tor-browser

predictor_enc.c (46398B)

---

// Copyright 2016 Google Inc. All Rights Reserved.
//
// Use of this source code is governed by a BSD-style license
// that can be found in the COPYING file in the root of the source
// tree. An additional intellectual property rights grant can be found
// in the file PATENTS. All contributing project authors may
// be found in the AUTHORS file in the root of the source tree.
// -----------------------------------------------------------------------------
//
// Image transform methods for lossless encoder.
//
// Authors: Vikas Arora (vikaas.arora@gmail.com)
//          Jyrki Alakuijala (jyrki@google.com)
//          Urvang Joshi (urvang@google.com)
//          Vincent Rabaud (vrabaud@google.com)

#include <assert.h>
#include <stdlib.h>
#include <string.h>

#include "src/dsp/lossless.h"
#include "src/dsp/lossless_common.h"
#include "src/enc/vp8i_enc.h"
#include "src/enc/vp8li_enc.h"
#include "src/utils/utils.h"
#include "src/webp/encode.h"
#include "src/webp/format_constants.h"
#include "src/webp/types.h"

#define HISTO_SIZE (4 * 256)
static const int64_t kSpatialPredictorBias = 15ll << LOG_2_PRECISION_BITS;
static const int kPredLowEffort = 11;
static const uint32_t kMaskAlpha = 0xff000000;
static const int kNumPredModes = 14;

// Mostly used to reduce code size + readability
static WEBP_INLINE int GetMin(int a, int b) { return (a > b) ? b : a; }
static WEBP_INLINE int GetMax(int a, int b) { return (a < b) ? b : a; }

//------------------------------------------------------------------------------
// Methods to calculate Entropy (Shannon).

// Compute a bias for prediction entropy using a global heuristic to favor
// values closer to 0. Hence the final negative sign.
// 'exp_val' has a scaling factor of 1/100.
static int64_t PredictionCostBias(const uint32_t counts[256], uint64_t weight_0,
                                 uint64_t exp_val) {
 const int significant_symbols = 256 >> 4;
 const uint64_t exp_decay_factor = 6;  // has a scaling factor of 1/10
 uint64_t bits = (weight_0 * counts[0]) << LOG_2_PRECISION_BITS;
 int i;
 exp_val <<= LOG_2_PRECISION_BITS;
 for (i = 1; i < significant_symbols; ++i) {
   bits += DivRound(exp_val * (counts[i] + counts[256 - i]), 100);
   exp_val = DivRound(exp_decay_factor * exp_val, 10);
 }
 return -DivRound((int64_t)bits, 10);
}

static int64_t PredictionCostSpatialHistogram(
   const uint32_t accumulated[HISTO_SIZE], const uint32_t tile[HISTO_SIZE],
   int mode, int left_mode, int above_mode) {
 int i;
 int64_t retval = 0;
 for (i = 0; i < 4; ++i) {
   const uint64_t kExpValue = 94;
   retval += PredictionCostBias(&tile[i * 256], 1, kExpValue);
   // Compute the new cost if 'tile' is added to 'accumulate' but also add the
   // cost of the current histogram to guide the spatial predictor selection.
   // Basically, favor low entropy, locally and globally.
   retval += (int64_t)VP8LCombinedShannonEntropy(&tile[i * 256],
                                                 &accumulated[i * 256]);
 }
 // Favor keeping the areas locally similar.
 if (mode == left_mode) retval -= kSpatialPredictorBias;
 if (mode == above_mode) retval -= kSpatialPredictorBias;
 return retval;
}

static WEBP_INLINE void UpdateHisto(uint32_t histo_argb[HISTO_SIZE],
                                   uint32_t argb) {
 ++histo_argb[0 * 256 + (argb >> 24)];
 ++histo_argb[1 * 256 + ((argb >> 16) & 0xff)];
 ++histo_argb[2 * 256 + ((argb >> 8) & 0xff)];
 ++histo_argb[3 * 256 + (argb & 0xff)];
}

//------------------------------------------------------------------------------
// Spatial transform functions.

static WEBP_INLINE void PredictBatch(int mode, int x_start, int y,
                                    int num_pixels, const uint32_t* current,
                                    const uint32_t* upper, uint32_t* out) {
 if (x_start == 0) {
   if (y == 0) {
     // ARGB_BLACK.
     VP8LPredictorsSub[0](current, NULL, 1, out);
   } else {
     // Top one.
     VP8LPredictorsSub[2](current, upper, 1, out);
   }
   ++x_start;
   ++out;
   --num_pixels;
 }
 if (y == 0) {
   // Left one.
   VP8LPredictorsSub[1](current + x_start, NULL, num_pixels, out);
 } else {
   VP8LPredictorsSub[mode](current + x_start, upper + x_start, num_pixels,
                           out);
 }
}

#if (WEBP_NEAR_LOSSLESS == 1)
static int MaxDiffBetweenPixels(uint32_t p1, uint32_t p2) {
 const int diff_a = abs((int)(p1 >> 24) - (int)(p2 >> 24));
 const int diff_r = abs((int)((p1 >> 16) & 0xff) - (int)((p2 >> 16) & 0xff));
 const int diff_g = abs((int)((p1 >> 8) & 0xff) - (int)((p2 >> 8) & 0xff));
 const int diff_b = abs((int)(p1 & 0xff) - (int)(p2 & 0xff));
 return GetMax(GetMax(diff_a, diff_r), GetMax(diff_g, diff_b));
}

static int MaxDiffAroundPixel(uint32_t current, uint32_t up, uint32_t down,
                             uint32_t left, uint32_t right) {
 const int diff_up = MaxDiffBetweenPixels(current, up);
 const int diff_down = MaxDiffBetweenPixels(current, down);
 const int diff_left = MaxDiffBetweenPixels(current, left);
 const int diff_right = MaxDiffBetweenPixels(current, right);
 return GetMax(GetMax(diff_up, diff_down), GetMax(diff_left, diff_right));
}

