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 "./av1_rtcd.h"
#include "av1/common/warped_motion.h"

/* 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 */

static ProjectPointsFunc get_project_points_type(TransformationType type) {
  switch (type) {
    case HOMOGRAPHY: return project_points_homography;
    case AFFINE: return project_points_affine;
    case ROTZOOM: return project_points_rotzoom;
    case TRANSLATION: return project_points_translation;
    default: assert(0); return NULL;
  }
}

void project_points_translation(const int32_t *mat, int *points, int *proj,
                                const int n, const int stride_points,
                                const int stride_proj, const int subsampling_x,
                                const int subsampling_y) {
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          ((x * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[0]),
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          ((x * (1 << WARPEDMODEL_PREC_BITS)) + mat[0]), WARPEDDIFF_PREC_BITS);
    if (subsampling_y)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          ((y * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[1]),
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          ((y * (1 << WARPEDMODEL_PREC_BITS))) + mat[1], WARPEDDIFF_PREC_BITS);
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_rotzoom(const int32_t *mat, int *points, int *proj,
                            const int n, const int stride_points,
                            const int stride_proj, const int subsampling_x,
                            const int subsampling_y) {
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
                                            WARPEDDIFF_PREC_BITS);
    if (subsampling_y)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          -mat[3] * 2 * x + mat[2] * 2 * y + mat[1] +
              (-mat[3] + mat[2] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(-mat[3] * x + mat[2] * y + mat[1],
                                            WARPEDDIFF_PREC_BITS);
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_affine(const int32_t *mat, int *points, int *proj,
                           const int n, const int stride_points,
                           const int stride_proj, const int subsampling_x,
                           const int subsampling_y) {
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
                                            WARPEDDIFF_PREC_BITS);
    if (subsampling_y)
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
          mat[4] * 2 * x + mat[5] * 2 * y + mat[1] +
              (mat[4] + mat[5] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
          WARPEDDIFF_PREC_BITS + 1);
    else
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[4] * x + mat[5] * y + mat[1],
                                            WARPEDDIFF_PREC_BITS);
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_hortrapezoid(const int32_t *mat, int *points, int *proj,
                                 const int n, const int stride_points,
                                 const int stride_proj, const int subsampling_x,
                                 const int subsampling_y) {
  int i;
  int64_t x, y, Z;
  int64_t xp, yp;
  for (i = 0; i < n; ++i) {
    x = *(points++), y = *(points++);
    x = (subsampling_x ? 4 * x + 1 : 2 * x);
    y = (subsampling_y ? 4 * y + 1 : 2 * y);

    Z = (mat[7] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
    xp = (mat[2] * x + mat[3] * y + 2 * mat[0]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
    yp = (mat[5] * y + 2 * mat[1]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));

    xp = xp > 0 ? (xp + Z / 2) / Z : (xp - Z / 2) / Z;
    yp = yp > 0 ? (yp + Z / 2) / Z : (yp - Z / 2) / Z;

    if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    *(proj++) = (int)xp;
    *(proj++) = (int)yp;

    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_vertrapezoid(const int32_t *mat, int *points, int *proj,
                                 const int n, const int stride_points,
                                 const int stride_proj, const int subsampling_x,
                                 const int subsampling_y) {
  int i;
  int64_t x, y, Z;
  int64_t xp, yp;
  for (i = 0; i < n; ++i) {
    x = *(points++), y = *(points++);
    x = (subsampling_x ? 4 * x + 1 : 2 * x);
    y = (subsampling_y ? 4 * y + 1 : 2 * y);

    Z = (mat[6] * x + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
    xp = (mat[2] * x + 2 * mat[0]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
    yp = (mat[4] * x + mat[5] * y + 2 * mat[1]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));

    xp = xp > 0 ? (xp + Z / 2) / Z : (xp - Z / 2) / Z;
    yp = yp > 0 ? (yp + Z / 2) / Z : (yp - Z / 2) / Z;

    if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    *(proj++) = (int)xp;
    *(proj++) = (int)yp;

    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_homography(const int32_t *mat, int *points, int *proj,
                               const int n, const int stride_points,
                               const int stride_proj, const int subsampling_x,
                               const int subsampling_y) {
  int i;
  int64_t x, y, Z;
  int64_t xp, yp;
  for (i = 0; i < n; ++i) {
    x = *(points++), y = *(points++);
    x = (subsampling_x ? 4 * x + 1 : 2 * x);
    y = (subsampling_y ? 4 * y + 1 : 2 * y);

