<commit_before><!--

Although you may be viewing an alternate representation, this document
is sourced in Markdown, a light-duty markup scheme, and is optimized for
the [kramdown](http://kramdown.rubyforge.org/) transformer.

See the accompanying README. External link targets are referenced at the
end of this file.

-->

Specification for WebP Lossless Bitstream 
=========================================

_2012-06-08_


Abstract
--------

WebP lossless is an image format for  lossless  compression
of ARGB images. The lossless format  stores  and  restores  the  pixel
values exactly, including the color values for zero alpha pixels.  The
format uses subresolution images, recursively embedded into the format
itself, for storing statistical data about the  images,  such  as  the
used entropy codes, spatial predictors, color  space  conversion,  and
color table. LZ77, Huffman coding, and a  color  cache  are  used  for
compression of the bulk data. Decoding speeds  faster  than  PNG  have
been demonstrated, as well as 25 % denser compression than what can be
achieved using today's PNG format.


* TOC placeholder
{:toc}


Nomenclature
------------

ARGB
: A pixel value consisting of alpha, red, green, and blue values.

ARGB image
: A two-dimensional array containing ARGB pixels.

color cache
: A small hash-addressed array to store recently used colors
  and to be able to recall them with shorter codes.

color indexing image
: A one-dimensional image of colors that can be
  indexed using a small integer (up to 256 within WebP lossless).

color transform image
: A two-dimensional subresolution image containing
  data about correlations of color components.

distance mapping
: Changes LZ77 distances to have the smallest values for
  pixels in 2d proximity.

entropy image
: A two-dimensional subresolution image indicating which
  entropy coding should be used in a respective square in the image,
  i.e., each pixel is a meta Huffman code.

Huffman code
: A classic way to do entropy coding where a smaller number of
  bits are used for more frequent codes.

LZ77
: Dictionary-based sliding window compression algorithm that either
  emits symbols or describes them as sequences of past symbols.

meta Huffman code
: A small integer (up to 16 bits) that indexes an element
  in the meta Huffman table.

predictor image
: A two-dimensional subresolution image indicating which
  spatial predictor is used for a particular square in the image.

prefix coding
: A way to entropy code larger integers that codes a few bits
  of the integer using an entropy code and codifies the remaining bits
  raw. This allows for the descriptions of the entropy codes to remain
  relatively small even when the range of symbols is large.

scan-line order
: A processing order of pixels, left-to-right, top-to-
  bottom, starting from the left-hand-top pixel, proceeding towards
  right. Once a row is completed, continue from the left-hand column of
  the next row.


Introduction
------------

This document describes the compressed data representation of a WebP
lossless image. It is intended as a detailed reference for WebP lossless
encoder and decoder implementation.

In this document, we use extensively the syntax of the C programming
language to describe the bitstream, and assume the existence of a function
for reading bits, ReadBits(n). The bytes are read in the natural order of
the stream containing them, and bits of each byte are read in the least-
significant-bit-first order. When multiple bits are read at the same time
the integer is constructed from the original data in the original order,
the most significant bits of the returned integer are also the most
significant bits of the original data. Thus the statement

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
b = ReadBits(2);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

is equivalent with the two statements below:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
b = ReadBits(1);         
b |= ReadBits(1) << 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We assume that each color component (e.g. alpha, red, blue and green) is
represented using an 8-bit byte. We define the corresponding type as uint8.
A whole ARGB pixel is represented by a type called uint32, an unsigned
integer consisting of 32 bits. In the code showing the behavior of the
transformations, alpha value is codified in bits 31..24, red in bits
23..16, green in bits 15..8 and blue in bits 7..0, but implementations of
the format are free to use another representation internally.

Broadly a WebP lossless image contains header data, transform information
and actual image data. Headers contain width and height of the image. A
WebP lossless image can go through five different types of transformation
before being entropy encoded. The transform information in the bitstream
contains the required data to apply the respective inverse transforms.


RIFF Header
-----------

The beginning of the header has the RIFF container. This consist of the
following 21 bytes:

   1. String "RIFF"
   2. A little-endian 32 bit value of the block length, the whole size of
      the block controlled by the RIFF header. Normally this equals the
      payload size (file size subtracted by 8 bytes, i.e., 4 bytes for
      'RIFF' identifier and 4 bytes for storing this value itself).
   3. String "WEBP" (RIFF container name).
   4. String "VP8L" (chunk tag for lossless encoded image data).
   5. A little-endian 32-bit value of the number of bytes in the lossless
      stream.
   6. One byte signature 0x64. Decoders need to accept also 0x65 as a valid
      stream, it has a planned future use. Today, a solid white image of the
      specified size should be shown for images having a 0x2f signature.

First 28 bits of the bitstream specify the width and height of the image.
Width and height are decoded as 14-bit integers as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int image_width = ReadBits(14) + 1;
int image_height = ReadBits(14) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The 14-bit dynamics for image size limit the maximum size of a WebP
lossless image to 16384✕16384 pixels.


Transformations
---------------

Transformations are reversible manipulations of the image data that can
reduce the remaining symbolic entropy by modeling spatial and color
correlations. Transformations can make the final compression more dense.

An image can go through four types of transformations. A 1 bit indicates
the presence of a transform. Every transform is allowed to be used only
once. The transformations are used only for the main level ARGB image -- the
subresolution images have no transforms, not even the 0 bit indicating the
end-of-transforms.

Typically an encoder would use these transforms to reduce the Shannon
entropy in the residual image. Also, the transform data can be decided
based on entropy minimization.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
while (ReadBits(1)) {  // Transform present.
  // Decode transform type.
  enum TransformType transform_type = ReadBits(2);
  // Decode transform data.
  ...
}

// Decode actual image data (section 4).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If a transform is present then the next two bits specify the transform
type. There are four types of transforms.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
enum TransformType {
  PREDICTOR_TRANSFORM             = 0,
  COLOR_TRANSFORM                 = 1,
  SUBTRACT_GREEN                  = 2,
  COLOR_INDEXING_TRANSFORM        = 3,
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The transform type is followed by the transform data. Transform data
contains the required information to apply the inverse transform and
depends on the transform type. Next we describe the transform data for
different types.


### Predictor transform

The predictor transform can be used to  reduce  entropy  by  exploiting  the
fact  that  neighboring  pixels  are  often  correlated.  In  the  predictor
transform, the current pixel value is  predicted  from  the  pixels  already
decoded  (in  scan-line  order)  and  only  the  residual  value  (actual  -
predicted)  is  encoded.  The  prediction  mode  determines  the   type   of
prediction to use. We divide the image into squares and all the pixels in  a
square use same prediction mode.

The first 4 bits of prediction data define the block  width  and  height  in
number of bits. The  number  of  block  columns,  block_xsize,  is  used  in
indexing two-dimensionally.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int size_bits = ReadBits(4);
int block_width = (1 << size_bits);
int block_height = (1 << size_bits);
#define DIV_ROUND_UP(num, den) ((num) + (den) - 1) / (den))
int block_xsize = DIV_ROUND_UP(image_width, 1 << size_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The transform data contains the prediction mode for each block of the
image. All the block_width * block_height pixels of a block use same
prediction mode. The prediction modes are treated as pixels of an image and
encoded using the same techniques described in chapter 4.

For a pixel x, y, one can compute the respective filter block address by:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int block_index = (y >> size_bits) * block_xsize +
                  (x >> size_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are 14 different prediction modes. In each prediction mode, the
current pixel value is predicted from one or more neighboring pixels whose
values are already known.

We choose the neighboring pixels (TL, T, TR, and L) of the current pixel
(P) as follows:


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
O    O    O    O    O    O    O    O    O    O    O
O    O    O    O    O    O    O    O    O    O    O
O    O    O    O    TL   T    TR   O    O    O    O
O    O    O    O    L    P    X    X    X    X    X
X    X    X    X    X    X    X    X    X    X    X
X    X    X    X    X    X    X    X    X    X    X
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

where TL means top-left, T top, TR top-right, L left pixel.
At the time of predicting a value for P, all pixels O, TL, T, TR and L have
been already processed, and pixel P and all pixels X are unknown.