static uint32_t AddGreenToBlueAndRed(uint32_t argb) {
 const uint32_t green = (argb >> 8) & 0xff;
 uint32_t red_blue = argb & 0x00ff00ffu;
 red_blue += (green << 16) | green;
 red_blue &= 0x00ff00ffu;
 return (argb & 0xff00ff00u) | red_blue;
}

static void MaxDiffsForRow(int width, int stride, const uint32_t* const argb,
                          uint8_t* const max_diffs, int used_subtract_green) {
 uint32_t current, up, down, left, right;
 int x;
 if (width <= 2) return;
 current = argb[0];
 right = argb[1];
 if (used_subtract_green) {
   current = AddGreenToBlueAndRed(current);
   right = AddGreenToBlueAndRed(right);
 }
 // max_diffs[0] and max_diffs[width - 1] are never used.
 for (x = 1; x < width - 1; ++x) {
   up = argb[-stride + x];
   down = argb[stride + x];
   left = current;
   current = right;
   right = argb[x + 1];
   if (used_subtract_green) {
     up = AddGreenToBlueAndRed(up);
     down = AddGreenToBlueAndRed(down);
     right = AddGreenToBlueAndRed(right);
   }
   max_diffs[x] = MaxDiffAroundPixel(current, up, down, left, right);
 }
}

// Quantize the difference between the actual component value and its prediction
// to a multiple of quantization, working modulo 256, taking care not to cross
// a boundary (inclusive upper limit).
static uint8_t NearLosslessComponent(uint8_t value, uint8_t predict,
                                    uint8_t boundary, int quantization) {
 const int residual = (value - predict) & 0xff;
 const int boundary_residual = (boundary - predict) & 0xff;
 const int lower = residual & ~(quantization - 1);
 const int upper = lower + quantization;
 // Resolve ties towards a value closer to the prediction (i.e. towards lower
 // if value comes after prediction and towards upper otherwise).
 const int bias = ((boundary - value) & 0xff) < boundary_residual;
 if (residual - lower < upper - residual + bias) {
   // lower is closer to residual than upper.
   if (residual > boundary_residual && lower <= boundary_residual) {
     // Halve quantization step to avoid crossing boundary. This midpoint is
     // on the same side of boundary as residual because midpoint >= residual
     // (since lower is closer than upper) and residual is above the boundary.
     return lower + (quantization >> 1);
   }
   return lower;
 } else {
   // upper is closer to residual than lower.
   if (residual <= boundary_residual && upper > boundary_residual) {
     // Halve quantization step to avoid crossing boundary. This midpoint is
     // on the same side of boundary as residual because midpoint <= residual
     // (since upper is closer than lower) and residual is below the boundary.
     return lower + (quantization >> 1);
   }
   return upper & 0xff;
 }
}

static WEBP_INLINE uint8_t NearLosslessDiff(uint8_t a, uint8_t b) {
 return (uint8_t)((((int)(a) - (int)(b))) & 0xff);
}

// Quantize every component of the difference between the actual pixel value and
// its prediction to a multiple of a quantization (a power of 2, not larger than
// max_quantization which is a power of 2, smaller than max_diff). Take care if
// value and predict have undergone subtract green, which means that red and
// blue are represented as offsets from green.
static uint32_t NearLossless(uint32_t value, uint32_t predict,
                            int max_quantization, int max_diff,
                            int used_subtract_green) {
 int quantization;
 uint8_t new_green = 0;
 uint8_t green_diff = 0;
 uint8_t a, r, g, b;
 if (max_diff <= 2) {
   return VP8LSubPixels(value, predict);
 }
 quantization = max_quantization;
 while (quantization >= max_diff) {
   quantization >>= 1;
 }
 if ((value >> 24) == 0 || (value >> 24) == 0xff) {
   // Preserve transparency of fully transparent or fully opaque pixels.
   a = NearLosslessDiff((value >> 24) & 0xff, (predict >> 24) & 0xff);
 } else {
   a = NearLosslessComponent(value >> 24, predict >> 24, 0xff, quantization);
 }
 g = NearLosslessComponent((value >> 8) & 0xff, (predict >> 8) & 0xff, 0xff,
                           quantization);
 if (used_subtract_green) {
   // The green offset will be added to red and blue components during decoding
   // to obtain the actual red and blue values.
   new_green = ((predict >> 8) + g) & 0xff;
   // The amount by which green has been adjusted during quantization. It is
   // subtracted from red and blue for compensation, to avoid accumulating two
   // quantization errors in them.
   green_diff = NearLosslessDiff(new_green, (value >> 8) & 0xff);
 }
 r = NearLosslessComponent(NearLosslessDiff((value >> 16) & 0xff, green_diff),
                           (predict >> 16) & 0xff, 0xff - new_green,
                           quantization);
 b = NearLosslessComponent(NearLosslessDiff(value & 0xff, green_diff),
                           predict & 0xff, 0xff - new_green, quantization);
 return ((uint32_t)a << 24) | ((uint32_t)r << 16) | ((uint32_t)g << 8) | b;
}
#endif  // (WEBP_NEAR_LOSSLESS == 1)

