path: root/media/libaom/src/av1/common/warped_motion.c

/*
 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
 *
 * 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.
 */

#include <stdio.h>
#include <stdlib.h>
#include <memory.h>
#include <math.h>
#include <assert.h>

#include "config/av1_rtcd.h"

#include "av1/common/warped_motion.h"
#include "av1/common/scale.h"

#define WARP_ERROR_BLOCK 32

/* clang-format off */
static const int error_measure_lut[512] = {
  // pow 0.7
  16384, 16339, 16294, 16249, 16204, 16158, 16113, 16068,
  16022, 15977, 15932, 15886, 15840, 15795, 15749, 15703,
  15657, 15612, 15566, 15520, 15474, 15427, 15381, 15335,
  15289, 15242, 15196, 15149, 15103, 15056, 15010, 14963,
  14916, 14869, 14822, 14775, 14728, 14681, 14634, 14587,
  14539, 14492, 14445, 14397, 14350, 14302, 14254, 14206,
  14159, 14111, 14063, 14015, 13967, 13918, 13870, 13822,
  13773, 13725, 13676, 13628, 13579, 13530, 13481, 13432,
  13383, 13334, 13285, 13236, 13187, 13137, 13088, 13038,
  12988, 12939, 12889, 12839, 12789, 12739, 12689, 12639,
  12588, 12538, 12487, 12437, 12386, 12335, 12285, 12234,
  12183, 12132, 12080, 12029, 11978, 11926, 11875, 11823,
  11771, 11719, 11667, 11615, 11563, 11511, 11458, 11406,
  11353, 11301, 11248, 11195, 11142, 11089, 11036, 10982,
  10929, 10875, 10822, 10768, 10714, 10660, 10606, 10552,
  10497, 10443, 10388, 10333, 10279, 10224, 10168, 10113,
  10058, 10002,  9947,  9891,  9835,  9779,  9723,  9666,
  9610, 9553, 9497, 9440, 9383, 9326, 9268, 9211,
  9153, 9095, 9037, 8979, 8921, 8862, 8804, 8745,
  8686, 8627, 8568, 8508, 8449, 8389, 8329, 8269,
  8208, 8148, 8087, 8026, 7965, 7903, 7842, 7780,
  7718, 7656, 7593, 7531, 7468, 7405, 7341, 7278,
  7214, 7150, 7086, 7021, 6956, 6891, 6826, 6760,
  6695, 6628, 6562, 6495, 6428, 6361, 6293, 6225,
  6157, 6089, 6020, 5950, 5881, 5811, 5741, 5670,
  5599, 5527, 5456, 5383, 5311, 5237, 5164, 5090,
  5015, 4941, 4865, 4789, 4713, 4636, 4558, 4480,
  4401, 4322, 4242, 4162, 4080, 3998, 3916, 3832,
  3748, 3663, 3577, 3490, 3402, 3314, 3224, 3133,
  3041, 2948, 2854, 2758, 2661, 2562, 2461, 2359,
  2255, 2148, 2040, 1929, 1815, 1698, 1577, 1452,
  1323, 1187, 1045,  894,  731,  550,  339,    0,
  339,  550,  731,  894, 1045, 1187, 1323, 1452,
  1577, 1698, 1815, 1929, 2040, 2148, 2255, 2359,
  2461, 2562, 2661, 2758, 2854, 2948, 3041, 3133,
  3224, 3314, 3402, 3490, 3577, 3663, 3748, 3832,
  3916, 3998, 4080, 4162, 4242, 4322, 4401, 4480,
  4558, 4636, 4713, 4789, 4865, 4941, 5015, 5090,
  5164, 5237, 5311, 5383, 5456, 5527, 5599, 5670,
  5741, 5811, 5881, 5950, 6020, 6089, 6157, 6225,
  6293, 6361, 6428, 6495, 6562, 6628, 6695, 6760,
  6826, 6891, 6956, 7021, 7086, 7150, 7214, 7278,
  7341, 7405, 7468, 7531, 7593, 7656, 7718, 7780,
  7842, 7903, 7965, 8026, 8087, 8148, 8208, 8269,
  8329, 8389, 8449, 8508, 8568, 8627, 8686, 8745,
  8804, 8862, 8921, 8979, 9037, 9095, 9153, 9211,
  9268, 9326, 9383, 9440, 9497, 9553, 9610, 9666,
  9723,  9779,  9835,  9891,  9947, 10002, 10058, 10113,
  10168, 10224, 10279, 10333, 10388, 10443, 10497, 10552,
  10606, 10660, 10714, 10768, 10822, 10875, 10929, 10982,
  11036, 11089, 11142, 11195, 11248, 11301, 11353, 11406,
  11458, 11511, 11563, 11615, 11667, 11719, 11771, 11823,
  11875, 11926, 11978, 12029, 12080, 12132, 12183, 12234,
  12285, 12335, 12386, 12437, 12487, 12538, 12588, 12639,
  12689, 12739, 12789, 12839, 12889, 12939, 12988, 13038,
  13088, 13137, 13187, 13236, 13285, 13334, 13383, 13432,
  13481, 13530, 13579, 13628, 13676, 13725, 13773, 13822,
  13870, 13918, 13967, 14015, 14063, 14111, 14159, 14206,
  14254, 14302, 14350, 14397, 14445, 14492, 14539, 14587,
  14634, 14681, 14728, 14775, 14822, 14869, 14916, 14963,
  15010, 15056, 15103, 15149, 15196, 15242, 15289, 15335,
  15381, 15427, 15474, 15520, 15566, 15612, 15657, 15703,
  15749, 15795, 15840, 15886, 15932, 15977, 16022, 16068,
  16113, 16158, 16204, 16249, 16294, 16339, 16384, 16384,
};
/* clang-format on */

// For warping, we really use a 6-tap filter, but we do blocks of 8 pixels
// at a time. The zoom/rotation/shear in the model are applied to the
// "fractional" position of each pixel, which therefore varies within
// [-1, 2) * WARPEDPIXEL_PREC_SHIFTS.
// We need an extra 2 taps to fit this in, for a total of 8 taps.
/* clang-format off */
const int16_t warped_filter[WARPEDPIXEL_PREC_SHIFTS * 3 + 1][8] = {
#if WARPEDPIXEL_PREC_BITS == 6
  // [-1, 0)
  { 0,   0, 127,   1,   0, 0, 0, 0 }, { 0, - 1, 127,   2,   0, 0, 0, 0 },
  { 1, - 3, 127,   4, - 1, 0, 0, 0 }, { 1, - 4, 126,   6, - 2, 1, 0, 0 },
  { 1, - 5, 126,   8, - 3, 1, 0, 0 }, { 1, - 6, 125,  11, - 4, 1, 0, 0 },
  { 1, - 7, 124,  13, - 4, 1, 0, 0 }, { 2, - 8, 123,  15, - 5, 1, 0, 0 },
  { 2, - 9, 122,  18, - 6, 1, 0, 0 }, { 2, -10, 121,  20, - 6, 1, 0, 0 },
  { 2, -11, 120,  22, - 7, 2, 0, 0 }, { 2, -12, 119,  25, - 8, 2, 0, 0 },
  { 3, -13, 117,  27, - 8, 2, 0, 0 }, { 3, -13, 116,  29, - 9, 2, 0, 0 },
  { 3, -14, 114,  32, -10, 3, 0, 0 }, { 3, -15, 113,  35, -10, 2, 0, 0 },
  { 3, -15, 111,  37, -11, 3, 0, 0 }, { 3, -16, 109,  40, -11, 3, 0, 0 },
  { 3, -16, 108,  42, -12, 3, 0, 0 }, { 4, -17, 106,  45, -13, 3, 0, 0 },
  { 4, -17, 104,  47, -13, 3, 0, 0 }, { 4, -17, 102,  50, -14, 3, 0, 0 },
  { 4, -17, 100,  52, -14, 3, 0, 0 }, { 4, -18,  98,  55, -15, 4, 0, 0 },
  { 4, -18,  96,  58, -15, 3, 0, 0 }, { 4, -18,  94,  60, -16, 4, 0, 0 },
  { 4, -18,  91,  63, -16, 4, 0, 0 }, { 4, -18,  89,  65, -16, 4, 0, 0 },
  { 4, -18,  87,  68, -17, 4, 0, 0 }, { 4, -18,  85,  70, -17, 4, 0, 0 },
  { 4, -18,  82,  73, -17, 4, 0, 0 }, { 4, -18,  80,  75, -17, 4, 0, 0 },
  { 4, -18,  78,  78, -18, 4, 0, 0 }, { 4, -17,  75,  80, -18, 4, 0, 0 },
  { 4, -17,  73,  82, -18, 4, 0, 0 }, { 4, -17,  70,  85, -18, 4, 0, 0 },
  { 4, -17,  68,  87, -18, 4, 0, 0 }, { 4, -16,  65,  89, -18, 4, 0, 0 },
  { 4, -16,  63,  91, -18, 4, 0, 0 }, { 4, -16,  60,  94, -18, 4, 0, 0 },
  { 3, -15,  58,  96, -18, 4, 0, 0 }, { 4, -15,  55,  98, -18, 4, 0, 0 },
  { 3, -14,  52, 100, -17, 4, 0, 0 }, { 3, -14,  50, 102, -17, 4, 0, 0 },
  { 3, -13,  47, 104, -17, 4, 0, 0 }, { 3, -13,  45, 106, -17, 4, 0, 0 },
  { 3, -12,  42, 108, -16, 3, 0, 0 }, { 3, -11,  40, 109, -16, 3, 0, 0 },
  { 3, -11,  37, 111, -15, 3, 0, 0 }, { 2, -10,  35, 113, -15, 3, 0, 0 },
  { 3, -10,  32, 114, -14, 3, 0, 0 }, { 2, - 9,  29, 116, -13, 3, 0, 0 },
  { 2, - 8,  27, 117, -13, 3, 0, 0 }, { 2, - 8,  25, 119, -12, 2, 0, 0 },
  { 2, - 7,  22, 120, -11, 2, 0, 0 }, { 1, - 6,  20, 121, -10, 2, 0, 0 },
  { 1, - 6,  18, 122, - 9, 2, 0, 0 }, { 1, - 5,  15, 123, - 8, 2, 0, 0 },
  { 1, - 4,  13, 124, - 7, 1, 0, 0 }, { 1, - 4,  11, 125, - 6, 1, 0, 0 },
  { 1, - 3,   8, 126, - 5, 1, 0, 0 }, { 1, - 2,   6, 126, - 4, 1, 0, 0 },
  { 0, - 1,   4, 127, - 3, 1, 0, 0 }, { 0,   0,   2, 127, - 1, 0, 0, 0 },

