warped_motion.c 55.3 KB
Newer Older
1
/*
2
 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
3
 *
4
5
6
7
8
9
 * 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.
10
11
12
13
14
15
16
17
 */

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

18
#include "./av1_rtcd.h"
19
#include "av1/common/warped_motion.h"
20
#include "av1/common/scale.h"
21

22
23
#define WARP_ERROR_BLOCK 32

24
25
/* clang-format off */
static const int error_measure_lut[512] = {
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
  // pow 0.7
  16384, 16339, 16294, 16249, 16204, 16158, 16113, 16068,
  16022, 15977, 15932, 15886, 15840, 15795, 15749, 15703,
  15657, 15612, 15566, 15520, 15474, 15427, 15381, 15335,
  15289, 15242, 15196, 15149, 15103, 15056, 15010, 14963,
  14916, 14869, 14822, 14775, 14728, 14681, 14634, 14587,
  14539, 14492, 14445, 14397, 14350, 14302, 14254, 14206,
  14159, 14111, 14063, 14015, 13967, 13918, 13870, 13822,
  13773, 13725, 13676, 13628, 13579, 13530, 13481, 13432,
  13383, 13334, 13285, 13236, 13187, 13137, 13088, 13038,
  12988, 12939, 12889, 12839, 12789, 12739, 12689, 12639,
  12588, 12538, 12487, 12437, 12386, 12335, 12285, 12234,
  12183, 12132, 12080, 12029, 11978, 11926, 11875, 11823,
  11771, 11719, 11667, 11615, 11563, 11511, 11458, 11406,
  11353, 11301, 11248, 11195, 11142, 11089, 11036, 10982,
  10929, 10875, 10822, 10768, 10714, 10660, 10606, 10552,
  10497, 10443, 10388, 10333, 10279, 10224, 10168, 10113,
  10058, 10002,  9947,  9891,  9835,  9779,  9723,  9666,
  9610, 9553, 9497, 9440, 9383, 9326, 9268, 9211,
  9153, 9095, 9037, 8979, 8921, 8862, 8804, 8745,
  8686, 8627, 8568, 8508, 8449, 8389, 8329, 8269,
  8208, 8148, 8087, 8026, 7965, 7903, 7842, 7780,
  7718, 7656, 7593, 7531, 7468, 7405, 7341, 7278,
  7214, 7150, 7086, 7021, 6956, 6891, 6826, 6760,
  6695, 6628, 6562, 6495, 6428, 6361, 6293, 6225,
  6157, 6089, 6020, 5950, 5881, 5811, 5741, 5670,
  5599, 5527, 5456, 5383, 5311, 5237, 5164, 5090,
  5015, 4941, 4865, 4789, 4713, 4636, 4558, 4480,
  4401, 4322, 4242, 4162, 4080, 3998, 3916, 3832,
  3748, 3663, 3577, 3490, 3402, 3314, 3224, 3133,
  3041, 2948, 2854, 2758, 2661, 2562, 2461, 2359,
  2255, 2148, 2040, 1929, 1815, 1698, 1577, 1452,
  1323, 1187, 1045,  894,  731,  550,  339,    0,
  339,  550,  731,  894, 1045, 1187, 1323, 1452,
  1577, 1698, 1815, 1929, 2040, 2148, 2255, 2359,
  2461, 2562, 2661, 2758, 2854, 2948, 3041, 3133,
  3224, 3314, 3402, 3490, 3577, 3663, 3748, 3832,
  3916, 3998, 4080, 4162, 4242, 4322, 4401, 4480,
  4558, 4636, 4713, 4789, 4865, 4941, 5015, 5090,
  5164, 5237, 5311, 5383, 5456, 5527, 5599, 5670,
  5741, 5811, 5881, 5950, 6020, 6089, 6157, 6225,
  6293, 6361, 6428, 6495, 6562, 6628, 6695, 6760,
  6826, 6891, 6956, 7021, 7086, 7150, 7214, 7278,
  7341, 7405, 7468, 7531, 7593, 7656, 7718, 7780,
  7842, 7903, 7965, 8026, 8087, 8148, 8208, 8269,
  8329, 8389, 8449, 8508, 8568, 8627, 8686, 8745,
  8804, 8862, 8921, 8979, 9037, 9095, 9153, 9211,
  9268, 9326, 9383, 9440, 9497, 9553, 9610, 9666,
  9723,  9779,  9835,  9891,  9947, 10002, 10058, 10113,
  10168, 10224, 10279, 10333, 10388, 10443, 10497, 10552,
  10606, 10660, 10714, 10768, 10822, 10875, 10929, 10982,
  11036, 11089, 11142, 11195, 11248, 11301, 11353, 11406,
  11458, 11511, 11563, 11615, 11667, 11719, 11771, 11823,
  11875, 11926, 11978, 12029, 12080, 12132, 12183, 12234,
  12285, 12335, 12386, 12437, 12487, 12538, 12588, 12639,
  12689, 12739, 12789, 12839, 12889, 12939, 12988, 13038,
  13088, 13137, 13187, 13236, 13285, 13334, 13383, 13432,
  13481, 13530, 13579, 13628, 13676, 13725, 13773, 13822,
  13870, 13918, 13967, 14015, 14063, 14111, 14159, 14206,
  14254, 14302, 14350, 14397, 14445, 14492, 14539, 14587,
  14634, 14681, 14728, 14775, 14822, 14869, 14916, 14963,
  15010, 15056, 15103, 15149, 15196, 15242, 15289, 15335,
  15381, 15427, 15474, 15520, 15566, 15612, 15657, 15703,
  15749, 15795, 15840, 15886, 15932, 15977, 16022, 16068,
  16113, 16158, 16204, 16249, 16294, 16339, 16384, 16384,
91
92
};
/* clang-format on */
93

Yaowu Xu's avatar
Yaowu Xu committed
94
95
96
97
void project_points_affine(const int32_t *mat, int *points, int *proj,
                           const int n, const int stride_points,
                           const int stride_proj, const int subsampling_x,
                           const int subsampling_y) {
98
99
100
101
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
102
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
103
104
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
105
106
          WARPEDDIFF_PREC_BITS + 1);
    else
107
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
108
                                            WARPEDDIFF_PREC_BITS);
109
    if (subsampling_y)
110
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
111
          mat[4] * 2 * x + mat[5] * 2 * y + mat[1] +
Sarah Parker's avatar
Sarah Parker committed
112
              (mat[4] + mat[5] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
113
114
          WARPEDDIFF_PREC_BITS + 1);
    else
115
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[4] * x + mat[5] * y + mat[1],
116
                                            WARPEDDIFF_PREC_BITS);
117
118
119
120
121
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

122
123
124
125
126
127
// For warping, we really use a 6-tap filter, but we do blocks of 8 pixels
// at a time. The zoom/rotation/shear in the model are applied to the
// "fractional" position of each pixel, which therefore varies within
// [-1, 2) * WARPEDPIXEL_PREC_SHIFTS.
// We need an extra 2 taps to fit this in, for a total of 8 taps.
/* clang-format off */
128
const int16_t warped_filter[WARPEDPIXEL_PREC_SHIFTS * 3 + 1][8] = {
129
#if WARPEDPIXEL_PREC_BITS == 6
130
  // [-1, 0)
131
  { 0,   0, 127,   1,   0, 0, 0, 0 }, { 0, - 1, 127,   2,   0, 0, 0, 0 },
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
  { 1, - 3, 127,   4, - 1, 0, 0, 0 }, { 1, - 4, 126,   6, - 2, 1, 0, 0 },
  { 1, - 5, 126,   8, - 3, 1, 0, 0 }, { 1, - 6, 125,  11, - 4, 1, 0, 0 },
  { 1, - 7, 124,  13, - 4, 1, 0, 0 }, { 2, - 8, 123,  15, - 5, 1, 0, 0 },
  { 2, - 9, 122,  18, - 6, 1, 0, 0 }, { 2, -10, 121,  20, - 6, 1, 0, 0 },
  { 2, -11, 120,  22, - 7, 2, 0, 0 }, { 2, -12, 119,  25, - 8, 2, 0, 0 },
  { 3, -13, 117,  27, - 8, 2, 0, 0 }, { 3, -13, 116,  29, - 9, 2, 0, 0 },
  { 3, -14, 114,  32, -10, 3, 0, 0 }, { 3, -15, 113,  35, -10, 2, 0, 0 },
  { 3, -15, 111,  37, -11, 3, 0, 0 }, { 3, -16, 109,  40, -11, 3, 0, 0 },
  { 3, -16, 108,  42, -12, 3, 0, 0 }, { 4, -17, 106,  45, -13, 3, 0, 0 },
  { 4, -17, 104,  47, -13, 3, 0, 0 }, { 4, -17, 102,  50, -14, 3, 0, 0 },
  { 4, -17, 100,  52, -14, 3, 0, 0 }, { 4, -18,  98,  55, -15, 4, 0, 0 },
  { 4, -18,  96,  58, -15, 3, 0, 0 }, { 4, -18,  94,  60, -16, 4, 0, 0 },
  { 4, -18,  91,  63, -16, 4, 0, 0 }, { 4, -18,  89,  65, -16, 4, 0, 0 },
  { 4, -18,  87,  68, -17, 4, 0, 0 }, { 4, -18,  85,  70, -17, 4, 0, 0 },
  { 4, -18,  82,  73, -17, 4, 0, 0 }, { 4, -18,  80,  75, -17, 4, 0, 0 },
  { 4, -18,  78,  78, -18, 4, 0, 0 }, { 4, -17,  75,  80, -18, 4, 0, 0 },
  { 4, -17,  73,  82, -18, 4, 0, 0 }, { 4, -17,  70,  85, -18, 4, 0, 0 },
  { 4, -17,  68,  87, -18, 4, 0, 0 }, { 4, -16,  65,  89, -18, 4, 0, 0 },
  { 4, -16,  63,  91, -18, 4, 0, 0 }, { 4, -16,  60,  94, -18, 4, 0, 0 },
  { 3, -15,  58,  96, -18, 4, 0, 0 }, { 4, -15,  55,  98, -18, 4, 0, 0 },
  { 3, -14,  52, 100, -17, 4, 0, 0 }, { 3, -14,  50, 102, -17, 4, 0, 0 },
  { 3, -13,  47, 104, -17, 4, 0, 0 }, { 3, -13,  45, 106, -17, 4, 0, 0 },
  { 3, -12,  42, 108, -16, 3, 0, 0 }, { 3, -11,  40, 109, -16, 3, 0, 0 },
  { 3, -11,  37, 111, -15, 3, 0, 0 }, { 2, -10,  35, 113, -15, 3, 0, 0 },
  { 3, -10,  32, 114, -14, 3, 0, 0 }, { 2, - 9,  29, 116, -13, 3, 0, 0 },
  { 2, - 8,  27, 117, -13, 3, 0, 0 }, { 2, - 8,  25, 119, -12, 2, 0, 0 },
  { 2, - 7,  22, 120, -11, 2, 0, 0 }, { 1, - 6,  20, 121, -10, 2, 0, 0 },
  { 1, - 6,  18, 122, - 9, 2, 0, 0 }, { 1, - 5,  15, 123, - 8, 2, 0, 0 },
  { 1, - 4,  13, 124, - 7, 1, 0, 0 }, { 1, - 4,  11, 125, - 6, 1, 0, 0 },
  { 1, - 3,   8, 126, - 5, 1, 0, 0 }, { 1, - 2,   6, 126, - 4, 1, 0, 0 },
162
  { 0, - 1,   4, 127, - 3, 1, 0, 0 }, { 0,   0,   2, 127, - 1, 0, 0, 0 },
163
164

