Name
OES_texture_compression_astc
Name Strings
GL_OES_texture_compression_astc
GL_KHR_texture_compression_astc_hdr
GL_KHR_texture_compression_astc_ldr
Contact
Sean Ellis (sean.ellis 'at' arm.com)
Contributors
Sean Ellis, ARM
Jorn Nystad, ARM
Tom Olson, ARM
Andy Pomianowski, AMD
Cass Everitt, NVIDIA
Walter Donovan, NVIDIA
Robert Simpson, Qualcomm
Maurice Ribble, Qualcomm
Larry Seiler, Intel
Daniel Koch, Transgaming
Anthony Wood, Imagination Technologies
Notice
Copyright (c) 2013 The Khronos Group Inc. Copyright terms at
http://www.khronos.org/registry/speccopyright.html
IP Status
No known issues.
Status
Ratified by the Khronos Board of Promoters, 27 September 2013
Version
Last Modified Date: June 25, 2013
Number
OpenGL ES Extension #162
Dependencies
Written based on the wording of the OpenGL ES 3.0 specification
Overview
Adaptive Scalable Texture Compression (ASTC) is a new texture
compression technology that offers unprecendented flexibility,
while producing better or comparable results than existing texture
compressions at all bit rates. It includes support for 2D and 3D
textures, with low and high dynamic range, at bitrates from below
1 bit/pixel up to 8 bits/pixel in fine steps.
The goal of this extension is to support the full profile of the
ASTC texture compression specification.
ASTC-compressed textures are handled in OpenGL ES and OpenGL by
adding new supported formats to the existing mechanisms for handling
compressed textures.
Issues
Interactions with Other Extensions
EXT_texture_storage affects the definition of this extension.
Extends extension KHR_texture_compression_astc_ldr and
KHR_texture_compression_astc_hdr.
Interactions with OpenGL 4.2
OpenGL 4.2 supports the feature that compressed textures can be
compressed online, by passing the compressed texture format enum as
the internal format when uploading a texture using TexImage1D,
TexImage2D or TexImage3D (see Section 3.9.3, Texture Image
Specification, subsection Encoding of Special Internal Formats).
Due to the complexity of the ASTC compression algorithm, it is not
usually suitable for online use, and therefore ASTC support will be
limited to pre-compressed textures only. Where on-device compression
is required, a domain-specific limited compressor will typically
be used, and this is therefore not suitable for implementation in
the driver.
In particular, the ASTC format specifiers will not be added to
Table 3.14, and thus will not be accepted by the TexImage*D
functions, and will not be returned by the (already deprecated)
COMPRESSED_TEXTURE_FORMATS query.
New Procedures and Functions
None
New Tokens
Accepted by the parameter of CompressedTexImage2D,
CompressedTexSubImage2D, TexStorage2D, TextureStorage2D, TexStorage3D,
and TextureStorage3D:
COMPRESSED_RGBA_ASTC_4x4_KHR 0x93B0
COMPRESSED_RGBA_ASTC_5x4_KHR 0x93B1
COMPRESSED_RGBA_ASTC_5x5_KHR 0x93B2
COMPRESSED_RGBA_ASTC_6x5_KHR 0x93B3
COMPRESSED_RGBA_ASTC_6x6_KHR 0x93B4
COMPRESSED_RGBA_ASTC_8x5_KHR 0x93B5
COMPRESSED_RGBA_ASTC_8x6_KHR 0x93B6
COMPRESSED_RGBA_ASTC_8x8_KHR 0x93B7
COMPRESSED_RGBA_ASTC_10x5_KHR 0x93B8
COMPRESSED_RGBA_ASTC_10x6_KHR 0x93B9
COMPRESSED_RGBA_ASTC_10x8_KHR 0x93BA
COMPRESSED_RGBA_ASTC_10x10_KHR 0x93BB
COMPRESSED_RGBA_ASTC_12x10_KHR 0x93BC
COMPRESSED_RGBA_ASTC_12x12_KHR 0x93BD
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4_KHR 0x93D0
COMPRESSED_SRGB8_ALPHA8_ASTC_5x4_KHR 0x93D1
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5_KHR 0x93D2
COMPRESSED_SRGB8_ALPHA8_ASTC_6x5_KHR 0x93D3
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6_KHR 0x93D4
COMPRESSED_SRGB8_ALPHA8_ASTC_8x5_KHR 0x93D5
COMPRESSED_SRGB8_ALPHA8_ASTC_8x6_KHR 0x93D6
COMPRESSED_SRGB8_ALPHA8_ASTC_8x8_KHR 0x93D7
COMPRESSED_SRGB8_ALPHA8_ASTC_10x5_KHR 0x93D8
COMPRESSED_SRGB8_ALPHA8_ASTC_10x6_KHR 0x93D9
COMPRESSED_SRGB8_ALPHA8_ASTC_10x8_KHR 0x93DA
COMPRESSED_SRGB8_ALPHA8_ASTC_10x10_KHR 0x93DB
COMPRESSED_SRGB8_ALPHA8_ASTC_12x10_KHR 0x93DC
COMPRESSED_SRGB8_ALPHA8_ASTC_12x12_KHR 0x93DD
If extension "EXT_texture_storage" is supported, these tokens are also
accepted by TexStorage2DEXT, TextureStorage2DEXT, TexStorage3DEXT and
TextureStorage3DEXT.
Accepted by the parameter of CompressedTexImage3D,
CompressedTexSubImage3D, TexStorage3D, and TextureStorage3D:
COMPRESSED_RGBA_ASTC_3x3x3_OES 0x93C0
COMPRESSED_RGBA_ASTC_4x3x3_OES 0x93C1
COMPRESSED_RGBA_ASTC_4x4x3_OES 0x93C2
COMPRESSED_RGBA_ASTC_4x4x4_OES 0x93C3
COMPRESSED_RGBA_ASTC_5x4x4_OES 0x93C4
COMPRESSED_RGBA_ASTC_5x5x4_OES 0x93C5
COMPRESSED_RGBA_ASTC_5x5x5_OES 0x93C6
COMPRESSED_RGBA_ASTC_6x5x5_OES 0x93C7
COMPRESSED_RGBA_ASTC_6x6x5_OES 0x93C8
COMPRESSED_RGBA_ASTC_6x6x6_OES 0x93C9
COMPRESSED_SRGB8_ALPHA8_ASTC_3x3x3_OES 0x93E0
COMPRESSED_SRGB8_ALPHA8_ASTC_4x3x3_OES 0x93E1
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4x3_OES 0x93E2
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4x4_OES 0x93E3
COMPRESSED_SRGB8_ALPHA8_ASTC_5x4x4_OES 0x93E4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5x4_OES 0x93E5
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5x5_OES 0x93E6
COMPRESSED_SRGB8_ALPHA8_ASTC_6x5x5_OES 0x93E7
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6x5_OES 0x93E8
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6x6_OES 0x93E9
If extension "EXT_texture_storage" is supported, these tokens are also
accepted by TexStorage3DEXT and TextureStorage3DEXT.