  // [0, 1)
  { 0,  0,   0, 127,   1,   0,  0,  0}, { 0,  0,  -1, 127,   2,   0,  0,  0},
  { 0,  1,  -3, 127,   4,  -2,  1,  0}, { 0,  1,  -5, 127,   6,  -2,  1,  0},
  { 0,  2,  -6, 126,   8,  -3,  1,  0}, {-1,  2,  -7, 126,  11,  -4,  2, -1},
  {-1,  3,  -8, 125,  13,  -5,  2, -1}, {-1,  3, -10, 124,  16,  -6,  3, -1},
  {-1,  4, -11, 123,  18,  -7,  3, -1}, {-1,  4, -12, 122,  20,  -7,  3, -1},
  {-1,  4, -13, 121,  23,  -8,  3, -1}, {-2,  5, -14, 120,  25,  -9,  4, -1},
  {-1,  5, -15, 119,  27, -10,  4, -1}, {-1,  5, -16, 118,  30, -11,  4, -1},
  {-2,  6, -17, 116,  33, -12,  5, -1}, {-2,  6, -17, 114,  35, -12,  5, -1},
  {-2,  6, -18, 113,  38, -13,  5, -1}, {-2,  7, -19, 111,  41, -14,  6, -2},
  {-2,  7, -19, 110,  43, -15,  6, -2}, {-2,  7, -20, 108,  46, -15,  6, -2},
  {-2,  7, -20, 106,  49, -16,  6, -2}, {-2,  7, -21, 104,  51, -16,  7, -2},
  {-2,  7, -21, 102,  54, -17,  7, -2}, {-2,  8, -21, 100,  56, -18,  7, -2},
  {-2,  8, -22,  98,  59, -18,  7, -2}, {-2,  8, -22,  96,  62, -19,  7, -2},
  {-2,  8, -22,  94,  64, -19,  7, -2}, {-2,  8, -22,  91,  67, -20,  8, -2},
  {-2,  8, -22,  89,  69, -20,  8, -2}, {-2,  8, -22,  87,  72, -21,  8, -2},
  {-2,  8, -21,  84,  74, -21,  8, -2}, {-2,  8, -22,  82,  77, -21,  8, -2},
  {-2,  8, -21,  79,  79, -21,  8, -2}, {-2,  8, -21,  77,  82, -22,  8, -2},
  {-2,  8, -21,  74,  84, -21,  8, -2}, {-2,  8, -21,  72,  87, -22,  8, -2},
  {-2,  8, -20,  69,  89, -22,  8, -2}, {-2,  8, -20,  67,  91, -22,  8, -2},
  {-2,  7, -19,  64,  94, -22,  8, -2}, {-2,  7, -19,  62,  96, -22,  8, -2},
  {-2,  7, -18,  59,  98, -22,  8, -2}, {-2,  7, -18,  56, 100, -21,  8, -2},
  {-2,  7, -17,  54, 102, -21,  7, -2}, {-2,  7, -16,  51, 104, -21,  7, -2},
  {-2,  6, -16,  49, 106, -20,  7, -2}, {-2,  6, -15,  46, 108, -20,  7, -2},
  {-2,  6, -15,  43, 110, -19,  7, -2}, {-2,  6, -14,  41, 111, -19,  7, -2},
  {-1,  5, -13,  38, 113, -18,  6, -2}, {-1,  5, -12,  35, 114, -17,  6, -2},
  {-1,  5, -12,  33, 116, -17,  6, -2}, {-1,  4, -11,  30, 118, -16,  5, -1},
  {-1,  4, -10,  27, 119, -15,  5, -1}, {-1,  4,  -9,  25, 120, -14,  5, -2},
  {-1,  3,  -8,  23, 121, -13,  4, -1}, {-1,  3,  -7,  20, 122, -12,  4, -1},
  {-1,  3,  -7,  18, 123, -11,  4, -1}, {-1,  3,  -6,  16, 124, -10,  3, -1},
  {-1,  2,  -5,  13, 125,  -8,  3, -1}, {-1,  2,  -4,  11, 126,  -7,  2, -1},
  { 0,  1,  -3,   8, 126,  -6,  2,  0}, { 0,  1,  -2,   6, 127,  -5,  1,  0},
  { 0,  1,  -2,   4, 127,  -3,  1,  0}, { 0,  0,   0,   2, 127,  -1,  0,  0},