Given the above neighboring pixels, the different prediction modes are
defined as follows.

| Mode   | Predicted value of each channel of the current pixel    |
| ------ | ------------------------------------------------------- |
|  0     | 0xff000000 (represents solid black color in ARGB)       |
|  1     | L                                                       |
|  2     | T                                                       |
|  3     | TR                                                      |
|  4     | TL                                                      |
|  5     | Average2(Average2(L, TR), T)                            |
|  6     | Average2(L, TL)                                         |
|  7     | Average2(L, T)                                          |
|  8     | Average2(TL, T)                                         |
|  9     | Average2(T, TR)                                         |
| 10     | Average2(Average2(L, TL), Average2(T, TR))              |
| 11     | Select(L, T, TL)                                        |
| 12     | ClampedAddSubtractFull(L, T, TL)                        |
| 13     | ClampedAddSubtractHalf(Average2(L, T), TL)              |


Average2 is defined as follows for each ARGB component:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
uint8 Average2(uint8 a, uint8 b) {
  return (a + b) / 2;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The Select predictor is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
uint32 Select(uint32 L, uint32 T, uint32 TL) {
  // L = left pixel, T = top pixel, TL = top left pixel.

  // ARGB component estimates for prediction.
  int pAlpha = ALPHA(L) + ALPHA(T) - ALPHA(TL);
  int pRed = RED(L) + RED(T) - RED(TL);
  int pGreen = GREEN(L) + GREEN(T) - GREEN(TL);
  int pBlue = BLUE(L) + BLUE(T) - BLUE(TL);

  // Manhattan distances to estimates for left and top pixels.
  int pL = abs(pAlpha - ALPHA(L)) + abs(pRed - RED(L)) +
           abs(pGreen - GREEN(L)) + abs(pBlue - BLUE(L));
  int pT = abs(pAlpha - ALPHA(T)) + abs(pRed - RED(T)) +
           abs(pGreen - GREEN(T)) + abs(pBlue - BLUE(T));

  // Return either left or top, the one closer to the prediction.
  if (pL <= pT) {
    return L;
  } else {
    return T;
  }
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The function ClampedAddSubstractFull and ClampedAddSubstractHalf are
performed for each ARGB component as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// Clamp the input value between 0 and 255.
int Clamp(int a) {
  return (a < 0) ? 0 : (a > 255) ?  255 : a;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int ClampAddSubtractFull(int a, int b, int c) {
  return Clamp(a + b - c);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int ClampAddSubtractHalf(int a, int b) {
  return Clamp(a + (a - b) / 2);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are special handling rules for some border pixels. If there is a
prediction transform, regardless of the mode [0..13] for these pixels, the
predicted value for the left-topmost pixel of the image is 0xff000000, L-
pixel for all pixels on the top row, and T-pixel for all pixels on the
leftmost column.

Addressing the TR-pixel for pixels on the rightmost column is exceptional.
The pixels on the rightmost column are predicted by using the modes [0..13]
just like pixels not on border, but by using the leftmost pixel on the same
row as the current TR-pixel. The TR-pixel offset in memory is the same fo
border and non-border pixels.


### Color Transform

The goal of the color transform is to decorrelate the R, G and B values of
each pixel. Color transform keeps the green (G) value as it is, transforms
red (R) based on green and transforms blue (B) based on green and then
based on red.

As is the case for the predictor transform, first the image is divided into
blocks and the same transform mode is used for all the pixels in a block.
For each block there are three types of color transform elements.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
typedef struct {
  uint8 green_to_red;
  uint8 green_to_blue;
  uint8 red_to_blue;
} ColorTransformElement;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The actual color transformation is done by defining a color transform
delta. The color transform delta depends on the ColorTransformElement which
is same for all the pixels in a particular block. The delta is added during
color transform. The inverse color transform then is just subtracting those
deltas.

The color transform function is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
 * Input:
 * red, green, blue values of the pixel
 * trans: Color transform element of the block where the
 *        pixel belongs to.
 *
 * Output:
 * *new_red = transformed value of red
 * *new_blue = transformed value of blue
 */
void ColorTransform(uint8 red, uint8 blue, uint8 green,
                    ColorTransformElement *trans,
                    uint8 *new_red, uint8 *new_blue) {
  // Transformed values of red and blue components
  uint32 tmp_red = red;
  uint32 tmp_blue = blue;

  // Applying transform is just adding the transform deltas
  tmp_red  += ColorTransformDelta(trans->green_to_red, green);
  tmp_blue += ColorTransformDelta(trans->green_to_blue, green);
  tmp_blue += ColorTransformDelta(trans->red_to_blue, red);

  *new_red = tmp_red & 0xff;
  *new_blue = tmp_blue & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ColorTransformDelta is computed using a signed 8-bit integer representing a
3.5-fixed-point number, and a signed 8-bit RGB color channel (c) [-
128..127] and is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int8 ColorTransformDelta(int8 t, int8 c) {
  return (t * c) >> 5;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The multiplication is to be done using more precision (with at least 16 bit
dynamics). The sign extension property of the shift operation does not
matter here: only the lowest 8 bits are used from the result, and there the
sign extension shifting and unsigned shifting are consistent with each
other.

Now we describe the contents of color transform data so that decoding can
apply the inverse color transform and recover the original red and blue
values. The first 4 bits of the color transform data contain the width and
height of the image block in number of bits, just like the predictor
transform:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int size_bits = ReadStream(4);
int block_width = 1 << size_bits;
int block_height = 1 << size_bits;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The remaining part of the color transform data contains
ColorTransformElement instances corresponding to each block of the image.
ColorTransformElement instances are treated as pixels of an image and
encoded using the methods described in section 4.

During decoding ColorTransformElement instances of the blocks are decoded
and the inverse color transform is applied on the ARGB values of the
pixels. As mentioned earlier that inverse color transform is just
subtracting ColorTransformElement values from the red and blue channels.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
 * Input:
 * red, blue and green values in the current state.
 * trans: Color transform element of the corresponding to the
 * block of the current pixel.
 *
 * Output:
 * new_red, new_blue: red, blue values after inverse transform.
 */
void InverseTransform(uint8 red, uint8 green, uint8 blue,
                      ColorTransfromElement *p,
                      uint8 *new_red, uint8 *new_blue) {
  // Applying inverse transform is just subtracting the
  // color transform deltas
  red  -= ColorTransformDelta(p->green_to_red_,  green);
  blue -= ColorTransformDelta(p->green_to_blue_, green);
  blue -= ColorTransformDelta(p->red_to_blue_, red & 0xff);

  *new_red = red & 0xff;
  *new_blue = blue & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


### Subtract Green Transform

The subtract green transform subtracts green values from red and blue
values of each pixel. When this transform is present, the decoder needs to
add the green value to both red and blue. There is no data associated with
this transform. The decoder applies the inverse transform as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
void AddGreenToBlueAndRed(uint8 green, uint8 *red, uint8 *blue) {
  *red  = (*red  + green) & 0xff;
  *blue = (*blue + green) & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This transform is redundant as it can be modeled using the color transform.
This transform is still often useful, and since it can extend the dynamics
of the color transform, and there is no additional data here, this
transform can be coded using less bits than a full blown color transform.


### Color Indexing Transform

If there are not many unique values of the pixels then it may be more
efficient to create a color index array and replace the pixel values by the
indices to this color index array. Color indexing transform is used to
achieve that. In the context of the WebP lossless, we specifically do not
call this transform a palette transform, since another slightly similar,
but more dynamic concept exists within WebP lossless encoding, called color
cache.

The color indexing transform checks for the number of unique ARGB values in
the image. If that number is below a threshold (256), it creates an array
of those ARGB values is created which replaces the pixel values with the
corresponding index. The green channel of the pixels are replaced with the
index, all alpha values are set to 255, all red and blue values to 0.

The transform data contains color table size and the entries in the color
table. The decoder reads the color indexing transform data as follow:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// 8 bit value for color table size
int color_table_size = ReadStream(8) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The color table is stored using the image storage format itself. The color
table can be obtained by reading an image, without the RIFF header, image
size, and transforms, assuming an height of one pixel, and a width of
color_table_size. The color table is always subtraction coded for reducing
the entropy of this image. The deltas of palette colors contain typically
much less entropy than the colors themselves leading to significant savings
for smaller images. In decoding, every final color in the color table can
be obtained by adding the previous color component values, by each ARGB-
component separately and storing the least significant 8 bits of the
result.

