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ul#markdown-toc + hr {
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+ ol ol { /* Format nested ordered lists */
+ list-style-type: lower-alpha;
+ }
+ dt {
+ font-style: italic;
+ font-weight: bold;
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diff --git a/doc/webp-lossless-bitstream-spec.txt b/doc/webp-lossless-bitstream-spec.txt
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+
+
+WebP Lossless Bitstream Specification
+=====================================
+
+_Working Draft, v0.2, 20120523_
+
+
+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.
+
+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).
+
+
+#### Basic structure
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ ::=
+ ::= () |
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+#### Structure of transforms
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ ::= 1-bit | 0-bit
+ ::= | | |
+
+ ::= 2-bit value 0; 4-bit sub-pixel code |
+ ::= 2-bit value 1; 4-bit sub-pixel code |
+ ::= 2-bit value 2
+ ::= 2-bit value 3; 8-bit color count |
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+#### Structure of the image data
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ ::=
+
+
+ ::= 1-bit value 0 |
+ (1-bit value 1;
+ )
+ ::= 4-bit subsample value;
+ ::= 4-bit length; meta Huffman size (subtracted by 2).
+ ::= 1 bit value 0 |
+ (1-bit value 1; 4-bit value for color cache size)
+ ::= |
+ ::= |
+ ::= see “Simple code length code” for details
+ ::= ; encoded code lengths
+ ::= see section “Normal code length code”
+ ::= ( | | ) |
+ ( | "")
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+A possible example sequence
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+1-bit
+1-bit0-bit
+
+
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+