// Stores the difference between the pixel and its prediction in "out".
// In case of a lossy encoding, updates the source image to avoid propagating
// the deviation further to pixels which depend on the current pixel for their
// predictions.
static WEBP_INLINE void GetResidual(
   int width, int height, uint32_t* const upper_row,
   uint32_t* const current_row, const uint8_t* const max_diffs, int mode,
   int x_start, int x_end, int y, int max_quantization, int exact,
   int used_subtract_green, uint32_t* const out) {
 if (exact) {
   PredictBatch(mode, x_start, y, x_end - x_start, current_row, upper_row,
                out);
 } else {
   const VP8LPredictorFunc pred_func = VP8LPredictors[mode];
   int x;
   for (x = x_start; x < x_end; ++x) {
     uint32_t predict;
     uint32_t residual;
     if (y == 0) {
       predict = (x == 0) ? ARGB_BLACK : current_row[x - 1];  // Left.
     } else if (x == 0) {
       predict = upper_row[x];  // Top.
     } else {
       predict = pred_func(&current_row[x - 1], upper_row + x);
     }
#if (WEBP_NEAR_LOSSLESS == 1)
     if (max_quantization == 1 || mode == 0 || y == 0 || y == height - 1 ||
         x == 0 || x == width - 1) {
       residual = VP8LSubPixels(current_row[x], predict);
     } else {
       residual = NearLossless(current_row[x], predict, max_quantization,
                               max_diffs[x], used_subtract_green);
       // Update the source image.
       current_row[x] = VP8LAddPixels(predict, residual);
       // x is never 0 here so we do not need to update upper_row like below.
     }
#else
     (void)max_diffs;
     (void)height;
     (void)max_quantization;
     (void)used_subtract_green;
     residual = VP8LSubPixels(current_row[x], predict);
#endif
     if ((current_row[x] & kMaskAlpha) == 0) {
       // If alpha is 0, cleanup RGB. We can choose the RGB values of the
       // residual for best compression. The prediction of alpha itself can be
       // non-zero and must be kept though. We choose RGB of the residual to be
       // 0.
       residual &= kMaskAlpha;
       // Update the source image.
       current_row[x] = predict & ~kMaskAlpha;
       // The prediction for the rightmost pixel in a row uses the leftmost
       // pixel
       // in that row as its top-right context pixel. Hence if we change the
       // leftmost pixel of current_row, the corresponding change must be
       // applied
       // to upper_row as well where top-right context is being read from.
       if (x == 0 && y != 0) upper_row[width] = current_row[0];
     }
     out[x - x_start] = residual;
   }
 }
}

// Accessors to residual histograms.
static WEBP_INLINE uint32_t* GetHistoArgb(uint32_t* const all_histos,
                                         int subsampling_index, int mode) {
 return &all_histos[(subsampling_index * kNumPredModes + mode) * HISTO_SIZE];
}

static WEBP_INLINE const uint32_t* GetHistoArgbConst(
   const uint32_t* const all_histos, int subsampling_index, int mode) {
 return &all_histos[subsampling_index * kNumPredModes * HISTO_SIZE +
                    mode * HISTO_SIZE];
}

// Accessors to accumulated residual histogram.
static WEBP_INLINE uint32_t* GetAccumulatedHisto(uint32_t* all_accumulated,
                                                int subsampling_index) {
 return &all_accumulated[subsampling_index * HISTO_SIZE];
}

// Find and store the best predictor for a tile at subsampling
// 'subsampling_index'.
static void GetBestPredictorForTile(const uint32_t* const all_argb,
                                   int subsampling_index, int tile_x,
                                   int tile_y, int tiles_per_row,
                                   uint32_t* all_accumulated_argb,
                                   uint32_t** const all_modes,
                                   uint32_t* const all_pred_histos) {
 uint32_t* const accumulated_argb =
     GetAccumulatedHisto(all_accumulated_argb, subsampling_index);
 uint32_t* const modes = all_modes[subsampling_index];
 uint32_t* const pred_histos =
     &all_pred_histos[subsampling_index * kNumPredModes];
 // Prediction modes of the left and above neighbor tiles.
 const int left_mode =
     (tile_x > 0) ? (modes[tile_y * tiles_per_row + tile_x - 1] >> 8) & 0xff
                  : 0xff;
 const int above_mode =
     (tile_y > 0) ? (modes[(tile_y - 1) * tiles_per_row + tile_x] >> 8) & 0xff
                  : 0xff;
 int mode;
 int64_t best_diff = WEBP_INT64_MAX;
 uint32_t best_mode = 0;
 const uint32_t* best_histo =
     GetHistoArgbConst(all_argb, /*subsampling_index=*/0, best_mode);
 for (mode = 0; mode < kNumPredModes; ++mode) {
   const uint32_t* const histo_argb =
       GetHistoArgbConst(all_argb, subsampling_index, mode);
   const int64_t cur_diff = PredictionCostSpatialHistogram(
       accumulated_argb, histo_argb, mode, left_mode, above_mode);

   if (cur_diff < best_diff) {
     best_histo = histo_argb;
     best_diff = cur_diff;
     best_mode = mode;
   }
 }
 // Update the accumulated histogram.
 VP8LAddVectorEq(best_histo, accumulated_argb, HISTO_SIZE);
 modes[tile_y * tiles_per_row + tile_x] = ARGB_BLACK | (best_mode << 8);
 ++pred_histos[best_mode];
}

