 75, 85, 92, 90, 87, 66, 61, 64, 73, 82, 92, 102, 105,
901
        /* Size 8x16 */
902
903
904
905
906
907
908
909
        32, 37, 48, 52, 57, 66, 68, 71, 30, 40, 46, 48, 52, 60, 63, 66, 33, 43,
        47, 47, 51, 59, 60, 63, 42, 47, 50, 50, 53, 60, 59, 62, 49, 48, 53, 54,
        57, 62, 62, 62, 49, 46, 53, 61, 64, 69, 66, 66, 50, 46, 54, 64, 67, 73,
        72, 70, 54, 49, 55, 68, 73, 80, 76, 75, 57, 50, 56, 70, 76, 84, 80, 79,
        63, 55, 60, 75, 82, 92, 87, 84, 64, 56, 61, 75, 83, 93, 93, 89, 68, 59,
        64, 74, 86, 94, 98, 94, 70, 62, 66, 73, 83, 96, 99, 98, 72, 64, 66, 75,
        83, 92, 101, 104, 74, 67, 66, 74, 84, 94, 103, 106, 76, 69, 67, 73, 82,
        91, 101, 109,
910
        /* Size 16x8 */
911
912
913
914
915
916
917
918
        32, 30, 33, 42, 49, 49, 50, 54, 57, 63, 64, 68, 70, 72, 74, 76, 37, 40,
        43, 47, 48, 46, 46, 49, 50, 55, 56, 59, 62, 64, 67, 69, 48, 46, 47, 50,
        53, 53, 54, 55, 56, 60, 61, 64, 66, 66, 66, 67, 52, 48, 47, 50, 54, 61,
        64, 68, 70, 75, 75, 74, 73, 75, 74, 73, 57, 52, 51, 53, 57, 64, 67, 73,
        76, 82, 83, 86, 83, 83, 84, 82, 66, 60, 59, 60, 62, 69, 73, 80, 84, 92,
        93, 94, 96, 92, 94, 91, 68, 63, 60, 59, 62, 66, 72, 76, 80, 87, 93, 98,
        99, 101, 103, 101, 71, 66, 63, 62, 62, 66, 70, 75, 79, 84, 89, 94, 98,
        104, 106, 109,
919
        /* Size 16x32 */
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
        32, 31, 37, 42, 48, 49, 52, 54, 57, 63, 66, 67, 68, 69, 71, 72, 31, 31,
        38, 42, 47, 47, 50, 52, 54, 60, 63, 64, 65, 66, 67, 68, 30, 32, 40, 42,
        46, 45, 48, 50, 52, 57, 60, 62, 63, 65, 66, 68, 32, 34, 41, 44, 46, 45,
        48, 49, 51, 57, 59, 61, 62, 63, 64, 65, 33, 36, 43, 45, 47, 46, 47, 49,
        51, 56, 59, 60, 60, 62, 63, 65, 37, 40, 47, 47, 47, 45, 47, 48, 50, 54,
        57, 58, 60, 61, 62, 63, 42, 43, 47, 48, 50, 49, 50, 52, 53, 57, 60, 58,
        59, 60, 62, 63, 45, 44, 47, 49, 51, 51, 52, 54, 55, 59, 61, 61, 61, 60,
        61, 61, 49, 46, 48, 50, 53, 53, 54, 55, 57, 60, 62, 63, 62, 63, 62, 62,
        48, 46, 47, 50, 53, 56, 57, 59, 60, 64, 66, 65, 65, 64, 64, 65, 49, 45,
        46, 49, 53, 58, 61, 62, 64, 67, 69, 67, 66, 66, 66, 65, 49, 46, 46, 49,
        53, 59, 62, 64, 65, 69, 71, 70, 68, 68, 67, 68, 50, 46, 46, 50, 54, 59,
        64, 65, 67, 71, 73, 72, 72, 70, 70, 69, 52, 48, 47, 50, 54, 61, 66, 68,
        71, 75, 77, 74, 73, 73, 71, 72, 54, 50, 49, 52, 55, 62, 68, 71, 73, 78,
        80, 78, 76, 74, 75, 73, 55, 51, 49, 52, 56, 63, 69, 72, 75, 80, 82, 80,
        79, 78, 76, 77, 57, 52, 50, 53, 56, 64, 70, 73, 76, 82, 84, 82, 80, 80,