    Z = (mat[6] * x + mat[7] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
    xp = (mat[2] * x + mat[3] * y + 2 * mat[0]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
    yp = (mat[4] * x + mat[5] * y + 2 * mat[1]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));

    xp = xp > 0 ? (xp + Z / 2) / Z : (xp - Z / 2) / Z;
    yp = yp > 0 ? (yp + Z / 2) / Z : (yp - Z / 2) / Z;

    if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    *(proj++) = (int)xp;
    *(proj++) = (int)yp;

    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

// 'points' are at original scale, output 'proj's are scaled up by
// 1 << WARPEDPIXEL_PREC_BITS
void project_points(const WarpedMotionParams *wm_params, int *points, int *proj,
                    const int n, const int stride_points, const int stride_proj,
                    const int subsampling_x, const int subsampling_y) {
  switch (wm_params->wmtype) {
    case AFFINE:
      project_points_affine(wm_params->wmmat, points, proj, n, stride_points,
                            stride_proj, subsampling_x, subsampling_y);
      break;
    case ROTZOOM:
      project_points_rotzoom(wm_params->wmmat, points, proj, n, stride_points,
                             stride_proj, subsampling_x, subsampling_y);
      break;
    case HOMOGRAPHY:
      project_points_homography(wm_params->wmmat, points, proj, n,
                                stride_points, stride_proj, subsampling_x,
                                subsampling_y);
      break;
    default: assert(0 && "Invalid warped motion type!"); return;
  }
}

static const int16_t
    filter_ntap[WARPEDPIXEL_PREC_SHIFTS][WARPEDPIXEL_FILTER_TAPS] = {
#if WARPEDPIXEL_PREC_BITS == 6
      { 0, 0, 128, 0, 0, 0 },      { 0, -1, 128, 2, -1, 0 },
      { 1, -3, 127, 4, -1, 0 },    { 1, -4, 126, 6, -2, 1 },
      { 1, -5, 126, 8, -3, 1 },    { 1, -6, 125, 11, -4, 1 },
      { 1, -7, 124, 13, -4, 1 },   { 2, -8, 123, 15, -5, 1 },
      { 2, -9, 122, 18, -6, 1 },   { 2, -10, 121, 20, -6, 1 },
      { 2, -11, 120, 22, -7, 2 },  { 2, -12, 119, 25, -8, 2 },
      { 3, -13, 117, 27, -8, 2 },  { 3, -13, 116, 29, -9, 2 },
      { 3, -14, 114, 32, -10, 3 }, { 3, -15, 113, 35, -10, 2 },
      { 3, -15, 111, 37, -11, 3 }, { 3, -16, 109, 40, -11, 3 },
      { 3, -16, 108, 42, -12, 3 }, { 4, -17, 106, 45, -13, 3 },
      { 4, -17, 104, 47, -13, 3 }, { 4, -17, 102, 50, -14, 3 },
      { 4, -17, 100, 52, -14, 3 }, { 4, -18, 98, 55, -15, 4 },
      { 4, -18, 96, 58, -15, 3 },  { 4, -18, 94, 60, -16, 4 },
      { 4, -18, 91, 63, -16, 4 },  { 4, -18, 89, 65, -16, 4 },
      { 4, -18, 87, 68, -17, 4 },  { 4, -18, 85, 70, -17, 4 },
      { 4, -18, 82, 73, -17, 4 },  { 4, -18, 80, 75, -17, 4 },
      { 4, -18, 78, 78, -18, 4 },  { 4, -17, 75, 80, -18, 4 },
      { 4, -17, 73, 82, -18, 4 },  { 4, -17, 70, 85, -18, 4 },
      { 4, -17, 68, 87, -18, 4 },  { 4, -16, 65, 89, -18, 4 },
      { 4, -16, 63, 91, -18, 4 },  { 4, -16, 60, 94, -18, 4 },
      { 3, -15, 58, 96, -18, 4 },  { 4, -15, 55, 98, -18, 4 },
      { 3, -14, 52, 100, -17, 4 }, { 3, -14, 50, 102, -17, 4 },
      { 3, -13, 47, 104, -17, 4 }, { 3, -13, 45, 106, -17, 4 },
      { 3, -12, 42, 108, -16, 3 }, { 3, -11, 40, 109, -16, 3 },
      { 3, -11, 37, 111, -15, 3 }, { 2, -10, 35, 113, -15, 3 },
      { 3, -10, 32, 114, -14, 3 }, { 2, -9, 29, 116, -13, 3 },
      { 2, -8, 27, 117, -13, 3 },  { 2, -8, 25, 119, -12, 2 },
      { 2, -7, 22, 120, -11, 2 },  { 1, -6, 20, 121, -10, 2 },
      { 1, -6, 18, 122, -9, 2 },   { 1, -5, 15, 123, -8, 2 },
      { 1, -4, 13, 124, -7, 1 },   { 1, -4, 11, 125, -6, 1 },
      { 1, -3, 8, 126, -5, 1 },    { 1, -2, 6, 126, -4, 1 },
      { 0, -1, 4, 127, -3, 1 },    { 0, -1, 2, 128, -1, 0 },
#elif WARPEDPIXEL_PREC_BITS == 5
      { 0, 0, 128, 0, 0, 0 },      { 1, -3, 127, 4, -1, 0 },
      { 1, -5, 126, 8, -3, 1 },    { 1, -7, 124, 13, -4, 1 },
      { 2, -9, 122, 18, -6, 1 },   { 2, -11, 120, 22, -7, 2 },
      { 3, -13, 117, 27, -8, 2 },  { 3, -14, 114, 32, -10, 3 },
      { 3, -15, 111, 37, -11, 3 }, { 3, -16, 108, 42, -12, 3 },
      { 4, -17, 104, 47, -13, 3 }, { 4, -17, 100, 52, -14, 3 },
      { 4, -18, 96, 58, -15, 3 },  { 4, -18, 91, 63, -16, 4 },
      { 4, -18, 87, 68, -17, 4 },  { 4, -18, 82, 73, -17, 4 },
      { 4, -18, 78, 78, -18, 4 },  { 4, -17, 73, 82, -18, 4 },
      { 4, -17, 68, 87, -18, 4 },  { 4, -16, 63, 91, -18, 4 },
      { 3, -15, 58, 96, -18, 4 },  { 3, -14, 52, 100, -17, 4 },
      { 3, -13, 47, 104, -17, 4 }, { 3, -12, 42, 108, -16, 3 },
      { 3, -11, 37, 111, -15, 3 }, { 3, -10, 32, 114, -14, 3 },
      { 2, -8, 27, 117, -13, 3 },  { 2, -7, 22, 120, -11, 2 },
      { 1, -6, 18, 122, -9, 2 },   { 1, -4, 13, 124, -7, 1 },
      { 1, -3, 8, 126, -5, 1 },    { 0, -1, 4, 127, -3, 1 },
#endif  // WARPEDPIXEL_PREC_BITS == 6
    };