// Computes the residuals for the different predictors.
// If max_quantization > 1, assumes that near lossless processing will be
// applied, quantizing residuals to multiples of quantization levels up to
// max_quantization (the actual quantization level depends on smoothness near
// the given pixel).
static void ComputeResidualsForTile(
   int width, int height, int tile_x, int tile_y, int min_bits,
   uint32_t update_up_to_index, uint32_t* const all_argb,
   uint32_t* const argb_scratch, const uint32_t* const argb,
   int max_quantization, int exact, int used_subtract_green) {
 const int start_x = tile_x << min_bits;
 const int start_y = tile_y << min_bits;
 const int tile_size = 1 << min_bits;
 const int max_y = GetMin(tile_size, height - start_y);
 const int max_x = GetMin(tile_size, width - start_x);
 // Whether there exist columns just outside the tile.
 const int have_left = (start_x > 0);
 // Position and size of the strip covering the tile and adjacent columns if
 // they exist.
 const int context_start_x = start_x - have_left;
#if (WEBP_NEAR_LOSSLESS == 1)
 const int context_width = max_x + have_left + (max_x < width - start_x);
#endif
 // The width of upper_row and current_row is one pixel larger than image width
 // to allow the top right pixel to point to the leftmost pixel of the next row
 // when at the right edge.
 uint32_t* upper_row = argb_scratch;
 uint32_t* current_row = upper_row + width + 1;
 uint8_t* const max_diffs = (uint8_t*)(current_row + width + 1);
 int mode;
 // Need pointers to be able to swap arrays.
 uint32_t residuals[1 << MAX_TRANSFORM_BITS];
 assert(max_x <= (1 << MAX_TRANSFORM_BITS));
 for (mode = 0; mode < kNumPredModes; ++mode) {
   int relative_y;
   uint32_t* const histo_argb =
       GetHistoArgb(all_argb, /*subsampling_index=*/0, mode);
   if (start_y > 0) {
     // Read the row above the tile which will become the first upper_row.
     // Include a pixel to the left if it exists; include a pixel to the right
     // in all cases (wrapping to the leftmost pixel of the next row if it does
     // not exist).
     memcpy(current_row + context_start_x,
            argb + (start_y - 1) * width + context_start_x,
            sizeof(*argb) * (max_x + have_left + 1));
   }
   for (relative_y = 0; relative_y < max_y; ++relative_y) {
     const int y = start_y + relative_y;
     int relative_x;
     uint32_t* tmp = upper_row;
     upper_row = current_row;
     current_row = tmp;
     // Read current_row. Include a pixel to the left if it exists; include a
     // pixel to the right in all cases except at the bottom right corner of
     // the image (wrapping to the leftmost pixel of the next row if it does
     // not exist in the current row).
     memcpy(current_row + context_start_x,
            argb + y * width + context_start_x,
            sizeof(*argb) * (max_x + have_left + (y + 1 < height)));
#if (WEBP_NEAR_LOSSLESS == 1)
     if (max_quantization > 1 && y >= 1 && y + 1 < height) {
       MaxDiffsForRow(context_width, width, argb + y * width + context_start_x,
                      max_diffs + context_start_x, used_subtract_green);
     }
#endif

     GetResidual(width, height, upper_row, current_row, max_diffs, mode,
                 start_x, start_x + max_x, y, max_quantization, exact,
                 used_subtract_green, residuals);
     for (relative_x = 0; relative_x < max_x; ++relative_x) {
       UpdateHisto(histo_argb, residuals[relative_x]);
     }
     if (update_up_to_index > 0) {
       uint32_t subsampling_index;
       for (subsampling_index = 1; subsampling_index <= update_up_to_index;
            ++subsampling_index) {
         uint32_t* const super_histo =
             GetHistoArgb(all_argb, subsampling_index, mode);
         for (relative_x = 0; relative_x < max_x; ++relative_x) {
           UpdateHisto(super_histo, residuals[relative_x]);
         }
       }
     }
   }
 }
}

// Converts pixels of the image to residuals with respect to predictions.
// If max_quantization > 1, applies near lossless processing, quantizing
// residuals to multiples of quantization levels up to max_quantization
// (the actual quantization level depends on smoothness near the given pixel).
static void CopyImageWithPrediction(int width, int height, int bits,
                                   const uint32_t* const modes,
                                   uint32_t* const argb_scratch,
                                   uint32_t* const argb, int low_effort,
                                   int max_quantization, int exact,
                                   int used_subtract_green) {
 const int tiles_per_row = VP8LSubSampleSize(width, bits);
 // The width of upper_row and current_row is one pixel larger than image width
 // to allow the top right pixel to point to the leftmost pixel of the next row
 // when at the right edge.
 uint32_t* upper_row = argb_scratch;
 uint32_t* current_row = upper_row + width + 1;
 uint8_t* current_max_diffs = (uint8_t*)(current_row + width + 1);
#if (WEBP_NEAR_LOSSLESS == 1)
 uint8_t* lower_max_diffs = current_max_diffs + width;
#endif
 int y;

 for (y = 0; y < height; ++y) {
   int x;
   uint32_t* const tmp32 = upper_row;
   upper_row = current_row;
   current_row = tmp32;
   memcpy(current_row, argb + y * width,
          sizeof(*argb) * (width + (y + 1 < height)));

   if (low_effort) {
     PredictBatch(kPredLowEffort, 0, y, width, current_row, upper_row,
                  argb + y * width);
   } else {
#if (WEBP_NEAR_LOSSLESS == 1)
     if (max_quantization > 1) {
       // Compute max_diffs for the lower row now, because that needs the
       // contents of argb for the current row, which we will overwrite with
       // residuals before proceeding with the next row.
       uint8_t* const tmp8 = current_max_diffs;
       current_max_diffs = lower_max_diffs;
       lower_max_diffs = tmp8;
       if (y + 2 < height) {
         MaxDiffsForRow(width, width, argb + (y + 1) * width, lower_max_diffs,
                        used_subtract_green);
       }
     }
#endif
     for (x = 0; x < width;) {
       const int mode =
           (modes[(y >> bits) * tiles_per_row + (x >> bits)] >> 8) & 0xff;
       int x_end = x + (1 << bits);
       if (x_end > width) x_end = width;
       GetResidual(width, height, upper_row, current_row, current_max_diffs,
                   mode, x, x_end, y, max_quantization, exact,
                   used_subtract_green, argb + y * width + x);
       x = x_end;
     }
   }
 }
}

// Checks whether 'image' can be subsampled by finding the biggest power of 2
// squares (defined by 'best_bits') of uniform value it is made out of.
void VP8LOptimizeSampling(uint32_t* const image, int full_width,
                         int full_height, int bits, int max_bits,
                         int* best_bits_out) {
 int width = VP8LSubSampleSize(full_width, bits);
 int height = VP8LSubSampleSize(full_height, bits);
 int old_width, x, y, square_size;
 int best_bits = bits;
 *best_bits_out = bits;
 // Check rows first.
 while (best_bits < max_bits) {
   const int new_square_size = 1 << (best_bits + 1 - bits);
   int is_good = 1;
   square_size = 1 << (best_bits - bits);
   for (y = 0; y + square_size < height; y += new_square_size) {
     // Check the first lines of consecutive line groups.
     if (memcmp(&image[y * width], &image[(y + square_size) * width],
                width * sizeof(*image)) != 0) {
       is_good = 0;
       break;
     }
   }
   if (is_good) {
     ++best_bits;
   } else {
     break;
   }
 }
 if (best_bits == bits) return;

