h274.c

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/*
 * H.274 film grain synthesis
 * Copyright (c) 2021 Niklas Haas <ffmpeg@haasn.xyz>
 *
 * This file is part of FFmpeg.
 *
 * FFmpeg is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * FFmpeg is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with FFmpeg; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 */
 
/**
 * @file
 * H.274 film grain synthesis.
 * @author Niklas Haas <ffmpeg@haasn.xyz>
 */
 
#include "libavutil/avassert.h"
#include "libavutil/imgutils.h"
 
#include "h274.h"
 
static const int8_t Gaussian_LUT[2048+4];
static const uint32_t Seed_LUT[256];
static const int8_t R64T[64][64];
 
static void prng_shift(uint32_t *state)
{
    // Primitive polynomial x^31 + x^3 + 1 (modulo 2)
    uint32_t x = *state;
    uint8_t feedback = 1u ^ (x >> 2) ^ (x >> 30);
    *state = (x << 1) | (feedback & 1u);
}
 
static void init_slice_c(int8_t out[64][64], uint8_t h, uint8_t v,
                         int16_t tmp[64][64])
{
    static const uint8_t deblock_factors[13] = {
        64, 71, 77, 84, 90, 96, 103, 109, 116, 122, 128, 128, 128
    };
 
    const uint8_t deblock_coeff = deblock_factors[v];
    const uint8_t freq_h = ((h + 3) << 2) - 1;
    const uint8_t freq_v = ((v + 3) << 2) - 1;
    uint32_t seed = Seed_LUT[h + v * 13];
 
    // Initialize with random gaussian values, using the output array as a
    // temporary buffer for these intermediate values.
    //
    // Note: To make the subsequent matrix multiplication cache friendlier, we
    // store each *column* of the starting image in a *row* of `out`
    for (int l = 0; l <= freq_v; l++) {
        for (int k = 0; k <= freq_h; k += 4) {
            uint16_t offset = seed % 2048;
            out[l][k + 0] = Gaussian_LUT[offset + 0];
            out[l][k + 1] = Gaussian_LUT[offset + 1];
            out[l][k + 2] = Gaussian_LUT[offset + 2];
            out[l][k + 3] = Gaussian_LUT[offset + 3];
            prng_shift(&seed);
        }
    }
 
    out[0][0] = 0;
 
    // 64x64 inverse integer transform
    for (int y = 0; y < 64; y++) {
        for (int x = 0; x <= freq_v; x++) {
            int32_t sum = 0;
            for (int p = 0; p <= freq_h; p++)
                sum += R64T[y][p] * out[x][p];
            tmp[y][x] = (sum + 128) >> 8;
        }
    }
 
    for (int y = 0; y < 64; y++) {
        for (int x = 0; x < 64; x++) {
            int32_t sum = 0;
            for (int p = 0; p <= freq_v; p++)
                sum += tmp[x][p] * R64T[y][p]; // R64T^T = R64
            // Renormalize and clip to [-127, 127]
            out[y][x] = av_clip((sum + 128) >> 8, -127, 127);
        }
    }
 
    // Deblock horizontal edges by simple attentuation of values
    for (int y = 0; y < 64; y += 8) {
        for (int x = 0; x < 64; x++) {
            out[y + 0][x] = (out[y + 0][x] * deblock_coeff) >> 7;
            out[y + 7][x] = (out[y + 7][x] * deblock_coeff) >> 7;
        }
    }
}
 
static void init_slice(H274FilmGrainDatabase *database, uint8_t h, uint8_t v)
{
    if (database->residency[h] & (1 << v))
        return;
 
    database->residency[h] |= (1 << v);
    init_slice_c(database->db[h][v], h, v, database->slice_tmp);
}
 
// Computes the average of an 8x8 block
static uint16_t avg_8x8_c(const uint8_t *in, int in_stride)
{
    uint16_t avg[8] = {0}; // summing over an array vectorizes better
 
    for (int y = 0; y < 8; y++) {
        for (int x = 0; x < 8; x++)
            avg[x] += in[x];
        in += in_stride;
    }
 
    return (avg[0] + avg[1] + avg[2] + avg[3] +
            avg[4] + avg[5] + avg[6] + avg[7]) >> 6;
}
 
// Synthesize an 8x8 block of film grain by copying the pattern from `db`
static void synth_grain_8x8_c(int8_t *out, const int out_stride,
                              const int16_t scale, const uint8_t shift,
                              const int8_t *db)
{
    for (int y = 0; y < 8; y++) {
        for (int x = 0; x < 8; x++)
            out[x] = (scale * db[x]) >> shift;
 
        out += out_stride;
        db += 64;
    }
}
 
// Deblock vertical edges of an 8x8 block, mixing with the previous block
static void deblock_8x8_c(int8_t *out, const int out_stride)
{
    for (int y = 0; y < 8; y++) {
        const int8_t l1 = out[-2], l0 = out[-1];
        const int8_t r0 = out[0], r1 = out[1];
        out[0]  = (l0 + r0 * 2 + r1) >> 2;
        out[-1] = (r0 + l0 * 2 + l1) >> 2;
        out += out_stride;
    }
}
 
// Generates a single 8x8 block of grain, optionally also applying the
// deblocking step (note that this implies writing to the previous block).
static av_always_inline void generate(int8_t *out, int out_stride,
                                      const uint8_t *in, int in_stride,
                                      H274FilmGrainDatabase *database,
                                      const AVFilmGrainH274Params *h274,
                                      int c, int invert, int deblock,
                                      int y_offset, int x_offset)
{
    const uint8_t shift = h274->log2_scale_factor + 6;
    const uint16_t avg = avg_8x8_c(in, in_stride);
    int16_t scale;
    uint8_t h, v;
    int8_t s = -1;
 