Additions to Chapter 2 of the OpenGL ES 3.0 Specification (OpenGL ES
Operation)
None
Additions to Chapter 3 of the OpenGL ES 3.0 Specification (Rasterization)
Added to Section 3.8.6, Compressed Texture Images
Add the tokens specified above to Table 3.16, Compressed Internal Formats.
In all cases, the base internal format will be RGBA. The encoding allows
images to be encoded with fewer channels, but this is always presented as
RGBA to the sampler.
After the paragraph discussing ETC2/EAC formats, add:
"If internalformat is one of the ASTC formats described in table 3.16,
the compressed image data is stored using one of the ASTC compressed
texture image encodings (see appendix C). The ASTC texture compression
algorithm supports both two- and three-dimensional images. If
internalformat is a 2D ASTC format, CompressedTexImage3D will accept an
array of compressed data consisting of multiple rows of compressed
blocks laid out as described in Section 3.8.3. The width and height of
each sub-image must be a multiple of the ASTC block size. If
internalformat is a 3D ASTC format, CompressedTexImage2D will generate
an INVALID_OPERATION error. If internalformat is a 3D ASTC format,
and only the ASTC LDR or HDR Profile is supported, then
CompressedTexImage3D will also generate an INVALID_OPERATION error."
At the end of the section, add:
"If internalformat is one of the ASTC formats described in table 3.16, the
texture is stored using one of the ASTC compressed texture image
encodings (see appendix C). Since ASTC images are easily edited along
block footprint boundaries, the limitations on subimage location and size
are as follows for CompressedTexSubImage2D and CompressedTexSubImage3D.
These commands will result in an INVALID_OPERATION error if one of the
following conditions occurs:
* width is not a multiple of the block width, and width + xoffset is not
equal to the width of the texture level.
* height is not a multiple of block height, and height+yoffset is not
equal to the height of the texture level.
* depth is not a multiple of block depth, and depth+zoffset is not
equal to the depth of the texture level. (If a 3D image is constructed
from 2D slices, the block depth is treated as 1.)
* xoffset, yoffset or zoffset is not a multiple of the corresponding
block dimension.
The contents of any block of texels of an ASTC compressed texture
image that does not intersect the area being modified are preserved
during valid CompressedTexSubImage* calls.
The block width, height and depth for each ASTC format are determined
according to Table 3.17:
--------------------------------------------------------------
Block
Compressed Internal Format Width Height Depth
--------------------------------------------------------------
COMPRESSED_RGBA_ASTC_4x4_KHR 4 4
COMPRESSED_RGBA_ASTC_5x4_KHR 5 4
COMPRESSED_RGBA_ASTC_5x5_KHR 5 5
COMPRESSED_RGBA_ASTC_6x5_KHR 6 5
COMPRESSED_RGBA_ASTC_6x6_KHR 6 6
COMPRESSED_RGBA_ASTC_8x5_KHR 8 5
COMPRESSED_RGBA_ASTC_8x6_KHR 8 6
COMPRESSED_RGBA_ASTC_8x8_KHR 8 8
COMPRESSED_RGBA_ASTC_10x5_KHR 10 5
COMPRESSED_RGBA_ASTC_10x6_KHR 10 6
COMPRESSED_RGBA_ASTC_10x8_KHR 10 8
COMPRESSED_RGBA_ASTC_10x10_KHR 10 10
COMPRESSED_RGBA_ASTC_12x10_KHR 12 10
COMPRESSED_RGBA_ASTC_12x12_KHR 12 12
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4_KHR 4 4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x4_KHR 5 4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5_KHR 5 5
COMPRESSED_SRGB8_ALPHA8_ASTC_6x5_KHR 6 5
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6_KHR 6 6
COMPRESSED_SRGB8_ALPHA8_ASTC_8x5_KHR 8 5
COMPRESSED_SRGB8_ALPHA8_ASTC_8x6_KHR 8 6
COMPRESSED_SRGB8_ALPHA8_ASTC_8x8_KHR 8 8
COMPRESSED_SRGB8_ALPHA8_ASTC_10x5_KHR 10 5
COMPRESSED_SRGB8_ALPHA8_ASTC_10x6_KHR 10 6
COMPRESSED_SRGB8_ALPHA8_ASTC_10x8_KHR 10 8
COMPRESSED_SRGB8_ALPHA8_ASTC_10x10_KHR 10 10
COMPRESSED_SRGB8_ALPHA8_ASTC_12x10_KHR 12 10
COMPRESSED_SRGB8_ALPHA8_ASTC_12x12_KHR 12 12
COMPRESSED_RGBA_ASTC_3x3x3_OES 3 3 3
COMPRESSED_RGBA_ASTC_4x3x3_OES 4 3 3
COMPRESSED_RGBA_ASTC_4x4x3_OES 4 4 3
COMPRESSED_RGBA_ASTC_4x4x4_OES 4 4 4
COMPRESSED_RGBA_ASTC_5x4x4_OES 5 4 4
COMPRESSED_RGBA_ASTC_5x5x4_OES 5 5 4
COMPRESSED_RGBA_ASTC_5x5x5_OES 5 5 5
COMPRESSED_RGBA_ASTC_6x5x5_OES 6 5 5
COMPRESSED_RGBA_ASTC_6x6x5_OES 6 6 5
COMPRESSED_RGBA_ASTC_6x6x6_OES 6 6 6
COMPRESSED_SRGB8_ALPHA8_ASTC_3x3x3_OES 3 3 3
COMPRESSED_SRGB8_ALPHA8_ASTC_4x3x3_OES 4 3 3
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4x3_OES 4 4 3
COMPRESSED_SRGB8_ALPHA8_ASTC_4x4x4_OES 4 4 4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x4x4_OES 5 4 4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5x4_OES 5 5 4
COMPRESSED_SRGB8_ALPHA8_ASTC_5x5x5_OES 5 5 5
COMPRESSED_SRGB8_ALPHA8_ASTC_6x5x5_OES 6 5 5
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6x5_OES 6 6 5
COMPRESSED_SRGB8_ALPHA8_ASTC_6x6x6_OES 6 6 6
--------------------------------------------------------------
Table 3.17: Compressed ASTC Format Block Sizes"
Added to Section 3.8.15:
The list of converted internal formats at the start of this section must
be expanded to include all of the COMPRESSED_SRGB8_ALPHA8_ASTC_*_KHR and
COMPRESSED_SRGB8_ALPHA8_ASTC_*_OES formats.
Additions to Chapter 4 of the OpenGL ES 3.0 Specification (Per-Fragment
Operations and the Framebuffer)
None
Additions to Chapter 5 of the OpenGL ES 3.0 Specification (Special Functions)
None
Additions to Chapter 6 of the OpenGL ES 3.0 Specification (State and
State Requests)
None
Additions to Appendix A of the OpenGL ES 3.0 Specification (Invariance)
None
Additions to Appendix B of the OpenGL ES 3.0 Specification (Corollaries)
None
Additions to Appendix C of the OpenGL ES 3.0 Specification (Compressed
Texture Image Formats)
Add a new sub-section on ASTC image formats, as follows:
C.2 ASTC Compressed Texture Image Formats
=========================================
C.2.1 What is ASTC?
