warped_motion.c

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

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

#include "av1/common/warped_motion.h"

/* clang-format off */
static const int error_measure_lut[512] = {
  // power 0.6
  255, 254, 254, 253, 253, 252, 251, 251,
  250, 250, 249, 248, 248, 247, 247, 246,
  245, 245, 244, 243, 243, 242, 242, 241,
  240, 240, 239, 238, 238, 237, 237, 236,
  235, 235, 234, 233, 233, 232, 231, 231,
  230, 230, 229, 228, 228, 227, 226, 226,
  225, 224, 224, 223, 222, 222, 221, 220,
  220, 219, 218, 218, 217, 216, 216, 215,
  214, 214, 213, 212, 212, 211, 210, 210,
  209, 208, 208, 207, 206, 206, 205, 204,
  203, 203, 202, 201, 201, 200, 199, 199,
  198, 197, 196, 196, 195, 194, 194, 193,
  192, 191, 191, 190, 189, 188, 188, 187,
  186, 185, 185, 184, 183, 182, 182, 181,
  180, 179, 179, 178, 177, 176, 176, 175,
  174, 173, 173, 172, 171, 170, 169, 169,
  168, 167, 166, 165, 165, 164, 163, 162,
  161, 161, 160, 159, 158, 157, 156, 156,
  155, 154, 153, 152, 151, 151, 150, 149,
  148, 147, 146, 145, 145, 144, 143, 142,
  141, 140, 139, 138, 137, 137, 136, 135,
  134, 133, 132, 131, 130, 129, 128, 127,
  126, 125, 124, 123, 122, 121, 120, 119,
  118, 117, 116, 115, 114, 113, 112, 111,
  110, 109, 108, 107, 106, 105, 104, 103,
  102, 100,  99,  98,  97,  96,  95,  94,
  92, 91, 90, 89, 88, 86, 85, 84,
  83, 81, 80, 79, 77, 76, 75, 73,
  72, 71, 69, 68, 66, 65, 63, 62,
  60, 59, 57, 55, 54, 52, 50, 48,
  47, 45, 43, 41, 39, 37, 34, 32,
  29, 27, 24, 21, 18, 14,  9,  0,
  9, 14, 18, 21, 24, 27, 29, 32,
  34, 37, 39, 41, 43, 45, 47, 48,
  50, 52, 54, 55, 57, 59, 60, 62,
  63, 65, 66, 68, 69, 71, 72, 73,
  75, 76, 77, 79, 80, 81, 83, 84,
  85, 86, 88, 89, 90, 91, 92, 94,
  95,  96,  97,  98,  99, 100, 102, 103,
  104, 105, 106, 107, 108, 109, 110, 111,
  112, 113, 114, 115, 116, 117, 118, 119,
  120, 121, 122, 123, 124, 125, 126, 127,
  128, 129, 130, 131, 132, 133, 134, 135,
  136, 137, 137, 138, 139, 140, 141, 142,
  143, 144, 145, 145, 146, 147, 148, 149,
  150, 151, 151, 152, 153, 154, 155, 156,
  156, 157, 158, 159, 160, 161, 161, 162,
  163, 164, 165, 165, 166, 167, 168, 169,
  169, 170, 171, 172, 173, 173, 174, 175,
  176, 176, 177, 178, 179, 179, 180, 181,
  182, 182, 183, 184, 185, 185, 186, 187,
  188, 188, 189, 190, 191, 191, 192, 193,
  194, 194, 195, 196, 196, 197, 198, 199,
  199, 200, 201, 201, 202, 203, 203, 204,
  205, 206, 206, 207, 208, 208, 209, 210,
  210, 211, 212, 212, 213, 214, 214, 215,
  216, 216, 217, 218, 218, 219, 220, 220,
  221, 222, 222, 223, 224, 224, 225, 226,
  226, 227, 228, 228, 229, 230, 230, 231,
  231, 232, 233, 233, 234, 235, 235, 236,
  237, 237, 238, 238, 239, 240, 240, 241,
  242, 242, 243, 243, 244, 245, 245, 246,
  247, 247, 248, 248, 249, 250, 250, 251,
  251, 252, 253, 253, 254, 254, 255, 255,
};
/* clang-format on */

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

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

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

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

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

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

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

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

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

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

static INLINE void get_subcolumn(int taps, 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 * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t bi_cubic_filter(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 * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

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

static uint8_t warp_interpolate(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 * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t v;

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

#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 * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint16_t)clip_pixel_highbd(val, bd);
}

static uint16_t highbd_bi_cubic_filter(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 * (1 << WARPEDPIXEL_PREC_BITS)));
  }
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint16_t)clip_pixel_highbd(val, bd);
}

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

static uint16_t highbd_warp_interpolate(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 * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
  int32_t v;

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

static INLINE int highbd_error_measure(int err, int bd) {
  const int b = bd - 8;
  const int bmask = (1 << b) - 1;
  const int v = (1 << b);
  int e1, e2;
  err = abs(err);
  e1 = err >> b;
  e2 = err & bmask;
  return error_measure_lut[255 + e1] * (v - e2) +
         error_measure_lut[256 + e1] * e2;
}

static 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;
  ProjectPointsFunc 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(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 + i * stride];
      gm_sumerr += highbd_error_measure(gm_err, bd);
      no_gm_sumerr += highbd_error_measure(no_gm_err, bd);
    }
  }
  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 ref_frm) {
  int i, j;
  ProjectPointsFunc 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(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      if (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);
    }
  }
}
#endif  // CONFIG_AOM_HIGHBITDEPTH

static INLINE int error_measure(int err) {
  return error_measure_lut[255 + err];
}

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;
  ProjectPointsFunc 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(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 + i * stride];
      gm_sumerr += error_measure(gm_err);
      no_gm_sumerr += error_measure(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 ref_frm) {
  int i, j;
  ProjectPointsFunc 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(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      if (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);
    }
  }
}

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);
#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, int ref_frm) {
#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, ref_frm);
  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, ref_frm);
}

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[6] =
          (int32_t)lrint(model[6] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
      wm->wmmat[7] =
          (int32_t)lrint(model[7] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
    /* fallthrough intended */
    case AFFINE:
      wm->wmmat[4] = (int32_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[5] = (int32_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS));
    /* fallthrough intended */
    case ROTZOOM:
      wm->wmmat[2] = (int32_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[3] = (int32_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS));
    /* fallthrough intended */
    case TRANSLATION:
      wm->wmmat[0] = (int32_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[1] = (int32_t)lrint(model[1] * (1 << WARPEDMODEL_PREC_BITS));
      break;
    default: assert(0 && "Invalid TransformationType");
  }
}

///////////////////////////////////////////////////////////////////////////////
// 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]);
      if (scale != 0.) {
        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]);
      if (scale != 0.) {
        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) {
      if (g != 0.) {
        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;
    if (g != 0.) {
      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) {
        aom_free(rv1);
        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;
        if (z != 0.) {
          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)) {
    aom_free(U);
    aom_free(W);
    aom_free(V);
    return 1;
  }
  for (i = 0; i < N; i++) {
    if (fabs(W[i]) < TINY_NEAR_ZERO) {
      aom_free(U);
      aom_free(W);
      aom_free(V);