The inverse transform for the image is simply replacing the pixel values
(which are indices to the color table) with the actual color table values.
The indexing is done based on the green component of the ARGB color.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// Inverse transform
argb = color_table[GREEN(argb)];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When the color table is of a small size (equal to or less than 16 colors),
several pixels are bundled into a single pixel. The pixel bundling packs
several (2, 4, or 8) pixels into a single pixel reducing the image width
respectively. Pixel bundling allows for a more efficient joint distribution
entropy coding of neighboring pixels, and gives some arithmetic coding like
benefits to the entropy code, but it can only be used when there is a small
amount of unique values.

color_table_size specifies how many pixels are combined together:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int width_bits = 0;
if (color_table_size <= 2) {
  width_bits = 3;
} else if (color_table_size <= 4) {
  width_bits = 2;
} else if (color_table_size <= 16) {
  width_bits = 1;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The width_bits has a value of 0, 1, 2 or 3. A value of 0 indicates no pixel
bundling to be done for the image. A value of 1 indicates that two pixels
are combined together, and each pixel has a range of [0..15]. A value of 2
indicates that four pixels are combined together, and each pixel has a
range of [0..3]. A value of 3 indicates that eight pixels are combined
together and each pixels has a range of [0..1], i.e., a binary value.

The values are packed into the green component as follows:

  * width_bits = 1: for every x value where x ≡ 0 (mod 2), a green value
    at x is positioned into the 4 least-significant bits of the green
    value at x / 2, a green value at x + 1 is positioned into the 4 most-
    significant bits of the green value at x / 2.
  * width_bits = 2: for every x value where x ≡ 0 (mod 4), a green value
    at x is positioned into the 2 least-significant bits of the green
    value at x / 4, green values at x + 1 to x + 3 in order to the more
    significant bits of the green value at x / 4.
  * width_bits = 3: for every x value where x ≡ 0 (mod 8), a green value
    at x is positioned into the least-significant bit of the green value
    at x / 8, green values at x + 1 to x + 7 in order to the more
    significant bits of the green value at x / 8.


Image Data
----------

Image data is an array of pixel values in scan-line order. We use image
data in five different roles: The main role, an auxiliary role related to
entropy coding, and three further roles related to transforms.

  1. ARGB image.
  2. Entropy image. The red and green components define the meta Huffman
     code used in a particular area of the image.
  3. Predictor image. The green component defines which of the 14 values is
     used within a particular square of the image.
  4. Color indexing image. An array of up to 256 ARGB colors are used for
     transforming a green-only image, using the green value as an index to
     this one-dimensional array.
  5. Color transformation image. Defines signed 3.5 fixed-point multipliers
     that are used to predict the red, green, blue components to reduce
     entropy.

To divide the image into multiple regions, the image is first divided into
a set of fixed-size blocks (typically 16x16 blocks). Each of these blocks
can be modeled using an entropy code, in a way where several blocks can
share the same entropy code. There is a cost in transmitting an entropy
code, and in order to minimize this cost, statistically similar blocks can
share an entropy code. The blocks sharing an entropy code can be found by
clustering their statistical properties, or by repeatedly joining two
randomly selected clusters when it reduces the overall amount of bits
needed to encode the image. [See section "Decoding of meta Huffman codes"
in Chapter 5 for an explanation of how this entropy image is stored.]

Each pixel is encoded using one of three possible methods:

  1. Huffman coded literals, where each channel (green, alpha, red, blue)
     is entropy-coded independently,
  2. LZ77, a sequence of pixels in scan-line order copied from elsewhere in
     the image, or,
  3. Color cache, using a short multiplicative hash code (color cache
     index) of a recently seen color.

In the following sections we introduce the main concepts in LZ77 prefix
coding, LZ77 entropy coding, LZ77 distance mapping, and color cache codes.
The actual details of the entropy code are described in more detail in
chapter 5.


### LZ77 prefix coding

Prefix coding divides large integer values into two parts, the prefix code
and the extra bits. The benefit of this approach is that entropy coding is
later used only for the prefix code, reducing the resources needed by the
entropy code. The extra bits are stored as they are, without an entropy
code.

This prefix code is used for coding backward reference lengths and
distances. The extra bits form an integer that is added to the lower value
of the range. Hence the LZ77 lengths and distances are divided into prefix
codes and extra bits performing the Huffman coding only on the prefixes
reduces the size of the Huffman codes to tens of values instead of
otherwise a million (distance) or several thousands (length).

| Prefix code | Value range     | Extra bits |
| ----------- | --------------- | ---------- |
| 0           | 1               | 0          |
| 1           | 2               | 0          |
| 2           | 3               | 0          |
| 3           | 4               | 0          |
| 4           | 5..6            | 1          |
| 5           | 7..8            | 1          |
| 6           | 9..12           | 2          |
| 7           | 13..16          | 2          |
| ...         | ...             | ...        |
| 38          | 262145..524288  | 17         |
| 39          | 524289..1048576 | 17         |

The code to obtain a value from the prefix code is as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if (prefix_code < 4) {
  return prefix_code;
}
uint32 extra_bits = (prefix_code - 2) >> 1;
uint32 offset = (2 + (prefix_code & 1)) << extra_bits;
return offset + ReadBits(extra_bits) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


### LZ77 backward reference entropy coding

Backward references are tuples of length and distance. Length indicates how
many pixels in scan-line order are to be copied. The length is codified in
two steps: prefix and extra bits. Only the first 24 prefix codes with their
respective extra bits are used for length codes, limiting the maximum
length to 4096. For distances, all 40 prefix codes are used.


### LZ77 distance mapping

120 smallest distance codes [1..120] are reserved for a close neighborhood
within the current pixel. The rest are pure distance codes in scan-line
order, just offset by 120. The smallest codes are coded into x and y
offsets by the following table. Each tuple shows the x and the y
coordinates in 2d offsets -- for example the first tuple (0, 1) means 0 for
no difference in x, and 1 pixel difference in y (indicating previous row).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(0, 1),  (1, 0),  (1, 1),  (-1, 1), (0, 2),  (2, 0),  (1, 2),  (-1, 2),
(2, 1),  (-2, 1), (2, 2),  (-2, 2), (0, 3),  (3, 0),  (1, 3),  (-1, 3),
(3, 1),  (-3, 1), (2, 3),  (-2, 3), (3, 2),  (-3, 2), (0, 4),  (4, 0),
(1, 4),  (-1, 4), (4, 1),  (-4, 1), (3, 3),  (-3, 3), (2, 4),  (-2, 4),
(4, 2),  (-4, 2), (0, 5),  (3, 4),  (-3, 4), (4, 3),  (-4, 3), (5, 0),
(1, 5),  (-1, 5), (5, 1),  (-5, 1), (2, 5),  (-2, 5), (5, 2),  (-5, 2),
(4, 4),  (-4, 4), (3, 5),  (-3, 5), (5, 3),  (-5, 3), (0, 6),  (6, 0),
(1, 6),  (-1, 6), (6, 1),  (-6, 1), (2, 6),  (-2, 6), (6, 2),  (-6, 2), 
(4, 5),  (-4, 5), (5, 4),  (-5, 4), (3, 6),  (-3, 6), (6, 3),  (-6, 3), 
(0, 7),  (7, 0),  (1, 7),  (-1, 7), (5, 5),  (-5, 5), (7, 1),  (-7, 1),
(4, 6),  (-4, 6), (6, 4),  (-6, 4), (2, 7),  (-2, 7), (7, 2),  (-7, 2),
(3, 7),  (-3, 7), (7, 3),  (-7, 3), (5, 6),  (-5, 6), (6, 5),  (-6, 5),
(8, 0),  (4, 7),  (-4, 7), (7, 4),  (-7, 4), (8, 1),  (8, 2),  (6, 6),
(-6, 6), (8, 3),  (5, 7),  (-5, 7), (7, 5),  (-7, 5), (8, 4),  (6, 7),
(-6, 7), (7, 6),  (-7, 6), (8, 5),  (7, 7),  (-7, 7), (8, 6),  (8, 7)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The distances codes that map into these tuples are changes into scan-line
order distances using the following formula: dist = x + y * xsize, where
xsize is the width of the image in pixels.