---------------------
ASTC stands for Adaptive Scalable Texture Compression.
The ASTC formats form a family of related compressed texture image
formats. They are all derived from a common set of definitions.
ASTC textures may be either 2D or 3D.
ASTC textures may be encoded using either high or low dynamic range.
Low dynamic range images may optionally be specified using the sRGB
color space.
Two sub-profiles ("LDR Profile" and "HDR Profile") may be implemented,
which support only 2D images at low or high dynamic range respectively.
The LDR profile is indicated by the presence of only the extension
string "GL_KHR_texture_compression_astc_ldr". If the HDR profile is
implemented, both "GL_KHR_texture_compression_astc_ldr"
and "GL_KHR_texture_compression_astc_hdr" must be published. If the full
profile (including 3D textures) is implemented, then all three extension
strings "GL_KHR_texture_compression_astc_ldr",
"GL_KHR_texture_compression_astc_hdr"
and "GL_OES_texture_compression_astc" must be published.
ASTC textures may be encoded as 1, 2, 3 or 4 components, but they are
all decoded into RGBA.
ASTC has a variable block size, and this is specified as part of the
name of the token passed to CompressedImage2D and its related functions.
C.2.2 Design Goals
--------------------
The design goals for the format are as follows:
* Random access. This is a must for any texture compression format.
* Bit exact decode. This is a must for conformance testing and
reproducibility.
* Suitable for mobile use. The format should be suitable for both
desktop and mobile GPU environments. It should be low bandwidth
and low in area.
* Flexible choice of bit rate. Current formats only offer a few bit
rates, leaving content developers with only coarse control over
the size/quality tradeoff.
* Scalable and long-lived. The format should support existing R, RG,
RGB and RGBA image types, and also have high "headroom", allowing
continuing use for several years and the ability to innovate in
encoders. Part of this is the choice to include HDR and 3D.
* Feature orthogonality. The choices for the various features of the
format are all orthogonal to each other. This has three effects:
first, it allows a large, flexible configuration space; second,
it makes that space easier to understand; and third, it makes
verification easier.
* Best in class at given bit rate. It should beat or match the current
best in class for peak signal-to-noise ratio (PSNR) at all bit rates.
* Fast decode. Texel throughput for a cached texture should be one
texel decode per clock cycle per decoder. Parallel decoding of several
texels from the same block should be possible at incremental cost.
* Low bandwidth. The encoding scheme should ensure that memory access
is kept to a minimum, cache reuse is high and memory bandwidth for
the format is low.
* Low area. It must occupy comparable die size to competing formats.
C.2.3 Basic Concepts
----------------------
ASTC is a block-based lossy compression format. The compressed image
is divided into a number of blocks of uniform size, which makes it
possible to quickly determine which block a given texel resides in.
Each block has a fixed memory footprint of 128 bits, but these bits
can represent varying numbers of texels (the block "footprint").
Block footprint sizes are not confined to powers-of-two, and are
also not confined to be square. They may be 2D, in which case the
block dimensions range from 4 to 12 texels, or 3D, in which case
the block dimensions range from 3 to 6 texels.
Decoding one texel requires only the data from a single block. This
simplifies cache design, reduces bandwidth and improves encoder throughput.
C.2.4 Block Encoding
----------------------
To understand how the blocks are stored and decoded, it is useful to start
with a simple example, and then introduce additional features.
The simplest block encoding starts by defining two color "endpoints". The
endpoints define two colors, and a number of additional colors are generated
by interpolating between them. We can define these colors using 1, 2, 3,
or 4 components (usually corresponding to R, RG, RGB and RGBA textures),
and using low or high dynamic range.
We then store a color interpolant weight for each texel in the image, which
specifies how to calculate the color to use. From this, a weighted average
of the two endpoint colors is used to generate the intermediate color,
which is the returned color for this texel.
There are several different ways of specifying the endpoint colors, and the
weights, but once they have been defined, calculation of the texel colors
proceeds identically for all of them. Each block is free to choose whichever
encoding scheme best represents its color endpoints, within the constraint
that all the data fits within the 128 bit block.
For blocks which have a large number of texels (e.g. a 12x12 block), there is
not enough space to explicitly store a weight for every texel. In this case,
a sparser grid with fewer weights is stored, and interpolation is used to
determine the effective weight to be used for each texel position. This allows
very low bit rates to be used with acceptable quality. This can also be used
to more efficiently encode blocks with low detail, or with strong vertical
or horizontal features.
For blocks which have a mixture of disparate colors, a single line in the
color space is not a good fit to the colors of the pixels in the original
image. It is therefore possible to partition the texels into multiple sets,
the pixels within each set having similar colors. For each of these
"partitions", we specify separate endpoint pairs, and choose which pair of
endpoints to use for a particular texel by looking up the partition index
from a partitioning pattern table. In ASTC, this partition table is actually
implemented as a function.
The endpoint encoding for each partition is independent.
For blocks which have uncorrelated channels - for example an image with a
transparency mask, or an image used as a normal map - it may be necessary
to specify two weights for each texel. Interpolation between the components
of the endpoint colors can then proceed independently for each "plane" of
the image. The assignment of channels to planes is selectable.
Since each of the above options is independent, it is possible to specify any
combination of channels, endpoint color encoding, weight encoding,
interpolation, multiple partitions and single or dual planes.
Since these values are specified per block, it is important that they are
represented with the minimum possible number of bits. As a result, these
values are packed together in ways which can be difficult to read, but
which are nevertheless highly amenable to hardware decode.
All of the values used as weights and color endpoint values can be specified
with a variable number of bits. The encoding scheme used allows a fine-
grained tradeoff between weight bits and color endpoint bits using "integer
sequence encoding". This can pack adjacent values together, allowing us to
use fractional numbers of bits per value.
Finally, a block may be just a single color. This is a so-called "void
extent block" and has a special coding which also allows it to identify
nearby regions of single color. This may be used to short-circuit fetching of
what would be identical blocks, and further reduce memory bandwidth.
C.2.5 LDR and HDR Modes
-------------------------
The decoding process for LDR content can be simplified if it is known in
advance that sRGB output is required. This selection is therefore included
as part of the global configuration.
The two modes differ in various ways.
-----------------------------------------------------------------------------
Operation LDR Mode HDR Mode
-----------------------------------------------------------------------------
Returned value Vector of FP16 values, Vector of FP16 values
or Vector of UNORM8 values.
sRGB compatible Yes No
LDR endpoint 16 bits, or 16 bits
decoding precision 8 bits for sRGB
HDR endpoint mode Error color As decoded
results
Error results Error color Vector of NaNs (0xFFFF)
-----------------------------------------------------------------------------
Table C.2.1 - Differences Between LDR and HDR Modes
The error color is opaque fully-saturated magenta
(R,G,B,A = 0xFF, 0x00, 0xFF, 0xFF). This has been chosen as it is much more
noticeable than black or white, and occurs far less often in valid images.
For linear RGB decode, the error color may be either opaque fully-saturated
magenta (R,G,B,A = 1.0, 0.0, 1.0, 1.0) or a vector of four NaNs
(R,G,B,A = NaN, NaN, NaN, NaN). In the latter case, the recommended NaN
value returned is 0xFFFF.