    // FIXME: This logic only generates grain with a single
    // intensity interval. Strictly speaking, the H.274 specification allows
    // for overlapping intensity intervals, however SMPTE RDD 5-2006 (which
    // concerns the implementation of H.274 for H.264) forbids this as it
    // requires a nontrivial grain synthesis process (FFT).
    //
    // In principle, we should detect this possibility ahead of time and warn
    // the user that the output is unlikely to be correct, or alternatively
    // return an AVERROR_PATCHWELCOME.
    for (int i = 0; i < h274->num_intensity_intervals[c]; i++) {
        if (avg >= h274->intensity_interval_lower_bound[c][i] &&
            avg <= h274->intensity_interval_upper_bound[c][i])
        {
            s = i;
            break;
        }
    }
 
    if (s < 0) {
        // No matching intensity interval, synthesize blank film grain
        for (int y = 0; y < 8; y++)
            memset(out + y * out_stride, 0, sizeof(int8_t[8]));
        return;
    }
 
    h = av_clip(h274->comp_model_value[c][s][1], 2, 14) - 2;
    v = av_clip(h274->comp_model_value[c][s][2], 2, 14) - 2;
    init_slice(database, h, v);
 
    scale = h274->comp_model_value[c][s][0];
    if (invert)
        scale = -scale;
 
    synth_grain_8x8_c(out, out_stride, scale, shift,
                      &database->db[h][v][y_offset][x_offset]);
 
    if (deblock)
        deblock_8x8_c(out, out_stride);
}
 
// Saturating 8-bit sum of a+b
static void add_8x8_clip_c(uint8_t *out, const uint8_t *a, const int8_t *b,
                           int n)
{
    for (int i = 0; i < n; i++)
        out[i] = av_clip_uint8(a[i] + b[i]);
}
 
int ff_h274_apply_film_grain(AVFrame *out_frame, const AVFrame *in_frame,
                             H274FilmGrainDatabase *database,
                             const AVFilmGrainParams *params)
{
    AVFilmGrainH274Params h274 = params->codec.h274;
    av_assert1(params->type == AV_FILM_GRAIN_PARAMS_H274);
    if (h274.model_id != 0)
        return AVERROR_PATCHWELCOME;
 
    av_assert1(out_frame->format == in_frame->format);
    if (in_frame->format != AV_PIX_FMT_YUV420P)
        return AVERROR_PATCHWELCOME;
 
    for (int c = 0; c < 3; c++) {
        static const uint8_t color_offset[3] = { 0, 85, 170 };
        uint32_t seed = Seed_LUT[(params->seed + color_offset[c]) % 256];
        const int width = c > 0 ? AV_CEIL_RSHIFT(out_frame->width, 1) : out_frame->width;
        const int height = c > 0 ? AV_CEIL_RSHIFT(out_frame->height, 1) : out_frame->height;
 
        uint8_t * const out = out_frame->data[c];
        const int out_stride = out_frame->linesize[c];
        int8_t * const grain = out_frame->data[c]; // re-use output buffer for grain
        const int grain_stride = out_stride;
        const uint8_t * const in = in_frame->data[c];
        const int in_stride = in_frame->linesize[c];
 
        if (!h274.component_model_present[c]) {
            av_image_copy_plane(out, out_stride, in, in_stride,
                                width * sizeof(uint8_t), height);
            continue;
        }
 
        if (c > 0) {
            // Adaptation for 4:2:0 chroma subsampling
            for (int i = 0; i < h274.num_intensity_intervals[c]; i++) {
                h274.comp_model_value[c][i][0] >>= 1;
                h274.comp_model_value[c][i][1] *= 2;
                h274.comp_model_value[c][i][2] *= 2;
            }
        }
 
        // Film grain synthesis is done in 8x8 blocks, but the PRNG state is
        // only advanced in 16x16 blocks, so use a nested loop
        for (int y = 0; y < height; y += 16) {
            for (int x = 0; x < width; x += 16) {
                uint16_t x_offset = (seed >> 16) % 52;
                uint16_t y_offset = (seed & 0xFFFF) % 56;
                const int invert = (seed & 0x1);
                x_offset &= 0xFFFC;
                y_offset &= 0xFFF8;
                prng_shift(&seed);
 
                for (int yy = 0; yy < 16 && y+yy < height; yy += 8) {
                    for (int xx = 0; xx < 16 && x+xx < width; xx += 8) {
                        generate(grain + (y+yy) * grain_stride + (x+xx), grain_stride,
                                 in + (y+yy) * in_stride + (x+xx), in_stride,
                                 database, &h274, c, invert, (x+xx) > 0,
                                 y_offset + yy, x_offset + xx);
                    }
                }
            }
        }
 