  // [1, 2)
  { 0, 0, 0,   1, 127,   0,   0, 0 }, { 0, 0, 0, - 1, 127,   2,   0, 0 },
  { 0, 0, 1, - 3, 127,   4, - 1, 0 }, { 0, 0, 1, - 4, 126,   6, - 2, 1 },
  { 0, 0, 1, - 5, 126,   8, - 3, 1 }, { 0, 0, 1, - 6, 125,  11, - 4, 1 },
  { 0, 0, 1, - 7, 124,  13, - 4, 1 }, { 0, 0, 2, - 8, 123,  15, - 5, 1 },
  { 0, 0, 2, - 9, 122,  18, - 6, 1 }, { 0, 0, 2, -10, 121,  20, - 6, 1 },
  { 0, 0, 2, -11, 120,  22, - 7, 2 }, { 0, 0, 2, -12, 119,  25, - 8, 2 },
  { 0, 0, 3, -13, 117,  27, - 8, 2 }, { 0, 0, 3, -13, 116,  29, - 9, 2 },
  { 0, 0, 3, -14, 114,  32, -10, 3 }, { 0, 0, 3, -15, 113,  35, -10, 2 },
  { 0, 0, 3, -15, 111,  37, -11, 3 }, { 0, 0, 3, -16, 109,  40, -11, 3 },
  { 0, 0, 3, -16, 108,  42, -12, 3 }, { 0, 0, 4, -17, 106,  45, -13, 3 },
  { 0, 0, 4, -17, 104,  47, -13, 3 }, { 0, 0, 4, -17, 102,  50, -14, 3 },
  { 0, 0, 4, -17, 100,  52, -14, 3 }, { 0, 0, 4, -18,  98,  55, -15, 4 },
  { 0, 0, 4, -18,  96,  58, -15, 3 }, { 0, 0, 4, -18,  94,  60, -16, 4 },
  { 0, 0, 4, -18,  91,  63, -16, 4 }, { 0, 0, 4, -18,  89,  65, -16, 4 },
  { 0, 0, 4, -18,  87,  68, -17, 4 }, { 0, 0, 4, -18,  85,  70, -17, 4 },
  { 0, 0, 4, -18,  82,  73, -17, 4 }, { 0, 0, 4, -18,  80,  75, -17, 4 },
  { 0, 0, 4, -18,  78,  78, -18, 4 }, { 0, 0, 4, -17,  75,  80, -18, 4 },
  { 0, 0, 4, -17,  73,  82, -18, 4 }, { 0, 0, 4, -17,  70,  85, -18, 4 },
  { 0, 0, 4, -17,  68,  87, -18, 4 }, { 0, 0, 4, -16,  65,  89, -18, 4 },
  { 0, 0, 4, -16,  63,  91, -18, 4 }, { 0, 0, 4, -16,  60,  94, -18, 4 },
  { 0, 0, 3, -15,  58,  96, -18, 4 }, { 0, 0, 4, -15,  55,  98, -18, 4 },
  { 0, 0, 3, -14,  52, 100, -17, 4 }, { 0, 0, 3, -14,  50, 102, -17, 4 },
  { 0, 0, 3, -13,  47, 104, -17, 4 }, { 0, 0, 3, -13,  45, 106, -17, 4 },
  { 0, 0, 3, -12,  42, 108, -16, 3 }, { 0, 0, 3, -11,  40, 109, -16, 3 },
  { 0, 0, 3, -11,  37, 111, -15, 3 }, { 0, 0, 2, -10,  35, 113, -15, 3 },
  { 0, 0, 3, -10,  32, 114, -14, 3 }, { 0, 0, 2, - 9,  29, 116, -13, 3 },
  { 0, 0, 2, - 8,  27, 117, -13, 3 }, { 0, 0, 2, - 8,  25, 119, -12, 2 },
  { 0, 0, 2, - 7,  22, 120, -11, 2 }, { 0, 0, 1, - 6,  20, 121, -10, 2 },
  { 0, 0, 1, - 6,  18, 122, - 9, 2 }, { 0, 0, 1, - 5,  15, 123, - 8, 2 },
  { 0, 0, 1, - 4,  13, 124, - 7, 1 }, { 0, 0, 1, - 4,  11, 125, - 6, 1 },
  { 0, 0, 1, - 3,   8, 126, - 5, 1 }, { 0, 0, 1, - 2,   6, 126, - 4, 1 },
  { 0, 0, 0, - 1,   4, 127, - 3, 1 }, { 0, 0, 0,   0,   2, 127, - 1, 0 },
  // dummy (replicate row index 191)
  { 0, 0, 0,   0,   2, 127, - 1, 0 },

#elif WARPEDPIXEL_PREC_BITS == 5
  // [-1, 0)
  {0,   0, 127,   1,   0, 0, 0, 0}, {1,  -3, 127,   4,  -1, 0, 0, 0},
  {1,  -5, 126,   8,  -3, 1, 0, 0}, {1,  -7, 124,  13,  -4, 1, 0, 0},
  {2,  -9, 122,  18,  -6, 1, 0, 0}, {2, -11, 120,  22,  -7, 2, 0, 0},
  {3, -13, 117,  27,  -8, 2, 0, 0}, {3, -14, 114,  32, -10, 3, 0, 0},
  {3, -15, 111,  37, -11, 3, 0, 0}, {3, -16, 108,  42, -12, 3, 0, 0},
  {4, -17, 104,  47, -13, 3, 0, 0}, {4, -17, 100,  52, -14, 3, 0, 0},
  {4, -18,  96,  58, -15, 3, 0, 0}, {4, -18,  91,  63, -16, 4, 0, 0},
  {4, -18,  87,  68, -17, 4, 0, 0}, {4, -18,  82,  73, -17, 4, 0, 0},
  {4, -18,  78,  78, -18, 4, 0, 0}, {4, -17,  73,  82, -18, 4, 0, 0},
  {4, -17,  68,  87, -18, 4, 0, 0}, {4, -16,  63,  91, -18, 4, 0, 0},
  {3, -15,  58,  96, -18, 4, 0, 0}, {3, -14,  52, 100, -17, 4, 0, 0},
  {3, -13,  47, 104, -17, 4, 0, 0}, {3, -12,  42, 108, -16, 3, 0, 0},
  {3, -11,  37, 111, -15, 3, 0, 0}, {3, -10,  32, 114, -14, 3, 0, 0},
  {2,  -8,  27, 117, -13, 3, 0, 0}, {2,  -7,  22, 120, -11, 2, 0, 0},
  {1,  -6,  18, 122,  -9, 2, 0, 0}, {1,  -4,  13, 124,  -7, 1, 0, 0},
  {1,  -3,   8, 126,  -5, 1, 0, 0}, {0,  -1,   4, 127,  -3, 1, 0, 0},
  // [0, 1)
  { 0,  0,   0, 127,   1,   0,   0,  0}, { 0,  1,  -3, 127,   4,  -2,   1,  0},
  { 0,  2,  -6, 126,   8,  -3,   1,  0}, {-1,  3,  -8, 125,  13,  -5,   2, -1},
  {-1,  4, -11, 123,  18,  -7,   3, -1}, {-1,  4, -13, 121,  23,  -8,   3, -1},
  {-1,  5, -15, 119,  27, -10,   4, -1}, {-2,  6, -17, 116,  33, -12,   5, -1},
  {-2,  6, -18, 113,  38, -13,   5, -1}, {-2,  7, -19, 110,  43, -15,   6, -2},
  {-2,  7, -20, 106,  49, -16,   6, -2}, {-2,  7, -21, 102,  54, -17,   7, -2},
  {-2,  8, -22,  98,  59, -18,   7, -2}, {-2,  8, -22,  94,  64, -19,   7, -2},
  {-2,  8, -22,  89,  69, -20,   8, -2}, {-2,  8, -21,  84,  74, -21,   8, -2},
  {-2,  8, -21,  79,  79, -21,   8, -2}, {-2,  8, -21,  74,  84, -21,   8, -2},
  {-2,  8, -20,  69,  89, -22,   8, -2}, {-2,  7, -19,  64,  94, -22,   8, -2},
  {-2,  7, -18,  59,  98, -22,   8, -2}, {-2,  7, -17,  54, 102, -21,   7, -2},
  {-2,  6, -16,  49, 106, -20,   7, -2}, {-2,  6, -15,  43, 110, -19,   7, -2},
  {-1,  5, -13,  38, 113, -18,   6, -2}, {-1,  5, -12,  33, 116, -17,   6, -2},
  {-1,  4, -10,  27, 119, -15,   5, -1}, {-1,  3,  -8,  23, 121, -13,   4, -1},
  {-1,  3,  -7,  18, 123, -11,   4, -1}, {-1,  2,  -5,  13, 125,  -8,   3, -1},
  { 0,  1,  -3,   8, 126,  -6,   2,  0}, { 0,  1,  -2,   4, 127,  -3,   1,  0},
  // [1, 2)
  {0, 0, 0,   1, 127,   0,   0, 0}, {0, 0, 1,  -3, 127,   4,  -1, 0},
  {0, 0, 1,  -5, 126,   8,  -3, 1}, {0, 0, 1,  -7, 124,  13,  -4, 1},
  {0, 0, 2,  -9, 122,  18,  -6, 1}, {0, 0, 2, -11, 120,  22,  -7, 2},
  {0, 0, 3, -13, 117,  27,  -8, 2}, {0, 0, 3, -14, 114,  32, -10, 3},
  {0, 0, 3, -15, 111,  37, -11, 3}, {0, 0, 3, -16, 108,  42, -12, 3},
  {0, 0, 4, -17, 104,  47, -13, 3}, {0, 0, 4, -17, 100,  52, -14, 3},
  {0, 0, 4, -18,  96,  58, -15, 3}, {0, 0, 4, -18,  91,  63, -16, 4},
  {0, 0, 4, -18,  87,  68, -17, 4}, {0, 0, 4, -18,  82,  73, -17, 4},
  {0, 0, 4, -18,  78,  78, -18, 4}, {0, 0, 4, -17,  73,  82, -18, 4},
  {0, 0, 4, -17,  68,  87, -18, 4}, {0, 0, 4, -16,  63,  91, -18, 4},
  {0, 0, 3, -15,  58,  96, -18, 4}, {0, 0, 3, -14,  52, 100, -17, 4},
  {0, 0, 3, -13,  47, 104, -17, 4}, {0, 0, 3, -12,  42, 108, -16, 3},
  {0, 0, 3, -11,  37, 111, -15, 3}, {0, 0, 3, -10,  32, 114, -14, 3},
  {0, 0, 2,  -8,  27, 117, -13, 3}, {0, 0, 2,  -7,  22, 120, -11, 2},
  {0, 0, 1,  -6,  18, 122,  -9, 2}, {0, 0, 1,  -4,  13, 124,  -7, 1},
  {0, 0, 1,  -3,   8, 126,  -5, 1}, {0, 0, 0,  -1,   4, 127,  -3, 1},
  // dummy (replicate row index 95)
  {0, 0, 0,  -1,   4, 127,  -3, 1},