  // [0, 1)
165
  { 0,  0,   0, 127,   1,   0,  0,  0}, { 0,  0,  -1, 127,   2,   0,  0,  0},
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
  { 0,  1,  -3, 127,   4,  -2,  1,  0}, { 0,  1,  -5, 127,   6,  -2,  1,  0},
  { 0,  2,  -6, 126,   8,  -3,  1,  0}, {-1,  2,  -7, 126,  11,  -4,  2, -1},
  {-1,  3,  -8, 125,  13,  -5,  2, -1}, {-1,  3, -10, 124,  16,  -6,  3, -1},
  {-1,  4, -11, 123,  18,  -7,  3, -1}, {-1,  4, -12, 122,  20,  -7,  3, -1},
  {-1,  4, -13, 121,  23,  -8,  3, -1}, {-2,  5, -14, 120,  25,  -9,  4, -1},
  {-1,  5, -15, 119,  27, -10,  4, -1}, {-1,  5, -16, 118,  30, -11,  4, -1},
  {-2,  6, -17, 116,  33, -12,  5, -1}, {-2,  6, -17, 114,  35, -12,  5, -1},
  {-2,  6, -18, 113,  38, -13,  5, -1}, {-2,  7, -19, 111,  41, -14,  6, -2},
  {-2,  7, -19, 110,  43, -15,  6, -2}, {-2,  7, -20, 108,  46, -15,  6, -2},
  {-2,  7, -20, 106,  49, -16,  6, -2}, {-2,  7, -21, 104,  51, -16,  7, -2},
  {-2,  7, -21, 102,  54, -17,  7, -2}, {-2,  8, -21, 100,  56, -18,  7, -2},
  {-2,  8, -22,  98,  59, -18,  7, -2}, {-2,  8, -22,  96,  62, -19,  7, -2},
  {-2,  8, -22,  94,  64, -19,  7, -2}, {-2,  8, -22,  91,  67, -20,  8, -2},
  {-2,  8, -22,  89,  69, -20,  8, -2}, {-2,  8, -22,  87,  72, -21,  8, -2},
  {-2,  8, -21,  84,  74, -21,  8, -2}, {-2,  8, -22,  82,  77, -21,  8, -2},
  {-2,  8, -21,  79,  79, -21,  8, -2}, {-2,  8, -21,  77,  82, -22,  8, -2},
  {-2,  8, -21,  74,  84, -21,  8, -2}, {-2,  8, -21,  72,  87, -22,  8, -2},
  {-2,  8, -20,  69,  89, -22,  8, -2}, {-2,  8, -20,  67,  91, -22,  8, -2},
  {-2,  7, -19,  64,  94, -22,  8, -2}, {-2,  7, -19,  62,  96, -22,  8, -2},
  {-2,  7, -18,  59,  98, -22,  8, -2}, {-2,  7, -18,  56, 100, -21,  8, -2},
  {-2,  7, -17,  54, 102, -21,  7, -2}, {-2,  7, -16,  51, 104, -21,  7, -2},
  {-2,  6, -16,  49, 106, -20,  7, -2}, {-2,  6, -15,  46, 108, -20,  7, -2},
  {-2,  6, -15,  43, 110, -19,  7, -2}, {-2,  6, -14,  41, 111, -19,  7, -2},
  {-1,  5, -13,  38, 113, -18,  6, -2}, {-1,  5, -12,  35, 114, -17,  6, -2},
  {-1,  5, -12,  33, 116, -17,  6, -2}, {-1,  4, -11,  30, 118, -16,  5, -1},
  {-1,  4, -10,  27, 119, -15,  5, -1}, {-1,  4,  -9,  25, 120, -14,  5, -2},
  {-1,  3,  -8,  23, 121, -13,  4, -1}, {-1,  3,  -7,  20, 122, -12,  4, -1},
  {-1,  3,  -7,  18, 123, -11,  4, -1}, {-1,  3,  -6,  16, 124, -10,  3, -1},
  {-1,  2,  -5,  13, 125,  -8,  3, -1}, {-1,  2,  -4,  11, 126,  -7,  2, -1},
  { 0,  1,  -3,   8, 126,  -6,  2,  0}, { 0,  1,  -2,   6, 127,  -5,  1,  0},
196
  { 0,  1,  -2,   4, 127,  -3,  1,  0}, { 0,  0,   0,   2, 127,  -1,  0,  0},
197
198

  // [1, 2)
199
  { 0, 0, 0,   1, 127,   0,   0, 0 }, { 0, 0, 0, - 1, 127,   2,   0, 0 },
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
  { 0, 0, 1, - 3, 127,   4, - 1, 0 }, { 0, 0, 1, - 4, 126,   6, - 2, 1 },
  { 0, 0, 1, - 5, 126,   8, - 3, 1 }, { 0, 0, 1, - 6, 125,  11, - 4, 1 },
  { 0, 0, 1, - 7, 124,  13, - 4, 1 }, { 0, 0, 2, - 8, 123,  15, - 5, 1 },
  { 0, 0, 2, - 9, 122,  18, - 6, 1 }, { 0, 0, 2, -10, 121,  20, - 6, 1 },
  { 0, 0, 2, -11, 120,  22, - 7, 2 }, { 0, 0, 2, -12, 119,  25, - 8, 2 },
  { 0, 0, 3, -13, 117,  27, - 8, 2 }, { 0, 0, 3, -13, 116,  29, - 9, 2 },
  { 0, 0, 3, -14, 114,  32, -10, 3 }, { 0, 0, 3, -15, 113,  35, -10, 2 },
  { 0, 0, 3, -15, 111,  37, -11, 3 }, { 0, 0, 3, -16, 109,  40, -11, 3 },
  { 0, 0, 3, -16, 108,  42, -12, 3 }, { 0, 0, 4, -17, 106,  45, -13, 3 },
  { 0, 0, 4, -17, 104,  47, -13, 3 }, { 0, 0, 4, -17, 102,  50, -14, 3 },
  { 0, 0, 4, -17, 100,  52, -14, 3 }, { 0, 0, 4, -18,  98,  55, -15, 4 },
  { 0, 0, 4, -18,  96,  58, -15, 3 }, { 0, 0, 4, -18,  94,  60, -16, 4 },
  { 0, 0, 4, -18,  91,  63, -16, 4 }, { 0, 0, 4, -18,  89,  65, -16, 4 },
  { 0, 0, 4, -18,  87,  68, -17, 4 }, { 0, 0, 4, -18,  85,  70, -17, 4 },
  { 0, 0, 4, -18,  82,  73, -17, 4 }, { 0, 0, 4, -18,  80,  75, -17, 4 },
  { 0, 0, 4, -18,  78,  78, -18, 4 }, { 0, 0, 4, -17,  75,  80, -18, 4 },
  { 0, 0, 4, -17,  73,  82, -18, 4 }, { 0, 0, 4, -17,  70,  85, -18, 4 },
  { 0, 0, 4, -17,  68,  87, -18, 4 }, { 0, 0, 4, -16,  65,  89, -18, 4 },
  { 0, 0, 4, -16,  63,  91, -18, 4 }, { 0, 0, 4, -16,  60,  94, -18, 4 },
  { 0, 0, 3, -15,  58,  96, -18, 4 }, { 0, 0, 4, -15,  55,  98, -18, 4 },
  { 0, 0, 3, -14,  52, 100, -17, 4 }, { 0, 0, 3, -14,  50, 102, -17, 4 },
  { 0, 0, 3, -13,  47, 104, -17, 4 }, { 0, 0, 3, -13,  45, 106, -17, 4 },
  { 0, 0, 3, -12,  42, 108, -16, 3 }, { 0, 0, 3, -11,  40, 109, -16, 3 },
  { 0, 0, 3, -11,  37, 111, -15, 3 }, { 0, 0, 2, -10,  35, 113, -15, 3 },
  { 0, 0, 3, -10,  32, 114, -14, 3 }, { 0, 0, 2, - 9,  29, 116, -13, 3 },
  { 0, 0, 2, - 8,  27, 117, -13, 3 }, { 0, 0, 2, - 8,  25, 119, -12, 2 },
  { 0, 0, 2, - 7,  22, 120, -11, 2 }, { 0, 0, 1, - 6,  20, 121, -10, 2 },
  { 0, 0, 1, - 6,  18, 122, - 9, 2 }, { 0, 0, 1, - 5,  15, 123, - 8, 2 },
  { 0, 0, 1, - 4,  13, 124, - 7, 1 }, { 0, 0, 1, - 4,  11, 125, - 6, 1 },
  { 0, 0, 1, - 3,   8, 126, - 5, 1 }, { 0, 0, 1, - 2,   6, 126, - 4, 1 },
230
  { 0, 0, 0, - 1,   4, 127, - 3, 1 }, { 0, 0, 0,   0,   2, 127, - 1, 0 },
231
232
  // dummy (replicate row index 191)
  { 0, 0, 0,   0,   2, 127, - 1, 0 },
233