 // Check columns.
 while (best_bits > bits) {
   int is_good = 1;
   square_size = 1 << (best_bits - bits);
   for (y = 0; is_good && y < height; ++y) {
     for (x = 0; is_good && x < width; x += square_size) {
       int i;
       for (i = x + 1; i < GetMin(x + square_size, width); ++i) {
         if (image[y * width + i] != image[y * width + x]) {
           is_good = 0;
           break;
         }
       }
     }
   }
   if (is_good) {
     break;
   }
   --best_bits;
 }
 if (best_bits == bits) return;

 // Subsample the image.
 old_width = width;
 square_size = 1 << (best_bits - bits);
 width = VP8LSubSampleSize(full_width, best_bits);
 height = VP8LSubSampleSize(full_height, best_bits);
 for (y = 0; y < height; ++y) {
   for (x = 0; x < width; ++x) {
     image[y * width + x] = image[square_size * (y * old_width + x)];
   }
 }
 *best_bits_out = best_bits;
}

// Computes the best predictor image.
// Finds the best predictors per tile. Once done, finds the best predictor image
// sampling.
// best_bits is set to 0 in case of error.
// The following requires some glossary:
// - a tile is a square of side 2^min_bits pixels.
// - a super-tile of a tile is a square of side 2^bits pixels with bits in
// [min_bits+1, max_bits].
// - the max-tile of a tile is the square of 2^max_bits pixels containing it.
//   If this max-tile crosses the border of an image, it is cropped.
// - tile, super-tiles and max_tile are aligned on powers of 2 in the original
//   image.
// - coordinates for tile, super-tile, max-tile are respectively named
//   tile_x, super_tile_x, max_tile_x at their bit scale.
// - in the max-tile, a tile has local coordinates (local_tile_x, local_tile_y).
// The tiles are processed in the following zigzag order to complete the
// super-tiles as soon as possible:
//   1  2|  5  6
//   3  4|  7  8
// --------------
//   9 10| 13 14
//  11 12| 15 16
// When computing the residuals for a tile, the histogram of the above
// super-tile is updated. If this super-tile is finished, its histogram is used
// to update the histogram of the next super-tile and so on up to the max-tile.
static void GetBestPredictorsAndSubSampling(
   int width, int height, const int min_bits, const int max_bits,
   uint32_t* const argb_scratch, const uint32_t* const argb,
   int max_quantization, int exact, int used_subtract_green,
   const WebPPicture* const pic, int percent_range, int* const percent,
   uint32_t** const all_modes, int* best_bits, uint32_t** best_mode) {
 const uint32_t tiles_per_row = VP8LSubSampleSize(width, min_bits);
 const uint32_t tiles_per_col = VP8LSubSampleSize(height, min_bits);
 int64_t best_cost;
 uint32_t subsampling_index;
 const uint32_t max_subsampling_index = max_bits - min_bits;
 // Compute the needed memory size for residual histograms, accumulated
 // residual histograms and predictor histograms.
 const int num_argb = (max_subsampling_index + 1) * kNumPredModes * HISTO_SIZE;
 const int num_accumulated_rgb = (max_subsampling_index + 1) * HISTO_SIZE;
 const int num_predictors = (max_subsampling_index + 1) * kNumPredModes;
 uint32_t* const raw_data = (uint32_t*)WebPSafeCalloc(
     num_argb + num_accumulated_rgb + num_predictors, sizeof(uint32_t));
 uint32_t* const all_argb = raw_data;
 uint32_t* const all_accumulated_argb = all_argb + num_argb;
 uint32_t* const all_pred_histos = all_accumulated_argb + num_accumulated_rgb;
 const int max_tile_size = 1 << max_subsampling_index;  // in tile size
 int percent_start = *percent;
 // When using the residuals of a tile for its super-tiles, you can either:
 // - use each residual to update the histogram of the super-tile, with a cost
 //   of 4 * (1<<n)^2 increment operations (4 for the number of channels, and
 //   (1<<n)^2 for the number of pixels in the tile)
 // - use the histogram of the tile to update the histogram of the super-tile,
 //   with a cost of HISTO_SIZE (1024)
 // The first method is therefore faster until n==4. 'update_up_to_index'
 // defines the maximum subsampling_index for which the residuals should be
 // individually added to the super-tile histogram.
 const uint32_t update_up_to_index =
     GetMax(GetMin(4, max_bits), min_bits) - min_bits;
 // Coordinates in the max-tile in tile units.
 uint32_t local_tile_x = 0, local_tile_y = 0;
 uint32_t max_tile_x = 0, max_tile_y = 0;
 uint32_t tile_x = 0, tile_y = 0;

 *best_bits = 0;
 *best_mode = NULL;
 if (raw_data == NULL) return;

 while (tile_y < tiles_per_col) {
   ComputeResidualsForTile(width, height, tile_x, tile_y, min_bits,
                           update_up_to_index, all_argb, argb_scratch, argb,
                           max_quantization, exact, used_subtract_green);

   // Update all the super-tiles that are complete.
   subsampling_index = 0;
   while (1) {
     const uint32_t super_tile_x = tile_x >> subsampling_index;
     const uint32_t super_tile_y = tile_y >> subsampling_index;
     const uint32_t super_tiles_per_row =
         VP8LSubSampleSize(width, min_bits + subsampling_index);
     GetBestPredictorForTile(all_argb, subsampling_index, super_tile_x,
                             super_tile_y, super_tiles_per_row,
                             all_accumulated_argb, all_modes, all_pred_histos);
     if (subsampling_index == max_subsampling_index) break;