        // Final output blend pass, done after grain synthesis is complete
        // because deblocking depends on previous grain values
        for (int y = 0; y < height; y++) {
            add_8x8_clip_c(out + y * out_stride, in + y * in_stride,
                           grain + y * grain_stride, width);
        }
    }
 
    return 0;
}
 
// These tables are all taken from the SMPTE RDD 5-2006 specification
static const int8_t Gaussian_LUT[2048+4] = {
    -11, 12, 103, -11, 42, -35, 12, 59, 77, 98, -87, 3, 65, -78, 45, 56, -51, 21,
    13, -11, -20, -19, 33, -127, 17, -6, -105, 18, 19, 71, 48, -10, -38, 42,
    -2, 75, -67, 52, -90, 33, -47, 21, -3, -56, 49, 1, -57, -42, -1, 120, -127,
    -108, -49, 9, 14, 127, 122, 109, 52, 127, 2, 7, 114, 19, 30, 12, 77, 112,
    82, -61, -127, 111, -52, -29, 2, -49, -24, 58, -29, -73, 12, 112, 67, 79,
    -3, -114, -87, -6, -5, 40, 58, -81, 49, -27, -31, -34, -105, 50, 16, -24,
    -35, -14, -15, -127, -55, -22, -55, -127, -112, 5, -26, -72, 127, 127, -2,
    41, 87, -65, -16, 55, 19, 91, -81, -65, -64, 35, -7, -54, 99, -7, 88, 125,
    -26, 91, 0, 63, 60, -14, -23, 113, -33, 116, 14, 26, 51, -16, 107, -8, 53,
    38, -34, 17, -7, 4, -91, 6, 63, 63, -15, 39, -36, 19, 55, 17, -51, 40, 33,
    -37, 126, -39, -118, 17, -30, 0, 19, 98, 60, 101, -12, -73, -17, -52, 98,
    3, 3, 60, 33, -3, -2, 10, -42, -106, -38, 14, 127, 16, -127, -31, -86, -39,
    -56, 46, -41, 75, 23, -19, -22, -70, 74, -54, -2, 32, -45, 17, -92, 59,
    -64, -67, 56, -102, -29, -87, -34, -92, 68, 5, -74, -61, 93, -43, 14, -26,
    -38, -126, -17, 16, -127, 64, 34, 31, 93, 17, -51, -59, 71, 77, 81, 127,
    127, 61, 33, -106, -93, 0, 0, 75, -69, 71, 127, -19, -111, 30, 23, 15, 2,
    39, 92, 5, 42, 2, -6, 38, 15, 114, -30, -37, 50, 44, 106, 27, 119, 7, -80,
    25, -68, -21, 92, -11, -1, 18, 41, -50, 79, -127, -43, 127, 18, 11, -21,
    32, -52, 27, -88, -90, -39, -19, -10, 24, -118, 72, -24, -44, 2, 12, 86,
    -107, 39, -33, -127, 47, 51, -24, -22, 46, 0, 15, -35, -69, -2, -74, 24,
    -6, 0, 29, -3, 45, 32, -32, 117, -45, 79, -24, -17, -109, -10, -70, 88,
    -48, 24, -91, 120, -37, 50, -127, 58, 32, -82, -10, -17, -7, 46, -127, -15,
    89, 127, 17, 98, -39, -33, 37, 42, -40, -32, -21, 105, -19, 19, 19, -59,
    -9, 30, 0, -127, 34, 127, -84, 75, 24, -40, -49, -127, -107, -14, 45, -75,
    1, 30, -20, 41, -68, -40, 12, 127, -3, 5, 20, -73, -59, -127, -3, -3, -53,
    -6, -119, 93, 120, -80, -50, 0, 20, -46, 67, 78, -12, -22, -127, 36, -41,
    56, 119, -5, -116, -22, 68, -14, -90, 24, -82, -44, -127, 107, -25, -37,
    40, -7, -7, -82, 5, -87, 44, -34, 9, -127, 39, 70, 49, -63, 74, -49, 109,
    -27, -89, -47, -39, 44, 49, -4, 60, -42, 80, 9, -127, -9, -56, -49, 125,
    -66, 47, 36, 117, 15, -11, -96, 109, 94, -17, -56, 70, 8, -14, -5, 50, 37,
    -45, 120, -30, -76, 40, -46, 6, 3, 69, 17, -78, 1, -79, 6, 127, 43, 26,
    127, -127, 28, -55, -26, 55, 112, 48, 107, -1, -77, -1, 53, -9, -22, -43,
    123, 108, 127, 102, 68, 46, 5, 1, 123, -13, -55, -34, -49, 89, 65, -105,
    -5, 94, -53, 62, 45, 30, 46, 18, -35, 15, 41, 47, -98, -24, 94, -75, 127,
    -114, 127, -68, 1, -17, 51, -95, 47, 12, 34, -45, -75, 89, -107, -9, -58,
    -29, -109, -24, 127, -61, -13, 77, -45, 17, 19, 83, -24, 9, 127, -66, 54,
    4, 26, 13, 111, 43, -113, -22, 10, -24, 83, 67, -14, 75, -123, 59, 127,
    -12, 99, -19, 64, -38, 54, 9, 7, 61, -56, 3, -57, 113, -104, -59, 3, -9,
