warped_motion.c 39.9 KB
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/*
 *  Copyright (c) 2015 The WebM project authors. All Rights Reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be
 *  found  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

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

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#include "av1/common/warped_motion.h"
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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(int16_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) {
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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[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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          ((x * (1 << WARPEDMODEL_PREC_BITS)) + mat[1]), 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[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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          ((y * (1 << WARPEDMODEL_PREC_BITS))) + mat[0], WARPEDDIFF_PREC_BITS);
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    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

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void project_points_rotzoom(int16_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) {
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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[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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    if (subsampling_y)
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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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    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

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void project_points_affine(int16_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) {
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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[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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    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[0] +
              (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[0],
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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_homography(int16_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) {
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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[7] * x + mat[6] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
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    xp = (mat[1] * x + mat[0] * y + 2 * mat[3]) *
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
    yp = (mat[2] * x + mat[5] * y + 2 * mat[4]) *
         (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++) = xp;
    *(proj++) = yp;

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

static const int16_t
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    filter_ntap[WARPEDPIXEL_PREC_SHIFTS][WARPEDPIXEL_FILTER_TAPS] = {
      { 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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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];
  } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
    return p[1];
  } 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 = 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];
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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)
    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);
    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);
  } else if (ix > width - 1) {
    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);
  } else if (iy > height - 1) {
    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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#if CONFIG_AOM_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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  } 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);
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    return clip_pixel_highbd(v, bd);
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  } else if (ix > width - 1) {
    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);
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    return clip_pixel_highbd(v, bd);
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  } else if (iy > height - 1) {
    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);
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    return clip_pixel_highbd(v, bd);
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  } 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);
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  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
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    return highbd_bi_cubic_filter(ref, x, y, stride, bd);
  } else {
    return highbd_bi_linear_filter(ref, x, y, stride, bd);
  }
}

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static double highbd_warp_erroradv(WarpedMotionParams *wm, uint8_t *ref8,
                                   int width, int height, int stride,
                                   uint8_t *dst8, 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 i, j;
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  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
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  uint16_t *dst = CONVERT_TO_SHORTPTR(dst8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
  int gm_err = 0, no_gm_err = 0;
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  int64_t gm_sumerr = 0, no_gm_sumerr = 0;
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  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;
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      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
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      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
               highbd_warp_interpolate(ref, out[0], out[1], width, height,
                                       stride, bd);
      no_gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
                  ref[(j - p_col) + (i - p_row) * stride];
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      gm_sumerr += (int64_t)gm_err * gm_err;
      no_gm_sumerr += (int64_t)no_gm_err * no_gm_err;
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    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

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static void highbd_warp_plane(WarpedMotionParams *wm, uint8_t *ref8, int width,
                              int height, int stride, uint8_t *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,
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                              int bd, int ref_frm) {
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  int i, j;
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  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
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  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
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  if (projectpoints == NULL) return;
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  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];
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      in[0] = j;
      in[1] = i;
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      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
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      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
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      if (ref_frm)
        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);
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    }
  }
}
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#endif  // CONFIG_AOM_HIGHBITDEPTH
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static double warp_erroradv(WarpedMotionParams *wm, uint8_t *ref, int width,
                            int height, int stride, uint8_t *dst, int p_col,
                            int p_row, int p_width, int p_height, int p_stride,
                            int subsampling_x, int subsampling_y, int x_scale,
                            int y_scale) {
  int gm_err = 0, no_gm_err = 0;
  int gm_sumerr = 0, no_gm_sumerr = 0;
  int i, j;
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  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
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  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;
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      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
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      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
               warp_interpolate(ref, out[0], out[1], width, height, stride);
      no_gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
                  ref[(j - p_col) + (i - p_row) * stride];
      gm_sumerr += gm_err * gm_err;
      no_gm_sumerr += no_gm_err * no_gm_err;
    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

static void warp_plane(WarpedMotionParams *wm, uint8_t *ref, int width,
                       int height, int stride, uint8_t *pred, int p_col,
                       int p_row, int p_width, int p_height, int p_stride,
                       int subsampling_x, int subsampling_y, int x_scale,
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                       int y_scale, int ref_frm) {
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  int i, j;
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  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
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  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;
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      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
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      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
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      if (ref_frm)
        pred[(j - p_col) + (i - p_row) * p_stride] = ROUND_POWER_OF_TWO(
            pred[(j - p_col) + (i - p_row) * p_stride] +
                warp_interpolate(ref, out[0], out[1], width, height, stride),
            1);
      else
        pred[(j - p_col) + (i - p_row) * p_stride] =
            warp_interpolate(ref, out[0], out[1], width, height, stride);
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    }
  }
}