     // Update the following super-tile histogram if it has not been updated
     // yet.
     ++subsampling_index;
     if (subsampling_index > update_up_to_index &&
         subsampling_index <= max_subsampling_index) {
       VP8LAddVectorEq(
           GetHistoArgbConst(all_argb, subsampling_index - 1, /*mode=*/0),
           GetHistoArgb(all_argb, subsampling_index, /*mode=*/0),
           HISTO_SIZE * kNumPredModes);
     }
     // Check whether the super-tile is not complete (if the smallest tile
     // is not at the end of a line/column or at the beginning of a super-tile
     // of size (1 << subsampling_index)).
     if (!((tile_x == (tiles_per_row - 1) ||
            (local_tile_x + 1) % (1 << subsampling_index) == 0) &&
           (tile_y == (tiles_per_col - 1) ||
            (local_tile_y + 1) % (1 << subsampling_index) == 0))) {
       --subsampling_index;
       // subsampling_index now is the index of the last finished super-tile.
       break;
     }
   }
   // Reset all the histograms belonging to finished tiles.
   memset(all_argb, 0,
          HISTO_SIZE * kNumPredModes * (subsampling_index + 1) *
              sizeof(*all_argb));

   if (subsampling_index == max_subsampling_index) {
     // If a new max-tile is started.
     if (tile_x == (tiles_per_row - 1)) {
       max_tile_x = 0;
       ++max_tile_y;
     } else {
       ++max_tile_x;
     }
     local_tile_x = 0;
     local_tile_y = 0;
   } else {
     // Proceed with the Z traversal.
     uint32_t coord_x = local_tile_x >> subsampling_index;
     uint32_t coord_y = local_tile_y >> subsampling_index;
     if (tile_x == (tiles_per_row - 1) && coord_x % 2 == 0) {
       ++coord_y;
     } else {
       if (coord_x % 2 == 0) {
         ++coord_x;
       } else {
         // Z traversal.
         ++coord_y;
         --coord_x;
       }
     }
     local_tile_x = coord_x << subsampling_index;
     local_tile_y = coord_y << subsampling_index;
   }
   tile_x = max_tile_x * max_tile_size + local_tile_x;
   tile_y = max_tile_y * max_tile_size + local_tile_y;

   if (tile_x == 0 &&
       !WebPReportProgress(
           pic, percent_start + percent_range * tile_y / tiles_per_col,
           percent)) {
     WebPSafeFree(raw_data);
     return;
   }
 }

 // Figure out the best sampling.
 best_cost = WEBP_INT64_MAX;
 for (subsampling_index = 0; subsampling_index <= max_subsampling_index;
      ++subsampling_index) {
   int plane;
   const uint32_t* const accumulated =
       GetAccumulatedHisto(all_accumulated_argb, subsampling_index);
   int64_t cost = VP8LShannonEntropy(
       &all_pred_histos[subsampling_index * kNumPredModes], kNumPredModes);
   for (plane = 0; plane < 4; ++plane) {
     cost += VP8LShannonEntropy(&accumulated[plane * 256], 256);
   }
   if (cost < best_cost) {
     best_cost = cost;
     *best_bits = min_bits + subsampling_index;
     *best_mode = all_modes[subsampling_index];
   }
 }

 WebPSafeFree(raw_data);

 VP8LOptimizeSampling(*best_mode, width, height, *best_bits,
                      MAX_TRANSFORM_BITS, best_bits);
}

// Finds the best predictor for each tile, and converts the image to residuals
// with respect to predictions. If near_lossless_quality < 100, applies
// near lossless processing, shaving off more bits of residuals for lower
// qualities.
int VP8LResidualImage(int width, int height, int min_bits, int max_bits,
                     int low_effort, uint32_t* const argb,
                     uint32_t* const argb_scratch, uint32_t* const image,
                     int near_lossless_quality, int exact,
                     int used_subtract_green, const WebPPicture* const pic,
                     int percent_range, int* const percent,
                     int* const best_bits) {
 int percent_start = *percent;
 const int max_quantization = 1 << VP8LNearLosslessBits(near_lossless_quality);
 if (low_effort) {
   const int tiles_per_row = VP8LSubSampleSize(width, max_bits);
   const int tiles_per_col = VP8LSubSampleSize(height, max_bits);
   int i;
   for (i = 0; i < tiles_per_row * tiles_per_col; ++i) {
     image[i] = ARGB_BLACK | (kPredLowEffort << 8);
   }
   *best_bits = max_bits;
 } else {
   // Allocate data to try all samplings from min_bits to max_bits.
   int bits;
   uint32_t sum_num_pixels = 0u;
   uint32_t *modes_raw, *best_mode;
   uint32_t* modes[MAX_TRANSFORM_BITS + 1];
   uint32_t num_pixels[MAX_TRANSFORM_BITS + 1];
   for (bits = min_bits; bits <= max_bits; ++bits) {
     const int tiles_per_row = VP8LSubSampleSize(width, bits);
     const int tiles_per_col = VP8LSubSampleSize(height, bits);
     num_pixels[bits] = tiles_per_row * tiles_per_col;
     sum_num_pixels += num_pixels[bits];
   }
   modes_raw = (uint32_t*)WebPSafeMalloc(sum_num_pixels, sizeof(*modes_raw));
   if (modes_raw == NULL) return 0;
   // Have modes point to the right global memory modes_raw.
   modes[min_bits] = modes_raw;
   for (bits = min_bits + 1; bits <= max_bits; ++bits) {
     modes[bits] = modes[bits - 1] + num_pixels[bits - 1];
   }
   // Find the best sampling.
   GetBestPredictorsAndSubSampling(
       width, height, min_bits, max_bits, argb_scratch, argb, max_quantization,
       exact, used_subtract_green, pic, percent_range, percent,
       &modes[min_bits], best_bits, &best_mode);
   if (*best_bits == 0) {
     WebPSafeFree(modes_raw);
     return 0;
   }
   // Keep the best predictor image.
   memcpy(image, best_mode,
          VP8LSubSampleSize(width, *best_bits) *
              VP8LSubSampleSize(height, *best_bits) * sizeof(*image));
   WebPSafeFree(modes_raw);
 }

 CopyImageWithPrediction(width, height, *best_bits, image, argb_scratch, argb,
                         low_effort, max_quantization, exact,
                         used_subtract_green);
 return WebPReportProgress(pic, percent_start + percent_range, percent);
}

//------------------------------------------------------------------------------
// Color transform functions.