        79, 77, 60, 54, 52, 55, 58, 65, 72, 75, 79, 85, 88, 86, 84, 82, 81, 81,
        63, 57, 55, 58, 60, 67, 75, 78, 82, 89, 92, 88, 87, 85, 84, 81, 64, 58,
        55, 58, 61, 68, 75, 78, 82, 89, 92, 90, 89, 87, 86, 86, 64, 59, 56, 58,
        61, 68, 75, 79, 83, 90, 93, 95, 93, 91, 89, 87, 67, 61, 58, 60, 63, 69,
        76, 79, 85, 92, 95, 96, 94, 92, 91, 91, 68, 62, 59, 60, 64, 71, 74, 78,
        86, 91, 94, 96, 98, 96, 94, 91, 69, 62, 60, 60, 65, 70, 72, 79, 85, 88,
        95, 98, 99, 98, 97, 96, 70, 63, 62, 60, 66, 69, 73, 81, 83, 89, 96, 97,
        99, 101, 98, 97, 71, 64, 63, 61, 67, 68, 74, 79, 82, 90, 93, 98, 102,
        102, 102, 101, 72, 65, 64, 62, 66, 68, 75, 78, 83, 89, 92, 100, 101,
        103, 104, 102, 73, 66, 65, 63, 66, 69, 75, 76, 84, 87, 93, 98, 102, 105,
        106, 107, 74, 67, 67, 64, 66, 70, 74, 77, 84, 86, 94, 96, 103, 105, 106,
        107, 75, 68, 68, 65, 66, 71, 74, 78, 83, 87, 93, 96, 103, 105, 109, 109,
        76, 69, 69, 66, 67, 72, 73, 80, 82, 88, 91, 97, 101, 107, 109, 110, 77,
        70, 70, 67, 67, 73, 73, 81, 81, 90, 90, 99, 99, 108, 108, 113,
949
        /* Size 32x16 */
950
        32, 31, 30, 32, 33, 37, 42, 45, 49, 48, 49, 49, 50, 52, 54, 55, 57, 60,
951
        63, 64, 64, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 31, 31, 32, 34,
952
        36, 40, 43, 44, 46, 46, 45, 46, 46, 48, 50, 51, 52, 54, 57, 58, 59, 61,
953
        62, 62, 63, 64, 65, 66, 67, 68, 69, 70, 37, 38, 40, 41, 43, 47, 47, 47,
954
        48, 47, 46, 46, 46, 47, 49, 49, 50, 52, 55, 55, 56, 58, 59, 60, 62, 63,
955
956
957
958
        64, 65, 67, 68, 69, 70, 42, 42, 42, 44, 45, 47, 48, 49, 50, 50, 49, 49,
        50, 50, 52, 52, 53, 55, 58, 58, 58, 60, 60, 60, 60, 61, 62, 63, 64, 65,
        66, 67, 48, 47, 46, 46, 47, 47, 50, 51, 53, 53, 53, 53, 54, 54, 55, 56,
        56, 58, 60, 61, 61, 63, 64, 65, 66, 67, 66, 66, 66, 66, 67, 67, 49, 47,
959
        45, 45, 46, 45, 49, 51, 53, 56, 58, 59, 59, 61, 62, 63, 64, 65, 67, 68,
960
961
962
963
964
965
        68, 69, 71, 70, 69, 68, 68, 69, 70, 71, 72, 73, 52, 50, 48, 48, 47, 47,
        50, 52, 54, 57, 61, 62, 64, 66, 68, 69, 70, 72, 75, 75, 75, 76, 74, 72,
        73, 74, 75, 75, 74, 74, 73, 73, 54, 52, 50, 49, 49, 48, 52, 54, 55, 59,
        62, 64, 65, 68, 71, 72, 73, 75, 78, 78, 79, 79, 78, 79, 81, 79, 78, 76,
        77, 78, 80, 81, 57, 54, 52, 51, 51, 50, 53, 55, 57, 60, 64, 65, 67, 71,
        73, 75, 76, 79, 82, 82, 83, 85, 86, 85, 83, 82, 83, 84, 84, 83, 82, 81,
966
        63, 60, 57, 57, 56, 54, 57, 59, 60, 64, 67, 69, 71, 75, 78, 80, 82, 85,
967
        89, 89, 90, 92, 91, 88, 89, 90, 89, 87, 86, 87, 88, 90, 66, 63, 60, 59,