static int32_t do_ntap_filter(const int32_t *const p, int x) {
  int i;
  int32_t sum = 0;
  for (i = 0; i < WARPEDPIXEL_FILTER_TAPS; ++i) {
    sum += p[i - WARPEDPIXEL_FILTER_TAPS / 2 + 1] * filter_ntap[x][i];
  }
  return sum;
}

static int32_t do_cubic_filter(const int32_t *const p, int x) {
  if (x == 0) {
    return p[0] * (1 << WARPEDPIXEL_FILTER_BITS);
  } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
    return p[1] * (1 << WARPEDPIXEL_FILTER_BITS);
  } else {
    const int64_t v1 = (int64_t)x * x * x * (3 * (p[0] - p[1]) + p[2] - p[-1]);
    const int64_t v2 =
        (int64_t)x * x * (2 * p[-1] - 5 * p[0] + 4 * p[1] - p[2]);
    const int64_t v3 = x * (p[1] - p[-1]);
    const int64_t v4 = 2 * p[0];
    return (int32_t)ROUND_POWER_OF_TWO_SIGNED(
        (v4 * (1 << (3 * WARPEDPIXEL_PREC_BITS))) +
            (v3 * (1 << (2 * WARPEDPIXEL_PREC_BITS))) +
            (v2 * (1 << WARPEDPIXEL_PREC_BITS)) + v1,
        3 * WARPEDPIXEL_PREC_BITS + 1 - WARPEDPIXEL_FILTER_BITS);
  }
}

static INLINE void get_subcolumn(int taps, const uint8_t *const ref,
                                 int32_t *col, int stride, int x, int y_start) {
  int i;
  for (i = 0; i < taps; ++i) {
    col[i] = ref[(i + y_start) * stride + x];
  }
}