The error color is returned as an informative response to invalid
conditions, including invalid block encodings or use of reserved endpoint
modes.
Future, forward-compatible extensions to OES_texture_compression_astc
may define valid interpretations of these conditions, which will decode to
some other color. Therefore, encoders and applications must not rely on
invalid encodings as a way of generating the error color.
C.2.6 Configuration Summary
-----------------------------
The global configuration data for the format is as follows:
* Block dimension (2D or 3D)
* Block footprint size
* sRGB output enabled or not
The data specified per block is as follows:
* Texel weight grid size
* Texel weight range
* Texel weight values
* Number of partitions
* Partition pattern index
* Color endpoint modes (includes LDR or HDR selection)
* Color endpoint data
* Number of planes
* Plane-to-channel assignment
C.2.7 Decode Procedure
------------------------
To decode one texel:
(Optimization: If within known void-extent, immediately return single
color)
Find block containing texel
Read block mode
If void-extent block, store void extent and immediately return single
color
For each plane in image
If block mode requires infill
Find and decode stored weights adjacent to texel, unquantize and
interpolate
Else
Find and decode weight for texel, and unquantize
Read number of partitions
If number of partitions > 1
Read partition table pattern index
Look up partition number from pattern
Read color endpoint mode and endpoint data for selected partition
Unquantize color endpoints
Interpolate color endpoints using weight (or weights in dual-plane mode)
Return interpolated color
C.2.8 Block Determination and Bit Rates
The block footprint is a global setting for any given texture, and is
therefore not encoded in the individual blocks.
For 2D textures, the block footprint's width and height are selectable
from a number of predefined sizes, namely 4, 5, 6, 8, 10 and 12 pixels.
For square and nearly-square blocks, this gives the following bit rates:
-------------------------------------
Footprint
Width Height Bit Rate Increment
-------------------------------------
4 4 8.00 125%
5 4 6.40 125%
5 5 5.12 120%
6 5 4.27 120%
6 6 3.56 114%
8 5 3.20 120%
8 6 2.67 105%
10 5 2.56 120%
10 6 2.13 107%
8 8 2.00 125%
10 8 1.60 125%
10 10 1.28 120%
12 10 1.07 120%
12 12 0.89
-------------------------------------
Table C.2.2 - 2D Footprint and Bit Rates
The block footprint is shown as width x height in the format enumerator,
so for example the enumerator COMPRESSED_RGBA_ASTC_8x6_KHR specifies an
image with a block width of 8 texels, and a block height of 6 texels.
The "Increment" column indicates the ratio of bit rate against the next
lower available rate. A consistent value in this column indicates an even
spread of bit rates.
For 3D textures, the block footprint's width, height and depth are
selectable from a number of predefined sizes, namely 3, 4, 5, and 6 pixels.
For cubic and near-cubic blocks, this gives the following bit rates:
-------------------------------------------
Block Footprint
Width Height Depth Bit Rate Increment
-------------------------------------------
3 3 3 4.74 133%
4 3 3 3.56 133%
4 4 3 2.67 133%
4 4 4 2.00 125%
5 4 4 1.60 125%
5 5 4 1.28 125%
5 5 5 1.02 120%
6 5 5 0.85 120%
6 6 5 0.71 120%
6 6 6 0.59
-------------------------------------------
Table C.2.3 - 3D Footprint and Bit Rates
The block footprint is shown as width x height x depth in the format
enumerator, so for example the enumerator COMPRESSED_RGBA_ASTC_5x4x4_OES
specifies an image with a block width of 5 texels, a block height of 4
texels and a block depth of 4 texels.
The full profile supports only those block footprints listed in Tables
C.2.2 and C.2.3. Other block sizes are not supported.
For images which are not an integer multiple of the block size, additional
texels are added to the edges with maximum X and Y (and Z for 3D textures).
These texels may be any color, as they will not be accessed.
Although these are not all powers of two, it is possible to calculate block
addresses and pixel addresses within the block, for legal image sizes,
without undue complexity.
Given an image which is W x H x D pixels in size, with block size
w x h x d, the size of the image in blocks is:
Bw = ceiling(W/w)
Bh = ceiling(H/h)
Bd = ceiling(D/d)
For a 3D image built from 2D slices, each 2D slice is a single texel thick,
so that for an image which is W x H x D pixels in size, with block size
w x h, the size of the image in blocks is:
Bw = ceiling(W/w)
Bh = ceiling(H/h)
Bd = D
C.2.9 Block Layout
--------------------
Each block in the image is stored as a single 128-bit block in memory. These
blocks are laid out in raster order, starting with the block at (0,0,0), then
ordered sequentially by X, Y and finally Z (if present). They are aligned to
128-bit boundaries in memory.
The bits in the block are labeled in little-endian order - the byte at the
lowest address contains bits 0..7. Bit 0 is the least significant bit in the
byte.
Each block has the same basic layout:
127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112
--------------------------------------------------------------
| Texel Weight Data (variable width) Fill direction ->
--------------------------------------------------------------
111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96
--------------------------------------------------------------
Texel Weight Data
--------------------------------------------------------------
95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80
--------------------------------------------------------------
Texel Weight Data
--------------------------------------------------------------
79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64
--------------------------------------------------------------
Texel Weight Data
--------------------------------------------------------------
63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48
--------------------------------------------------------------
: More config data :
--------------------------------------------------------------
47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32
--------------------------------------------------------------
<-Fill direction Color Endpoint Data
--------------------------------------------------------------
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
--------------------------------------------------------------
: Extra configuration data
--------------------------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
Extra | Part | Block mode |
--------------------------------------------------------------
Table C.2.4 - Block Layout Overview
Dotted partition lines indicate that the split position is not fixed.
The "Block mode" field specifies how the Texel Weight Data is encoded.
The "Part" field specifies the number of partitions, minus one. If dual
plane mode is enabled, the number of partitions must be 3 or fewer.
If 4 partitions are specified, the error value is returned for all
texels in the block.
The size and layout of the extra configuration data depends on the
number of partitions, and the number of planes in the image, as follows
(only the bottom 32 bits are shown):
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
--------------------------------------------------------------
<- Color endpoint data |CEM
--------------------------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
CEM | 0 0 | Block Mode |
--------------------------------------------------------------
Table C.2.5 - Single-partition Block Layout
CEM is the color endpoint mode field, which determines how the Color
Endpoint Data is encoded.
If dual-plane mode is active, the color component selector bits appear
directly below the weight bits.
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
--------------------------------------------------------------
| CEM | Partition Index
--------------------------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
Partition Index | Block Mode |
--------------------------------------------------------------
Table C.2.6 - Multi-partition Block Layout
The Partition Index field specifies which partition layout to use. CEM is
the first 6 bits of color endpoint mode information for the various
partitions. For modes which require more than 6 bits of CEM data, the
additional bits appear at a variable position directly beneath the texel
weight data.
If dual-plane mode is active, the color component selector bits then appear
directly below the additional CEM bits.