234
#elif WARPEDPIXEL_PREC_BITS == 5
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
  // [-1, 0)
  {0,   0, 127,   1,   0, 0, 0, 0}, {1,  -3, 127,   4,  -1, 0, 0, 0},
  {1,  -5, 126,   8,  -3, 1, 0, 0}, {1,  -7, 124,  13,  -4, 1, 0, 0},
  {2,  -9, 122,  18,  -6, 1, 0, 0}, {2, -11, 120,  22,  -7, 2, 0, 0},
  {3, -13, 117,  27,  -8, 2, 0, 0}, {3, -14, 114,  32, -10, 3, 0, 0},
  {3, -15, 111,  37, -11, 3, 0, 0}, {3, -16, 108,  42, -12, 3, 0, 0},
  {4, -17, 104,  47, -13, 3, 0, 0}, {4, -17, 100,  52, -14, 3, 0, 0},
  {4, -18,  96,  58, -15, 3, 0, 0}, {4, -18,  91,  63, -16, 4, 0, 0},
  {4, -18,  87,  68, -17, 4, 0, 0}, {4, -18,  82,  73, -17, 4, 0, 0},
  {4, -18,  78,  78, -18, 4, 0, 0}, {4, -17,  73,  82, -18, 4, 0, 0},
  {4, -17,  68,  87, -18, 4, 0, 0}, {4, -16,  63,  91, -18, 4, 0, 0},
  {3, -15,  58,  96, -18, 4, 0, 0}, {3, -14,  52, 100, -17, 4, 0, 0},
  {3, -13,  47, 104, -17, 4, 0, 0}, {3, -12,  42, 108, -16, 3, 0, 0},
  {3, -11,  37, 111, -15, 3, 0, 0}, {3, -10,  32, 114, -14, 3, 0, 0},
  {2,  -8,  27, 117, -13, 3, 0, 0}, {2,  -7,  22, 120, -11, 2, 0, 0},
  {1,  -6,  18, 122,  -9, 2, 0, 0}, {1,  -4,  13, 124,  -7, 1, 0, 0},
  {1,  -3,   8, 126,  -5, 1, 0, 0}, {0,  -1,   4, 127,  -3, 1, 0, 0},
  // [0, 1)
  { 0,  0,   0, 127,   1,   0,   0,  0}, { 0,  1,  -3, 127,   4,  -2,   1,  0},
  { 0,  2,  -6, 126,   8,  -3,   1,  0}, {-1,  3,  -8, 125,  13,  -5,   2, -1},
  {-1,  4, -11, 123,  18,  -7,   3, -1}, {-1,  4, -13, 121,  23,  -8,   3, -1},
  {-1,  5, -15, 119,  27, -10,   4, -1}, {-2,  6, -17, 116,  33, -12,   5, -1},
  {-2,  6, -18, 113,  38, -13,   5, -1}, {-2,  7, -19, 110,  43, -15,   6, -2},
  {-2,  7, -20, 106,  49, -16,   6, -2}, {-2,  7, -21, 102,  54, -17,   7, -2},
  {-2,  8, -22,  98,  59, -18,   7, -2}, {-2,  8, -22,  94,  64, -19,   7, -2},
  {-2,  8, -22,  89,  69, -20,   8, -2}, {-2,  8, -21,  84,  74, -21,   8, -2},
  {-2,  8, -21,  79,  79, -21,   8, -2}, {-2,  8, -21,  74,  84, -21,   8, -2},
  {-2,  8, -20,  69,  89, -22,   8, -2}, {-2,  7, -19,  64,  94, -22,   8, -2},
  {-2,  7, -18,  59,  98, -22,   8, -2}, {-2,  7, -17,  54, 102, -21,   7, -2},
  {-2,  6, -16,  49, 106, -20,   7, -2}, {-2,  6, -15,  43, 110, -19,   7, -2},
  {-1,  5, -13,  38, 113, -18,   6, -2}, {-1,  5, -12,  33, 116, -17,   6, -2},
  {-1,  4, -10,  27, 119, -15,   5, -1}, {-1,  3,  -8,  23, 121, -13,   4, -1},
  {-1,  3,  -7,  18, 123, -11,   4, -1}, {-1,  2,  -5,  13, 125,  -8,   3, -1},
  { 0,  1,  -3,   8, 126,  -6,   2,  0}, { 0,  1,  -2,   4, 127,  -3,   1,  0},
  // [1, 2)
  {0, 0, 0,   1, 127,   0,   0, 0}, {0, 0, 1,  -3, 127,   4,  -1, 0},
  {0, 0, 1,  -5, 126,   8,  -3, 1}, {0, 0, 1,  -7, 124,  13,  -4, 1},
  {0, 0, 2,  -9, 122,  18,  -6, 1}, {0, 0, 2, -11, 120,  22,  -7, 2},
  {0, 0, 3, -13, 117,  27,  -8, 2}, {0, 0, 3, -14, 114,  32, -10, 3},
  {0, 0, 3, -15, 111,  37, -11, 3}, {0, 0, 3, -16, 108,  42, -12, 3},
  {0, 0, 4, -17, 104,  47, -13, 3}, {0, 0, 4, -17, 100,  52, -14, 3},
  {0, 0, 4, -18,  96,  58, -15, 3}, {0, 0, 4, -18,  91,  63, -16, 4},
  {0, 0, 4, -18,  87,  68, -17, 4}, {0, 0, 4, -18,  82,  73, -17, 4},
  {0, 0, 4, -18,  78,  78, -18, 4}, {0, 0, 4, -17,  73,  82, -18, 4},
  {0, 0, 4, -17,  68,  87, -18, 4}, {0, 0, 4, -16,  63,  91, -18, 4},
  {0, 0, 3, -15,  58,  96, -18, 4}, {0, 0, 3, -14,  52, 100, -17, 4},
  {0, 0, 3, -13,  47, 104, -17, 4}, {0, 0, 3, -12,  42, 108, -16, 3},
  {0, 0, 3, -11,  37, 111, -15, 3}, {0, 0, 3, -10,  32, 114, -14, 3},
  {0, 0, 2,  -8,  27, 117, -13, 3}, {0, 0, 2,  -7,  22, 120, -11, 2},
  {0, 0, 1,  -6,  18, 122,  -9, 2}, {0, 0, 1,  -4,  13, 124,  -7, 1},
  {0, 0, 1,  -3,   8, 126,  -5, 1}, {0, 0, 0,  -1,   4, 127,  -3, 1},
286
287
  // dummy (replicate row index 95)
  {0, 0, 0,  -1,   4, 127,  -3, 1},
288
289

