/*

 * 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 WarpedFilterCoeff 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 WarpedFilterCoeff *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 WarpedFilterCoeff *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 WarpedFilterCoeff *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 WarpedFilterCoeff *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;

}