The final special case is that if bits [8:0] of the block are "111111100",
then the block is a void-extent block, which has a separate encoding
described in section C.2.22.
C.2.10 Block Mode
------------------
The Block Mode field specifies the width, height and depth of the grid of
weights, what range of values they use, and whether dual weight planes are
present. Since some these are not represented using powers of two (there
are 12 possible weight widths, for example), and not all combinations are
allowed, this is not a simple bit packing. However, it can be unpacked
quickly in hardware.
The weight ranges are encoded using a 3 bit value R, which is interpreted
together with a precision bit H, as follows:
Low Precision Range (H=0) High Precision Range (H=1)
R Weight Range Trits Quints Bits Weight Range Trits Quints Bits
-----------------------------------------------------------------------------
000 Invalid Invalid
001 Invalid Invalid
010 0..1 1 0..9 1 1
011 0..2 1 0..11 1 2
100 0..3 2 0..15 4
101 0..4 1 0..19 1 2
110 0..5 1 1 0..23 1 3
111 0..7 3 0..31 5
-----------------------------------------------------------------------------
Table C.2.7 - Weight Range Encodings
Each weight value is encoded using the specified number of Trits, Quints
and Bits. The details of this encoding can be found in Section C.3.12 -
Integer Sequence Encoding.
For 2D blocks, the Block Mode field is laid out as follows:
-------------------------------------------------------------------------
10 9 8 7 6 5 4 3 2 1 0 Width Height Notes
-------------------------------------------------------------------------
D H B A R0 0 0 R2 R1 B+4 A+2
D H B A R0 0 1 R2 R1 B+8 A+2
D H B A R0 1 0 R2 R1 A+2 B+8
D H 0 B A R0 1 1 R2 R1 A+2 B+6
D H 1 B A R0 1 1 R2 R1 B+2 A+2
D H 0 0 A R0 R2 R1 0 0 12 A+2
D H 0 1 A R0 R2 R1 0 0 A+2 12
D H 1 1 0 0 R0 R2 R1 0 0 6 10
D H 1 1 0 1 R0 R2 R1 0 0 10 6
B 1 0 A R0 R2 R1 0 0 A+6 B+6 D=0, H=0
x x 1 1 1 1 1 1 1 0 0 - - Void-extent
x x 1 1 1 x x x x 0 0 - - Reserved*
x x x x x x x 0 0 0 0 - - Reserved
-------------------------------------------------------------------------
Table C.2.8 - 2D Block Mode Layout
Note that, due to the encoding of the R field, as described in the
previous page, bits R2 and R1 cannot both be zero, which disambiguates
the first five rows from the rest of the table.
The penultimate row of the table is reserved only if bits [5:2] are not
all 1, in which case it encodes a void-extent block (as shown in the
previous row).
For 3D blocks, the Block Mode field is laid out as follows:
-------------------------------------------------------------------------
10 9 8 7 6 5 4 3 2 1 0 Width Height Depth Notes
-------------------------------------------------------------------------
D H B A R0 C R2 R1 A+2 B+2 C+2
B 0 0 A R0 R2 R1 0 0 6 B+2 A+2 D=0, H=0
B 0 1 A R0 R2 R1 0 0 A+2 6 B+2 D=0, H=0
B 1 0 A R0 R2 R1 0 0 A+2 B+2 6 D=0, H=0
D H 1 1 0 0 R0 R2 R1 0 0 6 2 2
D H 1 1 0 1 R0 R2 R1 0 0 2 6 2
D H 1 1 1 0 R0 R2 R1 0 0 2 2 6
x x 1 1 1 1 1 1 1 0 0 - - - Void-extent
x x 1 1 1 1 x x x 0 0 - - - Reserved*
x x x x x x x 0 0 0 0 - - - Reserved
------------------------------------------------------------------------
Table C.2.9 - 3D Block Mode Layout
The D bit is set to indicate dual-plane mode. In this mode, the maximum
allowed number of partitions is 3.
The penultimate row of the table is reserved only if bits [4:2] are not
all 1, in which case it encodes a void-extent block (as shown in the
previous row).
The size of the grid in each dimension must be less than or equal to
the corresponding dimension of the block footprint. If the grid size
is greater than the footprint dimension in any axis, then this is an
illegal block encoding and all texels will decode to the error color.
C.2.11 Color Endpoint Mode
---------------------------
In single-partition mode, the Color Endpoint Mode (CEM) field stores one
of 16 possible values. Each of these specifies how many raw data values
are encoded, and how to convert these raw values into two RGBA color
endpoints. They can be summarized as follows:
---------------------------------------------
CEM Description Class
---------------------------------------------
0 LDR Luminance, direct 0
1 LDR Luminance, base+offset 0
2 HDR Luminance, large range 0
3 HDR Luminance, small range 0
4 LDR Luminance+Alpha, direct 1
5 LDR Luminance+Alpha, base+offset 1
6 LDR RGB, base+scale 1
7 HDR RGB, base+scale 1
8 LDR RGB, direct 2
9 LDR RGB, base+offset 2
10 LDR RGB, base+scale plus two A 2
11 HDR RGB, direct 2
12 LDR RGBA, direct 3
13 LDR RGBA, base+offset 3
14 HDR RGB, direct + LDR Alpha 3
15 HDR RGB, direct + HDR Alpha 3
---------------------------------------------
Table C.2.10 - Color Endpoint Modes
In multi-partition mode, the CEM field is of variable width, from 6 to 14
bits. The lowest 2 bits of the CEM field specify how the endpoint mode
for each partition is calculated:
----------------------------------------------------
Value Meaning
----------------------------------------------------
00 All color endpoint pairs are of the same type.
A full 4-bit CEM is stored in block bits [28:25]
and is used for all partitions.
01 All endpoint pairs are of class 0 or 1.
10 All endpoint pairs are of class 1 or 2.
11 All endpoint pairs are of class 2 or 3.
----------------------------------------------------
Table C.2.11 - Multi-Partition Color Endpoint Modes
If the CEM selector value in bits [24:23] is not 00,
then data layout is as follows:
Part n m l k j i h g
------------------------------------------
2 ... Weight : M1 : ...
------------------------------------------
3 ... Weight : M2 : M1 :M0 : ...
------------------------------------------
4 ... Weight : M3 : M2 : M1 : M0 : ...
------------------------------------------
Part 28 27 26 25 24 23
----------------------
2 | M0 |C1 |C0 | CEM |
----------------------
3 |M0 |C2 |C1 |C0 | CEM |
----------------------
4 |C3 |C2 |C1 |C0 | CEM |
----------------------
Table C.2.12 - Multi-Partition Color Endpoint Modes
In this view, each partition i has two fields. Ci is the class selector
bit, choosing between the two possible CEM classes (0 indicates the
lower of the two classes), and Mi is a two-bit field specifying the low
bits of the color endpoint mode within that class. The additional bits
appear at a variable bit position, immediately below the texel weight
data.
The ranges used for the data values are not explicitly specified.
Instead, they are derived from the number of available bits remaining
after the configuration data and weight data have been specified.
Details of the decoding procedure for Color Endpoints can be found in
section C.2.13.