static uint8_t bi_ntap_filter(const uint8_t *const ref, int x, int y,
                              int stride) {
  int32_t val, arr[WARPEDPIXEL_FILTER_TAPS];
  int k;
  const int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  const int j = (int)y >> WARPEDPIXEL_PREC_BITS;
  for (k = 0; k < WARPEDPIXEL_FILTER_TAPS; ++k) {
    int32_t arr_temp[WARPEDPIXEL_FILTER_TAPS];
    get_subcolumn(WARPEDPIXEL_FILTER_TAPS, ref, arr_temp, stride,
                  i + k + 1 - WARPEDPIXEL_FILTER_TAPS / 2,
                  j + 1 - WARPEDPIXEL_FILTER_TAPS / 2);
    arr[k] = do_ntap_filter(arr_temp + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t bi_cubic_filter(const uint8_t *const ref, int x, int y,
                               int stride) {
  int32_t val, arr[4];
  int k;
  const int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  const int j = (int)y >> WARPEDPIXEL_PREC_BITS;
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
    get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t bi_linear_filter(const uint8_t *const ref, int x, int y,
                                int stride) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
              (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[iy * stride + ix + 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) * sx +
          ref[(iy + 1) * stride + ix] * sy * (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[(iy + 1) * stride + ix + 1] * sy * sx,
      WARPEDPIXEL_PREC_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t warp_interpolate(const uint8_t *const ref, int x, int y,
                                int width, int height, int stride) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t v;

  if (ix < 0 && iy < 0)
    return ref[0];
  else if (ix < 0 && iy >= height - 1)
    return ref[(height - 1) * stride];
  else if (ix >= width - 1 && iy < 0)
    return ref[width - 1];
  else if (ix >= width - 1 && iy >= height - 1)
    return ref[(height - 1) * stride + (width - 1)];
  else if (ix < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
            ref[(iy + 1) * stride] * sy,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (ix >= width - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride + width - 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
            ref[(iy + 1) * stride + width - 1] * sy,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (iy >= height - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[(height - 1) * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) +
            ref[(height - 1) * stride + ix + 1] * sx,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (ix >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             iy >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             ix < width - WARPEDPIXEL_FILTER_TAPS / 2 &&
             iy < height - WARPEDPIXEL_FILTER_TAPS / 2) {
    return bi_ntap_filter(ref, x, y, stride);
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
    return bi_cubic_filter(ref, x, y, stride);
  } else {
    return bi_linear_filter(ref, x, y, stride);
  }
}

// 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,
};

static INLINE uint16_t saturate_uint(int32_t v, int bits) {
  return (uint16_t)clamp(v, 0, (1 << bits) - 1);
}

#if CONFIG_WARPED_MOTION
// 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 e, 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.
  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];
}
#endif  // CONFIG_WARPED_MOTION

static int16_t resolve_divisor_32(uint32_t D, int16_t *shift) {
  int32_t e, f;
  *shift = get_msb(D);
  // e is obtained from D after resetting the most significant 1 bit.
  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;
  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);
  if (!is_affine_shear_allowed(wm->alpha, wm->beta, wm->gamma, wm->delta))
    return 0;

  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);
  return 1;
}

#if CONFIG_HIGHBITDEPTH
static INLINE void highbd_get_subcolumn(int taps, const uint16_t *const ref,
                                        int32_t *col, int stride, int x,
                                        int y_start) {
  int i;
  for (i = 0; i < taps; ++i) {
    col[i] = ref[(i + y_start) * stride + x];
  }
}

static uint16_t highbd_bi_ntap_filter(const uint16_t *const ref, int x, int y,
                                      int stride, int bd) {
  int32_t val, arr[WARPEDPIXEL_FILTER_TAPS];
  int k;
  const int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  const int j = (int)y >> WARPEDPIXEL_PREC_BITS;
  for (k = 0; k < WARPEDPIXEL_FILTER_TAPS; ++k) {
    int32_t arr_temp[WARPEDPIXEL_FILTER_TAPS];
    highbd_get_subcolumn(WARPEDPIXEL_FILTER_TAPS, ref, arr_temp, stride,
                         i + k + 1 - WARPEDPIXEL_FILTER_TAPS / 2,
                         j + 1 - WARPEDPIXEL_FILTER_TAPS / 2);
    arr[k] = do_ntap_filter(arr_temp + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint16_t)clip_pixel_highbd(val, bd);
}

static uint16_t highbd_bi_cubic_filter(const uint16_t *const ref, int x, int y,
                                       int stride, int bd) {
  int32_t val, arr[4];
  int k;
  const int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  const int j = (int)y >> WARPEDPIXEL_PREC_BITS;
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
    highbd_get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint16_t)clip_pixel_highbd(val, bd);
}