#endif  // WARPEDPIXEL_PREC_BITS == 6
290
};
291

292
293
/* clang-format on */

294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
#define DIV_LUT_PREC_BITS 14
#define DIV_LUT_BITS 8
#define DIV_LUT_NUM (1 << DIV_LUT_BITS)

static const uint16_t div_lut[DIV_LUT_NUM + 1] = {
  16384, 16320, 16257, 16194, 16132, 16070, 16009, 15948, 15888, 15828, 15768,
  15709, 15650, 15592, 15534, 15477, 15420, 15364, 15308, 15252, 15197, 15142,
  15087, 15033, 14980, 14926, 14873, 14821, 14769, 14717, 14665, 14614, 14564,
  14513, 14463, 14413, 14364, 14315, 14266, 14218, 14170, 14122, 14075, 14028,
  13981, 13935, 13888, 13843, 13797, 13752, 13707, 13662, 13618, 13574, 13530,
  13487, 13443, 13400, 13358, 13315, 13273, 13231, 13190, 13148, 13107, 13066,
  13026, 12985, 12945, 12906, 12866, 12827, 12788, 12749, 12710, 12672, 12633,
  12596, 12558, 12520, 12483, 12446, 12409, 12373, 12336, 12300, 12264, 12228,
  12193, 12157, 12122, 12087, 12053, 12018, 11984, 11950, 11916, 11882, 11848,
  11815, 11782, 11749, 11716, 11683, 11651, 11619, 11586, 11555, 11523, 11491,
  11460, 11429, 11398, 11367, 11336, 11305, 11275, 11245, 11215, 11185, 11155,
  11125, 11096, 11067, 11038, 11009, 10980, 10951, 10923, 10894, 10866, 10838,
  10810, 10782, 10755, 10727, 10700, 10673, 10645, 10618, 10592, 10565, 10538,
  10512, 10486, 10460, 10434, 10408, 10382, 10356, 10331, 10305, 10280, 10255,
  10230, 10205, 10180, 10156, 10131, 10107, 10082, 10058, 10034, 10010, 9986,
  9963,  9939,  9916,  9892,  9869,  9846,  9823,  9800,  9777,  9754,  9732,
  9709,  9687,  9664,  9642,  9620,  9598,  9576,  9554,  9533,  9511,  9489,
  9468,  9447,  9425,  9404,  9383,  9362,  9341,  9321,  9300,  9279,  9259,
  9239,  9218,  9198,  9178,  9158,  9138,  9118,  9098,  9079,  9059,  9039,
  9020,  9001,  8981,  8962,  8943,  8924,  8905,  8886,  8867,  8849,  8830,
  8812,  8793,  8775,  8756,  8738,  8720,  8702,  8684,  8666,  8648,  8630,
  8613,  8595,  8577,  8560,  8542,  8525,  8508,  8490,  8473,  8456,  8439,
  8422,  8405,  8389,  8372,  8355,  8339,  8322,  8306,  8289,  8273,  8257,
  8240,  8224,  8208,  8192,
};

#if CONFIG_WARPED_MOTION
// Decomposes a divisor D such that 1/D = y/2^shift, where y is returned
// at precision of DIV_LUT_PREC_BITS along with the shift.
static int16_t resolve_divisor_64(uint64_t D, int16_t *shift) {
  int64_t e, f;
330
331
  *shift = (int16_t)((D >> 32) ? get_msb((unsigned int)(D >> 32)) + 32
                               : get_msb((unsigned int)D));
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
  // e is obtained from D after resetting the most significant 1 bit.
  e = D - ((uint64_t)1 << *shift);
  // Get the most significant DIV_LUT_BITS (8) bits of e into f
  if (*shift > DIV_LUT_BITS)
    f = ROUND_POWER_OF_TWO_64(e, *shift - DIV_LUT_BITS);
  else
    f = e << (DIV_LUT_BITS - *shift);
  assert(f <= DIV_LUT_NUM);
  *shift += DIV_LUT_PREC_BITS;
  // Use f as lookup into the precomputed table of multipliers
  return div_lut[f];
}
#endif  // CONFIG_WARPED_MOTION

static int16_t resolve_divisor_32(uint32_t D, int16_t *shift) {
  int32_t e, f;
  *shift = get_msb(D);
  // e is obtained from D after resetting the most significant 1 bit.
  e = D - ((uint32_t)1 << *shift);
  // Get the most significant DIV_LUT_BITS (8) bits of e into f
  if (*shift > DIV_LUT_BITS)
    f = ROUND_POWER_OF_TWO(e, *shift - DIV_LUT_BITS);
  else
    f = e << (DIV_LUT_BITS - *shift);
  assert(f <= DIV_LUT_NUM);
  *shift += DIV_LUT_PREC_BITS;
  // Use f as lookup into the precomputed table of multipliers
  return div_lut[f];
}

Yaowu Xu's avatar
Yaowu Xu committed
362
static int is_affine_valid(const WarpedMotionParams *const wm) {
363
364
365
366
  const int32_t *mat = wm->wmmat;
  return (mat[2] > 0);
}

367
368
static int is_affine_shear_allowed(int16_t alpha, int16_t beta, int16_t gamma,
                                   int16_t delta) {
369
370
  if ((4 * abs(alpha) + 7 * abs(beta) >= (1 << WARPEDMODEL_PREC_BITS)) ||
      (4 * abs(gamma) + 4 * abs(delta) >= (1 << WARPEDMODEL_PREC_BITS)))
371
372
373
374
375
376
    return 0;
  else
    return 1;
}

// Returns 1 on success or 0 on an invalid affine set
377
int get_shear_params(WarpedMotionParams *wm) {
378
379
  const int32_t *mat = wm->wmmat;
  if (!is_affine_valid(wm)) return 0;
380
381
382
  wm->alpha =
      clamp(mat[2] - (1 << WARPEDMODEL_PREC_BITS), INT16_MIN, INT16_MAX);
  wm->beta = clamp(mat[3], INT16_MIN, INT16_MAX);
383
384
385
  int16_t shift;
  int16_t y = resolve_divisor_32(abs(mat[2]), &shift) * (mat[2] < 0 ? -1 : 1);
  int64_t v;
Yaowu Xu's avatar
Yaowu Xu committed
386
  v = ((int64_t)mat[4] * (1 << WARPEDMODEL_PREC_BITS)) * y;
387
  wm->gamma =
388
      clamp((int)ROUND_POWER_OF_TWO_SIGNED_64(v, shift), INT16_MIN, INT16_MAX);
389
  v = ((int64_t)mat[3] * mat[4]) * y;
390
  wm->delta = clamp(mat[5] - (int)ROUND_POWER_OF_TWO_SIGNED_64(v, shift) -
391
392
                        (1 << WARPEDMODEL_PREC_BITS),
                    INT16_MIN, INT16_MAX);
393
394
  if (!is_affine_shear_allowed(wm->alpha, wm->beta, wm->gamma, wm->delta))
    return 0;
395

396
397
398
399
400
401
402
403
  wm->alpha = ROUND_POWER_OF_TWO_SIGNED(wm->alpha, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);
  wm->beta = ROUND_POWER_OF_TWO_SIGNED(wm->beta, WARP_PARAM_REDUCE_BITS) *
             (1 << WARP_PARAM_REDUCE_BITS);
  wm->gamma = ROUND_POWER_OF_TWO_SIGNED(wm->gamma, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);
  wm->delta = ROUND_POWER_OF_TWO_SIGNED(wm->delta, WARP_PARAM_REDUCE_BITS) *
              (1 << WARP_PARAM_REDUCE_BITS);
404
405
406
  return 1;
}

407
#if CONFIG_HIGHBITDEPTH
408
409
410
static INLINE int highbd_error_measure(int err, int bd) {
  const int b = bd - 8;
  const int bmask = (1 << b) - 1;
411
  const int v = (1 << b);
412
413
414
415
416
417
418
419
  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;
}

David Barker's avatar
David Barker committed
420
421
422
/* Note: For an explanation of the warp algorithm, and some notes on bit widths
    for hardware implementations, see the comments above av1_warp_affine_c
*/
423
424
425
void av1_highbd_warp_affine_c(const int32_t *mat, const uint16_t *ref,
                              int width, int height, int stride, uint16_t *pred,
                              int p_col, int p_row, int p_width, int p_height,
clang-format's avatar
clang-format committed
426
                              int p_stride, int subsampling_x,
427
428
429
                              int subsampling_y, int bd,
                              ConvolveParams *conv_params, int16_t alpha,
                              int16_t beta, int16_t gamma, int16_t delta) {
David Barker's avatar
David Barker committed
430
  int32_t tmp[15 * 8];
431
  int i, j, k, l, m;
432
#if CONFIG_CONVOLVE_ROUND
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
  const int use_conv_params = conv_params->round == CONVOLVE_OPT_NO_ROUND;
  const int reduce_bits_horiz =
      use_conv_params ? conv_params->round_0 : HORSHEAR_REDUCE_PREC_BITS;
  const int max_bits_horiz =
      use_conv_params
          ? bd + FILTER_BITS + 1 - conv_params->round_0
          : bd + WARPEDPIXEL_FILTER_BITS + 1 - HORSHEAR_REDUCE_PREC_BITS;
  const int offset_bits_horiz =
      use_conv_params ? bd + FILTER_BITS - 1 : bd + WARPEDPIXEL_FILTER_BITS - 1;
  const int offset_bits_vert =
      use_conv_params
          ? bd + 2 * FILTER_BITS - conv_params->round_0
          : bd + 2 * WARPEDPIXEL_FILTER_BITS - HORSHEAR_REDUCE_PREC_BITS;
  if (use_conv_params) {
    conv_params->do_post_rounding = 1;
  }
449
  assert(FILTER_BITS == WARPEDPIXEL_FILTER_BITS);
450
451
452
453
454
455
456
457
458
#else
  const int reduce_bits_horiz = HORSHEAR_REDUCE_PREC_BITS;
  const int max_bits_horiz =
      bd + WARPEDPIXEL_FILTER_BITS + 1 - HORSHEAR_REDUCE_PREC_BITS;
  const int offset_bits_horiz = bd + WARPEDPIXEL_FILTER_BITS - 1;
  const int offset_bits_vert =
      bd + 2 * WARPEDPIXEL_FILTER_BITS - HORSHEAR_REDUCE_PREC_BITS;
#endif
  (void)max_bits_horiz;
459
460
461