#endif  // WARPEDPIXEL_PREC_BITS == 6
};

/* clang-format on */

#define DIV_LUT_PREC_BITS 14
#define DIV_LUT_BITS 8
#define DIV_LUT_NUM (1 << DIV_LUT_BITS)

static const uint16_t div_lut[DIV_LUT_NUM + 1] = {
  16384, 16320, 16257, 16194, 16132, 16070, 16009, 15948, 15888, 15828, 15768,
  15709, 15650, 15592, 15534, 15477, 15420, 15364, 15308, 15252, 15197, 15142,
  15087, 15033, 14980, 14926, 14873, 14821, 14769, 14717, 14665, 14614, 14564,
  14513, 14463, 14413, 14364, 14315, 14266, 14218, 14170, 14122, 14075, 14028,
  13981, 13935, 13888, 13843, 13797, 13752, 13707, 13662, 13618, 13574, 13530,
  13487, 13443, 13400, 13358, 13315, 13273, 13231, 13190, 13148, 13107, 13066,
  13026, 12985, 12945, 12906, 12866, 12827, 12788, 12749, 12710, 12672, 12633,
  12596, 12558, 12520, 12483, 12446, 12409, 12373, 12336, 12300, 12264, 12228,
  12193, 12157, 12122, 12087, 12053, 12018, 11984, 11950, 11916, 11882, 11848,
  11815, 11782, 11749, 11716, 11683, 11651, 11619, 11586, 11555, 11523, 11491,
  11460, 11429, 11398, 11367, 11336, 11305, 11275, 11245, 11215, 11185, 11155,
  11125, 11096, 11067, 11038, 11009, 10980, 10951, 10923, 10894, 10866, 10838,
  10810, 10782, 10755, 10727, 10700, 10673, 10645, 10618, 10592, 10565, 10538,
  10512, 10486, 10460, 10434, 10408, 10382, 10356, 10331, 10305, 10280, 10255,
  10230, 10205, 10180, 10156, 10131, 10107, 10082, 10058, 10034, 10010, 9986,
  9963,  9939,  9916,  9892,  9869,  9846,  9823,  9800,  9777,  9754,  9732,
  9709,  9687,  9664,  9642,  9620,  9598,  9576,  9554,  9533,  9511,  9489,
  9468,  9447,  9425,  9404,  9383,  9362,  9341,  9321,  9300,  9279,  9259,
  9239,  9218,  9198,  9178,  9158,  9138,  9118,  9098,  9079,  9059,  9039,
  9020,  9001,  8981,  8962,  8943,  8924,  8905,  8886,  8867,  8849,  8830,
  8812,  8793,  8775,  8756,  8738,  8720,  8702,  8684,  8666,  8648,  8630,
  8613,  8595,  8577,  8560,  8542,  8525,  8508,  8490,  8473,  8456,  8439,
  8422,  8405,  8389,  8372,  8355,  8339,  8322,  8306,  8289,  8273,  8257,
  8240,  8224,  8208,  8192,
};

// Decomposes a divisor D such that 1/D = y/2^shift, where y is returned
// at precision of DIV_LUT_PREC_BITS along with the shift.
static int16_t resolve_divisor_64(uint64_t D, int16_t *shift) {
  int64_t f;
  *shift = (int16_t)((D >> 32) ? get_msb((unsigned int)(D >> 32)) + 32
                               : get_msb((unsigned int)D));
  // e is obtained from D after resetting the most significant 1 bit.
  const int64_t e = D - ((uint64_t)1 << *shift);
  // Get the most significant DIV_LUT_BITS (8) bits of e into f
  if (*shift > DIV_LUT_BITS)
    f = ROUND_POWER_OF_TWO_64(e, *shift - DIV_LUT_BITS);
  else
    f = e << (DIV_LUT_BITS - *shift);
  assert(f <= DIV_LUT_NUM);
  *shift += DIV_LUT_PREC_BITS;
  // Use f as lookup into the precomputed table of multipliers
  return div_lut[f];
}

static int16_t resolve_divisor_32(uint32_t D, int16_t *shift) {
  int32_t f;
  *shift = get_msb(D);
  // e is obtained from D after resetting the most significant 1 bit.
  const int32_t e = D - ((uint32_t)1 << *shift);
  // Get the most significant DIV_LUT_BITS (8) bits of e into f
  if (*shift > DIV_LUT_BITS)
    f = ROUND_POWER_OF_TWO(e, *shift - DIV_LUT_BITS);
  else
    f = e << (DIV_LUT_BITS - *shift);
  assert(f <= DIV_LUT_NUM);
  *shift += DIV_LUT_PREC_BITS;
  // Use f as lookup into the precomputed table of multipliers
  return div_lut[f];
}

static int is_affine_valid(const WarpedMotionParams *const wm) {
  const int32_t *mat = wm->wmmat;
  return (mat[2] > 0);
}

static int is_affine_shear_allowed(int16_t alpha, int16_t beta, int16_t gamma,
                                   int16_t delta) {
  if ((4 * abs(alpha) + 7 * abs(beta) >= (1 << WARPEDMODEL_PREC_BITS)) ||
      (4 * abs(gamma) + 4 * abs(delta) >= (1 << WARPEDMODEL_PREC_BITS)))
    return 0;
  else
    return 1;
}

// Returns 1 on success or 0 on an invalid affine set
int get_shear_params(WarpedMotionParams *wm) {
  const int32_t *mat = wm->wmmat;
  if (!is_affine_valid(wm)) return 0;
  wm->alpha =
      clamp(mat[2] - (1 << WARPEDMODEL_PREC_BITS), INT16_MIN, INT16_MAX);
  wm->beta = clamp(mat[3], INT16_MIN, INT16_MAX);
  int16_t shift;
  int16_t y = resolve_divisor_32(abs(mat[2]), &shift) * (mat[2] < 0 ? -1 : 1);
  int64_t v = ((int64_t)mat[4] * (1 << WARPEDMODEL_PREC_BITS)) * y;
  wm->gamma =
      clamp((int)ROUND_POWER_OF_TWO_SIGNED_64(v, shift), INT16_MIN, INT16_MAX);
  v = ((int64_t)mat[3] * mat[4]) * y;
  wm->delta = clamp(mat[5] - (int)ROUND_POWER_OF_TWO_SIGNED_64(v, shift) -
                        (1 << WARPEDMODEL_PREC_BITS),
                    INT16_MIN, INT16_MAX);

  wm->alpha = ROUND_POWER_OF_TWO_SIGNED(wm->alpha, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);
  wm->beta = ROUND_POWER_OF_TWO_SIGNED(wm->beta, WARP_PARAM_REDUCE_BITS) *
             (1 << WARP_PARAM_REDUCE_BITS);
  wm->gamma = ROUND_POWER_OF_TWO_SIGNED(wm->gamma, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);
  wm->delta = ROUND_POWER_OF_TWO_SIGNED(wm->delta, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);

  if (!is_affine_shear_allowed(wm->alpha, wm->beta, wm->gamma, wm->delta))
    return 0;

  return 1;
}

static INLINE int highbd_error_measure(int err, int bd) {
  const int b = bd - 8;
  const int bmask = (1 << b) - 1;
  const int v = (1 << b);
  err = abs(err);
  const int e1 = err >> b;
  const int e2 = err & bmask;
  return error_measure_lut[255 + e1] * (v - e2) +
         error_measure_lut[256 + e1] * e2;
}