C.2.12 Integer Sequence Encoding
---------------------------------
Both the weight data and the endpoint color data are variable width, and
are specified using a sequence of integer values. The range of each
value in a sequence (e.g. a color weight) is constrained.
Since it is often the case that the most efficient range for these
values is not a power of two, each value sequence is encoded using a
technique known as "integer sequence encoding". This allows efficient,
hardware-friendly packing and unpacking of values with non-power-of-two
ranges.
In a sequence, each value has an identical range. The range is specified
in one of the following forms:
Value range MSB encoding LSB encoding
0 .. 2^n-1 - n bit value m (n <= 8)
0 .. (3 * 2^n)-1 Base-3 "trit" value t n bit value m (n <= 6)
0 .. (5 * 2^n)-1 Base-5 "quint" value q n bit value m (n <= 5)
Value range Value Block Packed block size
0 .. 2^n-1 m 1 n
0 .. (3 * 2^n)-1 t * 2^n + m 5 8 + 5*n
0 .. (5 * 2^n)-1 q * 2^n + m 3 7 + 3*n
Table C.2.13 -Encoding for Different Ranges
Since 3^5 is 243, it is possible to pack five trits into 8 bits(which has
256 possible values), so a trit can effectively be encoded as 1.6 bits.
Similarly, since 5^3 is 125, it is possible to pack three quints into
7 bits (which has 128 possible values), so a quint can be encoded as
2.33 bits.
The encoding scheme packs the trits or quints, and then interleaves the n
additional bits in positions that satisfy the requirements of an
arbitrary length stream. This makes it possible to correctly specify
lists of values whose length is not an integer multiple of 3 or 5 values.
It also makes it possible to easily select a value at random within the stream.
If there are insufficient bits in the stream to fill the final block, then
unused (higher order) bits are assumed to be 0 when decoding.
To decode the bits for value number i in a sequence of bits b, both
indexed from 0, perform the following:
If the range is encoded as n bits per value, then the value is bits
b[i*n+n-1:i*n] - a simple multiplexing operation.
If the range is encoded using a trit, then each block contains 5 values
(v0 to v4), each of which contains a trit (t0 to t4) and a corresponding
LSB value (m0 to m4). The first bit of the packed block is bit
floor(i/5)*(8+5*n). The bits in the block are packed as follows
(in this example, n is 4):
27 26 25 24 23 22 21 20 19 18 17 16
-----------------------------------------------
|T7 | m4 |T6 T5 | m3 |T4 |
-----------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
| m2 |T3 T2 | m1 |T1 T0 | m0 |
--------------------------------------------------------------
Table C.2.14 - Trit-based Packing
The five trits t0 to t4 are obtained by bit manipulations of the 8 bits
T[7:0] as follows:
if T[4:2] = 111
C = { T[7:5], T[1:0] }; t4 = t3 = 2
else
C = T[4:0]
if T[6:5] = 11
t4 = 2; t3 = T[7]
else
t4 = T[7]; t3 = T[6:5]
if C[1:0] = 11
t2 = 2; t1 = C[4]; t0 = { C[3], C[2]&~C[3] }
else if C[3:2] = 11
t2 = 2; t1 = 2; t0 = C[1:0]
else
t2 = C[4]; t1 = C[3:2]; t0 = { C[1], C[0]&~C[1] }
If the range is encoded using a quint, then each block contains 3 values
(v0 to v2), each of which contains a quint (q0 to q2) and a corresponding
LSB value (m0 to m2). The first bit of the packed block is bit
floor(i/3)*(7+3*n).
The bits in the block are packed as follows (in this example, n is 4):
18 17 16
-----------
|Q6 Q5 | m2
-----------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
---------------------------------------------------------------
m2 |Q4 Q3 | m1 |Q2 Q1 Q0 | m0 |
---------------------------------------------------------------
Table C.2.15 - Quint-based Packing
The three quints q0 to q2 are obtained by bit manipulations of the 7 bits
Q[6:0] as follows:
if Q[2:1] = 11 and Q[6:5] = 00
q2 = { Q[0], Q[4]&~Q[0], Q[3]&~Q[0] }; q1 = q0 = 4
else
if Q[2:1] = 11
q2 = 4; C = { Q[4:3], ~Q[6:5], Q[0] }
else
q2 = T[6:5]; C = Q[4:0]
if C[2:0] = 101
q1 = 4; q0 = C[4:3]
else
q1 = C[4:3]; q0 = C[2:0]
Both these procedures ensure a valid decoding for all 128 possible values
(even though a few are duplicates). They can also be implemented
efficiently in software using small tables.
Encoding methods are not specified here, although table-based mechanisms
work well.
C.2.13 Endpoint Unquantization
-------------------------------
Each color endpoint is specified as a sequence of integers in a given
range. These values are packed using integer sequence encoding, as a
stream of bits stored from just above the configuration data, and
growing upwards.
Once unpacked, the values must be unquantized from their storage range,
returning them to a standard range of 0..255.
For bit-only representations, this is simple bit replication from the
most significant bit of the value.
For trit or quint-based representations, this involves a set of bit
manipulations and adjustments to avoid the expense of full-width
multipliers. This procedure ensures correct scaling, but scrambles
the order of the decoded values relative to the encoded values.
This must be compensated for using a table in the encoder.
The initial inputs to the procedure are denoted A (9 bits), B (9 bits),
C (9 bits) and D (3 bits) and are decoded using the range as follows:
---------------------------------------------------------------
Range T Q B Bits A B C D
---------------------------------------------------------------
0..5 1 1 a aaaaaaaaa 000000000 204 Trit value
0..9 1 1 a aaaaaaaaa 000000000 113 Quint value
0..11 1 2 ba aaaaaaaaa b000b0bb0 93 Trit value
0..19 1 2 ba aaaaaaaaa b0000bb00 54 Quint value
0..23 1 3 cba aaaaaaaaa cb000cbcb 44 Trit value
0..39 1 3 cba aaaaaaaaa cb0000cbc 26 Quint value
0..47 1 4 dcba aaaaaaaaa dcb000dcb 22 Trit value
0..79 1 4 dcba aaaaaaaaa dcb0000dc 13 Quint value
0..95 1 5 edcba aaaaaaaaa edcb000ed 11 Trit value
0..159 1 5 edcba aaaaaaaaa edcb0000e 6 Quint value
0..191 1 6 fedcba aaaaaaaaa fedcb000f 5 Trit value
---------------------------------------------------------------
Table C.2.16 - Color Unquantization Parameters
These are then processed as follows:
T = D * C + B;
T = T ^ A;
T = (A & 0x80) | (T >> 2);
Note that the multiply in the first line is nearly trivial as it only
needs to multiply by 0, 1, 2, 3 or 4.
C.2.14 LDR Endpoint Decoding
-----------------------------
The decoding method used depends on the Color Endpoint Mode (CEM) field,
which specifies how many values are used to represent the endpoint.
The CEM field also specifies how to take the n unquantized color endpoint
values v0 to v[n-1] and convert them into two RGBA color endpoints e0
and e1.
The HDR Modes are more complex and do not fit neatly into this section.