  for (i = p_row; i < p_row + p_height; i += 8) {
    for (j = p_col; j < p_col + p_width; j += 8) {
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
      // Calculate the center of this 8x8 block,
      // project to luma coordinates (if in a subsampled chroma plane),
      // apply the affine transformation,
      // then convert back to the original coordinates (if necessary)
      const int32_t src_x = (j + 4) << subsampling_x;
      const int32_t src_y = (i + 4) << subsampling_y;
      const int32_t dst_x = mat[2] * src_x + mat[3] * src_y + mat[0];
      const int32_t dst_y = mat[4] * src_x + mat[5] * src_y + mat[1];
      const int32_t x4 = dst_x >> subsampling_x;
      const int32_t y4 = dst_y >> subsampling_y;

      int32_t ix4 = x4 >> WARPEDMODEL_PREC_BITS;
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      int32_t iy4 = y4 >> WARPEDMODEL_PREC_BITS;
      int32_t sy4 = y4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508

      sx4 += alpha * (-4) + beta * (-4);
      sy4 += gamma * (-4) + delta * (-4);

      sx4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);
      sy4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);

      // Horizontal filter
      for (k = -7; k < 8; ++k) {
        int iy = iy4 + k;
        if (iy < 0)
          iy = 0;
        else if (iy > height - 1)
          iy = height - 1;

        int sx = sx4 + beta * (k + 4);
        for (l = -4; l < 4; ++l) {
          int ix = ix4 + l - 3;
          const int offs = ROUND_POWER_OF_TWO(sx, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_horiz;
          for (m = 0; m < 8; ++m) {
            int sample_x = ix + m;
            if (sample_x < 0)
              sample_x = 0;
            else if (sample_x > width - 1)
              sample_x = width - 1;
            sum += ref[iy * stride + sample_x] * coeffs[m];
          }
509
510
          sum = ROUND_POWER_OF_TWO(sum, reduce_bits_horiz);
          assert(0 <= sum && sum < (1 << max_bits_horiz));
511
512
513
514
515
516
517
518
          tmp[(k + 7) * 8 + (l + 4)] = sum;
          sx += alpha;
        }
      }

      // Vertical filter
      for (k = -4; k < AOMMIN(4, p_row + p_height - i - 4); ++k) {
        int sy = sy4 + delta * (k + 4);
519
        for (l = -4; l < AOMMIN(4, p_col + p_width - j - 4); ++l) {
520
521
522
523
524
525
526
527
528
          const int offs = ROUND_POWER_OF_TWO(sy, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_vert;
          for (m = 0; m < 8; ++m) {
            sum += tmp[(k + m + 4) * 8 + (l + 4)] * coeffs[m];
          }
529
530
531
532
533
534
535
536
537
538
#if CONFIG_CONVOLVE_ROUND
          if (use_conv_params) {
            CONV_BUF_TYPE *p =
                &conv_params
                     ->dst[(i - p_row + k + 4) * conv_params->dst_stride +
                           (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, conv_params->round_1) -
                  (1 << (offset_bits_horiz + FILTER_BITS -
                         conv_params->round_0 - conv_params->round_1)) -
                  (1 << (offset_bits_vert - conv_params->round_1));
539
540
541
542
            if (conv_params->do_average)
              *p += sum;
            else
              *p = sum;
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
          } else {
#else
          {
#endif
            uint16_t *p =
                &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, VERSHEAR_REDUCE_PREC_BITS);
            assert(0 <= sum && sum < (1 << (bd + 2)));
            uint16_t px =
                clip_pixel_highbd(sum - (1 << (bd - 1)) - (1 << bd), bd);
            if (conv_params->do_average)
              *p = ROUND_POWER_OF_TWO(*p + px, 1);
            else
              *p = px;
          }
558
559
560
561
562
563
564
          sy += gamma;
        }
      }
    }
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
565
566
567
568
569
static void highbd_warp_plane(WarpedMotionParams *wm, const uint8_t *const ref8,
                              int width, int height, int stride,
                              const uint8_t *const pred8, int p_col, int p_row,
                              int p_width, int p_height, int p_stride,
                              int subsampling_x, int subsampling_y, int x_scale,
570
571
                              int y_scale, int bd,
                              ConvolveParams *conv_params) {
572
  assert(wm->wmtype <= AFFINE);
573
574
575
576
  if (wm->wmtype == ROTZOOM) {
    wm->wmmat[5] = wm->wmmat[2];
    wm->wmmat[4] = -wm->wmmat[3];
  }
577
  if (x_scale == SCALE_SUBPEL_SHIFTS && y_scale == SCALE_SUBPEL_SHIFTS) {
Yaowu Xu's avatar
Yaowu Xu committed
578
    const int32_t *const mat = wm->wmmat;
579
580
581
582
    const int16_t alpha = wm->alpha;
    const int16_t beta = wm->beta;
    const int16_t gamma = wm->gamma;
    const int16_t delta = wm->delta;
583

Yaowu Xu's avatar
Yaowu Xu committed
584
    const uint16_t *const ref = CONVERT_TO_SHORTPTR(ref8);
585
586
587
    uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
    av1_highbd_warp_affine(mat, ref, width, height, stride, pred, p_col, p_row,
                           p_width, p_height, p_stride, subsampling_x,
588
                           subsampling_y, bd, conv_params, alpha, beta, gamma,
589
                           delta);
590
  } else {
591
    assert(0);
592
593
594
  }
}

595
static int64_t highbd_frame_error(const uint16_t *const ref, int stride,
596
597
                                  const uint16_t *const dst, int p_width,
                                  int p_height, int p_stride, int bd) {
598
599
600
  int64_t sum_error = 0;
  for (int i = 0; i < p_height; ++i) {
    for (int j = 0; j < p_width; ++j) {
601
602
      sum_error +=
          highbd_error_measure(dst[j + i * p_stride] - ref[j + i * stride], bd);
603
604
605
606
607
608
    }
  }
  return sum_error;
}

static int64_t highbd_warp_error(
Yaowu Xu's avatar
Yaowu Xu committed
609
610
611
    WarpedMotionParams *wm, const uint8_t *const ref8, int width, int height,
    int stride, const uint8_t *const dst8, int p_col, int p_row, int p_width,
    int p_height, int p_stride, int subsampling_x, int subsampling_y,
612
    int x_scale, int y_scale, int bd, int64_t best_error) {
613
  int64_t gm_sumerr = 0;
614
615
616
617
618
  int warp_w, warp_h;
  int error_bsize_w = AOMMIN(p_width, WARP_ERROR_BLOCK);
  int error_bsize_h = AOMMIN(p_height, WARP_ERROR_BLOCK);
  uint16_t tmp[WARP_ERROR_BLOCK * WARP_ERROR_BLOCK];

619
  ConvolveParams conv_params = get_conv_params(0, 0, 0);
620
621
622
623
624
625
626
627
628
  for (int i = p_row; i < p_row + p_height; i += WARP_ERROR_BLOCK) {
    for (int j = p_col; j < p_col + p_width; j += WARP_ERROR_BLOCK) {
      // avoid warping extra 8x8 blocks in the padded region of the frame
      // when p_width and p_height are not multiples of WARP_ERROR_BLOCK
      warp_w = AOMMIN(error_bsize_w, p_col + p_width - j);
      warp_h = AOMMIN(error_bsize_h, p_row + p_height - i);
      highbd_warp_plane(wm, ref8, width, height, stride,
                        CONVERT_TO_BYTEPTR(tmp), j, i, warp_w, warp_h,
                        WARP_ERROR_BLOCK, subsampling_x, subsampling_y, x_scale,
629
                        y_scale, bd, &conv_params);
630
631
632
633
634
635
636

      gm_sumerr += highbd_frame_error(
          tmp, WARP_ERROR_BLOCK, CONVERT_TO_SHORTPTR(dst8) + j + i * p_stride,
          warp_w, warp_h, p_stride, bd);
      if (gm_sumerr > best_error) return gm_sumerr;
    }
  }
637
  return gm_sumerr;
638
}
639
#endif  // CONFIG_HIGHBITDEPTH
640

641
642
643
644
static INLINE int error_measure(int err) {
  return error_measure_lut[255 + err];
}

645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
/* The warp filter for ROTZOOM and AFFINE models works as follows:
   * Split the input into 8x8 blocks
   * For each block, project the point (4, 4) within the block, to get the
     overall block position. Split into integer and fractional coordinates,
     maintaining full WARPEDMODEL precision
   * Filter horizontally: Generate 15 rows of 8 pixels each. Each pixel gets a
     variable horizontal offset. This means that, while the rows of the
     intermediate buffer align with the rows of the *reference* image, the
     columns align with the columns of the *destination* image.
   * Filter vertically: Generate the output block (up to 8x8 pixels, but if the
     destination is too small we crop the output at this stage). Each pixel has
     a variable vertical offset, so that the resulting rows are aligned with
     the rows of the destination image.