### Color Cache Code

Color cache stores a set of colors that have been recently used in the
image. Using the color cache code, the color cache colors can be referred
more efficiently than emitting the respective ARGB values independently or
by sending them as backward references with a length of one pixel.

Color cache codes are coded as follows. First, there is a bit that
indicates if the color cache is used or not. If this bit is 0, no color
cache codes exist, and they are not transmitted in the Huffman code that
decodes the green symbols and the length prefix codes. However, if this bit
is 1, the color cache size is read:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int color_cache_code_bits = ReadBits(br, 4);
int color_cache_size = 1 << color_cache_code_bits;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color_cache_code_bits defines the size of the color_cache by (1 <<
color_cache_code_bits). The range of allowed values for
color_cache_code_bits is [1..11]. Compliant decoders must indicate a
corrupted bit stream for other values.

A color cache is an array of the size color_cache_size. Each entry stores
one ARGB color. Colors are looked up by indexing them by (0x1e35a7bd *
color) >> (32 - color_cache_code_bits). Only one lookup is done in a color
cache, there is no conflict resolution.

In the beginning of decoding or encoding of an image, all entries in all
color cache values are set to zero. The color cache code is converted to
this color at decoding time. The state of the color cache is maintained by
inserting every pixel, be it produced by backward referencing or as
literals, into the cache in the order they appear in the stream.


Entropy Code
------------

### Huffman coding

Most of the data is coded using a canonical Huffman code. This includes the
following:

  * A combined code that defines either the value of the green
    component, a color cache code, or a prefix of the length codes,
  * the data for alpha, red and blue components, and
  * prefixes of the distance codes.

The Huffman codes are transmitted by sending the code lengths, the actual
symbols are implicit and done in order for each length. The Huffman code
lengths are run-length-encoded using three different prefixes, and the
result of this coding is further Huffman coded.


### Spatially-variant Huffman coding

For every pixel (x, y) in the image, there is a definition of which entropy
code to use. First, there is an integer called 'meta Huffman code' that can
be obtained from a subresolution 2d image. This meta Huffman code
identifies a set of five Huffman codes, one for green (along with length
codes and color cache codes), one for each of red, blue and alpha, and one
for distance. The Huffman codes are identified by their position in a table
by an integer.

### Decoding flow of image data

Read next symbol S

  1. S < 256
     1. Use S as green component
     2. read alpha
     3. read red
     4. read blue
  2. S < 256 + 24
     1. Use S - 256 as a length prefix code
     2. read length extra bits
     3. read distance prefix code
     4. read distance extra bits
  3. S >= 256 + 24
     1. Use ARGB color from the color cache, at index S - 256 + 24


### Decoding the code lengths

There are two different ways to encode the code lengths of a Huffman code,
indicated by the first bit of the code: simple code length code (1), and
normal code length code (0).


#### Simple code length code

This variant can codify 1 or 2 non-zero length codes in the range of [0,
255]. All other code lengths are implicitly zeros.

The first bit indicates the number of codes:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int num_symbols = ReadBits(1) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The first symbol is stored either using a 1-bit code for values of 0 and 1,
or using a 8-bit code for values in range [0, 255]. The second symbol, when
present, is coded as an 8-bit code.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int first_symbol_len_code = VP8LReadBits(br, 1);
symbols[0] = ReadBits(1 + 7 * first_symbol_len_code);
if (num_symbols == 2) {
  symbols[1] = ReadBits(8);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Empty trees can be coded as trees that contain one 0 symbol, and can be
codified using four bits. For example, a distance tree can be empty if
there are no backward references. Similarly, alpha, red, and blue trees can
be empty if all pixels within the same meta Huffman code are produced using
the color cache.


#### Normal code length code

The code lengths of a Huffman code are read as follows. num_codes specifies
the number of code lengths, the rest of the codes lengths (according to the
order in kCodeLengthCodeOrder) are zeros.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int kCodeLengthCodes = 19;
int kCodeLengthCodeOrder[kCodeLengthCodes] = {
  17, 18, 0, 1, 2, 3, 4, 5, 16, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
};
int num_codes = 4 + ReadStream(4);
for (i = 0; i < num_codes; ++i) {
  code_lengths[kCodeLengthCodeOrder[i]] = ReadBits(3);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  * Code length code [0..15] indicate literal code lengths. 
    * Value 0 means no symbols have been coded, 
    * Values [1..15] indicate the bit length of the respective code. 
  * Code 16 repeats the previous non-zero value [3..6] times, i.e., 3 + ReadStream(2) times.  If code 16 is used before a non-zero value has been emitted, a value of 8 is repeated. 
  * Code 17 emits a streak of zeros [3..10], i.e., 3 + ReadStream(3) times. 
  * Code 18 emits a streak of zeros of length [11..138], i.e., 11 + ReadStream(7) times.

The entropy codes for alpha, red and blue have a total of 256 symbols. The
entropy code for distance prefix codes has 40 symbols. The entropy code for
green has 256 + 24 + color_cache_size, 256 symbols for different green
symbols, 24 length code prefix symbols, and symbols for the color cache.

The meta Huffman code, specified in the next section, defines how many
Huffman codes there are. There are always 5 times the number of Huffman
codes to the number of meta Huffman codes.


### Decoding of meta Huffman codes

There are two ways to code the meta Huffman codes, indicated by one bit
for the ARGB image and is an implicit zero, i.e., not present in the
stream for all predictor images and Huffman image itself. 

If this bit is zero, there is only one meta Huffman code, using Huffman
codes 0, 1, 2, 3 and 4 for green, alpha, red, blue and distance,
respectively. This meta Huffman code is used everywhere in the image.

If this bit is one, the meta Huffman codes are controlled by the entropy
image, where the index of the meta Huffman code is codified in the red and
green components. The index can be obtained from the uint32 value by
((pixel >> 8) & 0xffff), thus there can be up to 65536 unique meta Huffman
codes. When decoding a Huffman encoded symbol at a pixel x, y, one chooses
the meta Huffman code respective to these coordinates. However, not all
bits of the coordinates are used for choosing the meta Huffman code, i.e.,
the entropy image is of subresolution to the real image.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int huffman_bits = ReadBits(4);
int huffman_xsize = DIV_ROUND_UP(xsize, 1 << huffman_bits);
int huffman_ysize = DIV_ROUND_UP(ysize, 1 << huffman_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

huffman_bits gives the amount of subsampling in the entropy image.

After reading the huffman_bits, an entropy image stream of size
huffman_xsize, huffman_ysize is read.

The meta Huffman code, identifying the five Huffman codes per meta Huffman
code, is coded only by the number of codes:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int num_meta_codes = max(entropy_image) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, we can obtain the five Huffman codes for green, alpha, red, blue and
distance for a given (x, y) by the following expression:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
meta_codes[(entropy_image[(y >> huffman_bits) * huffman_xsize +
                          (x >> huffman_bits)] >> 8) & 0xffff]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The huffman_code[5 * meta_code + k], codes with k == 0 are for the green &
length code, k == 4 for the distance code, and the codes at k == 1, 2, and
3, are for codes of length 256 for red, blue and alpha, respectively.

The value of k for the reference position in meta_code determines the
length of the Huffman code:

  * k = 0; length = 256 + 24 + cache_size
  * k = 1, 2, or 3;  length = 256
  * k = 4, length = 40.


Overall Structure of the Format
-------------------------------

Below there is a eagles-eye-view into the format in Backus-Naur form. It 
does not cover all details. End-of-image EOI is only implicitly coded into
the number of pixels (xsize * ysize).<commit_msg>Apply inline emphasis and monospacing, per gdoc / PDF<commit_after><!--

Although you may be viewing an alternate representation, this document
is sourced in Markdown, a light-duty markup scheme, and is optimized for
the [kramdown](http://kramdown.rubyforge.org/) transformer.