/* Note: For an explanation of the warp algorithm, and some notes on bit widths
    for hardware implementations, see the comments above av1_warp_affine_c
*/
void av1_highbd_warp_affine_c(const int32_t *mat, const uint16_t *ref,
                              int width, int height, int stride, uint16_t *pred,
                              int p_col, int p_row, int p_width, int p_height,
                              int p_stride, int subsampling_x,
                              int subsampling_y, int bd,
                              ConvolveParams *conv_params, int16_t alpha,
                              int16_t beta, int16_t gamma, int16_t delta) {
  int32_t tmp[15 * 8];
  const int reduce_bits_horiz =
      conv_params->round_0 +
      AOMMAX(bd + FILTER_BITS - conv_params->round_0 - 14, 0);
  const int reduce_bits_vert = conv_params->is_compound
                                   ? conv_params->round_1
                                   : 2 * FILTER_BITS - reduce_bits_horiz;
  const int max_bits_horiz = bd + FILTER_BITS + 1 - reduce_bits_horiz;
  const int offset_bits_horiz = bd + FILTER_BITS - 1;
  const int offset_bits_vert = bd + 2 * FILTER_BITS - reduce_bits_horiz;
  const int round_bits =
      2 * FILTER_BITS - conv_params->round_0 - conv_params->round_1;
  const int offset_bits = bd + 2 * FILTER_BITS - conv_params->round_0;
  (void)max_bits_horiz;
  assert(IMPLIES(conv_params->is_compound, conv_params->dst != NULL));

  for (int i = p_row; i < p_row + p_height; i += 8) {
    for (int j = p_col; j < p_col + p_width; j += 8) {
      // Calculate the center of this 8x8 block,
      // project to luma coordinates (if in a subsampled chroma plane),
      // apply the affine transformation,
      // then convert back to the original coordinates (if necessary)
      const int32_t src_x = (j + 4) << subsampling_x;
      const int32_t src_y = (i + 4) << subsampling_y;
      const int32_t dst_x = mat[2] * src_x + mat[3] * src_y + mat[0];
      const int32_t dst_y = mat[4] * src_x + mat[5] * src_y + mat[1];
      const int32_t x4 = dst_x >> subsampling_x;
      const int32_t y4 = dst_y >> subsampling_y;

      const int32_t ix4 = x4 >> WARPEDMODEL_PREC_BITS;
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      const int32_t iy4 = y4 >> WARPEDMODEL_PREC_BITS;
      int32_t sy4 = y4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);

      sx4 += alpha * (-4) + beta * (-4);
      sy4 += gamma * (-4) + delta * (-4);

      sx4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);
      sy4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);

      // Horizontal filter
      for (int k = -7; k < 8; ++k) {
        const int iy = clamp(iy4 + k, 0, height - 1);

        int sx = sx4 + beta * (k + 4);
        for (int l = -4; l < 4; ++l) {
          int ix = ix4 + l - 3;
          const int offs = ROUND_POWER_OF_TWO(sx, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_horiz;
          for (int m = 0; m < 8; ++m) {
            const int sample_x = clamp(ix + m, 0, width - 1);
            sum += ref[iy * stride + sample_x] * coeffs[m];
          }
          sum = ROUND_POWER_OF_TWO(sum, reduce_bits_horiz);
          assert(0 <= sum && sum < (1 << max_bits_horiz));
          tmp[(k + 7) * 8 + (l + 4)] = sum;
          sx += alpha;
        }
      }

      // Vertical filter
      for (int k = -4; k < AOMMIN(4, p_row + p_height - i - 4); ++k) {
        int sy = sy4 + delta * (k + 4);
        for (int l = -4; l < AOMMIN(4, p_col + p_width - j - 4); ++l) {
          const int offs = ROUND_POWER_OF_TWO(sy, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_vert;
          for (int m = 0; m < 8; ++m) {
            sum += tmp[(k + m + 4) * 8 + (l + 4)] * coeffs[m];
          }

          if (conv_params->is_compound) {
            CONV_BUF_TYPE *p =
                &conv_params
                     ->dst[(i - p_row + k + 4) * conv_params->dst_stride +
                           (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, reduce_bits_vert);
            if (conv_params->do_average) {
              uint16_t *dst16 =
                  &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
              int32_t tmp32 = *p;
              if (conv_params->use_jnt_comp_avg) {
                tmp32 = tmp32 * conv_params->fwd_offset +
                        sum * conv_params->bck_offset;
                tmp32 = tmp32 >> DIST_PRECISION_BITS;
              } else {
                tmp32 += sum;
                tmp32 = tmp32 >> 1;
              }
              tmp32 = tmp32 - (1 << (offset_bits - conv_params->round_1)) -
                      (1 << (offset_bits - conv_params->round_1 - 1));
              *dst16 =
                  clip_pixel_highbd(ROUND_POWER_OF_TWO(tmp32, round_bits), bd);
            } else {
              *p = sum;
            }
          } else {
            uint16_t *p =
                &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, reduce_bits_vert);
            assert(0 <= sum && sum < (1 << (bd + 2)));
            *p = clip_pixel_highbd(sum - (1 << (bd - 1)) - (1 << bd), bd);
          }
          sy += gamma;
        }
      }
    }
  }
}

static void highbd_warp_plane(WarpedMotionParams *wm, const uint8_t *const ref8,
                              int width, int height, int stride,
                              const uint8_t *const pred8, int p_col, int p_row,
                              int p_width, int p_height, int p_stride,
                              int subsampling_x, int subsampling_y, int bd,
                              ConvolveParams *conv_params) {
  assert(wm->wmtype <= AFFINE);
  if (wm->wmtype == ROTZOOM) {
    wm->wmmat[5] = wm->wmmat[2];
    wm->wmmat[4] = -wm->wmmat[3];
  }
  const int32_t *const mat = wm->wmmat;
  const int16_t alpha = wm->alpha;
  const int16_t beta = wm->beta;
  const int16_t gamma = wm->gamma;
  const int16_t delta = wm->delta;

  const uint16_t *const ref = CONVERT_TO_SHORTPTR(ref8);
  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  av1_highbd_warp_affine(mat, ref, width, height, stride, pred, p_col, p_row,
                         p_width, p_height, p_stride, subsampling_x,
                         subsampling_y, bd, conv_params, alpha, beta, gamma,
                         delta);
}

static int64_t highbd_frame_error(const uint16_t *const ref, int stride,
                                  const uint16_t *const dst, int p_width,
                                  int p_height, int p_stride, int bd) {
  int64_t sum_error = 0;
  for (int i = 0; i < p_height; ++i) {
    for (int j = 0; j < p_width; ++j) {
      sum_error +=
          highbd_error_measure(dst[j + i * p_stride] - ref[j + i * stride], bd);
    }
  }
  return sum_error;
}

static int64_t highbd_warp_error(
    WarpedMotionParams *wm, const uint8_t *const ref8, int width, int height,
    int stride, const uint8_t *const dst8, int p_col, int p_row, int p_width,
    int p_height, int p_stride, int subsampling_x, int subsampling_y, int bd,
    int64_t best_error) {
  int64_t gm_sumerr = 0;
  const int error_bsize_w = AOMMIN(p_width, WARP_ERROR_BLOCK);
  const int error_bsize_h = AOMMIN(p_height, WARP_ERROR_BLOCK);
  uint16_t tmp[WARP_ERROR_BLOCK * WARP_ERROR_BLOCK];

  ConvolveParams conv_params = get_conv_params(0, 0, bd);
  conv_params.use_jnt_comp_avg = 0;
  for (int i = p_row; i < p_row + p_height; i += WARP_ERROR_BLOCK) {
    for (int j = p_col; j < p_col + p_width; j += WARP_ERROR_BLOCK) {
      // avoid warping extra 8x8 blocks in the padded region of the frame
      // when p_width and p_height are not multiples of WARP_ERROR_BLOCK
      const int warp_w = AOMMIN(error_bsize_w, p_col + p_width - j);
      const int warp_h = AOMMIN(error_bsize_h, p_row + p_height - i);
      highbd_warp_plane(wm, ref8, width, height, stride,
                        CONVERT_TO_BYTEPTR(tmp), j, i, warp_w, warp_h,
                        WARP_ERROR_BLOCK, subsampling_x, subsampling_y, bd,
                        &conv_params);

      gm_sumerr += highbd_frame_error(
          tmp, WARP_ERROR_BLOCK, CONVERT_TO_SHORTPTR(dst8) + j + i * p_stride,
          warp_w, warp_h, p_stride, bd);
      if (gm_sumerr > best_error) return gm_sumerr;
    }
  }
  return gm_sumerr;
}

static INLINE int error_measure(int err) {
  return error_measure_lut[255 + err];
}

/* The warp filter for ROTZOOM and AFFINE models works as follows:
   * Split the input into 8x8 blocks
   * For each block, project the point (4, 4) within the block, to get the
     overall block position. Split into integer and fractional coordinates,
     maintaining full WARPEDMODEL precision
   * Filter horizontally: Generate 15 rows of 8 pixels each. Each pixel gets a
     variable horizontal offset. This means that, while the rows of the
     intermediate buffer align with the rows of the *reference* image, the
     columns align with the columns of the *destination* image.
   * Filter vertically: Generate the output block (up to 8x8 pixels, but if the
     destination is too small we crop the output at this stage). Each pixel has
     a variable vertical offset, so that the resulting rows are aligned with
     the rows of the destination image.