static WEBP_INLINE void MultipliersClear(VP8LMultipliers* const m) {
 m->green_to_red = 0;
 m->green_to_blue = 0;
 m->red_to_blue = 0;
}

static WEBP_INLINE void ColorCodeToMultipliers(uint32_t color_code,
                                              VP8LMultipliers* const m) {
 m->green_to_red  = (color_code >>  0) & 0xff;
 m->green_to_blue = (color_code >>  8) & 0xff;
 m->red_to_blue   = (color_code >> 16) & 0xff;
}

static WEBP_INLINE uint32_t MultipliersToColorCode(
   const VP8LMultipliers* const m) {
 return 0xff000000u |
        ((uint32_t)(m->red_to_blue) << 16) |
        ((uint32_t)(m->green_to_blue) << 8) |
        m->green_to_red;
}

static int64_t PredictionCostCrossColor(const uint32_t accumulated[256],
                                       const uint32_t counts[256]) {
 // Favor low entropy, locally and globally.
 // Favor small absolute values for PredictionCostSpatial
 static const uint64_t kExpValue = 240;
 return (int64_t)VP8LCombinedShannonEntropy(counts, accumulated) +
        PredictionCostBias(counts, 3, kExpValue);
}

static int64_t GetPredictionCostCrossColorRed(
   const uint32_t* argb, int stride, int tile_width, int tile_height,
   VP8LMultipliers prev_x, VP8LMultipliers prev_y, int green_to_red,
   const uint32_t accumulated_red_histo[256]) {
 uint32_t histo[256] = { 0 };
 int64_t cur_diff;

 VP8LCollectColorRedTransforms(argb, stride, tile_width, tile_height,
                               green_to_red, histo);

 cur_diff = PredictionCostCrossColor(accumulated_red_histo, histo);
 if ((uint8_t)green_to_red == prev_x.green_to_red) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if ((uint8_t)green_to_red == prev_y.green_to_red) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if (green_to_red == 0) {
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 return cur_diff;
}

static void GetBestGreenToRed(const uint32_t* argb, int stride, int tile_width,
                             int tile_height, VP8LMultipliers prev_x,
                             VP8LMultipliers prev_y, int quality,
                             const uint32_t accumulated_red_histo[256],
                             VP8LMultipliers* const best_tx) {
 const int kMaxIters = 4 + ((7 * quality) >> 8);  // in range [4..6]
 int green_to_red_best = 0;
 int iter, offset;
 int64_t best_diff = GetPredictionCostCrossColorRed(
     argb, stride, tile_width, tile_height, prev_x, prev_y, green_to_red_best,
     accumulated_red_histo);
 for (iter = 0; iter < kMaxIters; ++iter) {
   // ColorTransformDelta is a 3.5 bit fixed point, so 32 is equal to
   // one in color computation. Having initial delta here as 1 is sufficient
   // to explore the range of (-2, 2).
   const int delta = 32 >> iter;
   // Try a negative and a positive delta from the best known value.
   for (offset = -delta; offset <= delta; offset += 2 * delta) {
     const int green_to_red_cur = offset + green_to_red_best;
     const int64_t cur_diff = GetPredictionCostCrossColorRed(
         argb, stride, tile_width, tile_height, prev_x, prev_y,
         green_to_red_cur, accumulated_red_histo);
     if (cur_diff < best_diff) {
       best_diff = cur_diff;
       green_to_red_best = green_to_red_cur;
     }
   }
 }
 best_tx->green_to_red = (green_to_red_best & 0xff);
}

static int64_t GetPredictionCostCrossColorBlue(
   const uint32_t* argb, int stride, int tile_width, int tile_height,
   VP8LMultipliers prev_x, VP8LMultipliers prev_y, int green_to_blue,
   int red_to_blue, const uint32_t accumulated_blue_histo[256]) {
 uint32_t histo[256] = { 0 };
 int64_t cur_diff;

 VP8LCollectColorBlueTransforms(argb, stride, tile_width, tile_height,
                                green_to_blue, red_to_blue, histo);

 cur_diff = PredictionCostCrossColor(accumulated_blue_histo, histo);
 if ((uint8_t)green_to_blue == prev_x.green_to_blue) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if ((uint8_t)green_to_blue == prev_y.green_to_blue) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if ((uint8_t)red_to_blue == prev_x.red_to_blue) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if ((uint8_t)red_to_blue == prev_y.red_to_blue) {
   // favor keeping the areas locally similar
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if (green_to_blue == 0) {
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 if (red_to_blue == 0) {
   cur_diff -= 3ll << LOG_2_PRECISION_BITS;
 }
 return cur_diff;
}

#define kGreenRedToBlueNumAxis 8
#define kGreenRedToBlueMaxIters 7
static void GetBestGreenRedToBlue(const uint32_t* argb, int stride,
                                 int tile_width, int tile_height,
                                 VP8LMultipliers prev_x,
                                 VP8LMultipliers prev_y, int quality,
                                 const uint32_t accumulated_blue_histo[256],
                                 VP8LMultipliers* const best_tx) {
 const int8_t offset[kGreenRedToBlueNumAxis][2] =
     {{0, -1}, {0, 1}, {-1, 0}, {1, 0}, {-1, -1}, {-1, 1}, {1, -1}, {1, 1}};
 const int8_t delta_lut[kGreenRedToBlueMaxIters] = { 16, 16, 8, 4, 2, 2, 2 };
 const int iters =
     (quality < 25) ? 1 : (quality > 50) ? kGreenRedToBlueMaxIters : 4;
 int green_to_blue_best = 0;
 int red_to_blue_best = 0;
 int iter;
 // Initial value at origin:
 int64_t best_diff = GetPredictionCostCrossColorBlue(
     argb, stride, tile_width, tile_height, prev_x, prev_y, green_to_blue_best,
     red_to_blue_best, accumulated_blue_histo);
 for (iter = 0; iter < iters; ++iter) {
   const int delta = delta_lut[iter];
   int axis;
   for (axis = 0; axis < kGreenRedToBlueNumAxis; ++axis) {
     const int green_to_blue_cur =
         offset[axis][0] * delta + green_to_blue_best;
     const int red_to_blue_cur = offset[axis][1] * delta + red_to_blue_best;
     const int64_t cur_diff = GetPredictionCostCrossColorBlue(
         argb, stride, tile_width, tile_height, prev_x, prev_y,
         green_to_blue_cur, red_to_blue_cur, accumulated_blue_histo);
     if (cur_diff < best_diff) {
       best_diff = cur_diff;
       green_to_blue_best = green_to_blue_cur;
       red_to_blue_best = red_to_blue_cur;
     }
     if (quality < 25 && iter == 4) {
       // Only axis aligned diffs for lower quality.
       break;  // next iter.
     }
   }
   if (delta == 2 && green_to_blue_best == 0 && red_to_blue_best == 0) {
     // Further iterations would not help.
     break;  // out of iter-loop.
   }
 }
 best_tx->green_to_blue = green_to_blue_best & 0xff;
 best_tx->red_to_blue = red_to_blue_best & 0xff;
}
#undef kGreenRedToBlueMaxIters
#undef kGreenRedToBlueNumAxis

