warped_motion.c 75.9 KB
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/*
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 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
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 *
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 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
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 */

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

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#include "./av1_rtcd.h"
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#include "av1/common/warped_motion.h"
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/* clang-format off */
static const int error_measure_lut[512] = {
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  // 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,
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};
/* clang-format on */
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static ProjectPointsFunc get_project_points_type(TransformationType type) {
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  switch (type) {
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    case HOMOGRAPHY: return project_points_homography;
    case AFFINE: return project_points_affine;
    case ROTZOOM: return project_points_rotzoom;
    case TRANSLATION: return project_points_translation;
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    default: assert(0); return NULL;
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  }
}

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

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

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

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void project_points_hortrapezoid(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;
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    *(proj++) = (int)xp;
    *(proj++) = (int)yp;
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    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

void project_points_vertrapezoid(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;
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    *(proj++) = (int)xp;
    *(proj++) = (int)yp;
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    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

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void project_points_homography(int32_t *mat, int *points, int *proj,
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                               const int n, const int stride_points,
                               const int stride_proj, const int subsampling_x,
                               const int subsampling_y) {
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  int i;
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  int64_t x, y, Z;
  int64_t xp, yp;
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  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);

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

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

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// 'points' are at original scale, output 'proj's are scaled up by
// 1 << WARPEDPIXEL_PREC_BITS
void project_points(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;
  }
}

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static const int16_t
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    filter_ntap[WARPEDPIXEL_PREC_SHIFTS][WARPEDPIXEL_FILTER_TAPS] = {
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#if WARPEDPIXEL_PREC_BITS == 6
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      { 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 },
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#elif WARPEDPIXEL_PREC_BITS == 5
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      { 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
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    };
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static int32_t do_ntap_filter(int32_t *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(int32_t *p, int x) {
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  if (x == 0) {
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    return p[0] * (1 << WARPEDPIXEL_FILTER_BITS);
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  } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
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    return p[1] * (1 << WARPEDPIXEL_FILTER_BITS);
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  } else {
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    const int64_t v1 = (int64_t)x * x * x * (3 * (p[0] - p[1]) + p[2] - p[-1]);
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    const int64_t v2 =
        (int64_t)x * x * (2 * p[-1] - 5 * p[0] + 4 * p[1] - p[2]);
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    const int64_t v3 = x * (p[1] - p[-1]);
    const int64_t v4 = 2 * p[0];
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    return (int32_t)ROUND_POWER_OF_TWO_SIGNED(
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        (v4 * (1 << (3 * WARPEDPIXEL_PREC_BITS))) +
            (v3 * (1 << (2 * WARPEDPIXEL_PREC_BITS))) +
            (v2 * (1 << WARPEDPIXEL_PREC_BITS)) + v1,
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        3 * WARPEDPIXEL_PREC_BITS + 1 - WARPEDPIXEL_FILTER_BITS);
  }
}

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

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

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

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

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

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// 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 */
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const int16_t warped_filter[WARPEDPIXEL_PREC_SHIFTS * 3 + 1][8] = {
503
#if WARPEDPIXEL_PREC_BITS == 6
504
  // [-1, 0)
505
  { 0,   0, 127,   1,   0, 0, 0, 0 }, { 0, - 1, 127,   2,   0, 0, 0, 0 },
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  { 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 },
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  { 0, - 1,   4, 127, - 3, 1, 0, 0 }, { 0,   0,   2, 127, - 1, 0, 0, 0 },
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  // [0, 1)
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  { 0,  0,   0, 127,   1,   0,  0,  0}, { 0,  0,  -1, 127,   2,   0,  0,  0},
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  { 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},
570
  { 0,  1,  -2,   4, 127,  -3,  1,  0}, { 0,  0,   0,   2, 127,  -1,  0,  0},
571 572

  // [1, 2)
573
  { 0, 0, 0,   1, 127,   0,   0, 0 }, { 0, 0, 0, - 1, 127,   2,   0, 0 },
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  { 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 },
604
  { 0, 0, 0, - 1,   4, 127, - 3, 1 }, { 0, 0, 0,   0,   2, 127, - 1, 0 },
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  // dummy (replicate row index 191)
  { 0, 0, 0,   0,   2, 127, - 1, 0 },
607

608
#elif WARPEDPIXEL_PREC_BITS == 5
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  // [-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},
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  // dummy (replicate row index 95)
  {0, 0, 0,  -1,   4, 127,  -3, 1},
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#endif  // WARPEDPIXEL_PREC_BITS == 6
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};
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/* clang-format on */

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#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,
};

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static INLINE int16_t saturate_int16(int32_t v) {
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  if (v > 32767)
    return 32767;
  else if (v < -32768)
    return -32768;
  return v;
}

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#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;
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  *shift = (int16_t)((D >> 32) ? get_msb((unsigned int)(D >> 32)) + 32
                               : get_msb((unsigned int)D));
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  // 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(WarpedMotionParams *wm) {
  const int32_t *mat = wm->wmmat;
  return (mat[2] > 0);
}

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

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

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#if CONFIG_HIGHBITDEPTH
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static INLINE void highbd_get_subcolumn(int taps, uint16_t *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];
  }
}

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

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

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

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

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  if (ix < 0 && iy < 0)
    return ref[0];
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  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) +
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            ref[(iy + 1) * stride] * sy,
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        WARPEDPIXEL_PREC_BITS);
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    return clip_pixel_highbd(v, bd);
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