   To accomplish these alignments, we factor the warp matrix as a
   product of two shear / asymmetric zoom matrices:
   / a b \  = /   1       0    \ * / 1+alpha  beta \
   \ c d /    \ gamma  1+delta /   \    0      1   /
   where a, b, c, d are wmmat[2], wmmat[3], wmmat[4], wmmat[5] respectively.
   The horizontal shear (with alpha and beta) is applied first,
   then the vertical shear (with gamma and delta) is applied second.

   The only limitation is that, to fit this in a fixed 8-tap filter size,
   the fractional pixel offsets must be at most +-1. Since the horizontal filter
   generates 15 rows of 8 columns, and the initial point we project is at (4, 4)
   within the block, the parameters must satisfy
   4 * |alpha| + 7 * |beta| <= 1   and   4 * |gamma| + 4 * |delta| <= 1
   for this filter to be applicable.

   Note: This function assumes that the caller has done all of the relevant
   checks, ie. that we have a ROTZOOM or AFFINE model, that wm[4] and wm[5]
   are set appropriately (if using a ROTZOOM model), and that alpha, beta,
   gamma, delta are all in range.

   TODO(david.barker): Maybe support scaled references?
*/
/* A note on hardware implementation:
    The warp filter is intended to be implementable using the same hardware as
    the high-precision convolve filters from the loop-restoration and
    convolve-round experiments.

    For a single filter stage, considering all of the coefficient sets for the
    warp filter and the regular convolution filter, an input in the range
    [0, 2^k - 1] is mapped into the range [-56 * (2^k - 1), 184 * (2^k - 1)]
    before rounding.

    Allowing for some changes to the filter coefficient sets, call the range
    [-64 * 2^k, 192 * 2^k]. Then, if we initialize the accumulator to 64 * 2^k,
    we can replace this by the range [0, 256 * 2^k], which can be stored in an
    unsigned value with 8 + k bits.

    This allows the derivation of the appropriate bit widths and offsets for
    the various intermediate values: If

    F := FILTER_BITS = 7 (or else the above ranges need adjusting)
         So a *single* filter stage maps a k-bit input to a (k + F + 1)-bit
         intermediate value.
    H := ROUND0_BITS
    V := VERSHEAR_REDUCE_PREC_BITS
    (and note that we must have H + V = 2*F for the output to have the same
     scale as the input)

    then we end up with the following offsets and ranges:
    Horizontal filter: Apply an offset of 1 << (bd + F - 1), sum fits into a
                       uint{bd + F + 1}
    After rounding: The values stored in 'tmp' fit into a uint{bd + F + 1 - H}.
    Vertical filter: Apply an offset of 1 << (bd + 2*F - H), sum fits into a
                     uint{bd + 2*F + 2 - H}
    After rounding: The final value, before undoing the offset, fits into a
                    uint{bd + 2}.

    Then we need to undo the offsets before clamping to a pixel. Note that,
    if we do this at the end, the amount to subtract is actually independent
    of H and V:

    offset to subtract = (1 << ((bd + F - 1) - H + F - V)) +
                         (1 << ((bd + 2*F - H) - V))
                      == (1 << (bd - 1)) + (1 << bd)

    This allows us to entirely avoid clamping in both the warp filter and
    the convolve-round experiment. As of the time of writing, the Wiener filter
    from loop-restoration can encode a central coefficient up to 216, which
    leads to a maximum value of about 282 * 2^k after applying the offset.
    So in that case we still need to clamp.
*/
void av1_warp_affine_c(const int32_t *mat, const uint8_t *ref, int width,
                       int height, int stride, uint8_t *pred, int p_col,
                       int p_row, int p_width, int p_height, int p_stride,
                       int subsampling_x, int subsampling_y,
                       ConvolveParams *conv_params, int16_t alpha, int16_t beta,
                       int16_t gamma, int16_t delta) {
  int32_t tmp[15 * 8];
  const int bd = 8;
  const int reduce_bits_horiz = conv_params->round_0;
  const int reduce_bits_vert = conv_params->is_compound
                                   ? conv_params->round_1
                                   : 2 * FILTER_BITS - reduce_bits_horiz;
  const int max_bits_horiz = bd + FILTER_BITS + 1 - reduce_bits_horiz;
  const int offset_bits_horiz = bd + FILTER_BITS - 1;
  const int offset_bits_vert = bd + 2 * FILTER_BITS - reduce_bits_horiz;
  const int round_bits =
      2 * FILTER_BITS - conv_params->round_0 - conv_params->round_1;
  const int offset_bits = bd + 2 * FILTER_BITS - conv_params->round_0;
  (void)max_bits_horiz;
  assert(IMPLIES(conv_params->is_compound, conv_params->dst != NULL));
  assert(IMPLIES(conv_params->do_average, conv_params->is_compound));

  for (int i = p_row; i < p_row + p_height; i += 8) {
    for (int j = p_col; j < p_col + p_width; j += 8) {
      // Calculate the center of this 8x8 block,
      // project to luma coordinates (if in a subsampled chroma plane),
      // apply the affine transformation,
      // then convert back to the original coordinates (if necessary)
      const int32_t src_x = (j + 4) << subsampling_x;
      const int32_t src_y = (i + 4) << subsampling_y;
      const int32_t dst_x = mat[2] * src_x + mat[3] * src_y + mat[0];
      const int32_t dst_y = mat[4] * src_x + mat[5] * src_y + mat[1];
      const int32_t x4 = dst_x >> subsampling_x;
      const int32_t y4 = dst_y >> subsampling_y;

      int32_t ix4 = x4 >> WARPEDMODEL_PREC_BITS;
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      int32_t iy4 = y4 >> WARPEDMODEL_PREC_BITS;
      int32_t sy4 = y4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);

      sx4 += alpha * (-4) + beta * (-4);
      sy4 += gamma * (-4) + delta * (-4);

      sx4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);
      sy4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);

      // Horizontal filter
      for (int k = -7; k < 8; ++k) {
        // Clamp to top/bottom edge of the frame
        const int iy = clamp(iy4 + k, 0, height - 1);

        int sx = sx4 + beta * (k + 4);

        for (int l = -4; l < 4; ++l) {
          int ix = ix4 + l - 3;
          // At this point, sx = sx4 + alpha * l + beta * k
          const int offs = ROUND_POWER_OF_TWO(sx, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_horiz;
          for (int m = 0; m < 8; ++m) {
            // Clamp to left/right edge of the frame
            const int sample_x = clamp(ix + m, 0, width - 1);

            sum += ref[iy * stride + sample_x] * coeffs[m];
          }
          sum = ROUND_POWER_OF_TWO(sum, reduce_bits_horiz);
          assert(0 <= sum && sum < (1 << max_bits_horiz));
          tmp[(k + 7) * 8 + (l + 4)] = sum;
          sx += alpha;
        }
      }

