warped_motion.c

/*
 *  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>

#include "av1/common/warped_motion.h"

static ProjectPointsType get_project_points_type(TransformationType type) {
  switch (type) {
    case HOMOGRAPHY: return projectPointsHomography;
    case AFFINE: return projectPointsAffine;
    case ROTZOOM: return projectPointsRotZoom;
    case TRANSLATION: return projectPointsTranslation;
    default: assert(0); return NULL;
  }
}

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

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

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

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

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

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

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

static const int16_t filter_4tap[WARPEDPIXEL_PREC_SHIFTS][4] = {
  { 0, 128, 0, 0 },     { -1, 127, 2, 0 },    { -2, 127, 4, -1 },
  { -3, 126, 6, -1 },   { -3, 125, 8, -2 },   { -4, 124, 11, -3 },
  { -5, 123, 13, -3 },  { -5, 121, 15, -3 },  { -6, 120, 18, -4 },
  { -7, 119, 20, -4 },  { -7, 118, 22, -5 },  { -8, 116, 25, -5 },
  { -8, 115, 27, -6 },  { -9, 113, 30, -6 },  { -9, 112, 32, -7 },
  { -9, 110, 34, -7 },  { -10, 108, 37, -7 }, { -10, 107, 39, -8 },
  { -10, 105, 41, -8 }, { -11, 103, 44, -8 }, { -11, 101, 47, -9 },
  { -11, 99, 49, -9 },  { -11, 97, 51, -9 },  { -11, 95, 54, -10 },
  { -11, 93, 56, -10 }, { -12, 91, 59, -10 }, { -12, 89, 61, -10 },
  { -12, 87, 64, -11 }, { -12, 85, 66, -11 }, { -12, 82, 69, -11 },
  { -12, 80, 71, -11 }, { -12, 78, 73, -11 }, { -11, 75, 75, -11 },
  { -11, 73, 78, -12 }, { -11, 71, 80, -12 }, { -11, 69, 82, -12 },
  { -11, 66, 85, -12 }, { -11, 64, 87, -12 }, { -10, 61, 89, -12 },
  { -10, 59, 91, -12 }, { -10, 56, 93, -11 }, { -10, 54, 95, -11 },
  { -9, 51, 97, -11 },  { -9, 49, 99, -11 },  { -9, 47, 101, -11 },
  { -8, 44, 103, -11 }, { -8, 41, 105, -10 }, { -8, 39, 107, -10 },
  { -7, 37, 108, -10 }, { -7, 34, 110, -9 },  { -7, 32, 112, -9 },
  { -6, 30, 113, -9 },  { -6, 27, 115, -8 },  { -5, 25, 116, -8 },
  { -5, 22, 118, -7 },  { -4, 20, 119, -7 },  { -4, 18, 120, -6 },
  { -3, 15, 121, -5 },  { -3, 13, 123, -5 },  { -3, 11, 124, -4 },
  { -2, 8, 125, -3 },   { -1, 6, 126, -3 },   { -1, 4, 127, -2 },
  { 0, 2, 127, -1 },
};

static const int16_t
    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 },
    };

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

/*
static int32_t do_linear_filter(int32_t *p, int x) {
  int32_t sum = 0;
  sum = p[0] * (WARPEDPIXEL_PREC_SHIFTS - x) + p[1] * x;
  sum <<= (WARPEDPIXEL_FILTER_BITS - WARPEDPIXEL_PREC_BITS);
  return sum;
}

static int32_t do_4tap_filter(int32_t *p, int x) {
  int i;
  int32_t sum = 0;
  for (i = 0; i < 4; ++i) {
    sum += p[i - 1] * filter_4tap[x][i];
  }
  return sum;
}
*/

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

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

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

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

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

#if CONFIG_AOM_HIGHBITDEPTH
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];
  }
}

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

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

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

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

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

static 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;
  ProjectPointsType projectpoints = get_project_points_type(wm->wmtype);
  uint16_t *dst = CONVERT_TO_SHORTPTR(dst8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
  int gm_err = 0, no_gm_err = 0;
  int64_t gm_sumerr = 0, no_gm_sumerr = 0;
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      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];
      gm_sumerr += (int64_t)gm_err * gm_err;
      no_gm_sumerr += (int64_t)no_gm_err * no_gm_err;
    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

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,
                              int bd) {
  int i, j;
  ProjectPointsType projectpoints = get_project_points_type(wm->wmtype);
  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
  if (projectpoints == NULL) return;
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      pred[(j - p_col) + (i - p_row) * p_stride] = highbd_warp_interpolate(
          ref, out[0], out[1], width, height, stride, bd);
    }
  }
}
#endif  // CONFIG_AOM_HIGHBITDEPTH

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;
  ProjectPointsType projectpoints = get_project_points_type(wm->wmtype);
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      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,
                       int y_scale) {
  int i, j;
  ProjectPointsType projectpoints = get_project_points_type(wm->wmtype);
  if (projectpoints == NULL) return;
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
      projectpoints((int16_t *)wm->wmmat, in, out, 1, 2, 2, subsampling_x,
                    subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      pred[(j - p_col) + (i - p_row) * p_stride] =
          warp_interpolate(ref, out[0], out[1], width, height, stride);
    }
  }
}

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
  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);
  else
#endif  // CONFIG_AOM_HIGHBITDEPTH
    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);
}

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,
                    int subsampling_y, int x_scale, int y_scale) {
#if CONFIG_AOM_HIGHBITDEPTH
  if (use_hbd)
    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
                      x_scale, y_scale, bd);
  else
#endif  // CONFIG_AOM_HIGHBITDEPTH
    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, x_scale,
               y_scale);
}

void av1_integerize_model(const double *model, TransformationType wmtype,
                          WarpedMotionParams *wm) {
  wm->wmtype = wmtype;
  switch (wmtype) {
    case HOMOGRAPHY:
      assert(fabs(model[8] - 1.0) < 1e-12);
      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));
    /* fallthrough intended */
    case AFFINE:
      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));
    /* fallthrough intended */
    case ROTZOOM:
      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));
    /* fallthrough intended */
    case TRANSLATION:
      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));
      break;
    default: assert(0 && "Invalid TransformationType");
  }
}