static VP8LMultipliers GetBestColorTransformForTile(
   int tile_x, int tile_y, int bits, VP8LMultipliers prev_x,
   VP8LMultipliers prev_y, int quality, int xsize, int ysize,
   const uint32_t accumulated_red_histo[256],
   const uint32_t accumulated_blue_histo[256], const uint32_t* const argb) {
 const int max_tile_size = 1 << bits;
 const int tile_y_offset = tile_y * max_tile_size;
 const int tile_x_offset = tile_x * max_tile_size;
 const int all_x_max = GetMin(tile_x_offset + max_tile_size, xsize);
 const int all_y_max = GetMin(tile_y_offset + max_tile_size, ysize);
 const int tile_width = all_x_max - tile_x_offset;
 const int tile_height = all_y_max - tile_y_offset;
 const uint32_t* const tile_argb = argb + tile_y_offset * xsize
                                 + tile_x_offset;
 VP8LMultipliers best_tx;
 MultipliersClear(&best_tx);

 GetBestGreenToRed(tile_argb, xsize, tile_width, tile_height,
                   prev_x, prev_y, quality, accumulated_red_histo, &best_tx);
 GetBestGreenRedToBlue(tile_argb, xsize, tile_width, tile_height,
                       prev_x, prev_y, quality, accumulated_blue_histo,
                       &best_tx);
 return best_tx;
}

static void CopyTileWithColorTransform(int xsize, int ysize,
                                      int tile_x, int tile_y,
                                      int max_tile_size,
                                      VP8LMultipliers color_transform,
                                      uint32_t* argb) {
 const int xscan = GetMin(max_tile_size, xsize - tile_x);
 int yscan = GetMin(max_tile_size, ysize - tile_y);
 argb += tile_y * xsize + tile_x;
 while (yscan-- > 0) {
   VP8LTransformColor(&color_transform, argb, xscan);
   argb += xsize;
 }
}

int VP8LColorSpaceTransform(int width, int height, int bits, int quality,
                           uint32_t* const argb, uint32_t* image,
                           const WebPPicture* const pic, int percent_range,
                           int* const percent, int* const best_bits) {
 const int max_tile_size = 1 << bits;
 const int tile_xsize = VP8LSubSampleSize(width, bits);
 const int tile_ysize = VP8LSubSampleSize(height, bits);
 int percent_start = *percent;
 uint32_t accumulated_red_histo[256] = { 0 };
 uint32_t accumulated_blue_histo[256] = { 0 };
 int tile_x, tile_y;
 VP8LMultipliers prev_x, prev_y;
 MultipliersClear(&prev_y);
 MultipliersClear(&prev_x);
 for (tile_y = 0; tile_y < tile_ysize; ++tile_y) {
   for (tile_x = 0; tile_x < tile_xsize; ++tile_x) {
     int y;
     const int tile_x_offset = tile_x * max_tile_size;
     const int tile_y_offset = tile_y * max_tile_size;
     const int all_x_max = GetMin(tile_x_offset + max_tile_size, width);
     const int all_y_max = GetMin(tile_y_offset + max_tile_size, height);
     const int offset = tile_y * tile_xsize + tile_x;
     if (tile_y != 0) {
       ColorCodeToMultipliers(image[offset - tile_xsize], &prev_y);
     }
     prev_x = GetBestColorTransformForTile(tile_x, tile_y, bits,
                                           prev_x, prev_y,
                                           quality, width, height,
                                           accumulated_red_histo,
                                           accumulated_blue_histo,
                                           argb);
     image[offset] = MultipliersToColorCode(&prev_x);
     CopyTileWithColorTransform(width, height, tile_x_offset, tile_y_offset,
                                max_tile_size, prev_x, argb);

     // Gather accumulated histogram data.
     for (y = tile_y_offset; y < all_y_max; ++y) {
       int ix = y * width + tile_x_offset;
       const int ix_end = ix + all_x_max - tile_x_offset;
       for (; ix < ix_end; ++ix) {
         const uint32_t pix = argb[ix];
         if (ix >= 2 &&
             pix == argb[ix - 2] &&
             pix == argb[ix - 1]) {
           continue;  // repeated pixels are handled by backward references
         }
         if (ix >= width + 2 &&
             argb[ix - 2] == argb[ix - width - 2] &&
             argb[ix - 1] == argb[ix - width - 1] &&
             pix == argb[ix - width]) {
           continue;  // repeated pixels are handled by backward references
         }
         ++accumulated_red_histo[(pix >> 16) & 0xff];
         ++accumulated_blue_histo[(pix >> 0) & 0xff];
       }
     }
   }
   if (!WebPReportProgress(
           pic, percent_start + percent_range * tile_y / tile_ysize,
           percent)) {
     return 0;
   }
 }
 VP8LOptimizeSampling(image, width, height, bits, MAX_TRANSFORM_BITS,
                      best_bits);
 return 1;
}