    -47, 74, 85, -55, -34, 12, 118, 28, 93, -72, 13, -99, -72, -20, 30, 72,
    -94, 19, -54, 64, -12, -63, -25, 65, 72, -10, 127, 0, -127, 103, -20, -73,
    -112, -103, -6, 28, -42, -21, -59, -29, -26, 19, -4, -51, 94, -58, -95,
    -37, 35, 20, -69, 127, -19, -127, -22, -120, -53, 37, 74, -127, -1, -12,
    -119, -53, -28, 38, 69, 17, 16, -114, 89, 62, 24, 37, -23, 49, -101, -32,
    -9, -95, -53, 5, 93, -23, -49, -8, 51, 3, -75, -90, -10, -39, 127, -86,
    -22, 20, 20, 113, 75, 52, -31, 92, -63, 7, -12, 46, 36, 101, -43, -17, -53,
    -7, -38, -76, -31, -21, 62, 31, 62, 20, -127, 31, 64, 36, 102, -85, -10,
    77, 80, 58, -79, -8, 35, 8, 80, -24, -9, 3, -17, 72, 127, 83, -87, 55, 18,
    -119, -123, 36, 10, 127, 56, -55, 113, 13, 26, 32, -13, -48, 22, -13, 5,
    58, 27, 24, 26, -11, -36, 37, -92, 78, 81, 9, 51, 14, 67, -13, 0, 32, 45,
    -76, 32, -39, -22, -49, -127, -27, 31, -9, 36, 14, 71, 13, 57, 12, -53,
    -86, 53, -44, -35, 2, 127, 12, -66, -44, 46, -115, 3, 10, 56, -35, 119,
    -19, -61, 52, -59, -127, -49, -23, 4, -5, 17, -82, -6, 127, 25, 79, 67, 64,
    -25, 14, -64, -37, -127, -28, 21, -63, 66, -53, -41, 109, -62, 15, -22, 13,
    29, -63, 20, 27, 95, -44, -59, -116, -10, 79, -49, 22, -43, -16, 46, -47,
    -120, -36, -29, -52, -44, 29, 127, -13, 49, -9, -127, 75, -28, -23, 88, 59,
    11, -95, 81, -59, 58, 60, -26, 40, -92, -3, -22, -58, -45, -59, -22, -53,
    71, -29, 66, -32, -23, 14, -17, -66, -24, -28, -62, 47, 38, 17, 16, -37,
    -24, -11, 8, -27, -19, 59, 45, -49, -47, -4, -22, -81, 30, -67, -127, 74,
    102, 5, -18, 98, 34, -66, 42, -52, 7, -59, 24, -58, -19, -24, -118, -73,
    91, 15, -16, 79, -32, -79, -127, -36, 41, 77, -83, 2, 56, 22, -75, 127,
    -16, -21, 12, 31, 56, -113, -127, 90, 55, 61, 12, 55, -14, -113, -14, 32,
    49, -67, -17, 91, -10, 1, 21, 69, -70, 99, -19, -112, 66, -90, -10, -9,
    -71, 127, 50, -81, -49, 24, 61, -61, -111, 7, -41, 127, 88, -66, 108, -127,
    -6, 36, -14, 41, -50, 14, 14, 73, -101, -28, 77, 127, -8, -100, 88, 38,
    121, 88, -125, -60, 13, -94, -115, 20, -67, -87, -94, -119, 44, -28, -30,
    18, 5, -53, -61, 20, -43, 11, -77, -60, 13, 29, 3, 6, -72, 38, -60, -11,
    108, -53, 41, 66, -12, -127, -127, -49, 24, 29, 46, 36, 91, 34, -33, 116,
    -51, -34, -52, 91, 7, -83, 73, -26, -103, 24, -10, 76, 84, 5, 68, -80, -13,
    -17, -32, -48, 20, 50, 26, 10, 63, -104, -14, 37, 127, 114, 97, 35, 1, -33,
    -55, 127, -124, -33, 61, -7, 119, -32, -127, -53, -42, 63, 3, -5, -26, 70,
    -58, -33, -44, -43, 34, -56, -127, 127, 25, -35, -11, 16, -81, 29, -58, 40,
    -127, -127, 20, -47, -11, -36, -63, -52, -32, -82, 78, -76, -73, 8, 27,
    -72, -9, -74, -85, -86, -57, 25, 78, -10, -97, 35, -65, 8, -59, 14, 1, -42,
    32, -88, -44, 17, -3, -9, 59, 40, 12, -108, -40, 24, 34, 18, -28, 2, 51,
    -110, -4, 100, 1, 65, 22, 0, 127, 61, 45, 25, -31, 6, 9, -7, -48, 99, 16,
    44, -2, -40, 32, -39, -52, 10, -110, -19, 56, -127, 69, 26, 51, 92, 40, 61,
    -52, 45, -38, 13, 85, 122, 27, 66, 45, -111, -83, -3, 31, 37, 19, -36, 58,
    71, 39, -78, -47, 58, -78, 8, -62, -36, -14, 61, 42, -127, 71, -4, 24, -54,
    52, -127, 67, -4, -42, 30, -63, 59, -3, -1, -18, -46, -92, -81, -96, -14,
    -53, -10, -11, -77, 13, 1, 8, -67, -127, 127, -28, 26, -14, 18, -13, -26,
    2, 10, -46, -32, -15, 27, -31, -59, 59, 77, -121, 28, 40, -54, -62, -31,