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double av1_warp_erroradv(WarpedMotionParams *wm,
#if CONFIG_AOM_HIGHBITDEPTH
                         int use_hbd, int bd,
#endif  // CONFIG_AOM_HIGHBITDEPTH
                         uint8_t *ref, int width, int height, int stride,
                         uint8_t *dst, int p_col, int p_row, int p_width,
                         int p_height, int p_stride, int subsampling_x,
                         int subsampling_y, int x_scale, int y_scale) {
#if CONFIG_AOM_HIGHBITDEPTH
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  if (use_hbd)
    return highbd_warp_erroradv(
        wm, ref, width, height, stride, dst, p_col, p_row, p_width, p_height,
        p_stride, subsampling_x, subsampling_y, x_scale, y_scale, bd);
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#endif  // CONFIG_AOM_HIGHBITDEPTH
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  return warp_erroradv(wm, ref, width, height, stride, dst, p_col, p_row,
                       p_width, p_height, p_stride, subsampling_x,
                       subsampling_y, x_scale, y_scale);
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}

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void av1_warp_plane(WarpedMotionParams *wm,
#if CONFIG_AOM_HIGHBITDEPTH
                    int use_hbd, int bd,
#endif  // CONFIG_AOM_HIGHBITDEPTH
                    uint8_t *ref, int width, int height, int stride,
                    uint8_t *pred, int p_col, int p_row, int p_width,
                    int p_height, int p_stride, int subsampling_x,
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                    int subsampling_y, int x_scale, int y_scale, int ref_frm) {
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#if CONFIG_AOM_HIGHBITDEPTH
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  if (use_hbd)
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    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
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                      x_scale, y_scale, bd, ref_frm);
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  else
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#endif  // CONFIG_AOM_HIGHBITDEPTH
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    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, x_scale,
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               y_scale, ref_frm);
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}
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void av1_integerize_model(const double *model, TransformationType wmtype,
                          WarpedMotionParams *wm) {
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  wm->wmtype = wmtype;
  switch (wmtype) {
    case HOMOGRAPHY:
      assert(fabs(model[8] - 1.0) < 1e-12);
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      wm->wmmat[3].as_mv.row =
          (int16_t)lrint(model[6] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
      wm->wmmat[3].as_mv.col =
          (int16_t)lrint(model[7] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
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    /* fallthrough intended */
    case AFFINE:
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      wm->wmmat[2].as_mv.row =
          (int16_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[2].as_mv.col =
          (int16_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS));
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    /* fallthrough intended */
    case ROTZOOM:
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      wm->wmmat[1].as_mv.row =
          (int16_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[1].as_mv.col =
          (int16_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS));
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    /* fallthrough intended */
    case TRANSLATION:
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      wm->wmmat[0].as_mv.row =
          (int16_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[0].as_mv.col =
          (int16_t)lrint(model[1] * (1 << WARPEDMODEL_PREC_BITS));
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      break;
    default: assert(0 && "Invalid TransformationType");
  }
}
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///////////////////////////////////////////////////////////////////////////////
// svdcmp
// Adopted from Numerical Recipes in C

static const double TINY_NEAR_ZERO = 1.0E-12;

static INLINE double sign(double a, double b) {
  return ((b) >= 0 ? fabs(a) : -fabs(a));
}

static INLINE double pythag(double a, double b) {
  double ct;
  const double absa = fabs(a);
  const double absb = fabs(b);

  if (absa > absb) {
    ct = absb / absa;
    return absa * sqrt(1.0 + ct * ct);
  } else {
    ct = absa / absb;
    return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);
  }
}

static void multiply_mat(const double *m1, const double *m2, double *res,
                         const int m1_rows, const int inner_dim,
                         const int m2_cols) {
  double sum;

  int row, col, inner;
  for (row = 0; row < m1_rows; ++row) {
    for (col = 0; col < m2_cols; ++col) {
      sum = 0;
      for (inner = 0; inner < inner_dim; ++inner)
        sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + col];
      *(res++) = sum;
    }
  }
}