static uint16_t highbd_bi_linear_filter(const uint16_t *const ref, int x, int y,
                                        int stride, int bd) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
              (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[iy * stride + ix + 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) * sx +
          ref[(iy + 1) * stride + ix] * sy * (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[(iy + 1) * stride + ix + 1] * sy * sx,
      WARPEDPIXEL_PREC_BITS * 2);
  return (uint16_t)clip_pixel_highbd(val, bd);
}

static uint16_t highbd_warp_interpolate(const uint16_t *const ref, int x, int y,
                                        int width, int height, int stride,
                                        int bd) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t v;

  if (ix < 0 && iy < 0)
    return ref[0];
  else if (ix < 0 && iy > height - 1)
    return ref[(height - 1) * stride];
  else if (ix > width - 1 && iy < 0)
    return ref[width - 1];
  else if (ix > width - 1 && iy > height - 1)
    return ref[(height - 1) * stride + (width - 1)];
  else if (ix < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
            ref[(iy + 1) * stride] * sy,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel_highbd(v, bd);
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel_highbd(v, bd);
  } else if (ix > width - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride + width - 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
            ref[(iy + 1) * stride + width - 1] * sy,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel_highbd(v, bd);
  } else if (iy > height - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[(height - 1) * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) +
            ref[(height - 1) * stride + ix + 1] * sx,
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel_highbd(v, bd);
  } else if (ix >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             iy >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             ix < width - WARPEDPIXEL_FILTER_TAPS / 2 &&
             iy < height - WARPEDPIXEL_FILTER_TAPS / 2) {
    return highbd_bi_ntap_filter(ref, x, y, stride, bd);
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
    return highbd_bi_cubic_filter(ref, x, y, stride, bd);
  } else {
    return highbd_bi_linear_filter(ref, x, y, stride, bd);
  }
}

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);
  int e1, e2;
  err = abs(err);
  e1 = err >> b;
  e2 = err & bmask;
  return error_measure_lut[255 + e1] * (v - e2) +
         error_measure_lut[256 + e1] * e2;
}

static void highbd_warp_plane_old(
    const WarpedMotionParams *const 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 x_scale, int y_scale, int bd, int comp_avg) {
  int i, j;
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  const uint16_t *const ref = CONVERT_TO_SHORTPTR(ref8);
  if (projectpoints == NULL) return;
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      if (comp_avg)
        pred[(j - p_col) + (i - p_row) * p_stride] = ROUND_POWER_OF_TWO(
            pred[(j - p_col) + (i - p_row) * p_stride] +
                highbd_warp_interpolate(ref, out[0], out[1], width, height,
                                        stride, bd),
            1);
      else
        pred[(j - p_col) + (i - p_row) * p_stride] = highbd_warp_interpolate(
            ref, out[0], out[1], width, height, stride, bd);
    }
  }
}

// Note: For an explanation of the warp algorithm, see the comment
// above warp_plane()
//
// Note also: The "worst case" in terms of modulus of the data stored into 'tmp'
// (ie, the result of 'sum' in the horizontal filter) occurs when:
// coeffs = { -2,   8, -22,  87,  72, -21,   8, -2}, and
// ref =    {  0, 255,   0, 255, 255,   0, 255,  0}
// Before rounding, this gives sum = 716625. After rounding,
// HORSHEAR_REDUCE_PREC_BITS = 4 => sum = 44789 > 2^15
// HORSHEAR_REDUCE_PREC_BITS = 5 => sum = 22395 < 2^15
//
// So, as long as HORSHEAR_REDUCE_PREC_BITS >= 5, we can safely use a 16-bit
// intermediate array.
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, int comp_avg,
                              int16_t alpha, int16_t beta, int16_t gamma,
                              int16_t delta) {
#if HORSHEAR_REDUCE_PREC_BITS >= 5
  int16_t tmp[15 * 8];
#else
  int32_t tmp[15 * 8];
#endif
  int i, j, k, l, m;

  /* Note: For this code to work, the left/right frame borders need to be
     extended by at least 13 pixels each. By the time we get here, other
     code will have set up this border, but we allow an explicit check
     for debugging purposes.
  */
  /*for (i = 0; i < height; ++i) {
    for (j = 0; j < 13; ++j) {
      assert(ref[i * stride - 13 + j] == ref[i * stride]);
      assert(ref[i * stride + width + j] == ref[i * stride + (width - 1)]);
    }
  }*/

  for (i = p_row; i < p_row + p_height; i += 8) {
    for (j = p_col; j < p_col + p_width; j += 8) {
      int32_t x4, y4, ix4, sx4, iy4, sy4;
      if (subsampling_x)