    -21, -37, -32, -6, -127, -25, -60, 70, -127, 112, -127, 127, 88, -7, 116,
    110, 53, 87, -127, 3, 16, 23, 74, -106, -51, 3, 74, -82, -112, -74, 65, 81,
    25, 53, 127, -45, -50, -103, -41, -65, -29, 79, -67, 64, -33, -30, -8, 127,
    0, -13, -51, 67, -14, 5, -92, 29, -35, -8, -90, -57, -3, 36, 43, 44, -31,
    -69, -7, 36, 39, -51, 43, -81, 58, 6, 127, 12, 57, 66, 46, 59, -43, -42,
    41, -15, -120, 24, 3, -11, 19, -13, 51, 28, 3, 55, -48, -12, -1, 2, 97,
    -19, 29, 42, 13, 43, 78, -44, 56, -108, -43, -19, 127, 15, -11, -18, -81,
    83, -37, 77, -109, 15, 65, -50, 43, 12, 13, 27, 28, 61, 57, 30, 26, 106,
    -18, 56, 13, 97, 4, -8, -62, -103, 94, 108, -44, 52, 27, -47, -9, 105, -53,
    46, 89, 103, -33, 38, -34, 55, 51, 70, -94, -35, -87, -107, -19, -31, 9,
    -19, 79, -14, 77, 5, -19, -107, 85, 21, -45, -39, -42, 9, -29, 74, 47, -75,
    60, -127, 120, -112, -57, -32, 41, 7, 79, 76, 66, 57, 41, -25, 31, 37, -47,
    -36, 43, -73, -37, 63, 127, -69, -52, 90, -33, -61, 60, -55, 44, 15, 4,
    -67, 13, -92, 64, 29, -39, -3, 83, -2, -38, -85, -86, 58, 35, -69, -61, 29,
    -37, -95, -78, 4, 30, -4, -32, -80, -22, -9, -77, 46, 7, -93, -71, 65, 9,
    -50, 127, -70, 26, -12, -39, -114, 63, -127, -100, 4, -32, 111, 22, -60,
    65, -101, 26, -42, 21, -59, -27, -74, 2, -94, 6, 126, 5, 76, -88, -9, -43,
    -101, 127, 1, 125, 92, -63, 52, 56, 4, 81, -127, 127, 80, 127, -29, 30,
    116, -74, -17, -57, 105, 48, 45, 25, -72, 48, -38, -108, 31, -34, 4, -11,
    41, -127, 52, -104, -43, -37, 52, 2, 47, 87, -9, 77, 27, -41, -25, 90, 86,
    -56, 75, 10, 33, 78, 58, 127, 127, -7, -73, 49, -33, -106, -35, 38, 57, 53,
    -17, -4, 83, 52, -108, 54, -125, 28, 23, 56, -43, -88, -17, -6, 47, 23, -9,
    0, -13, 111, 75, 27, -52, -38, -34, 39, 30, 66, 39, 38, -64, 38, 3, 21,
    -32, -51, -28, 54, -38, -87, 20, 52, 115, 18, -81, -70, 0, -14, -46, -46,
    -3, 125, 16, -14, 23, -82, -84, -69, -20, -65, -127, 9, 81, -49, 61, 7,
    -36, -45, -42, 57, -26, 47, 20, -85, 46, -13, 41, -37, -75, -60, 86, -78,
    -127, 12, 50, 2, -3, 13, 47, 5, 19, -78, -55, -27, 65, -71, 12, -108, 20,
    -16, 11, -31, 63, -55, 37, 75, -17, 127, -73, -33, -28, -120, 105, 68, 106,
    -103, -106, 71, 61, 2, 23, -3, 33, -5, -15, -67, -15, -23, -54, 15, -63,
    76, 58, -110, 1, 83, -27, 22, 75, -39, -17, -11, 64, -17, -127, -54, -66,
    31, 96, 116, 3, -114, -7, -108, -63, 97, 9, 50, 8, 75, -28, 72, 112, -36,
    -112, 95, -50, 23, -13, -19, 55, 21, 23, 92, 91, 22, -49, 16, -75, 23, 9,
    -49, -97, -37, 49, -36, 36, -127, -86, 43, 127, -24, -24, 84, 83, -35, -34,
    -12, 109, 102, -38, 51, -68, 34, 19, -22, 49, -32, 127, 40, 24, -93, -4,
    -3, 105, 3, -58, -18, 8, 127, -18, 125, 68, 69, -62, 30, -36, 54, -57, -24,
    17, 43, -36, -27, -57, -67, -21, -10, -49, 68, 12, 65, 4, 48, 55, 127, -75,
    44, 89, -66, -13, -78, -82, -91, 22, 30, 33, -40, -87, -34, 96, -91, 39,
    10, -64, -3, -12, 127, -50, -37, -56, 23, -35, -36, -54, 90, -91, 2, 50,
    77, -6, -127, 16, 46, -5, -73, 0, -56, -18, -72, 28, 93, 60, 49, 20, 18,
    111, -111, 32, -83, 47, 47, -10, 35, -88, 43, 57, -98, 127, -17, 0, 1, -39,
    -127, -2, 0, 63, 93, 0, 36, -66, -61, -19, 39, -127, 58, 50, -17, 127, 88,
    -43, -108, -51, -16, 7, -36, 68, 46, -14, 107, 40, 57, 7, 19, 8, 3, 88,
    -90, -92, -18, -21, -24, 13, 7, -4, -78, -91, -4, 8, -35, -5, 19, 2, -111,
    4, -66, -81, 122, -20, -34, -37, -84, 127, 68, 46, 17, 47,
 