      // Vertical filter
      for (int k = -4; k < AOMMIN(4, p_row + p_height - i - 4); ++k) {
        int sy = sy4 + delta * (k + 4);
        for (int l = -4; l < AOMMIN(4, p_col + p_width - j - 4); ++l) {
          // At this point, sy = sy4 + gamma * l + delta * k
          const int offs = ROUND_POWER_OF_TWO(sy, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_vert;
          for (int m = 0; m < 8; ++m) {
            sum += tmp[(k + m + 4) * 8 + (l + 4)] * coeffs[m];
          }

          if (conv_params->is_compound) {
            CONV_BUF_TYPE *p =
                &conv_params
                     ->dst[(i - p_row + k + 4) * conv_params->dst_stride +
                           (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, reduce_bits_vert);
            if (conv_params->do_average) {
              uint8_t *dst8 =
                  &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
              int32_t tmp32 = *p;
              if (conv_params->use_jnt_comp_avg) {
                tmp32 = tmp32 * conv_params->fwd_offset +
                        sum * conv_params->bck_offset;
                tmp32 = tmp32 >> DIST_PRECISION_BITS;
              } else {
                tmp32 += sum;
                tmp32 = tmp32 >> 1;
              }
              tmp32 = tmp32 - (1 << (offset_bits - conv_params->round_1)) -
                      (1 << (offset_bits - conv_params->round_1 - 1));
              *dst8 = clip_pixel(ROUND_POWER_OF_TWO(tmp32, round_bits));
            } else {
              *p = sum;
            }
          } else {
            uint8_t *p =
                &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, reduce_bits_vert);
            assert(0 <= sum && sum < (1 << (bd + 2)));
            *p = clip_pixel(sum - (1 << (bd - 1)) - (1 << bd));
          }
          sy += gamma;
        }
      }
    }
  }
}

static void warp_plane(WarpedMotionParams *wm, const uint8_t *const ref,
                       int width, int height, int stride, uint8_t *pred,
                       int p_col, int p_row, int p_width, int p_height,
                       int p_stride, int subsampling_x, int subsampling_y,
                       ConvolveParams *conv_params) {
  assert(wm->wmtype <= AFFINE);
  if (wm->wmtype == ROTZOOM) {
    wm->wmmat[5] = wm->wmmat[2];
    wm->wmmat[4] = -wm->wmmat[3];
  }
  const int32_t *const mat = wm->wmmat;
  const int16_t alpha = wm->alpha;
  const int16_t beta = wm->beta;
  const int16_t gamma = wm->gamma;
  const int16_t delta = wm->delta;
  av1_warp_affine(mat, ref, width, height, stride, pred, p_col, p_row, p_width,
                  p_height, p_stride, subsampling_x, subsampling_y, conv_params,
                  alpha, beta, gamma, delta);
}

static int64_t frame_error(const uint8_t *const ref, int stride,
                           const uint8_t *const dst, int p_width, int p_height,
                           int p_stride) {
  int64_t sum_error = 0;
  for (int i = 0; i < p_height; ++i) {
    for (int j = 0; j < p_width; ++j) {
      sum_error +=
          (int64_t)error_measure(dst[j + i * p_stride] - ref[j + i * stride]);
    }
  }
  return sum_error;
}

static int64_t warp_error(WarpedMotionParams *wm, const uint8_t *const ref,
                          int width, int height, int stride,
                          const uint8_t *const dst, int p_col, int p_row,
                          int p_width, int p_height, int p_stride,
                          int subsampling_x, int subsampling_y,
                          int64_t best_error) {
  int64_t gm_sumerr = 0;
  int warp_w, warp_h;
  int error_bsize_w = AOMMIN(p_width, WARP_ERROR_BLOCK);
  int error_bsize_h = AOMMIN(p_height, WARP_ERROR_BLOCK);
  uint8_t tmp[WARP_ERROR_BLOCK * WARP_ERROR_BLOCK];
  ConvolveParams conv_params = get_conv_params(0, 0, 8);
  conv_params.use_jnt_comp_avg = 0;

  for (int i = p_row; i < p_row + p_height; i += WARP_ERROR_BLOCK) {
    for (int j = p_col; j < p_col + p_width; j += WARP_ERROR_BLOCK) {
      // avoid warping extra 8x8 blocks in the padded region of the frame
      // when p_width and p_height are not multiples of WARP_ERROR_BLOCK
      warp_w = AOMMIN(error_bsize_w, p_col + p_width - j);
      warp_h = AOMMIN(error_bsize_h, p_row + p_height - i);
      warp_plane(wm, ref, width, height, stride, tmp, j, i, warp_w, warp_h,
                 WARP_ERROR_BLOCK, subsampling_x, subsampling_y, &conv_params);

      gm_sumerr += frame_error(tmp, WARP_ERROR_BLOCK, dst + j + i * p_stride,
                               warp_w, warp_h, p_stride);
      if (gm_sumerr > best_error) return gm_sumerr;
    }
  }
  return gm_sumerr;
}

int64_t av1_frame_error(int use_hbd, int bd, const uint8_t *ref, int stride,
                        uint8_t *dst, int p_width, int p_height, int p_stride) {
  if (use_hbd) {
    return highbd_frame_error(CONVERT_TO_SHORTPTR(ref), stride,
                              CONVERT_TO_SHORTPTR(dst), p_width, p_height,
                              p_stride, bd);
  }
  return frame_error(ref, stride, dst, p_width, p_height, p_stride);
}

int64_t av1_warp_error(WarpedMotionParams *wm, int use_hbd, int bd,
                       const uint8_t *ref, int width, int height, int stride,
                       uint8_t *dst, int p_col, int p_row, int p_width,
                       int p_height, int p_stride, int subsampling_x,
                       int subsampling_y, int64_t best_error) {
  if (wm->wmtype <= AFFINE)
    if (!get_shear_params(wm)) return 1;
  if (use_hbd)
    return highbd_warp_error(wm, ref, width, height, stride, dst, p_col, p_row,
                             p_width, p_height, p_stride, subsampling_x,
                             subsampling_y, bd, best_error);
  return warp_error(wm, ref, width, height, stride, dst, p_col, p_row, p_width,
                    p_height, p_stride, subsampling_x, subsampling_y,
                    best_error);
}

void av1_warp_plane(WarpedMotionParams *wm, int use_hbd, int bd,
                    const uint8_t *ref, int width, int height, int stride,
                    uint8_t *pred, int p_col, int p_row, int p_width,
                    int p_height, int p_stride, int subsampling_x,
                    int subsampling_y, ConvolveParams *conv_params) {
  if (use_hbd)
    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
                      bd, conv_params);
  else
    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, conv_params);
}

#define LS_MV_MAX 256  // max mv in 1/8-pel
// Use LS_STEP = 8 so that 2 less bits needed for A, Bx, By.
#define LS_STEP 8

// Assuming LS_MV_MAX is < MAX_SB_SIZE * 8,
// the precision needed is:
//   (MAX_SB_SIZE_LOG2 + 3) [for sx * sx magnitude] +
//   (MAX_SB_SIZE_LOG2 + 4) [for sx * dx magnitude] +
//   1 [for sign] +
//   LEAST_SQUARES_SAMPLES_MAX_BITS
//        [for adding up to LEAST_SQUARES_SAMPLES_MAX samples]
// The value is 23
#define LS_MAT_RANGE_BITS \
  ((MAX_SB_SIZE_LOG2 + 4) * 2 + LEAST_SQUARES_SAMPLES_MAX_BITS)

// Bit-depth reduction from the full-range
#define LS_MAT_DOWN_BITS 2

// bits range of A, Bx and By after downshifting
#define LS_MAT_BITS (LS_MAT_RANGE_BITS - LS_MAT_DOWN_BITS)
#define LS_MAT_MIN (-(1 << (LS_MAT_BITS - 1)))
#define LS_MAT_MAX ((1 << (LS_MAT_BITS - 1)) - 1)

// By setting LS_STEP = 8, the least 2 bits of every elements in A, Bx, By are
// 0. So, we can reduce LS_MAT_RANGE_BITS(2) bits here.
#define LS_SQUARE(a)                                          \
  (((a) * (a)*4 + (a)*4 * LS_STEP + LS_STEP * LS_STEP * 2) >> \
   (2 + LS_MAT_DOWN_BITS))
#define LS_PRODUCT1(a, b)                                           \
  (((a) * (b)*4 + ((a) + (b)) * 2 * LS_STEP + LS_STEP * LS_STEP) >> \
   (2 + LS_MAT_DOWN_BITS))
#define LS_PRODUCT2(a, b)                                               \
  (((a) * (b)*4 + ((a) + (b)) * 2 * LS_STEP + LS_STEP * LS_STEP * 2) >> \
   (2 + LS_MAT_DOWN_BITS))