They are documented in following section.
The methods can be summarized as follows.
-------------------------------------------------
CEM Range Description n
-------------------------------------------------
0 LDR Luminance, direct 2
1 LDR Luminance, base+offset 2
2 HDR Luminance, large range 2
3 HDR Luminance, small range 2
4 LDR Luminance+Alpha, direct 4
5 LDR Luminance+Alpha, base+offset 4
6 LDR RGB, base+scale 4
7 HDR RGB, base+scale 4
8 LDR RGB, direct 6
9 LDR RGB, base+offset 6
10 LDR RGB, base+scale plus two A 6
11 HDR RGB 6
12 LDR RGBA, direct 8
13 LDR RGBA, base+offset 8
14 HDR RGB + LDR Alpha 8
15 HDR RGB + HDR Alpha 8
-------------------------------------------------
Table C.2.17 -Color Endpoint Modes
Mode 14 is special in that the alpha values are interpolated linearly,
but the color components are interpolated logarithmically. This is the
only endpoint format with mixed-mode operation, and will return the
error value if encountered in LDR mode.
Decode the different LDR endpoint modes as follows:
Mode 0 LDR Luminance, direct
e0=(v0,v0,v0,0xFF); e1=(v1,v1,v1,0xFF);
Mode 1 LDR Luminance, base+offset
L0 = (v0>>2)|(v1&0xC0); L1=L0+(v1&0x3F);
if (L1>0xFF) { L1=0xFF; }
e0=(L0,L0,L0,0xFF); e1=(L1,L1,L1,0xFF);
Mode 4 LDR Luminance+Alpha,direct
e0=(v0,v0,v0,v2);
e1=(v1,v1,v1,v3);
Mode 5 LDR Luminance+Alpha, base+offset
bit_transfer_signed(v1,v0); bit_transfer_signed(v3,v2);
e0=(v0,v0,v0,v2); e1=(v0+v1,v0+v1,v0+v1,v2+v3);
clamp_unorm8(e0); clamp_unorm8(e1);
Mode 6 LDR RGB, base+scale
e0=(v0*v3>>8,v1*v3>>8,v2*v3>>8, 0xFF);
e1=(v0,v1,v2,0xFF);
Mode 8 LDR RGB, Direct
s0= v0+v2+v4; s1= v1+v3+v5;
if (s1>=s0){e0=(v0,v2,v4,0xFF);
e1=(v1,v3,v5,0xFF); }
else { e0=blue_contract(v1,v3,v5,0xFF);
e1=blue_contract(v0,v2,v4,0xFF); }
Mode 9 LDR RGB, base+offset
bit_transfer_signed(v1,v0);
bit_transfer_signed(v3,v2);
bit_transfer_signed(v5,v4);
if(v1+v3+v5 >= 0)
{ e0=(v0,v2,v4,0xFF); e1=(v0+v1,v2+v3,v4+v5,0xFF); }
else
{ e0=blue_contract(v0+v1,v2+v3,v4+v5,0xFF);
e1=blue_contract(v0,v2,v4,0xFF); }
clamp_unorm8(e0); clamp_unorm8(e1);
Mode 10 LDR RGB, base+scale plus two A
e0=(v0*v3>>8,v1*v3>>8,v2*v3>>8, v4);
e1=(v0,v1,v2, v5);
Mode 12 LDR RGBA, direct
s0= v0+v2+v4; s1= v1+v3+v5;
if (s1>=s0){e0=(v0,v2,v4,v6);
e1=(v1,v3,v5,v7); }
else { e0=blue_contract(v1,v3,v5,v7);
e1=blue_contract(v0,v2,v4,v6); }
Mode 13 LDR RGBA, base+offset
bit_transfer_signed(v1,v0);
bit_transfer_signed(v3,v2);
bit_transfer_signed(v5,v4);
bit_transfer_signed(v7,v6);
if(v1+v3+v5>=0) { e0=(v0,v2,v4,v6);
e1=(v0+v1,v2+v3,v4+v5,v6+v7); }
else { e0=blue_contract(v0+v1,v2+v3,v4+v5,v6+v7);
e1=blue_contract(v0,v2,v4,v6); }
clamp_unorm8(e0); clamp_unorm8(e1);
The bit_transfer_signed procedure transfers a bit from one value (a)
to another (b). Initially, both a and b are in the range 0..255.
After calling this procedure, a's range becomes -32..31, and b remains
in the range 0..255. Note that, as is often the case, this is easier to
express in hardware than in C:
bit_transfer_signed(int& a, int& b)
{
b >>= 1;
b |= a & 0x80;
a >>= 1;
a &= 0x3F;
if( (a&0x20)!=0 ) a-=0x40;
}
The blue_contract procedure is used to give additional precision to
RGB colors near grey:
color blue_contract( int r, int g, int b, int a )
{
color c;
c.r = (r+b) >> 1;
c.g = (g+b) >> 1;
c.b = b;
c.a = a;
return c;
}
The clamp_unorm8 procedure is used to clamp a color into the UNORM8 range:
void clamp_unorm8(color c)
{
if(c.r < 0) {c.r=0;} else if(c.r > 255) {c.r=255;}
if(c.g < 0) {c.g=0;} else if(c.g > 255) {c.g=255;}
if(c.b < 0) {c.b=0;} else if(c.b > 255) {c.b=255;}
if(c.a < 0) {c.a=0;} else if(c.a > 255) {c.a=255;}
}
C.2.15 HDR Endpoint Decoding
-------------------------
For HDR endpoint modes, color values are represented in a 12-bit
pseudo-logarithmic representation.
HDR Endpoint Mode 2
Mode 2 represents luminance-only data with a large range. It encodes
using two values (v0, v1). The complete decoding procedure is as follows:
if(v1 >= v0)
{
y0 = (v0 << 4);
y1 = (v1 << 4);
}
else
{
y0 = (v1 << 4) + 8;
y1 = (v0 << 4) - 8;
}
// Construct RGBA result (0x780 is 1.0f)
e0 = (y0, y0, y0, 0x780);
e1 = (y1, y1, y1, 0x780);
HDR Endpoint Mode 3
Mode 3 represents luminance-only data with a small range. It packs the
bits for a base luminance value, together with an offset, into two values
(v0, v1):
Value 7 6 5 4 3 2 1 0
----- ------------------------------
v0 |M | L[6:0] |
------------------------------
v1 | X[3:0] | d[3:0] |
------------------------------
Table C.2.18 - HDR Mode 3 Value Layout
The bit field marked as X allocates different bits to L or d depending
on the value of the mode bit M.