See the accompanying README. External link targets are referenced at the
end of this file.

-->

Specification for WebP Lossless Bitstream 
=========================================

_2012-06-08_


Abstract
--------

WebP lossless is an image format for  lossless  compression
of ARGB images. The lossless format  stores  and  restores  the  pixel
values exactly, including the color values for zero alpha pixels.  The
format uses subresolution images, recursively embedded into the format
itself, for storing statistical data about the  images,  such  as  the
used entropy codes, spatial predictors, color  space  conversion,  and
color table. LZ77, Huffman coding, and a  color  cache  are  used  for
compression of the bulk data. Decoding speeds  faster  than  PNG  have
been demonstrated, as well as 25 % denser compression than what can be
achieved using today's PNG format.


* TOC placeholder
{:toc}


Nomenclature
------------

ARGB
: A pixel value consisting of alpha, red, green, and blue values.

ARGB image
: A two-dimensional array containing ARGB pixels.

color cache
: A small hash-addressed array to store recently used colors
  and to be able to recall them with shorter codes.

color indexing image
: A one-dimensional image of colors that can be
  indexed using a small integer (up to 256 within WebP lossless).

color transform image
: A two-dimensional subresolution image containing
  data about correlations of color components.

distance mapping
: Changes LZ77 distances to have the smallest values for
  pixels in 2d proximity.

entropy image
: A two-dimensional subresolution image indicating which
  entropy coding should be used in a respective square in the image,
  i.e., each pixel is a meta Huffman code.

Huffman code
: A classic way to do entropy coding where a smaller number of
  bits are used for more frequent codes.

LZ77
: Dictionary-based sliding window compression algorithm that either
  emits symbols or describes them as sequences of past symbols.

meta Huffman code
: A small integer (up to 16 bits) that indexes an element
  in the meta Huffman table.

predictor image
: A two-dimensional subresolution image indicating which
  spatial predictor is used for a particular square in the image.

prefix coding
: A way to entropy code larger integers that codes a few bits
  of the integer using an entropy code and codifies the remaining bits
  raw. This allows for the descriptions of the entropy codes to remain
  relatively small even when the range of symbols is large.

scan-line order
: A processing order of pixels, left-to-right, top-to-
  bottom, starting from the left-hand-top pixel, proceeding towards
  right. Once a row is completed, continue from the left-hand column of
  the next row.


Introduction
------------

This document describes the compressed data representation of a WebP
lossless image. It is intended as a detailed reference for WebP lossless
encoder and decoder implementation.

In this document, we use extensively the syntax of the C programming
language to describe the bitstream, and assume the existence of a
function for reading bits, `ReadBits(n)`. The bytes are read in the
natural order of the stream containing them, and bits of each byte are
read in the least-significant-bit-first order. When multiple bits are
read at the same time the integer is constructed from the original data
in the original order, the most significant bits of the returned
integer are also the most significant bits of the original data. Thus
the statement

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
b = ReadBits(2);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

is equivalent with the two statements below:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
b = ReadBits(1);         
b |= ReadBits(1) << 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We assume that each color component (e.g. alpha, red, blue and green) is
represented using an 8-bit byte. We define the corresponding type as uint8.
A whole ARGB pixel is represented by a type called uint32, an unsigned
integer consisting of 32 bits. In the code showing the behavior of the
transformations, alpha value is codified in bits 31..24, red in bits
23..16, green in bits 15..8 and blue in bits 7..0, but implementations of
the format are free to use another representation internally.

Broadly a WebP lossless image contains header data, transform information
and actual image data. Headers contain width and height of the image. A
WebP lossless image can go through five different types of transformation
before being entropy encoded. The transform information in the bitstream
contains the required data to apply the respective inverse transforms.


RIFF Header
-----------

The beginning of the header has the RIFF container. This consist of the
following 21 bytes:

   1. String "RIFF"
   2. A little-endian 32 bit value of the block length, the whole size of
      the block controlled by the RIFF header. Normally this equals the
      payload size (file size subtracted by 8 bytes, i.e., 4 bytes for
      'RIFF' identifier and 4 bytes for storing this value itself).
   3. String "WEBP" (RIFF container name).
   4. String "VP8L" (chunk tag for lossless encoded image data).
   5. A little-endian 32-bit value of the number of bytes in the lossless
      stream.
   6. One byte signature 0x64. Decoders need to accept also 0x65 as a valid
      stream, it has a planned future use. Today, a solid white image of the
      specified size should be shown for images having a 0x2f signature.

First 28 bits of the bitstream specify the width and height of the image.
Width and height are decoded as 14-bit integers as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int image_width = ReadBits(14) + 1;
int image_height = ReadBits(14) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The 14-bit dynamics for image size limit the maximum size of a WebP
lossless image to 16384✕16384 pixels.


Transformations
---------------

Transformations are reversible manipulations of the image data that can
reduce the remaining symbolic entropy by modeling spatial and color
correlations. Transformations can make the final compression more dense.

An image can go through four types of transformations. A 1 bit indicates
the presence of a transform. Every transform is allowed to be used only
once. The transformations are used only for the main level ARGB image -- the
subresolution images have no transforms, not even the 0 bit indicating the
end-of-transforms.

Typically an encoder would use these transforms to reduce the Shannon
entropy in the residual image. Also, the transform data can be decided
based on entropy minimization.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
while (ReadBits(1)) {  // Transform present.
  // Decode transform type.
  enum TransformType transform_type = ReadBits(2);
  // Decode transform data.
  ...
}

// Decode actual image data (section 4).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If a transform is present then the next two bits specify the transform
type. There are four types of transforms.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
enum TransformType {
  PREDICTOR_TRANSFORM             = 0,
  COLOR_TRANSFORM                 = 1,
  SUBTRACT_GREEN                  = 2,
  COLOR_INDEXING_TRANSFORM        = 3,
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The transform type is followed by the transform data. Transform data
contains the required information to apply the inverse transform and
depends on the transform type. Next we describe the transform data for
different types.


### Predictor transform

The predictor transform can be used to reduce entropy by exploiting the
fact that neighboring pixels are often correlated. In the predictor
transform, the current pixel value is predicted from the pixels already
decoded (in scan-line order) and only the residual value (actual -
predicted) is encoded. The _prediction mode_ determines the type of
prediction to use. We divide the image into squares and all the pixels
in a square use same prediction mode.

The first 4 bits of prediction data define the block width and height in
number of bits. The number of block columns, _block_xsize_, is used in
indexing two-dimensionally.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int size_bits = ReadBits(4);
int block_width = (1 << size_bits);
int block_height = (1 << size_bits);
#define DIV_ROUND_UP(num, den) ((num) + (den) - 1) / (den))
int block_xsize = DIV_ROUND_UP(image_width, 1 << size_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The transform data contains the prediction mode for each block of the
image. All the `block_width * block_height` pixels of a block use same
prediction mode. The prediction modes are treated as pixels of an image
and encoded using the same techniques described in chapter 4.

For a pixel _x, y_, one can compute the respective filter block address
by:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int block_index = (y >> size_bits) * block_xsize +
                  (x >> size_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are 14 different prediction modes. In each prediction mode, the
current pixel value is predicted from one or more neighboring pixels whose
values are already known.

We choose the neighboring pixels (TL, T, TR, and L) of the current pixel
(P) as follows:


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
O    O    O    O    O    O    O    O    O    O    O
O    O    O    O    O    O    O    O    O    O    O
O    O    O    O    TL   T    TR   O    O    O    O
O    O    O    O    L    P    X    X    X    X    X
X    X    X    X    X    X    X    X    X    X    X
X    X    X    X    X    X    X    X    X    X    X
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

where TL means top-left, T top, TR top-right, L left pixel.
At the time of predicting a value for P, all pixels O, TL, T, TR and L have
been already processed, and pixel P and all pixels X are unknown.