static int svdcmp(double **u, int m, int n, double w[], double **v) {
  const int max_its = 30;
  int flag, i, its, j, jj, k, l, nm;
  double anorm, c, f, g, h, s, scale, x, y, z;
  double *rv1 = (double *)aom_malloc(sizeof(*rv1) * (n + 1));
  g = scale = anorm = 0.0;
  for (i = 0; i < n; i++) {
    l = i + 1;
    rv1[i] = scale * g;
    g = s = scale = 0.0;
    if (i < m) {
      for (k = i; k < m; k++) scale += fabs(u[k][i]);
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      if (scale != 0.) {
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        for (k = i; k < m; k++) {
          u[k][i] /= scale;
          s += u[k][i] * u[k][i];
        }
        f = u[i][i];
        g = -sign(sqrt(s), f);
        h = f * g - s;
        u[i][i] = f - g;
        for (j = l; j < n; j++) {
          for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];
          f = s / h;
          for (k = i; k < m; k++) u[k][j] += f * u[k][i];
        }
        for (k = i; k < m; k++) u[k][i] *= scale;
      }
    }
    w[i] = scale * g;
    g = s = scale = 0.0;
    if (i < m && i != n - 1) {
      for (k = l; k < n; k++) scale += fabs(u[i][k]);
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      if (scale != 0.) {
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        for (k = l; k < n; k++) {
          u[i][k] /= scale;
          s += u[i][k] * u[i][k];
        }
        f = u[i][l];
        g = -sign(sqrt(s), f);
        h = f * g - s;
        u[i][l] = f - g;
        for (k = l; k < n; k++) rv1[k] = u[i][k] / h;
        for (j = l; j < m; j++) {
          for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];
          for (k = l; k < n; k++) u[j][k] += s * rv1[k];
        }
        for (k = l; k < n; k++) u[i][k] *= scale;
      }
    }
    anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));
  }

  for (i = n - 1; i >= 0; i--) {
    if (i < n - 1) {
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      if (g != 0.) {
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        for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;
        for (j = l; j < n; j++) {
          for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];
          for (k = l; k < n; k++) v[k][j] += s * v[k][i];
        }
      }
      for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
    }
    v[i][i] = 1.0;
    g = rv1[i];
    l = i;
  }
  for (i = AOMMIN(m, n) - 1; i >= 0; i--) {
    l = i + 1;
    g = w[i];
    for (j = l; j < n; j++) u[i][j] = 0.0;
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    if (g != 0.) {
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      g = 1.0 / g;
      for (j = l; j < n; j++) {
        for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];
        f = (s / u[i][i]) * g;
        for (k = i; k < m; k++) u[k][j] += f * u[k][i];
      }
      for (j = i; j < m; j++) u[j][i] *= g;
    } else {
      for (j = i; j < m; j++) u[j][i] = 0.0;
    }
    ++u[i][i];
  }
  for (k = n - 1; k >= 0; k--) {
    for (its = 0; its < max_its; its++) {
      flag = 1;
      for (l = k; l >= 0; l--) {
        nm = l - 1;
        if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {
          flag = 0;
          break;
        }
        if ((double)(fabs(w[nm]) + anorm) == anorm) break;
      }
      if (flag) {
        c = 0.0;
        s = 1.0;
        for (i = l; i <= k; i++) {
          f = s * rv1[i];
          rv1[i] = c * rv1[i];
          if ((double)(fabs(f) + anorm) == anorm) break;
          g = w[i];
          h = pythag(f, g);
          w[i] = h;
          h = 1.0 / h;
          c = g * h;
          s = -f * h;
          for (j = 0; j < m; j++) {
            y = u[j][nm];
            z = u[j][i];
            u[j][nm] = y * c + z * s;
            u[j][i] = z * c - y * s;
          }
        }
      }
      z = w[k];
      if (l == k) {
        if (z < 0.0) {
          w[k] = -z;
          for (j = 0; j < n; j++) v[j][k] = -v[j][k];
        }
        break;
      }
      if (its == max_its - 1) {
        return 1;
      }
      assert(k > 0);
      x = w[l];
      nm = k - 1;
      y = w[nm];
      g = rv1[nm];
      h = rv1[k];
      f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
      g = pythag(f, 1.0);
      f = ((x - z) * (x + z) + h * ((y / (f + sign(g, f))) - h)) / x;
      c = s = 1.0;
      for (j = l; j <= nm; j++) {
        i = j + 1;
        g = rv1[i];
        y = w[i];
        h = s * g;
        g = c * g;
        z = pythag(f, h);
        rv1[j] = z;
        c = f / z;
        s = h / z;
        f = x * c + g * s;
        g = g * c - x * s;
        h = y * s;
        y *= c;
        for (jj = 0; jj < n; jj++) {
          x = v[jj][j];
          z = v[jj][i];
          v[jj][j] = x * c + z * s;
          v[jj][i] = z * c - x * s;
        }
        z = pythag(f, h);
        w[j] = z;
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        if (z != 0.) {
827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208
          z = 1.0 / z;
          c = f * z;
          s = h * z;
        }
        f = c * g + s * y;
        x = c * y - s * g;
        for (jj = 0; jj < m; jj++) {
          y = u[jj][j];
          z = u[jj][i];
          u[jj][j] = y * c + z * s;
          u[jj][i] = z * c - y * s;
        }
      }
      rv1[l] = 0.0;
      rv1[k] = f;
      w[k] = x;
    }
  }
  aom_free(rv1);
  return 0;
}