    // Repeat the beginning of the array to allow wrapping reads
    -11, 12, 103, -11,
};
 
static const uint32_t Seed_LUT[256] = {
    747538460, 1088979410, 1744950180, 1767011913, 1403382928,
    521866116, 1060417601, 2110622736, 1557184770, 105289385, 585624216,
    1827676546, 1191843873, 1018104344, 1123590530, 663361569, 2023850500,
    76561770, 1226763489, 80325252, 1992581442, 502705249, 740409860,
    516219202, 557974537, 1883843076, 720112066, 1640137737, 1820967556,
    40667586, 155354121, 1820967557, 1115949072, 1631803309, 98284748,
    287433856, 2119719977, 988742797, 1827432592, 579378475, 1017745956,
    1309377032, 1316535465, 2074315269, 1923385360, 209722667, 1546228260,
    168102420, 135274561, 355958469, 248291472, 2127839491, 146920100,
    585982612, 1611702337, 696506029, 1386498192, 1258072451, 1212240548,
    1043171860, 1217404993, 1090770605, 1386498193, 169093201, 541098240,
    1468005469, 456510673, 1578687785, 1838217424, 2010752065, 2089828354,
    1362717428, 970073673, 854129835, 714793201, 1266069081, 1047060864,
    1991471829, 1098097741, 913883585, 1669598224, 1337918685, 1219264706,
    1799741108, 1834116681, 683417731, 1120274457, 1073098457, 1648396544,
    176642749, 31171789, 718317889, 1266977808, 1400892508, 549749008,
    1808010512, 67112961, 1005669825, 903663673, 1771104465, 1277749632,
    1229754427, 950632997, 1979371465, 2074373264, 305357524, 1049387408,
    1171033360, 1686114305, 2147468765, 1941195985, 117709841, 809550080,
    991480851, 1816248997, 1561503561, 329575568, 780651196, 1659144592,
    1910793616, 604016641, 1665084765, 1530186961, 1870928913, 809550081,
    2079346113, 71307521, 876663040, 1073807360, 832356664, 1573927377,
    204073344, 2026918147, 1702476788, 2043881033, 57949587, 2001393952,
    1197426649, 1186508931, 332056865, 950043140, 890043474, 349099312,
    148914948, 236204097, 2022643605, 1441981517, 498130129, 1443421481,
    924216797, 1817491777, 1913146664, 1411989632, 929068432, 495735097,
    1684636033, 1284520017, 432816184, 1344884865, 210843729, 676364544,
    234449232, 12112337, 1350619139, 1753272996, 2037118872, 1408560528,
    533334916, 1043640385, 357326099, 201376421, 110375493, 541106497,
    416159637, 242512193, 777294080, 1614872576, 1535546636, 870600145,
    910810409, 1821440209, 1605432464, 1145147393, 951695441, 1758494976,
    1506656568, 1557150160, 608221521, 1073840384, 217672017, 684818688,
    1750138880, 16777217, 677990609, 953274371, 1770050213, 1359128393,
    1797602707, 1984616737, 1865815816, 2120835200, 2051677060, 1772234061,
    1579794881, 1652821009, 1742099468, 1887260865, 46468113, 1011925248,
    1134107920, 881643832, 1354774993, 472508800, 1892499769, 1752793472,
    1962502272, 687898625, 883538000, 1354355153, 1761673473, 944820481,
    2020102353, 22020353, 961597696, 1342242816, 964808962, 1355809701,
    17016649, 1386540177, 647682692, 1849012289, 751668241, 1557184768,
    127374604, 1927564752, 1045744913, 1614921984, 43588881, 1016185088,
    1544617984, 1090519041, 136122424, 215038417, 1563027841, 2026918145,
    1688778833, 701530369, 1372639488, 1342242817, 2036945104, 953274369,
    1750192384, 16842753, 964808960, 1359020032, 1358954497
};
 