Given the above neighboring pixels, the different prediction modes are
defined as follows.

| Mode   | Predicted value of each channel of the current pixel    |
| ------ | ------------------------------------------------------- |
|  0     | 0xff000000 (represents solid black color in ARGB)       |
|  1     | L                                                       |
|  2     | T                                                       |
|  3     | TR                                                      |
|  4     | TL                                                      |
|  5     | Average2(Average2(L, TR), T)                            |
|  6     | Average2(L, TL)                                         |
|  7     | Average2(L, T)                                          |
|  8     | Average2(TL, T)                                         |
|  9     | Average2(T, TR)                                         |
| 10     | Average2(Average2(L, TL), Average2(T, TR))              |
| 11     | Select(L, T, TL)                                        |
| 12     | ClampedAddSubtractFull(L, T, TL)                        |
| 13     | ClampedAddSubtractHalf(Average2(L, T), TL)              |


`Average2` is defined as follows for each ARGB component:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
uint8 Average2(uint8 a, uint8 b) {
  return (a + b) / 2;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The Select predictor is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
uint32 Select(uint32 L, uint32 T, uint32 TL) {
  // L = left pixel, T = top pixel, TL = top left pixel.

  // ARGB component estimates for prediction.
  int pAlpha = ALPHA(L) + ALPHA(T) - ALPHA(TL);
  int pRed = RED(L) + RED(T) - RED(TL);
  int pGreen = GREEN(L) + GREEN(T) - GREEN(TL);
  int pBlue = BLUE(L) + BLUE(T) - BLUE(TL);

  // Manhattan distances to estimates for left and top pixels.
  int pL = abs(pAlpha - ALPHA(L)) + abs(pRed - RED(L)) +
           abs(pGreen - GREEN(L)) + abs(pBlue - BLUE(L));
  int pT = abs(pAlpha - ALPHA(T)) + abs(pRed - RED(T)) +
           abs(pGreen - GREEN(T)) + abs(pBlue - BLUE(T));

  // Return either left or top, the one closer to the prediction.
  if (pL <= pT) {
    return L;
  } else {
    return T;
  }
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The function `ClampedAddSubstractFull` and `ClampedAddSubstractHalf` are
performed for each ARGB component as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// Clamp the input value between 0 and 255.
int Clamp(int a) {
  return (a < 0) ? 0 : (a > 255) ?  255 : a;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int ClampAddSubtractFull(int a, int b, int c) {
  return Clamp(a + b - c);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int ClampAddSubtractHalf(int a, int b) {
  return Clamp(a + (a - b) / 2);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are special handling rules for some border pixels. If there is a
prediction transform, regardless of the mode [0..13] for these pixels, the
predicted value for the left-topmost pixel of the image is 0xff000000, L-
pixel for all pixels on the top row, and T-pixel for all pixels on the
leftmost column.

Addressing the TR-pixel for pixels on the rightmost column is exceptional.
The pixels on the rightmost column are predicted by using the modes [0..13]
just like pixels not on border, but by using the leftmost pixel on the same
row as the current TR-pixel. The TR-pixel offset in memory is the same fo
border and non-border pixels.


### Color Transform

The goal of the color transform is to decorrelate the R, G and B values of
each pixel. Color transform keeps the green (G) value as it is, transforms
red (R) based on green and transforms blue (B) based on green and then
based on red.

As is the case for the predictor transform, first the image is divided into
blocks and the same transform mode is used for all the pixels in a block.
For each block there are three types of color transform elements.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
typedef struct {
  uint8 green_to_red;
  uint8 green_to_blue;
  uint8 red_to_blue;
} ColorTransformElement;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The actual color transformation is done by defining a color transform
delta. The color transform delta depends on the `ColorTransformElement`
which is same for all the pixels in a particular block. The delta is
added during color transform. The inverse color transform then is just
subtracting those deltas.

The color transform function is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
 * Input:
 * red, green, blue values of the pixel
 * trans: Color transform element of the block where the
 *        pixel belongs to.
 *
 * Output:
 * *new_red = transformed value of red
 * *new_blue = transformed value of blue
 */
void ColorTransform(uint8 red, uint8 blue, uint8 green,
                    ColorTransformElement *trans,
                    uint8 *new_red, uint8 *new_blue) {
  // Transformed values of red and blue components
  uint32 tmp_red = red;
  uint32 tmp_blue = blue;

  // Applying transform is just adding the transform deltas
  tmp_red  += ColorTransformDelta(trans->green_to_red, green);
  tmp_blue += ColorTransformDelta(trans->green_to_blue, green);
  tmp_blue += ColorTransformDelta(trans->red_to_blue, red);

  *new_red = tmp_red & 0xff;
  *new_blue = tmp_blue & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`ColorTransformDelta` is computed using a signed 8-bit integer
representing a 3.5-fixed-point number, and a signed 8-bit RGB color
channel (c) [-128..127] and is defined as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int8 ColorTransformDelta(int8 t, int8 c) {
  return (t * c) >> 5;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The multiplication is to be done using more precision (with at least 16 bit
dynamics). The sign extension property of the shift operation does not
matter here: only the lowest 8 bits are used from the result, and there the
sign extension shifting and unsigned shifting are consistent with each
other.

Now we describe the contents of color transform data so that decoding can
apply the inverse color transform and recover the original red and blue
values. The first 4 bits of the color transform data contain the width and
height of the image block in number of bits, just like the predictor
transform:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int size_bits = ReadStream(4);
int block_width = 1 << size_bits;
int block_height = 1 << size_bits;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The remaining part of the color transform data contains
ColorTransformElement instances corresponding to each block of the image.
ColorTransformElement instances are treated as pixels of an image and
encoded using the methods described in section 4.

During decoding ColorTransformElement instances of the blocks are decoded
and the inverse color transform is applied on the ARGB values of the
pixels. As mentioned earlier that inverse color transform is just
subtracting ColorTransformElement values from the red and blue channels.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
 * Input:
 * red, blue and green values in the current state.
 * trans: Color transform element of the corresponding to the
 * block of the current pixel.
 *
 * Output:
 * new_red, new_blue: red, blue values after inverse transform.
 */
void InverseTransform(uint8 red, uint8 green, uint8 blue,
                      ColorTransfromElement *p,
                      uint8 *new_red, uint8 *new_blue) {
  // Applying inverse transform is just subtracting the
  // color transform deltas
  red  -= ColorTransformDelta(p->green_to_red_,  green);
  blue -= ColorTransformDelta(p->green_to_blue_, green);
  blue -= ColorTransformDelta(p->red_to_blue_, red & 0xff);

  *new_red = red & 0xff;
  *new_blue = blue & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


### Subtract Green Transform

The subtract green transform subtracts green values from red and blue
values of each pixel. When this transform is present, the decoder needs to
add the green value to both red and blue. There is no data associated with
this transform. The decoder applies the inverse transform as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
void AddGreenToBlueAndRed(uint8 green, uint8 *red, uint8 *blue) {
  *red  = (*red  + green) & 0xff;
  *blue = (*blue + green) & 0xff;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This transform is redundant as it can be modeled using the color transform.
This transform is still often useful, and since it can extend the dynamics
of the color transform, and there is no additional data here, this
transform can be coded using less bits than a full blown color transform.


### Color Indexing Transform

If there are not many unique values of the pixels then it may be more
efficient to create a color index array and replace the pixel values by the
indices to this color index array. Color indexing transform is used to
achieve that. In the context of the WebP lossless, we specifically do not
call this transform a palette transform, since another slightly similar,
but more dynamic concept exists within WebP lossless encoding, called color
cache.

The color indexing transform checks for the number of unique ARGB values in
the image. If that number is below a threshold (256), it creates an array
of those ARGB values is created which replaces the pixel values with the
corresponding index. The green channel of the pixels are replaced with the
index, all alpha values are set to 255, all red and blue values to 0.

The transform data contains color table size and the entries in the color
table. The decoder reads the color indexing transform data as follow:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// 8 bit value for color table size
int color_table_size = ReadStream(8) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The color table is stored using the image storage format itself. The color
table can be obtained by reading an image, without the RIFF header, image
size, and transforms, assuming an height of one pixel, and a width of
color_table_size. The color table is always subtraction coded for reducing
the entropy of this image. The deltas of palette colors contain typically
much less entropy than the colors themselves leading to significant savings
for smaller images. In decoding, every final color in the color table can
be obtained by adding the previous color component values, by each ARGB-
component separately and storing the least significant 8 bits of the
result.