968
        59, 57, 60, 61, 62, 66, 69, 71, 73, 77, 80, 82, 84, 88, 92, 92, 93, 95,
969
970
971
972
973
974
975
976
977
978
        94, 95, 96, 93, 92, 93, 94, 93, 91, 90, 67, 64, 62, 61, 60, 58, 58, 61,
        63, 65, 67, 70, 72, 74, 78, 80, 82, 86, 88, 90, 95, 96, 96, 98, 97, 98,
        100, 98, 96, 96, 97, 99, 68, 65, 63, 62, 60, 60, 59, 61, 62, 65, 66, 68,
        72, 73, 76, 79, 80, 84, 87, 89, 93, 94, 98, 99, 99, 102, 101, 102, 103,
        103, 101, 99, 69, 66, 65, 63, 62, 61, 60, 60, 63, 64, 66, 68, 70, 73,
        74, 78, 80, 82, 85, 87, 91, 92, 96, 98, 101, 102, 103, 105, 105, 105,
        107, 108, 71, 67, 66, 64, 63, 62, 62, 61, 62, 64, 66, 67, 70, 71, 75,
        76, 79, 81, 84, 86, 89, 91, 94, 97, 98, 102, 104, 106, 106, 109, 109,
        108, 72, 68, 68, 65, 65, 63, 63, 61, 62, 65, 65, 68, 69, 72, 73, 77, 77,
        81, 81, 86, 87, 91, 91, 96, 97, 101, 102, 107, 107, 109, 110, 113,
979
        /* Size 4x16 */
980
981
982
983
        31, 49, 63, 69, 32, 45, 57, 65, 36, 46, 56, 62, 43, 49, 57, 60, 46, 53,
        60, 63, 45, 58, 67, 66, 46, 59, 71, 70, 50, 62, 78, 74, 52, 64, 82, 80,
        57, 67, 89, 85, 59, 68, 90, 91, 62, 71, 91, 96, 63, 69, 89, 101, 65, 68,
        89, 103, 67, 70, 86, 105, 69, 72, 88, 107,
984
        /* Size 16x4 */
985
986
987
988
        31, 32, 36, 43, 46, 45, 46, 50, 52, 57, 59, 62, 63, 65, 67, 69, 49, 45,
        46, 49, 53, 58, 59, 62, 64, 67, 68, 71, 69, 68, 70, 72, 63, 57, 56, 57,
        60, 67, 71, 78, 82, 89, 90, 91, 89, 89, 86, 88, 69, 65, 62, 60, 63, 66,
        70, 74, 80, 85, 91, 96, 101, 103, 105, 107,
989
        /* Size 8x32 */
990
991
992
993
994
995
996
997
998
999
1000
        32, 37, 48, 52, 57, 66, 68, 71, 31, 38, 47, 50, 54, 63, 65, 67, 30, 40,
        46, 48, 52, 60, 63, 66, 32, 41, 46, 48, 51, 59, 62, 64, 33, 43, 47, 47,
        51, 59, 60, 63, 37, 47, 47, 47, 50, 57, 60, 62, 42, 47, 50, 50, 53, 60,
        59, 62, 45, 47, 51, 52, 55, 61, 61, 61, 49, 48, 53, 54, 57, 62, 62, 62,
        48, 47, 53, 57, 60, 66, 65, 64, 49, 46, 53, 61, 64, 69, 66, 66, 49, 46,
        53, 62, 65, 71, 68, 67, 50, 46, 54, 64, 67, 73, 72, 70, 52, 47, 54, 66,
        71, 77, 73, 71, 54, 49, 55, 68, 73, 80, 76, 75, 55, 49, 56, 69, 75, 82,
        79, 76, 57, 50, 56, 70, 76, 84, 80, 79, 60, 52, 58, 72, 79, 88, 84, 81,
        63, 55, 60, 75, 82, 92, 87, 84, 64, 55, 61, 75, 82, 92, 89, 86, 64, 56,
        61, 75, 83, 93, 93, 89, 67, 58, 63, 76, 85, 95, 94, 91, 68, 59, 64, 74,
        86, 94, 98, 94, 69, 60, 65, 72, 85, 95, 99, 97, 70, 62, 66, 73, 83, 96,
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