// Note: This is pre-transposed, i.e. stored column-major order
static const int8_t R64T[64][64] = {
    {
         32,  45,  45,  45,  45,  45,  45,  45,  44,  44,  44,  44,  43,  43,  43,  42,
         42,  41,  41,  40,  40,  39,  39,  38,  38,  37,  36,  36,  35,  34,  34,  33,
         32,  31,  30,  30,  29,  28,  27,  26,  25,  24,  23,  22,  21,  20,  19,  18,
         17,  16,  15,  14,  13,  12,  11,  10,   9,   8,   7,   6,   4,   3,   2,   1,
    }, {
         32,  45,  45,  44,  43,  42,  41,  39,  38,  36,  34,  31,  29,  26,  23,  20,
         17,  14,  11,   8,   4,   1,  -2,  -6,  -9, -12, -15, -18, -21, -24, -27, -30,
        -32, -34, -36, -38, -40, -41, -43, -44, -44, -45, -45, -45, -45, -45, -44, -43,
        -42, -40, -39, -37, -35, -33, -30, -28, -25, -22, -19, -16, -13, -10,  -7,  -3,
    }, {
         32,  45,  44,  42,  40,  37,  34,  30,  25,  20,  15,  10,   4,  -1,  -7, -12,
        -17, -22, -27, -31, -35, -38, -41, -43, -44, -45, -45, -45, -43, -41, -39, -36,
        -32, -28, -23, -18, -13,  -8,  -2,   3,   9,  14,  19,  24,  29,  33,  36,  39,
         42,  44,  45,  45,  45,  44,  43,  40,  38,  34,  30,  26,  21,  16,  11,   6,
    }, {
         32,  45,  43,  39,  35,  30,  23,  16,   9,   1,  -7, -14, -21, -28, -34, -38,
        -42, -44, -45, -45, -43, -40, -36, -31, -25, -18, -11,  -3,   4,  12,  19,  26,
         32,  37,  41,  44,  45,  45,  44,  41,  38,  33,  27,  20,  13,   6,  -2, -10,
        -17, -24, -30, -36, -40, -43, -45, -45, -44, -42, -39, -34, -29, -22, -15,  -8,
    }, {
         32,  44,  41,  36,  29,  20,  11,   1,  -9, -18, -27, -34, -40, -44, -45, -45,
        -42, -37, -30, -22, -13,  -3,   7,  16,  25,  33,  39,  43,  45,  45,  43,  38,
         32,  24,  15,   6,  -4, -14, -23, -31, -38, -42, -45, -45, -43, -39, -34, -26,
        -17,  -8,   2,  12,  21,  30,  36,  41,  44,  45,  44,  40,  35,  28,  19,  10,
    }, {
         32,  44,  39,  31,  21,  10,  -2, -14, -25, -34, -41, -45, -45, -42, -36, -28,
        -17,  -6,   7,  18,  29,  37,  43,  45,  44,  40,  34,  24,  13,   1, -11, -22,
        -32, -39, -44, -45, -43, -38, -30, -20,  -9,   3,  15,  26,  35,  41,  45,  45,
         42,  36,  27,  16,   4,  -8, -19, -30, -38, -43, -45, -44, -40, -33, -23, -12,
    }, {
         32,  43,  36,  26,  13,  -1, -15, -28, -38, -44, -45, -42, -35, -24, -11,   3,
         17,  30,  39,  44,  45,  41,  34,  22,   9,  -6, -19, -31, -40, -45, -45, -40,
        -32, -20,  -7,   8,  21,  33,  41,  45,  44,  39,  30,  18,   4, -10, -23, -34,
        -42, -45, -44, -38, -29, -16,  -2,  12,  25,  36,  43,  45,  43,  37,  27,  14,
    }, {
         32,  42,  34,  20,   4, -12, -27, -38, -44, -45, -39, -28, -13,   3,  19,  33,
         42,  45,  43,  34,  21,   6, -11, -26, -38, -44, -45, -39, -29, -14,   2,  18,
         32,  41,  45,  43,  35,  22,   7, -10, -25, -37, -44, -45, -40, -30, -15,   1,
         17,  31,  41,  45,  43,  36,  23,   8,  -9, -24, -36, -44, -45, -40, -30, -16,
    }, {
         32,  41,  30,  14,  -4, -22, -36, -44, -44, -37, -23,  -6,  13,  30,  41,  45,
         42,  31,  15,  -3, -21, -36, -44, -45, -38, -24,  -7,  12,  29,  40,  45,  42,
         32,  16,  -2, -20, -35, -44, -45, -38, -25,  -8,  11,  28,  40,  45,  43,  33,
         17,  -1, -19, -34, -43, -45, -39, -26,  -9,  10,  27,  39,  45,  43,  34,  18,
    }, {
         32,  40,  27,   8, -13, -31, -43, -45, -38, -22,  -2,  18,  35,  44,  44,  34,
         17,  -3, -23, -38, -45, -42, -30, -12,   9,  28,  41,  45,  40,  26,   7, -14,
        -32, -43, -45, -37, -21,  -1,  19,  36,  44,  44,  34,  16,  -4, -24, -39, -45,
        -42, -30, -11,  10,  29,  41,  45,  39,  25,   6, -15, -33, -43, -45, -36, -20,
    }, {
         32,  39,  23,   1, -21, -38, -45, -40, -25,  -3,  19,  37,  45,  41,  27,   6,
        -17, -36, -45, -42, -29,  -8,  15,  34,  44,  43,  30,  10, -13, -33, -44, -44,
        -32, -12,  11,  31,  43,  44,  34,  14,  -9, -30, -43, -45, -35, -16,   7,  28,
         42,  45,  36,  18,  -4, -26, -41, -45, -38, -20,   2,  24,  40,  45,  39,  22,
    }, {
         32,  38,  19,  -6, -29, -43, -44, -31,  -9,  16,  36,  45,  40,  22,  -2, -26,
        -42, -45, -34, -12,  13,  34,  45,  41,  25,   1, -23, -40, -45, -36, -15,  10,
         32,  44,  43,  28,   4, -20, -39, -45, -38, -18,   7,  30,  43,  44,  30,   8,
        -17, -37, -45, -39, -21,   3,  27,  42,  44,  33,  11, -14, -35, -45, -41, -24,
    }, {
         32,  37,  15, -12, -35, -45, -39, -18,   9,  33,  45,  40,  21,  -6, -30, -44,
        -42, -24,   2,  28,  43,  43,  27,   1, -25, -42, -44, -30,  -4,  22,  41,  45,
         32,   8, -19, -39, -45, -34, -11,  16,  38,  45,  36,  14, -13, -36, -45, -38,
