webp/doc/webp-lossless-bitstream-spec.txt

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

_Jyrki Alakuijala, Ph.D., Google, Inc., 2012-06-19_


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 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, 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 to the right. Once a row is
  completed, continue from the left-hand column of the next row.


1 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 extensively use C programming language syntax 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
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 four different types of
transformation before being entropy encoded. The transform information
in the bitstream contains the data required to apply the respective
inverse transforms.


2 RIFF Header
-------------

The beginning of the header has the RIFF container. This consists 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 minus 8 bytes: 4 bytes for the 'RIFF'
      identifier and 4 bytes for storing the 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 0x2f.

The 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.

The alpha_is_used bit is a hint only, and should not impact decoding.
It should be set to 0 when all alpha values are 255 in the picture, and
1 otherwise.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int alpha_is_used = ReadBits(1);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The version_number is a 3 bit code that must be discarded by the decoder
at this time. Complying encoders write a 3-bit value 0.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int version_number = ReadBits(3);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


3 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 transformation. A 1 bit indicates
the presence of a transform. Each 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 information required 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 3 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(3) + 2;
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](#image-data).

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     | ClampAddSubtractFull(L, T, TL)                          |
| 13     | ClampAddSubtractHalf(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 functions `ClampAddSubtractFull` and `ClampAddSubtractHalf` 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 for 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 the 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:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 3 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(3) + 2;
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
[Chapter 4](#image-data).

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
void InverseTransform(uint8 red, uint8 green, uint8 blue,
                      ColorTransformElement *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, but it is still often useful. Since it can extend the
dynamics of the color transform and there is no additional data here,
the subtract green transform can be coded using fewer bits than a
full-blown color transform.


### Color Indexing Transform

If there are not many unique pixel values, it may be more efficient to
create a color index array and replace the pixel values by the array's
indices. The color indexing transform achieves this. (In the context of
WebP lossless, we specifically do not call this a palette transform
because a similar but more dynamic concept exists in WebP lossless
encoding: 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, which is then used to replace 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
follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// 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 a height of one pixel and
a width of `color_table_size`. The color table is always
subtraction-coded to reduce image entropy. 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 small (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 are a small number of unique values.

`color_table_size` specifies how many pixels are combined together:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int width_bits;
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;
} else {
  width_bits = 0;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`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 pixel 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.


4 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 is used for
     transforming a green-only image, using the green value as an index
     to this one-dimensional array.
  5. Color transform image. It is created by `ColorTransformElement` values
     (defined in [Color Transform](#color-transform)) for different blocks of
     the image. Each `ColorTransformElement` `'cte'` is treated as a pixel whose
     alpha component is `255`, red component is `cte.red_to_blue`, green
     component is `cte.green_to_blue` and blue component is `cte.green_to_red`.

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 the section
[Decoding of Meta Huffman Codes](#decoding-of-meta-huffman-codes) in
[Chapter 5](#entropy-code) 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](#entropy-code).


### 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 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  | 18         |
| 39          | 524289..1048576 | 18         |

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if (prefix_code < 4) {
  return prefix_code + 1;
}
int extra_bits = (prefix_code - 2) >> 1;
int 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. If a decoder detects a computed _dist_ value smaller than 1,
the value of 1 is used instead.


### 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 to more efficiently than emitting the respective ARGB values
independently or 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 bitstream 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.


5 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 the entropy image. This
meta Huffman code identifies a set of five Huffman codes:

  * Huffman code #1: used for green channel, backward-reference length and
    color cache
  * Huffman code #2, #3 and #4: used for red, blue and alpha channels
    respectively.
  * Huffman code #5: used for backward-reference distance.


### Decoding Flow of Image Data

Read next symbol S from the bitsteam using Huffman code #1. Note that S is any
integer in the range `0` to `(256 + 24 + `
[`color_cache_size`](#color-cache-code)`- 1)`.

The interpretation of S depends on its value:

  1. if S < 256
     1. Use S as the green component
     1. Read red from the bitstream using Huffman code #2
     1. Read blue from the bitstream using Huffman code #3
     1. Read alpha from the bitstream using Huffman code #4
  1. if S < 256 + 24
     1. Use S - 256 as a length prefix code
     1. Read extra bits for length from the bitstream
     1. Determine backward-reference length L from length prefix code and the
        extra bits read.
     1. Read distance prefix code from the bitstream using Huffman code #5
     1. Read extra bits for distance from the bitstream
     1. Determine backward-reference distance D from distance prefix code and
        the extra bits read.
     1. Copy the L pixels (in scan-line order) from the sequence of pixels
        prior to them by D pixels.
  1. if S >= 256 + 24
     1. Use S - (256 + 24) as the index into the color cache.
     1. Get ARGB color from the color cache at that index.


### 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 code 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] indicates 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 transform images and the entropy 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(3) + 2;
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.


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

Below is a 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).


#### Basic Structure

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
<format> ::= <RIFF header><image size><image stream>
<image stream> ::= <optional-transform><spatially-coded image>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


#### Structure of Transforms

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
<optional-transform> ::= (1-bit value 1; <transform> <optional-transform>) |
                         1-bit value 0
<transform> ::= <predictor-tx> | <color-tx> | <subtract-green-tx> |
                <color-indexing-tx>
<predictor-tx> ::= 2-bit value 0; <predictor image>
<predictor image> ::= 3-bit sub-pixel code | <entropy-coded image>
<color-tx> ::= 2-bit value 1; <color image>
<color image> ::= 3-bit sub-pixel code | <entropy-coded image>
<subtract-green-tx> ::= 2-bit value 2
<color-indexing-tx> ::= 2-bit value 3; <color-indexing image>
<color-indexing image> ::= 8-bit color count; <entropy-coded image>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


#### Structure of the Image Data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
<spatially-coded image> ::= <meta huffman><entropy-coded image>
<entropy-coded image> ::= <color cache info><huffman codes><lz77-coded image>
<meta huffman> ::= 1-bit value 0 |
                   (1-bit value 1; <entropy image>)
<entropy image> ::= 3-bit subsample value; <entropy-coded image>
<color cache info> ::= 1 bit value 0 |
                       (1-bit value 1; 4-bit value for color cache size)
<huffman codes> ::= <huffman code> | <huffman code><huffman codes>
<huffman code> ::= <simple huffman code> | <normal huffman code>
<simple huffman code> ::= see "Simple code length code" for details
<normal huffman code> ::= <code length code>; encoded code lengths
<code length code> ::= see section "Normal code length code"
<lz77-coded image> ::= ((<argb-pixel> | <lz77-copy> | <color-cache-code>)
                       <lz77-coded image>) | ""
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A possible example sequence:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
<RIFF header><image size>1-bit value 1<subtract-green-tx>
1-bit value 1<predictor-tx>1-bit value 0<meta huffman>
<color cache info><huffman codes>
<lz77-coded image>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~