   To accomplish these alignments, we factor the warp matrix as a
   product of two shear / asymmetric zoom matrices:
   / a b \  = /   1       0    \ * / 1+alpha  beta \
   \ c d /    \ gamma  1+delta /   \    0      1   /
   where a, b, c, d are wmmat[2], wmmat[3], wmmat[4], wmmat[5] respectively.
David Barker's avatar
David Barker committed
664
665
   The horizontal shear (with alpha and beta) is applied first,
   then the vertical shear (with gamma and delta) is applied second.
666
667
668
669
670

   The only limitation is that, to fit this in a fixed 8-tap filter size,
   the fractional pixel offsets must be at most +-1. Since the horizontal filter
   generates 15 rows of 8 columns, and the initial point we project is at (4, 4)
   within the block, the parameters must satisfy
David Barker's avatar
David Barker committed
671
   4 * |alpha| + 7 * |beta| <= 1   and   4 * |gamma| + 4 * |delta| <= 1
672
673
   for this filter to be applicable.

David Barker's avatar
David Barker committed
674
   Note: This function assumes that the caller has done all of the relevant
675
676
677
678
679
680
   checks, ie. that we have a ROTZOOM or AFFINE model, that wm[4] and wm[5]
   are set appropriately (if using a ROTZOOM model), and that alpha, beta,
   gamma, delta are all in range.

   TODO(david.barker): Maybe support scaled references?
*/
David Barker's avatar
David Barker committed
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
/* A note on hardware implementation:
    The warp filter is intended to be implementable using the same hardware as
    the high-precision convolve filters from the loop-restoration and
    convolve-round experiments.

    For a single filter stage, considering all of the coefficient sets for the
    warp filter and the regular convolution filter, an input in the range
    [0, 2^k - 1] is mapped into the range [-56 * (2^k - 1), 184 * (2^k - 1)]
    before rounding.

    Allowing for some changes to the filter coefficient sets, call the range
    [-64 * 2^k, 192 * 2^k]. Then, if we initialize the accumulator to 64 * 2^k,
    we can replace this by the range [0, 256 * 2^k], which can be stored in an
    unsigned value with 8 + k bits.

    This allows the derivation of the appropriate bit widths and offsets for
    the various intermediate values: If

    F := WARPEDPIXEL_FILTER_BITS = 7 (or else the above ranges need adjusting)
         So a *single* filter stage maps a k-bit input to a (k + F + 1)-bit
         intermediate value.
    H := HORSHEAR_REDUCE_PREC_BITS
    V := VERSHEAR_REDUCE_PREC_BITS
    (and note that we must have H + V = 2*F for the output to have the same
     scale as the input)

    then we end up with the following offsets and ranges:
    Horizontal filter: Apply an offset of 1 << (bd + F - 1), sum fits into a
                       uint{bd + F + 1}
    After rounding: The values stored in 'tmp' fit into a uint{bd + F + 1 - H}.
    Vertical filter: Apply an offset of 1 << (bd + 2*F - H), sum fits into a
                     uint{bd + 2*F + 2 - H}
    After rounding: The final value, before undoing the offset, fits into a
                    uint{bd + 2}.

    Then we need to undo the offsets before clamping to a pixel. Note that,
    if we do this at the end, the amount to subtract is actually independent
    of H and V:

    offset to subtract = (1 << ((bd + F - 1) - H + F - V)) +
                         (1 << ((bd + 2*F - H) - V))
                      == (1 << (bd - 1)) + (1 << bd)

    This allows us to entirely avoid clamping in both the warp filter and
    the convolve-round experiment. As of the time of writing, the Wiener filter
    from loop-restoration can encode a central coefficient up to 216, which
    leads to a maximum value of about 282 * 2^k after applying the offset.
    So in that case we still need to clamp.
*/
730
731
732
void av1_warp_affine_c(const int32_t *mat, const 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,
733
734
735
                       int subsampling_x, int subsampling_y,
                       ConvolveParams *conv_params, int16_t alpha, int16_t beta,
                       int16_t gamma, int16_t delta) {
David Barker's avatar
David Barker committed
736
  int32_t tmp[15 * 8];
737
  int i, j, k, l, m;
738
  const int bd = 8;
739
#if CONFIG_CONVOLVE_ROUND
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
  const int use_conv_params = conv_params->round == CONVOLVE_OPT_NO_ROUND;
  const int reduce_bits_horiz =
      use_conv_params ? conv_params->round_0 : HORSHEAR_REDUCE_PREC_BITS;
  const int max_bits_horiz =
      use_conv_params
          ? bd + FILTER_BITS + 1 - conv_params->round_0
          : bd + WARPEDPIXEL_FILTER_BITS + 1 - HORSHEAR_REDUCE_PREC_BITS;
  const int offset_bits_horiz =
      use_conv_params ? bd + FILTER_BITS - 1 : bd + WARPEDPIXEL_FILTER_BITS - 1;
  const int offset_bits_vert =
      use_conv_params
          ? bd + 2 * FILTER_BITS - conv_params->round_0
          : bd + 2 * WARPEDPIXEL_FILTER_BITS - HORSHEAR_REDUCE_PREC_BITS;
  if (use_conv_params) {
    conv_params->do_post_rounding = 1;
  }
756
  assert(FILTER_BITS == WARPEDPIXEL_FILTER_BITS);
757
758
759
760
761
762
763
764
765
#else
  const int reduce_bits_horiz = HORSHEAR_REDUCE_PREC_BITS;
  const int max_bits_horiz =
      bd + WARPEDPIXEL_FILTER_BITS + 1 - HORSHEAR_REDUCE_PREC_BITS;
  const int offset_bits_horiz = bd + WARPEDPIXEL_FILTER_BITS - 1;
  const int offset_bits_vert =
      bd + 2 * WARPEDPIXEL_FILTER_BITS - HORSHEAR_REDUCE_PREC_BITS;
#endif
  (void)max_bits_horiz;
766
767
768

  for (i = p_row; i < p_row + p_height; i += 8) {
    for (j = p_col; j < p_col + p_width; j += 8) {
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
      // Calculate the center of this 8x8 block,
      // project to luma coordinates (if in a subsampled chroma plane),
      // apply the affine transformation,
      // then convert back to the original coordinates (if necessary)
      const int32_t src_x = (j + 4) << subsampling_x;
      const int32_t src_y = (i + 4) << subsampling_y;
      const int32_t dst_x = mat[2] * src_x + mat[3] * src_y + mat[0];
      const int32_t dst_y = mat[4] * src_x + mat[5] * src_y + mat[1];
      const int32_t x4 = dst_x >> subsampling_x;
      const int32_t y4 = dst_y >> subsampling_y;

      int32_t ix4 = x4 >> WARPEDMODEL_PREC_BITS;
      int32_t sx4 = x4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
      int32_t iy4 = y4 >> WARPEDMODEL_PREC_BITS;
      int32_t sy4 = y4 & ((1 << WARPEDMODEL_PREC_BITS) - 1);
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820

      sx4 += alpha * (-4) + beta * (-4);
      sy4 += gamma * (-4) + delta * (-4);

      sx4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);
      sy4 &= ~((1 << WARP_PARAM_REDUCE_BITS) - 1);

      // Horizontal filter
      for (k = -7; k < 8; ++k) {
        // Clamp to top/bottom edge of the frame
        int iy = iy4 + k;
        if (iy < 0)
          iy = 0;
        else if (iy > height - 1)
          iy = height - 1;

        int sx = sx4 + beta * (k + 4);

        for (l = -4; l < 4; ++l) {
          int ix = ix4 + l - 3;
          // At this point, sx = sx4 + alpha * l + beta * k
          const int offs = ROUND_POWER_OF_TWO(sx, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_horiz;
          for (m = 0; m < 8; ++m) {
            // Clamp to left/right edge of the frame
            int sample_x = ix + m;
            if (sample_x < 0)
              sample_x = 0;
            else if (sample_x > width - 1)
              sample_x = width - 1;

            sum += ref[iy * stride + sample_x] * coeffs[m];
          }
821
822
          sum = ROUND_POWER_OF_TWO(sum, reduce_bits_horiz);
          assert(0 <= sum && sum < (1 << max_bits_horiz));
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
          tmp[(k + 7) * 8 + (l + 4)] = sum;
          sx += alpha;
        }
      }