static int SVD(double *U, double *W, double *V, double *matx, int M, int N) {
  // Assumes allocation for U is MxN
  double **nrU = (double **)aom_malloc((M) * sizeof(*nrU));
  double **nrV = (double **)aom_malloc((N) * sizeof(*nrV));
  int problem, i;

  problem = !(nrU && nrV);
  if (!problem) {
    for (i = 0; i < M; i++) {
      nrU[i] = &U[i * N];
    }
    for (i = 0; i < N; i++) {
      nrV[i] = &V[i * N];
    }
  } else {
    if (nrU) aom_free(nrU);
    if (nrV) aom_free(nrV);
    return 1;
  }

  /* copy from given matx into nrU */
  for (i = 0; i < M; i++) {
    memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));
  }

  /* HERE IT IS: do SVD */
  if (svdcmp(nrU, M, N, W, nrV)) {
    aom_free(nrU);
    aom_free(nrV);
    return 1;
  }

  /* aom_free Numerical Recipes arrays */
  aom_free(nrU);
  aom_free(nrV);

  return 0;
}

int pseudo_inverse(double *inv, double *matx, const int M, const int N) {
  double ans;
  int i, j, k;
  double *const U = (double *)aom_malloc(M * N * sizeof(*matx));
  double *const W = (double *)aom_malloc(N * sizeof(*matx));
  double *const V = (double *)aom_malloc(N * N * sizeof(*matx));

  if (!(U && W && V)) {
    return 1;
  }
  if (SVD(U, W, V, matx, M, N)) {
    return 1;
  }
  for (i = 0; i < N; i++) {
    if (fabs(W[i]) < TINY_NEAR_ZERO) {
      return 1;
    }
  }

  for (i = 0; i < N; i++) {
    for (j = 0; j < M; j++) {
      ans = 0;
      for (k = 0; k < N; k++) {
        ans += V[k + N * i] * U[k + N * j] / W[k];
      }
      inv[j + M * i] = ans;
    }
  }
  aom_free(U);
  aom_free(W);
  aom_free(V);
  return 0;
}

static void normalize_homography(double *pts, int n, double *T) {
  // Assume the points are 2d coordinates with scale = 1
  double *p = pts;
  double mean[2] = { 0, 0 };
  double msqe = 0;
  double scale;
  int i;
  for (i = 0; i < n; ++i, p += 2) {
    mean[0] += p[0];
    mean[1] += p[1];
  }
  mean[0] /= n;
  mean[1] /= n;
  for (p = pts, i = 0; i < n; ++i, p += 2) {
    p[0] -= mean[0];
    p[1] -= mean[1];
    msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
  }
  msqe /= n;
  scale = sqrt(2) / msqe;
  T[0] = scale;
  T[1] = 0;
  T[2] = -scale * mean[0];
  T[3] = 0;
  T[4] = scale;
  T[5] = -scale * mean[1];
  T[6] = 0;
  T[7] = 0;
  T[8] = 1;
  for (p = pts, i = 0; i < n; ++i, p += 2) {
    p[0] *= scale;
    p[1] *= scale;
  }
}

static void invnormalize_mat(double *T, double *iT) {
  double is = 1.0 / T[0];
  double m0 = -T[2] * is;
  double m1 = -T[5] * is;
  iT[0] = is;
  iT[1] = 0;
  iT[2] = m0;
  iT[3] = 0;
  iT[4] = is;
  iT[5] = m1;
  iT[6] = 0;
  iT[7] = 0;
  iT[8] = 1;
}

static void denormalize_homography(