The inverse transform for the image is simply replacing the pixel values
(which are indices to the color table) with the actual color table values.
The indexing is done based on the green component of the ARGB color.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// Inverse transform
argb = color_table[GREEN(argb)];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When the color table is of a small size (equal to or less than 16 colors),
several pixels are bundled into a single pixel. The pixel bundling packs
several (2, 4, or 8) pixels into a single pixel reducing the image width
respectively. Pixel bundling allows for a more efficient joint distribution
entropy coding of neighboring pixels, and gives some arithmetic coding like
benefits to the entropy code, but it can only be used when there is a small
amount of unique values.

color_table_size specifies how many pixels are combined together:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int width_bits = 0;
if (color_table_size <= 2) {
  width_bits = 3;
} else if (color_table_size <= 4) {
  width_bits = 2;
} else if (color_table_size <= 16) {
  width_bits = 1;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The _width_bits_ has a value of 0, 1, 2 or 3. A value of 0 indicates no
pixel bundling to be done for the image. A value of 1 indicates that two
pixels are combined together, and each pixel has a range of [0..15]. A
value of 2 indicates that four pixels are combined together, and each
pixel has a range of [0..3]. A value of 3 indicates that eight pixels
are combined together and each pixels has a range of [0..1], i.e., a
binary value.

The values are packed into the green component as follows:

  * _width_bits_ = 1: for every x value where x ≡ 0 (mod 2), a green value
    at x is positioned into the 4 least-significant bits of the green
    value at x / 2, a green value at x + 1 is positioned into the 4 most-
    significant bits of the green value at x / 2.
  * _width_bits_ = 2: for every x value where x ≡ 0 (mod 4), a green value
    at x is positioned into the 2 least-significant bits of the green
    value at x / 4, green values at x + 1 to x + 3 in order to the more
    significant bits of the green value at x / 4.
  * _width_bits_ = 3: for every x value where x ≡ 0 (mod 8), a green value
    at x is positioned into the least-significant bit of the green value
    at x / 8, green values at x + 1 to x + 7 in order to the more
    significant bits of the green value at x / 8.


Image Data
----------

Image data is an array of pixel values in scan-line order. We use image
data in five different roles: The main role, an auxiliary role related to
entropy coding, and three further roles related to transforms.

  1. ARGB image.
  2. Entropy image. The red and green components define the meta Huffman
     code used in a particular area of the image.
  3. Predictor image. The green component defines which of the 14 values is
     used within a particular square of the image.
  4. Color indexing image. An array of up to 256 ARGB colors are used for
     transforming a green-only image, using the green value as an index to
     this one-dimensional array.
  5. Color transformation image. Defines signed 3.5 fixed-point multipliers
     that are used to predict the red, green, blue components to reduce
     entropy.

To divide the image into multiple regions, the image is first divided into
a set of fixed-size blocks (typically 16x16 blocks). Each of these blocks
can be modeled using an entropy code, in a way where several blocks can
share the same entropy code. There is a cost in transmitting an entropy
code, and in order to minimize this cost, statistically similar blocks can
share an entropy code. The blocks sharing an entropy code can be found by
clustering their statistical properties, or by repeatedly joining two
randomly selected clusters when it reduces the overall amount of bits
needed to encode the image. [See section _"Decoding of meta Huffman codes"_
in Chapter 5 for an explanation of how this _entropy image_ is stored.]

Each pixel is encoded using one of three possible methods:

  1. Huffman coded literals, where each channel (green, alpha, red, blue)
     is entropy-coded independently,
  2. LZ77, a sequence of pixels in scan-line order copied from elsewhere in
     the image, or,
  3. Color cache, using a short multiplicative hash code (color cache
     index) of a recently seen color.

In the following sections we introduce the main concepts in LZ77 prefix
coding, LZ77 entropy coding, LZ77 distance mapping, and color cache codes.
The actual details of the entropy code are described in more detail in
chapter 5.


### LZ77 prefix coding

Prefix coding divides large integer values into two parts, the prefix code
and the extra bits. The benefit of this approach is that entropy coding is
later used only for the prefix code, reducing the resources needed by the
entropy code. The extra bits are stored as they are, without an entropy
code.

This prefix code is used for coding backward reference lengths and
distances. The extra bits form an integer that is added to the lower value
of the range. Hence the LZ77 lengths and distances are divided into prefix
codes and extra bits performing the Huffman coding only on the prefixes
reduces the size of the Huffman codes to tens of values instead of
otherwise a million (distance) or several thousands (length).

| Prefix code | Value range     | Extra bits |
| ----------- | --------------- | ---------- |
| 0           | 1               | 0          |
| 1           | 2               | 0          |
| 2           | 3               | 0          |
| 3           | 4               | 0          |
| 4           | 5..6            | 1          |
| 5           | 7..8            | 1          |
| 6           | 9..12           | 2          |
| 7           | 13..16          | 2          |
| ...         | ...             | ...        |
| 38          | 262145..524288  | 17         |
| 39          | 524289..1048576 | 17         |

The code to obtain a value from the prefix code is as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if (prefix_code < 4) {
  return prefix_code;
}
uint32 extra_bits = (prefix_code - 2) >> 1;
uint32 offset = (2 + (prefix_code & 1)) << extra_bits;
return offset + ReadBits(extra_bits) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


### LZ77 backward reference entropy coding

Backward references are tuples of length and distance. Length indicates how
many pixels in scan-line order are to be copied. The length is codified in
two steps: prefix and extra bits. Only the first 24 prefix codes with their
respective extra bits are used for length codes, limiting the maximum
length to 4096. For distances, all 40 prefix codes are used.


### LZ77 distance mapping

120 smallest distance codes [1..120] are reserved for a close neighborhood
within the current pixel. The rest are pure distance codes in scan-line
order, just offset by 120. The smallest codes are coded into x and y
offsets by the following table. Each tuple shows the x and the y
coordinates in 2d offsets -- for example the first tuple (0, 1) means 0 for
no difference in x, and 1 pixel difference in y (indicating previous row).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(0, 1),  (1, 0),  (1, 1),  (-1, 1), (0, 2),  (2, 0),  (1, 2),  (-1, 2),
(2, 1),  (-2, 1), (2, 2),  (-2, 2), (0, 3),  (3, 0),  (1, 3),  (-1, 3),
(3, 1),  (-3, 1), (2, 3),  (-2, 3), (3, 2),  (-3, 2), (0, 4),  (4, 0),
(1, 4),  (-1, 4), (4, 1),  (-4, 1), (3, 3),  (-3, 3), (2, 4),  (-2, 4),
(4, 2),  (-4, 2), (0, 5),  (3, 4),  (-3, 4), (4, 3),  (-4, 3), (5, 0),
(1, 5),  (-1, 5), (5, 1),  (-5, 1), (2, 5),  (-2, 5), (5, 2),  (-5, 2),
(4, 4),  (-4, 4), (3, 5),  (-3, 5), (5, 3),  (-5, 3), (0, 6),  (6, 0),
(1, 6),  (-1, 6), (6, 1),  (-6, 1), (2, 6),  (-2, 6), (6, 2),  (-6, 2), 
(4, 5),  (-4, 5), (5, 4),  (-5, 4), (3, 6),  (-3, 6), (6, 3),  (-6, 3), 
(0, 7),  (7, 0),  (1, 7),  (-1, 7), (5, 5),  (-5, 5), (7, 1),  (-7, 1),
(4, 6),  (-4, 6), (6, 4),  (-6, 4), (2, 7),  (-2, 7), (7, 2),  (-7, 2),
(3, 7),  (-3, 7), (7, 3),  (-7, 3), (5, 6),  (-5, 6), (6, 5),  (-6, 5),
(8, 0),  (4, 7),  (-4, 7), (7, 4),  (-7, 4), (8, 1),  (8, 2),  (6, 6),
(-6, 6), (8, 3),  (5, 7),  (-5, 7), (7, 5),  (-7, 5), (8, 4),  (6, 7),
(-6, 7), (7, 6),  (-7, 6), (8, 5),  (7, 7),  (-7, 7), (8, 6),  (8, 7)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The distances codes that map into these tuples are changes into scan-line
order distances using the following formula: _dist = x + y * xsize_, where
_xsize_ is the width of the image in pixels.