#define USE_LIMITED_PREC_MULT 0

#if USE_LIMITED_PREC_MULT

#define MUL_PREC_BITS 16
static uint16_t resolve_multiplier_64(uint64_t D, int16_t *shift) {
  int msb = 0;
  uint16_t mult = 0;
  *shift = 0;
  if (D != 0) {
    msb = (int16_t)((D >> 32) ? get_msb((unsigned int)(D >> 32)) + 32
                              : get_msb((unsigned int)D));
    if (msb >= MUL_PREC_BITS) {
      mult = (uint16_t)ROUND_POWER_OF_TWO_64(D, msb + 1 - MUL_PREC_BITS);
      *shift = msb + 1 - MUL_PREC_BITS;
    } else {
      mult = (uint16_t)D;
      *shift = 0;
    }
  }
  return mult;
}

static int32_t get_mult_shift_ndiag(int64_t Px, int16_t iDet, int shift) {
  int32_t ret;
  int16_t mshift;
  uint16_t Mul = resolve_multiplier_64(llabs(Px), &mshift);
  int32_t v = (int32_t)Mul * (int32_t)iDet * (Px < 0 ? -1 : 1);
  shift -= mshift;
  if (shift > 0) {
    return (int32_t)clamp(ROUND_POWER_OF_TWO_SIGNED(v, shift),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  } else {
    return (int32_t)clamp(v * (1 << (-shift)),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  }
  return ret;
}

static int32_t get_mult_shift_diag(int64_t Px, int16_t iDet, int shift) {
  int16_t mshift;
  uint16_t Mul = resolve_multiplier_64(llabs(Px), &mshift);
  int32_t v = (int32_t)Mul * (int32_t)iDet * (Px < 0 ? -1 : 1);
  shift -= mshift;
  if (shift > 0) {
    return (int32_t)clamp(
        ROUND_POWER_OF_TWO_SIGNED(v, shift),
        (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
        (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  } else {
    return (int32_t)clamp(
        v * (1 << (-shift)),
        (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
        (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  }
}

#else

static int32_t get_mult_shift_ndiag(int64_t Px, int16_t iDet, int shift) {
  int64_t v = Px * (int64_t)iDet;
  return (int32_t)clamp64(ROUND_POWER_OF_TWO_SIGNED_64(v, shift),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
}

static int32_t get_mult_shift_diag(int64_t Px, int16_t iDet, int shift) {
  int64_t v = Px * (int64_t)iDet;
  return (int32_t)clamp64(
      ROUND_POWER_OF_TWO_SIGNED_64(v, shift),
      (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
      (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
}
#endif  // USE_LIMITED_PREC_MULT

static int find_affine_int(int np, const int *pts1, const int *pts2,
                           BLOCK_SIZE bsize, int mvy, int mvx,
                           WarpedMotionParams *wm, int mi_row, int mi_col) {
  int32_t A[2][2] = { { 0, 0 }, { 0, 0 } };
  int32_t Bx[2] = { 0, 0 };
  int32_t By[2] = { 0, 0 };
  int i;

  const int bw = block_size_wide[bsize];
  const int bh = block_size_high[bsize];
  const int rsuy = (AOMMAX(bh, MI_SIZE) / 2 - 1);
  const int rsux = (AOMMAX(bw, MI_SIZE) / 2 - 1);
  const int suy = rsuy * 8;
  const int sux = rsux * 8;
  const int duy = suy + mvy;
  const int dux = sux + mvx;
  const int isuy = (mi_row * MI_SIZE + rsuy);
  const int isux = (mi_col * MI_SIZE + rsux);

  // Assume the center pixel of the block has exactly the same motion vector
  // as transmitted for the block. First shift the origin of the source
  // points to the block center, and the origin of the destination points to
  // the block center added to the motion vector transmitted.
  // Let (xi, yi) denote the source points and (xi', yi') denote destination
  // points after origin shfifting, for i = 0, 1, 2, .... n-1.
  // Then if  P = [x0, y0,
  //               x1, y1
  //               x2, y1,
  //                ....
  //              ]
  //          q = [x0', x1', x2', ... ]'
  //          r = [y0', y1', y2', ... ]'
  // the least squares problems that need to be solved are:
  //          [h1, h2]' = inv(P'P)P'q and
  //          [h3, h4]' = inv(P'P)P'r
  // where the affine transformation is given by:
  //          x' = h1.x + h2.y
  //          y' = h3.x + h4.y
  //
  // The loop below computes: A = P'P, Bx = P'q, By = P'r
  // We need to just compute inv(A).Bx and inv(A).By for the solutions.
  // Contribution from neighbor block
  for (i = 0; i < np; i++) {
    const int dx = pts2[i * 2] - dux;
    const int dy = pts2[i * 2 + 1] - duy;
    const int sx = pts1[i * 2] - sux;
    const int sy = pts1[i * 2 + 1] - suy;
    // (TODO)yunqing: This comparison wouldn't be necessary if the sample
    // selection is done in find_samples(). Also, global offset can be removed
    // while collecting samples.
    if (abs(sx - dx) < LS_MV_MAX && abs(sy - dy) < LS_MV_MAX) {
      A[0][0] += LS_SQUARE(sx);
      A[0][1] += LS_PRODUCT1(sx, sy);
      A[1][1] += LS_SQUARE(sy);
      Bx[0] += LS_PRODUCT2(sx, dx);
      Bx[1] += LS_PRODUCT1(sy, dx);
      By[0] += LS_PRODUCT1(sx, dy);
      By[1] += LS_PRODUCT2(sy, dy);
    }
  }

  // Just for debugging, and can be removed later.
  assert(A[0][0] >= LS_MAT_MIN && A[0][0] <= LS_MAT_MAX);
  assert(A[0][1] >= LS_MAT_MIN && A[0][1] <= LS_MAT_MAX);
  assert(A[1][1] >= LS_MAT_MIN && A[1][1] <= LS_MAT_MAX);
  assert(Bx[0] >= LS_MAT_MIN && Bx[0] <= LS_MAT_MAX);
  assert(Bx[1] >= LS_MAT_MIN && Bx[1] <= LS_MAT_MAX);
  assert(By[0] >= LS_MAT_MIN && By[0] <= LS_MAT_MAX);
  assert(By[1] >= LS_MAT_MIN && By[1] <= LS_MAT_MAX);

  int64_t Det;
  int16_t iDet, shift;

  // Compute Determinant of A
  Det = (int64_t)A[0][0] * A[1][1] - (int64_t)A[0][1] * A[0][1];
  if (Det == 0) return 1;
  iDet = resolve_divisor_64(llabs(Det), &shift) * (Det < 0 ? -1 : 1);
  shift -= WARPEDMODEL_PREC_BITS;
  if (shift < 0) {
    iDet <<= (-shift);
    shift = 0;
  }

  int64_t Px[2], Py[2];

  // These divided by the Det, are the least squares solutions
  Px[0] = (int64_t)A[1][1] * Bx[0] - (int64_t)A[0][1] * Bx[1];
  Px[1] = -(int64_t)A[0][1] * Bx[0] + (int64_t)A[0][0] * Bx[1];
  Py[0] = (int64_t)A[1][1] * By[0] - (int64_t)A[0][1] * By[1];
  Py[1] = -(int64_t)A[0][1] * By[0] + (int64_t)A[0][0] * By[1];

  wm->wmmat[2] = get_mult_shift_diag(Px[0], iDet, shift);
  wm->wmmat[3] = get_mult_shift_ndiag(Px[1], iDet, shift);
  wm->wmmat[4] = get_mult_shift_ndiag(Py[0], iDet, shift);
  wm->wmmat[5] = get_mult_shift_diag(Py[1], iDet, shift);

  // Note: In the vx, vy expressions below, the max value of each of the
  // 2nd and 3rd terms are (2^16 - 1) * (2^13 - 1). That leaves enough room
  // for the first term so that the overall sum in the worst case fits
  // within 32 bits overall.
  int32_t vx = mvx * (1 << (WARPEDMODEL_PREC_BITS - 3)) -
               (isux * (wm->wmmat[2] - (1 << WARPEDMODEL_PREC_BITS)) +
                isuy * wm->wmmat[3]);
  int32_t vy = mvy * (1 << (WARPEDMODEL_PREC_BITS - 3)) -
               (isux * wm->wmmat[4] +
                isuy * (wm->wmmat[5] - (1 << WARPEDMODEL_PREC_BITS)));
  wm->wmmat[0] =
      clamp(vx, -WARPEDMODEL_TRANS_CLAMP, WARPEDMODEL_TRANS_CLAMP - 1);
  wm->wmmat[1] =
      clamp(vy, -WARPEDMODEL_TRANS_CLAMP, WARPEDMODEL_TRANS_CLAMP - 1);

  wm->wmmat[6] = wm->wmmat[7] = 0;
  return 0;
}

int find_projection(int np, int *pts1, int *pts2, BLOCK_SIZE bsize, int mvy,
                    int mvx, WarpedMotionParams *wm_params, int mi_row,
                    int mi_col) {
  assert(wm_params->wmtype == AFFINE);

  if (find_affine_int(np, pts1, pts2, bsize, mvy, mvx, wm_params, mi_row,
                      mi_col))
    return 1;

  // check compatibility with the fast warp filter
  if (!get_shear_params(wm_params)) return 1;

  return 0;
}