xref: /aosp_15_r20/external/libaom/av1/common/warped_motion.c (revision 77c1e3ccc04c968bd2bc212e87364f250e820521)

/*
 * 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/av1_common_int.h"
#include "av1/common/warped_motion.h"
#include "av1/common/scale.h"

// 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 av1_warped_filter[WARPEDPIXEL_PREC_SHIFTS * 3 + 1][8] = {
  // [-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 },
};

/* 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;
}

#ifndef NDEBUG
// Check that the given warp model satisfies the relevant constraints for
// its stated model type
static void check_model_consistency(WarpedMotionParams *wm) {
  switch (wm->wmtype) {
    case IDENTITY:
      assert(wm->wmmat[0] == 0);
      assert(wm->wmmat[1] == 0);
      AOM_FALLTHROUGH_INTENDED;
    case TRANSLATION:
      assert(wm->wmmat[2] == 1 << WARPEDMODEL_PREC_BITS);
      assert(wm->wmmat[3] == 0);
      AOM_FALLTHROUGH_INTENDED;
    case ROTZOOM:
      assert(wm->wmmat[4] == -wm->wmmat[3]);
      assert(wm->wmmat[5] == wm->wmmat[2]);
      AOM_FALLTHROUGH_INTENDED;
    case AFFINE: break;
    default: assert(0 && "Bad wmtype");
  }
}
#endif  // NDEBUG

// Returns 1 on success or 0 on an invalid affine set
int av1_get_shear_params(WarpedMotionParams *wm) {
#ifndef NDEBUG
  // Check that models have been constructed sensibly
  // This is a good place to check, because this function does not need to
  // be called until after model construction is complete, but must be called
  // before the model can be used for prediction.
  check_model_consistency(wm);
#endif  // NDEBUG

  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;
}

#if CONFIG_AV1_HIGHBITDEPTH
/* 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;
  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));

  // Check that, even with 12-bit input, the intermediate values will fit
  // into an unsigned 16-bit intermediate array.
  assert(bd + FILTER_BITS + 2 - conv_params->round_0 <= 16);

  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 int64_t dst_x =
          (int64_t)mat[2] * src_x + (int64_t)mat[3] * src_y + (int64_t)mat[0];
      const int64_t dst_y =
          (int64_t)mat[4] * src_x + (int64_t)mat[5] * src_y + (int64_t)mat[1];
      const int64_t x4 = dst_x >> subsampling_x;
      const int64_t y4 = dst_y >> subsampling_y;

      const int32_t ix4 = (int32_t)(x4 >> WARPEDMODEL_PREC_BITS);
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      const int32_t iy4 = (int32_t)(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 = av1_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 = av1_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_dist_wtd_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;
        }
      }
    }
  }
}

void highbd_warp_plane(WarpedMotionParams *wm, const uint16_t *const ref,
                       int width, int height, int stride, uint16_t *const 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) {
  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_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);
}
#endif  // CONFIG_AV1_HIGHBITDEPTH

/* 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(rachelbarker): 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 int64_t dst_x =
          (int64_t)mat[2] * src_x + (int64_t)mat[3] * src_y + (int64_t)mat[0];
      const int64_t dst_y =
          (int64_t)mat[4] * src_x + (int64_t)mat[5] * src_y + (int64_t)mat[1];
      const int64_t x4 = dst_x >> subsampling_x;
      const int64_t y4 = dst_y >> subsampling_y;

      int32_t ix4 = (int32_t)(x4 >> WARPEDMODEL_PREC_BITS);
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      int32_t iy4 = (int32_t)(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 = av1_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 = av1_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_dist_wtd_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;
        }
      }
    }
  }
}

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) {
  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);
}

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 CONFIG_AV1_HIGHBITDEPTH
  if (use_hbd)
    highbd_warp_plane(wm, CONVERT_TO_SHORTPTR(ref), width, height, stride,
                      CONVERT_TO_SHORTPTR(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);
#else
  (void)use_hbd;
  (void)bd;
  warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
             p_height, p_stride, subsampling_x, subsampling_y, conv_params);
#endif
}

#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 };

  const int bw = block_size_wide[bsize];
  const int bh = block_size_high[bsize];
  const int rsuy = bh / 2 - 1;
  const int rsux = bw / 2 - 1;
  const int suy = rsuy * 8;
  const int sux = rsux * 8;
  const int duy = suy + mvy;
  const int dux = sux + mvx;

  // 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 (int 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);

  // Compute Determinant of A
  const int64_t Det = (int64_t)A[0][0] * A[1][1] - (int64_t)A[0][1] * A[0][1];
  if (Det == 0) return 1;

  int16_t shift;
  int16_t 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);

  const int isuy = (mi_row * MI_SIZE + rsuy);
  const int isux = (mi_col * MI_SIZE + rsux);
  // 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.
  const int32_t vx = mvx * (1 << (WARPEDMODEL_PREC_BITS - 3)) -
                     (isux * (wm->wmmat[2] - (1 << WARPEDMODEL_PREC_BITS)) +
                      isuy * wm->wmmat[3]);
  const 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);
  return 0;
}

int av1_find_projection(int np, const int *pts1, const 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 (!av1_get_shear_params(wm_params)) return 1;

  return 0;
}