### Color Cache Code

Color cache stores a set of colors that have been recently used in the
image. Using the color cache code, the color cache colors can be referred
more efficiently than emitting the respective ARGB values independently or
by sending them as backward references with a length of one pixel.

Color cache codes are coded as follows. First, there is a bit that
indicates if the color cache is used or not. If this bit is 0, no color
cache codes exist, and they are not transmitted in the Huffman code that
decodes the green symbols and the length prefix codes. However, if this bit
is 1, the color cache size is read:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int color_cache_code_bits = ReadBits(br, 4);
int color_cache_size = 1 << color_cache_code_bits;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_color_cache_code_bits_ defines the size of the color_cache by (1 <<
_color_cache_code_bits_). The range of allowed values for
_color_cache_code_bits_ is [1..11]. Compliant decoders must indicate a
corrupted bit stream for other values.

A color cache is an array of the size _color_cache_size_. Each entry stores
one ARGB color. Colors are looked up by indexing them by (0x1e35a7bd *
_color_) >> (32 - _color_cache_code_bits_). Only one lookup is done in a
color cache, there is no conflict resolution.

In the beginning of decoding or encoding of an image, all entries in all
color cache values are set to zero. The color cache code is converted to
this color at decoding time. The state of the color cache is maintained by
inserting every pixel, be it produced by backward referencing or as
literals, into the cache in the order they appear in the stream.


Entropy Code
------------

### Huffman coding

Most of the data is coded using a canonical Huffman code. This includes the
following:

  * A combined code that defines either the value of the green
    component, a color cache code, or a prefix of the length codes,
  * the data for alpha, red and blue components, and
  * prefixes of the distance codes.

The Huffman codes are transmitted by sending the code lengths, the actual
symbols are implicit and done in order for each length. The Huffman code
lengths are run-length-encoded using three different prefixes, and the
result of this coding is further Huffman coded.


### Spatially-variant Huffman coding

For every pixel (x, y) in the image, there is a definition of which entropy
code to use. First, there is an integer called 'meta Huffman code' that can
be obtained from a subresolution 2d image. This meta Huffman code
identifies a set of five Huffman codes, one for green (along with length
codes and color cache codes), one for each of red, blue and alpha, and one
for distance. The Huffman codes are identified by their position in a table
by an integer.

### Decoding flow of image data

Read next symbol S

  1. S < 256
     1. Use S as green component
     2. read alpha
     3. read red
     4. read blue
  2. S < 256 + 24
     1. Use S - 256 as a length prefix code
     2. read length extra bits
     3. read distance prefix code
     4. read distance extra bits
  3. S >= 256 + 24
     1. Use ARGB color from the color cache, at index S - 256 + 24


### Decoding the code lengths

There are two different ways to encode the code lengths of a Huffman code,
indicated by the first bit of the code: _simple code length code_ (1), and
_normal code length code_ (0).


#### Simple code length code

This variant can codify 1 or 2 non-zero length codes in the range of [0,
255]. All other code lengths are implicitly zeros.

The first bit indicates the number of codes:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int num_symbols = ReadBits(1) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The first symbol is stored either using a 1-bit code for values of 0 and 1,
or using a 8-bit code for values in range [0, 255]. The second symbol, when
present, is coded as an 8-bit code.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int first_symbol_len_code = VP8LReadBits(br, 1);
symbols[0] = ReadBits(1 + 7 * first_symbol_len_code);
if (num_symbols == 2) {
  symbols[1] = ReadBits(8);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Empty trees can be coded as trees that contain one 0 symbol, and can be
codified using four bits. For example, a distance tree can be empty if
there are no backward references. Similarly, alpha, red, and blue trees can
be empty if all pixels within the same meta Huffman code are produced using
the color cache.


#### Normal code length code

The code lengths of a Huffman code are read as follows. _num_codes_ specifies
the number of code lengths, the rest of the codes lengths (according to the
order in _kCodeLengthCodeOrder_) are zeros.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int kCodeLengthCodes = 19;
int kCodeLengthCodeOrder[kCodeLengthCodes] = {
  17, 18, 0, 1, 2, 3, 4, 5, 16, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
};
int num_codes = 4 + ReadStream(4);
for (i = 0; i < num_codes; ++i) {
  code_lengths[kCodeLengthCodeOrder[i]] = ReadBits(3);
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  * Code length code [0..15] indicate literal code lengths. 
    * Value 0 means no symbols have been coded, 
    * Values [1..15] indicate the bit length of the respective code. 
  * Code 16 repeats the previous non-zero value [3..6] times, i.e., 3 + ReadStream(2) times.  If code 16 is used before a non-zero value has been emitted, a value of 8 is repeated. 
  * Code 17 emits a streak of zeros [3..10], i.e., 3 + ReadStream(3) times. 
  * Code 18 emits a streak of zeros of length [11..138], i.e., 11 + ReadStream(7) times.

The entropy codes for alpha, red and blue have a total of 256 symbols. The
entropy code for distance prefix codes has 40 symbols. The entropy code for
green has 256 + 24 + _color_cache_size_, 256 symbols for different green
symbols, 24 length code prefix symbols, and symbols for the color cache.

The meta Huffman code, specified in the next section, defines how many
Huffman codes there are. There are always 5 times the number of Huffman
codes to the number of meta Huffman codes.


### Decoding of meta Huffman codes

There are two ways to code the meta Huffman codes, indicated by one bit
for the ARGB image and is an implicit zero, i.e., not present in the
stream for all predictor images and Huffman image itself. 

If this bit is zero, there is only one meta Huffman code, using Huffman
codes 0, 1, 2, 3 and 4 for green, alpha, red, blue and distance,
respectively. This meta Huffman code is used everywhere in the image.

If this bit is one, the meta Huffman codes are controlled by the entropy
image, where the index of the meta Huffman code is codified in the red and
green components. The index can be obtained from the uint32 value by
_((pixel >> 8) & 0xffff)_, thus there can be up to 65536 unique meta Huffman
codes. When decoding a Huffman encoded symbol at a pixel x, y, one chooses
the meta Huffman code respective to these coordinates. However, not all
bits of the coordinates are used for choosing the meta Huffman code, i.e.,
the entropy image is of subresolution to the real image.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int huffman_bits = ReadBits(4);
int huffman_xsize = DIV_ROUND_UP(xsize, 1 << huffman_bits);
int huffman_ysize = DIV_ROUND_UP(ysize, 1 << huffman_bits);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_huffman_bits_ gives the amount of subsampling in the entropy image.

After reading the _huffman_bits_, an entropy image stream of size
_huffman_xsize_, _huffman_ysize_ is read.

The meta Huffman code, identifying the five Huffman codes per meta Huffman
code, is coded only by the number of codes:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int num_meta_codes = max(entropy_image) + 1;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, we can obtain the five Huffman codes for green, alpha, red, blue and
distance for a given (x, y) by the following expression:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
meta_codes[(entropy_image[(y >> huffman_bits) * huffman_xsize +
                          (x >> huffman_bits)] >> 8) & 0xffff]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The _huffman_code[5 * meta_code + k]_, codes with _k_ == 0 are for the green &
length code, _k_ == 4 for the distance code, and the codes at _k_ == 1, 2, and
3, are for codes of length 256 for red, blue and alpha, respectively.

The value of k for the reference position in _meta_code_ determines the
length of the Huffman code:

  * k = 0; length = 256 + 24 + cache_size
  * k = 1, 2, or 3;  length = 256
  * k = 4, length = 40.


Overall Structure of the Format
-------------------------------

Below there is a eagles-eye-view into the format in Backus-Naur form. It 
does not cover all details. End-of-image EOI is only implicitly coded into
the number of pixels (xsize * ysize).
{'fraction_non_alphanumeric': 0.11849120134685533, 'fraction_numerical': 0.023329458451918066, 'mean_word_length': 3.302500718597298, 'pattern_counts': {'":': 0, '<': 67, '<?xml version=': 0, '>': 57, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 58, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '4874743', 'n_tokens_mistral': 22005, 'n_tokens_neox': 20135, 'n_words': 10835}