        -17,  10,  34,  45,  40,  20,  -7, -31, -44, -41, -23,   3,  29,  44,  43,  26,
    }, {
         32,  36,  11, -18, -40, -45, -30,  -3,  25,  43,  43,  24,  -4, -31, -45, -39,
        -17,  12,  36,  45,  35,  10, -19, -40, -44, -30,  -2,  26,  43,  42,  23,  -6,
        -32, -45, -39, -16,  13,  37,  45,  34,   9, -20, -41, -44, -29,  -1,  27,  44,
         42,  22,  -7, -33, -45, -38, -15,  14,  38,  45,  34,   8, -21, -41, -44, -28,
    }, {
         32,  34,   7, -24, -43, -41, -19,  12,  38,  45,  30,   1, -29, -45, -39, -14,
         17,  40,  44,  26,  -4, -33, -45, -36,  -9,  22,  43,  42,  21, -10, -36, -45,
        -32,  -3,  27,  44,  40,  16, -15, -39, -44, -28,   2,  31,  45,  37,  11, -20,
        -42, -43, -23,   8,  35,  45,  34,   6, -25, -44, -41, -18,  13,  38,  45,  30,
    }, {
         32,  33,   2, -30, -45, -36,  -7,  26,  44,  38,  11, -22, -43, -40, -15,  18,
         42,  42,  19, -14, -40, -44, -23,  10,  38,  45,  27,  -6, -35, -45, -30,   1,
         32,  45,  34,   3, -29, -45, -36,  -8,  25,  44,  39,  12, -21, -43, -41, -16,
         17,  41,  43,  20, -13, -39, -44, -24,   9,  37,  45,  28,  -4, -34, -45, -31,
    }, {
         32,  31,  -2, -34, -45, -28,   7,  37,  44,  24, -11, -39, -43, -20,  15,  41,
         42,  16, -19, -43, -40, -12,  23,  44,  38,   8, -27, -45, -35,  -3,  30,  45,
         32,  -1, -34, -45, -29,   6,  36,  45,  25, -10, -39, -44, -21,  14,  41,  42,
         17, -18, -43, -40, -13,  22,  44,  38,   9, -26, -45, -36,  -4,  30,  45,  33,
    }, {
         32,  30,  -7, -38, -43, -18,  19,  44,  38,   6, -30, -45, -29,   8,  39,  43,
         17, -20, -44, -37,  -4,  31,  45,  28,  -9, -39, -43, -16,  21,  44,  36,   3,
        -32, -45, -27,  10,  40,  42,  15, -22, -44, -36,  -2,  33,  45,  26, -11, -40,
        -42, -14,  23,  45,  35,   1, -34, -45, -25,  12,  41,  41,  13, -24, -45, -34,
    }, {
         32,  28, -11, -41, -40,  -8,  30,  45,  25, -14, -43, -38,  -4,  33,  45,  22,
        -17, -44, -36,  -1,  35,  44,  19, -20, -44, -34,   2,  37,  43,  16, -23, -45,
        -32,   6,  39,  42,  13, -26, -45, -30,   9,  40,  41,  10, -29, -45, -27,  12,
         42,  39,   7, -31, -45, -24,  15,  43,  38,   3, -34, -45, -21,  18,  44,  36,
    }, {
         32,  26, -15, -44, -35,   3,  39,  41,   9, -31, -45, -20,  21,  45,  30, -10,
        -42, -38,  -2,  36,  43,  14, -27, -45, -25,  16,  44,  34,  -4, -39, -41,  -8,
         32,  45,  19, -22, -45, -30,  11,  42,  38,   1, -36, -43, -13,  28,  45,  24,
        -17, -44, -34,   6,  40,  40,   7, -33, -44, -18,  23,  45,  29, -12, -43, -37,
    }, {
         32,  24, -19, -45, -29,  14,  44,  33,  -9, -42, -36,   3,  40,  39,   2, -37,
        -42,  -8,  34,  44,  13, -30, -45, -18,  25,  45,  23, -20, -45, -28,  15,  44,
         32, -10, -43, -36,   4,  40,  39,   1, -38, -41,  -7,  34,  43,  12, -30, -45,
        -17,  26,  45,  22, -21, -45, -27,  16,  44,  31, -11, -43, -35,   6,  41,  38,
    }, {
         32,  22, -23, -45, -21,  24,  45,  20, -25, -45, -19,  26,  45,  18, -27, -45,
        -17,  28,  45,  16, -29, -45, -15,  30,  44,  14, -30, -44, -13,  31,  44,  12,
        -32, -44, -11,  33,  43,  10, -34, -43,  -9,  34,  43,   8, -35, -42,  -7,  36,
         42,   6, -36, -41,  -4,  37,  41,   3, -38, -40,  -2,  38,  40,   1, -39, -39,
    }, {
         32,  20, -27, -45, -13,  33,  43,   6, -38, -39,   2,  41,  35, -10, -44, -30,
         17,  45,  23, -24, -45, -16,  30,  44,   9, -36, -41,  -1,  40,  37,  -7, -43,
        -32,  14,  45,  26, -21, -45, -19,  28,  44,  12, -34, -42,  -4,  38,  39,  -3,
        -42, -34,  11,  44,  29, -18, -45, -22,  25,  45,  15, -31, -43,  -8,  36,  40,
    }, {
         32,  18, -30, -43,  -4,  39,  36, -10, -44, -26,  23,  45,  13, -34, -41,   1,
         42,  33, -15, -45, -21,  28,  44,   8, -38, -38,   7,  44,  29, -20, -45, -16,
         32,  42,   2, -40, -35,  12,  45,  24, -25, -45, -11,  36,  40,  -3, -43, -31,
         17,  45,  19, -30, -43,  -6,  39,  37,  -9, -44, -27,  22,  45,  14, -34, -41,
    }, {
         32,  16, -34, -40,   4,  44,  27, -24, -44,  -8,  39,  36, -13, -45, -19,  31,
         42,  -1, -43, -30,  21,  45,  11, -37, -38,  10,  45,  22, -29, -43,  -2,  41,
         32, -18, -45, -14,  35,  39,  -7, -44, -25,  26,  44,   6, -40, -34,  15,  45,
         17, -33, -41,   3,  43,  28, -23, -45,  -9,  38,  36, -12, -45, -20,  30,  42,
    }, {
         32,  14, -36, -37,  13,  45,  15, -36, -38,  12,  45,  16, -35, -38,  11,  45,
         17, -34, -39,  10,  45,  18, -34, -39,   9,  45,  19, -33, -40,   8,  45,  20,
        -32, -40,   7,  45,  21, -31, -41,   6,  44,  22, -30, -41,   4,  44,  23, -30,
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