      // Vertical filter
      for (k = -4; k < AOMMIN(4, p_row + p_height - i - 4); ++k) {
        int sy = sy4 + delta * (k + 4);
        for (l = -4; l < AOMMIN(4, p_col + p_width - j - 4); ++l) {
          // At this point, sy = sy4 + gamma * l + delta * k
          const int offs = ROUND_POWER_OF_TWO(sy, WARPEDDIFF_PREC_BITS) +
                           WARPEDPIXEL_PREC_SHIFTS;
          assert(offs >= 0 && offs <= WARPEDPIXEL_PREC_SHIFTS * 3);
          const int16_t *coeffs = warped_filter[offs];

          int32_t sum = 1 << offset_bits_vert;
          for (m = 0; m < 8; ++m) {
            sum += tmp[(k + m + 4) * 8 + (l + 4)] * coeffs[m];
          }
842
843
844
845
846
847
848
849
850
851
#if CONFIG_CONVOLVE_ROUND
          if (use_conv_params) {
            CONV_BUF_TYPE *p =
                &conv_params
                     ->dst[(i - p_row + k + 4) * conv_params->dst_stride +
                           (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, conv_params->round_1) -
                  (1 << (offset_bits_horiz + FILTER_BITS -
                         conv_params->round_0 - conv_params->round_1)) -
                  (1 << (offset_bits_vert - conv_params->round_1));
852
853
854
855
            if (conv_params->do_average)
              *p += sum;
            else
              *p = sum;
856
857
858
859
860
861
862
863
864
865
866
867
868
869
          } else {
#else
          {
#endif
            uint8_t *p =
                &pred[(i - p_row + k + 4) * p_stride + (j - p_col + l + 4)];
            sum = ROUND_POWER_OF_TWO(sum, VERSHEAR_REDUCE_PREC_BITS);
            assert(0 <= sum && sum < (1 << (bd + 2)));
            uint8_t px = clip_pixel(sum - (1 << (bd - 1)) - (1 << bd));
            if (conv_params->do_average)
              *p = ROUND_POWER_OF_TWO(*p + px, 1);
            else
              *p = px;
          }
870
871
872
873
874
875
876
          sy += gamma;
        }
      }
    }
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
877
878
879
880
static void warp_plane(WarpedMotionParams *wm, const uint8_t *const 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,
881
                       int x_scale, int y_scale, ConvolveParams *conv_params) {
882
  assert(wm->wmtype <= AFFINE);
883
884
885
886
  if (wm->wmtype == ROTZOOM) {
    wm->wmmat[5] = wm->wmmat[2];
    wm->wmmat[4] = -wm->wmmat[3];
  }
887
  if (x_scale == SCALE_SUBPEL_SHIFTS && y_scale == SCALE_SUBPEL_SHIFTS) {
Yaowu Xu's avatar
Yaowu Xu committed
888
    const int32_t *const mat = wm->wmmat;
889
890
891
892
    const int16_t alpha = wm->alpha;
    const int16_t beta = wm->beta;
    const int16_t gamma = wm->gamma;
    const int16_t delta = wm->delta;
893

894
895
    av1_warp_affine(mat, ref, width, height, stride, pred, p_col, p_row,
                    p_width, p_height, p_stride, subsampling_x, subsampling_y,
896
                    conv_params, alpha, beta, gamma, delta);
897
  } else {
898
    assert(0);
899
900
901
  }
}

902
static int64_t frame_error(const uint8_t *const ref, int stride,
903
904
                           const uint8_t *const dst, int p_width, int p_height,
                           int p_stride) {
905
906
907
  int64_t sum_error = 0;
  for (int i = 0; i < p_height; ++i) {
    for (int j = 0; j < p_width; ++j) {
908
909
      sum_error +=
          (int64_t)error_measure(dst[j + i * p_stride] - ref[j + i * stride]);
910
911
912
913
914
915
916
917
918
919
    }
  }
  return sum_error;
}

static int64_t warp_error(WarpedMotionParams *wm, const uint8_t *const ref,
                          int width, int height, int stride,
                          const uint8_t *const 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,
920
                          int y_scale, int64_t best_error) {
921
  int64_t gm_sumerr = 0;
922
923
924
925
  int warp_w, warp_h;
  int error_bsize_w = AOMMIN(p_width, WARP_ERROR_BLOCK);
  int error_bsize_h = AOMMIN(p_height, WARP_ERROR_BLOCK);
  uint8_t tmp[WARP_ERROR_BLOCK * WARP_ERROR_BLOCK];
926
  ConvolveParams conv_params = get_conv_params(0, 0, 0);
927
928
929
930
931
932
933
934
935

  for (int i = p_row; i < p_row + p_height; i += WARP_ERROR_BLOCK) {
    for (int j = p_col; j < p_col + p_width; j += WARP_ERROR_BLOCK) {
      // avoid warping extra 8x8 blocks in the padded region of the frame
      // when p_width and p_height are not multiples of WARP_ERROR_BLOCK
      warp_w = AOMMIN(error_bsize_w, p_col + p_width - j);
      warp_h = AOMMIN(error_bsize_h, p_row + p_height - i);
      warp_plane(wm, ref, width, height, stride, tmp, j, i, warp_w, warp_h,
                 WARP_ERROR_BLOCK, subsampling_x, subsampling_y, x_scale,
936
                 y_scale, &conv_params);
937
938
939
940
941
942

      gm_sumerr += frame_error(tmp, WARP_ERROR_BLOCK, dst + j + i * p_stride,
                               warp_w, warp_h, p_stride);
      if (gm_sumerr > best_error) return gm_sumerr;
    }
  }
943
944
945
946
947
948
949
  return gm_sumerr;
}

int64_t av1_frame_error(
#if CONFIG_HIGHBITDEPTH
    int use_hbd, int bd,
#endif  // CONFIG_HIGHBITDEPTH
950
951
    const uint8_t *ref, int stride, uint8_t *dst, int p_width, int p_height,
    int p_stride) {
952
953
954
#if CONFIG_HIGHBITDEPTH
  if (use_hbd) {
    return highbd_frame_error(CONVERT_TO_SHORTPTR(ref), stride,
955
956
                              CONVERT_TO_SHORTPTR(dst), p_width, p_height,
                              p_stride, bd);
957
958
  }
#endif  // CONFIG_HIGHBITDEPTH
959
  return frame_error(ref, stride, dst, p_width, p_height, p_stride);
960
961
}

962
int64_t av1_warp_error(WarpedMotionParams *wm,
963
#if CONFIG_HIGHBITDEPTH
964
                       int use_hbd, int bd,
965
#endif  // CONFIG_HIGHBITDEPTH
966
967
968
                       const 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,
969
970
                       int subsampling_y, int x_scale, int y_scale,
                       int64_t best_error) {
971
972
  if (wm->wmtype <= AFFINE)
    if (!get_shear_params(wm)) return 1;
973
#if CONFIG_HIGHBITDEPTH
974
  if (use_hbd)
975
976
    return highbd_warp_error(wm, ref, width, height, stride, dst, p_col, p_row,
                             p_width, p_height, p_stride, subsampling_x,
977
                             subsampling_y, x_scale, y_scale, bd, best_error);
978
#endif  // CONFIG_HIGHBITDEPTH
979
980
  return warp_error(wm, ref, width, height, stride, dst, p_col, p_row, p_width,
                    p_height, p_stride, subsampling_x, subsampling_y, x_scale,
981
                    y_scale, best_error);
982
983
}

Yaowu Xu's avatar
Yaowu Xu committed
984
void av1_warp_plane(WarpedMotionParams *wm,
985
#if CONFIG_HIGHBITDEPTH
Yaowu Xu's avatar
Yaowu Xu committed
986
                    int use_hbd, int bd,
987
#endif  // CONFIG_HIGHBITDEPTH
Yaowu Xu's avatar
Yaowu Xu committed
988
                    const uint8_t *ref, int width, int height, int stride,
Yaowu Xu's avatar
Yaowu Xu committed
989
990
                    uint8_t *pred, int p_col, int p_row, int p_width,
                    int p_height, int p_stride, int subsampling_x,
991
992
                    int subsampling_y, int x_scale, int y_scale,
                    ConvolveParams *conv_params) {
993
#if CONFIG_HIGHBITDEPTH
994
  if (use_hbd)
clang-format's avatar
clang-format committed
995
996
    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
997
                      x_scale, y_scale, bd, conv_params);
998
  else
999
#endif  // CONFIG_HIGHBITDEPTH
clang-format's avatar
clang-format committed
1000
1001
    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, x_scale,
1002
               y_scale, conv_params);
1003
}
1004

1005
#if CONFIG_WARPED_MOTION
1006
#define LEAST_SQUARES_ORDER 2
1007

1008
#define LS_MV_MAX 256  // max mv in 1/8-pel
1009
1010
#define LS_STEP 2

1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
// Assuming LS_MV_MAX is < MAX_SB_SIZE * 8,
// the precision needed is:
//   (MAX_SB_SIZE_LOG2 + 3) [for sx * sx magnitude] +
//   (MAX_SB_SIZE_LOG2 + 4) [for sx * dx magnitude] +
//   1 [for sign] +
//   LEAST_SQUARES_SAMPLES_MAX_BITS
//        [for adding up to LEAST_SQUARES_SAMPLES_MAX samples]
// The value is 23
#define LS_MAT_RANGE_BITS \
  ((MAX_SB_SIZE_LOG2 + 4) * 2 + LEAST_SQUARES_SAMPLES_MAX_BITS)

// Bit-depth reduction from the full-range
#define LS_MAT_DOWN_BITS 2

// bits range of A, Bx and By after downshifting
#define LS_MAT_BITS (LS_MAT_RANGE_BITS - LS_MAT_DOWN_BITS)
#define LS_MAT_MIN (-(1 << (LS_MAT_BITS - 1)))
#define LS_MAT_MAX ((1 << (LS_MAT_BITS - 1)) - 1)

1030
#define LS_SUM(a) ((a)*4 + LS_STEP * 2)
1031
1032
#define LS_SQUARE(a) \
  (((a) * (a)*4 + (a)*4 * LS_STEP + LS_STEP * LS_STEP * 2) >> 2)
1033
#define LS_PRODUCT1(a, b) \
1034
  (((a) * (b)*4 + ((a) + (b)) * 2 * LS_STEP + LS_STEP * LS_STEP) >> 2)
1035
#define LS_PRODUCT2(a, b) \
1036
  (((a) * (b)*4 + ((a) + (b)) * 2 * LS_STEP + LS_STEP * LS_STEP * 2) >> 2)
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
#define USE_LIMITED_PREC_MULT 0

#if USE_LIMITED_PREC_MULT

#define MUL_PREC_BITS 16
static uint16_t resolve_multiplier_64(uint64_t D, int16_t *shift) {
  int msb = 0;
  uint16_t mult = 0;
  *shift = 0;
  if (D != 0) {
    msb = (int16_t)((D >> 32) ? get_msb((unsigned int)(D >> 32)) + 32
                              : get_msb((unsigned int)D));
    if (msb >= MUL_PREC_BITS) {
      mult = (uint16_t)ROUND_POWER_OF_TWO_64(D, msb + 1 - MUL_PREC_BITS);
      *shift = msb + 1 - MUL_PREC_BITS;
    } else {
      mult = (uint16_t)D;
      *shift = 0;
    }
  }
  return mult;
}

static int32_t get_mult_shift_ndiag(int64_t Px, int16_t iDet, int shift) {
  int32_t ret;
  int16_t mshift;
  uint16_t Mul = resolve_multiplier_64(llabs(Px), &mshift);
  int32_t v = (int32_t)Mul * (int32_t)iDet * (Px < 0 ? -1 : 1);
  shift -= mshift;
  if (shift > 0) {
    return (int32_t)clamp(ROUND_POWER_OF_TWO_SIGNED(v, shift),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  } else {
    return (int32_t)clamp(v * (1 << (-shift)),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  }
  return ret;
}

static int32_t get_mult_shift_diag(int64_t Px, int16_t iDet, int shift) {
  int16_t mshift;
  uint16_t Mul = resolve_multiplier_64(llabs(Px), &mshift);
  int32_t v = (int32_t)Mul * (int32_t)iDet * (Px < 0 ? -1 : 1);
  shift -= mshift;
  if (shift > 0) {
    return (int32_t)clamp(
        ROUND_POWER_OF_TWO_SIGNED(v, shift),
        (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
        (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  } else {
    return (int32_t)clamp(
        v * (1 << (-shift)),
        (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
        (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
  }
}

#else

static int32_t get_mult_shift_ndiag(int64_t Px, int16_t iDet, int shift) {
  int64_t v = Px * (int64_t)iDet;
  return (int32_t)clamp64(ROUND_POWER_OF_TWO_SIGNED_64(v, shift),
                          -WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
                          WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
}

static int32_t get_mult_shift_diag(int64_t Px, int16_t iDet, int shift) {
  int64_t v = Px * (int64_t)iDet;
  return (int32_t)clamp64(
      ROUND_POWER_OF_TWO_SIGNED_64(v, shift),
      (1 << WARPEDMODEL_PREC_BITS) - WARPEDMODEL_NONDIAGAFFINE_CLAMP + 1,
      (1 << WARPEDMODEL_PREC_BITS) + WARPEDMODEL_NONDIAGAFFINE_CLAMP - 1);
}
#endif  // USE_LIMITED_PREC_MULT

1115
1116
1117
static int find_affine_int(int np, const int *pts1, const int *pts2,
                           BLOCK_SIZE bsize, int mvy, int mvx,
                           WarpedMotionParams *wm, int mi_row, int mi_col) {
1118
1119
1120
  int32_t A[2][2] = { { 0, 0 }, { 0, 0 } };
  int32_t Bx[2] = { 0, 0 };
  int32_t By[2] = { 0, 0 };
1121
  int i, n = 0;
1122
1123
1124

  const int bw = block_size_wide[bsize];
  const int bh = block_size_high[bsize];
1125
1126
1127
1128
  const int isuy = (mi_row * MI_SIZE + AOMMAX(bh, MI_SIZE) / 2 - 1);
  const int isux = (mi_col * MI_SIZE + AOMMAX(bw, MI_SIZE) / 2 - 1);
  const int suy = isuy * 8;
  const int sux = isux * 8;
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
  const int duy = suy + mvy;
  const int dux = sux + mvx;

  // Assume the center pixel of the block has exactly the same motion vector
  // as transmitted for the block. First shift the origin of the source
  // points to the block center, and the origin of the destination points to
  // the block center added to the motion vector transmitted.
  // Let (xi, yi) denote the source points and (xi', yi') denote destination
  // points after origin shfifting, for i = 0, 1, 2, .... n-1.
  // Then if  P = [x0, y0,
  //               x1, y1
  //               x2, y1,
  //                ....
  //              ]
  //          q = [x0', x1', x2', ... ]'
  //          r = [y0', y1', y2', ... ]'
  // the least squares problems that need to be solved are:
  //          [h1, h2]' = inv(P'P)P'q and
  //          [h3, h4]' = inv(P'P)P'r
  // where the affine transformation is given by:
  //          x' = h1.x + h2.y
  //          y' = h3.x + h4.y
  //
  // The loop below computes: A = P'P, Bx = P'q, By = P'r
  // We need to just compute inv(A).Bx and inv(A).By for the solutions.
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
  int sx, sy, dx, dy;
  // Contribution from neighbor block
  for (i = 0; i < np && n < LEAST_SQUARES_SAMPLES_MAX; i++) {
    dx = pts2[i * 2] - dux;
    dy = pts2[i * 2 + 1] - duy;
    sx = pts1[i * 2] - sux;
    sy = pts1[i * 2 + 1] - suy;
    if (abs(sx - dx) < LS_MV_MAX && abs(sy - dy) < LS_MV_MAX) {
      A[0][0] += LS_SQUARE(sx);
      A[0][1] += LS_PRODUCT1(sx, sy);
      A[1][1] += LS_SQUARE(sy);
      Bx[0] += LS_PRODUCT2(sx, dx);
      Bx[1] += LS_PRODUCT1(sy, dx);
      By[0] += LS_PRODUCT1(sx, dy);
      By[1] += LS_PRODUCT2(sy, dy);
      n++;
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
  int downshift;
  if (n >= 4)
    downshift = LS_MAT_DOWN_BITS;
  else if (n >= 2)
    downshift = LS_MAT_DOWN_BITS - 1;
  else
    downshift = LS_MAT_DOWN_BITS - 2;

  // Reduce precision by downshift bits
  A[0][0] = clamp(ROUND_POWER_OF_TWO_SIGNED(A[0][0], downshift), LS_MAT_MIN,
                  LS_MAT_MAX);
  A[0][1] = clamp(ROUND_POWER_OF_TWO_SIGNED(A[0][1], downshift), LS_MAT_MIN,
                  LS_MAT_MAX);
  A[1][1] = clamp(ROUND_POWER_OF_TWO_SIGNED(A[1][1], downshift), LS_MAT_MIN,
                  LS_MAT_MAX);
  Bx[0] = clamp(ROUND_POWER_OF_TWO_SIGNED(Bx[0], downshift), LS_MAT_MIN,
                LS_MAT_MAX);
  Bx[1] = clamp(ROUND_POWER_OF_TWO_SIGNED(Bx[1], downshift), LS_MAT_MIN,
                LS_MAT_MAX);
  By[0] = clamp(ROUND_POWER_OF_TWO_SIGNED(By[0], downshift), LS_MAT_MIN,
                LS_MAT_MAX);
  By[1] = clamp(ROUND_POWER_OF_TWO_SIGNED(By[1], downshift), LS_MAT_MIN,
                LS_MAT_MAX);

  int64_t Px[2], Py[2], Det;
  int16_t iDet, shift;
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207

  // These divided by the Det, are the least squares solutions
  Px[0] = (int64_t)A[1][1] * Bx[0] - (int64_t)A[0][1] * Bx[1];
  Px[1] = -(int64_t)A[0][1] * Bx[0] + (int64_t)A[0][0] * Bx[1];
  Py[0] = (int64_t)A[1][1] * By[0] - (int64_t)A[0][1] * By[1];
  Py[1] = -(int64_t)A[0][1] * By[0] + (int64_t)A[0][0] * By[1];

  // Compute Determinant of A
  Det = (int64_t)A[0][0] * A[1][1] - (int64_t)A[0][1] * A[0][1];
  if (Det == 0) return 1;
Yaowu Xu's avatar
Yaowu Xu committed
1208
  iDet = resolve_divisor_64(llabs(Det), &shift) * (Det < 0 ? -1 : 1);
1209
1210
1211
1212
  shift -= WARPEDMODEL_PREC_BITS;
  if (shift < 0) {
    iDet <<= (-shift);
    shift = 0;
1213
1214
  }

1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225