The complete decoding procedure is as follows:
// Check mode bit and extract.
if((v0&0x80) !=0)
{
y0 = ((v1 & 0xE0) << 4) | ((v0 & 0x7F) << 2);
d = (v1 & 0x1F) << 2;
}
else
{
y0 = ((v1 & 0xF0) << 4) | ((v0 & 0x7F) << 1);
d = (v1 & 0x0F) << 1;
}
// Add delta and clamp
y1 = y0 + d;
if(y1 > 0xFFF) { y1 = 0xFFF; }
// Construct RGBA result (0x780 is 1.0f)
e0 = (y0, y0, y0, 0x780);
e1 = (y1, y1, y1, 0x780);
HDR Endpoint Mode 7
Mode 7 packs the bits for a base RGB value, a scale factor, and some
mode bits into the four values (v0, v1, v2, v3):
Value 7 6 5 4 3 2 1 0
----- ------------------------------
v0 |M[3:2] | R[5:0] |
----- ------------------------------
v1 |M1 |X0 |X1 | G[4:0] |
----- ------------------------------
v2 |M0 |X2 |X3 | B[4:0] |
----- ------------------------------
v3 |X4 |X5 |X6 | S[4:0] |
----- ------------------------------
Table C.2.19 - HDR Mode 7 Value Layout
The mode bits M0 to M3 are a packed representation of an endpoint bit
mode, together with the major component index. For modes 0 to 4, the
component (red, green, or blue) with the largest magnitude is identified,
and the values swizzled to ensure that it is decoded from the red channel.
The endpoint bit mode is used to determine the number of bits assigned
to each component of the endpoint, and the destination of each of the
extra bits X0 to X6, as follows:
------------------------------------------------------
Number of bits Destination of extra bits
Mode R G B S X0 X1 X2 X3 X4 X5 X6
------------------------------------------------------
0 11 5 5 7 R9 R8 R7 R10 R6 S6 S5
1 11 6 6 5 R8 G5 R7 B5 R6 R10 R9
2 10 5 5 8 R9 R8 R7 R6 S7 S6 S5
3 9 6 6 7 R8 G5 R7 B5 R6 S6 S5
4 8 7 7 6 G6 G5 B6 B5 R6 R7 S5
5 7 7 7 7 G6 G5 B6 B5 R6 S6 S5
------------------------------------------------------
Table C.2.20 - Endpoint Bit Mode
As noted before, this appears complex when expressed in C, but much
easier to achieve in hardware - bit masking, extraction, shifting
and assignment usually ends up as a single wire or multiplexer.
The complete decoding procedure is as follows:
// Extract mode bits and unpack to major component and mode.
int modeval = ((v0&0xC0)>>6) | ((v1&0x80)>>5) | ((v2&0x80)>>4);
int majcomp;
int mode;
if( (modeval & 0xC ) != 0xC )
{
majcomp = modeval >> 2; mode = modeval & 3;
}
else if( modeval != 0xF )
{
majcomp = modeval & 3; mode = 4;
}
else
{
majcomp = 0; mode = 5;
}
// Extract low-order bits of r, g, b, and s.
int red = v0 & 0x3f;
int green = v1 & 0x1f;
int blue = v2 & 0x1f;
int scale = v3 & 0x1f;
// Extract high-order bits, which may be assigned depending on mode
int x0 = (v1 >> 6) & 1; int x1 = (v1 >> 5) & 1;
int x2 = (v2 >> 6) & 1; int x3 = (v2 >> 5) & 1;
int x4 = (v3 >> 7) & 1; int x5 = (v3 >> 6) & 1;
int x6 = (v3 >> 5) & 1;
// Now move the high-order xs into the right place.
int ohm = 1 << mode;
if( ohm & 0x30 ) green |= x0 << 6;
if( ohm & 0x3A ) green |= x1 << 5;
if( ohm & 0x30 ) blue |= x2 << 6;
if( ohm & 0x3A ) blue |= x3 << 5;
if( ohm & 0x3D ) scale |= x6 << 5;
if( ohm & 0x2D ) scale |= x5 << 6;
if( ohm & 0x04 ) scale |= x4 << 7;
if( ohm & 0x3B ) red |= x4 << 6;
if( ohm & 0x04 ) red |= x3 << 6;
if( ohm & 0x10 ) red |= x5 << 7;
if( ohm & 0x0F ) red |= x2 << 7;
if( ohm & 0x05 ) red |= x1 << 8;
if( ohm & 0x0A ) red |= x0 << 8;
if( ohm & 0x05 ) red |= x0 << 9;
if( ohm & 0x02 ) red |= x6 << 9;
if( ohm & 0x01 ) red |= x3 << 10;
if( ohm & 0x02 ) red |= x5 << 10;
// Shift the bits to the top of the 12-bit result.
static const int shamts[6] = { 1,1,2,3,4,5 };
int shamt = shamts[mode];
red <<= shamt; green <<= shamt; blue <<= shamt; scale <<= shamt;
// Minor components are stored as differences
if( mode != 5 ) { green = red - green; blue = red - blue; }
// Swizzle major component into place
if( majcomp == 1 ) swap( red, green );
if( majcomp == 2 ) swap( red, blue );
// Clamp output values, set alpha to 1.0
e1.r = clamp( red, 0, 0xFFF );
e1.g = clamp( green, 0, 0xFFF );
e1.b = clamp( blue, 0, 0xFFF );
e1.alpha = 0x780;
e0.r = clamp( red - scale, 0, 0xFFF );
e0.g = clamp( green - scale, 0, 0xFFF );
e0.b = clamp( blue - scale, 0, 0xFFF );
e0.alpha = 0x780;
HDR Endpoint Mode 11
Mode 11 specifies two RGB values, which it calculates from a number of
bitfields (a, b0, b1, c, d0 and d1) which are packed together with some
mode bits into the six values (v0, v1, v2, v3, v4, v5):
Value 7 6 5 4 3 2 1 0
----- ------------------------------
v0 | a[7:0] |
----- ------------------------------
v1 |m0 |a8 | c[5:0] |
----- ------------------------------
v2 |m1 |X0 | b0[5:0] |
----- ------------------------------
v3 |m2 |X1 | b1[5:0] |
----- ------------------------------
v4 |mj0|X2 |X4 | d0[4:0] |
----- ------------------------------
v5 |mj1|X3 |X5 | d1[4:0] |
----- ------------------------------
Table C.2.21 - HDR Mode 11 Value Layout
If the major component bits mj[1:0 ] are both 1, then the RGB values
are specified directly
Value 7 6 5 4 3 2 1 0
----- ------------------------------
v0 | R0[11:4] |
----- ------------------------------
v1 | R1[11:4] |
----- ------------------------------
v2 | G0[11:4] |
----- ------------------------------
v3 | G1[11:4] |
----- ------------------------------
v4 | 1 | B0[11:5] |
----- ------------------------------
v5 | 1 | B1[11:5] |
----- ------------------------------
Table C.2.22 - HDR Mode 11 Value Layout
The mode bits m[2:0] specify the bit allocation for the different
values, and the destinations of the extra bits X0 to X5:
-------------------------------------------------------------------------
Number of bits Destination of extra bits
Mode a b c d X0 X1 X2 X3 X4 X5
-------------------------------------------------------------------------
0 9 7 6 7 b0[6] b1[6] d0[6] d1[6] d0[5] d1[5]
1 9 8 6 6 b0[6] b1[6] b0[7] b1[7] d0[5] d1[5]
2 10 6 7 7 a[9] c[6] d0[6] d1[6] d0[5] d1[5]
3 10 7 7 6 b0[6] b1[6] a[9] c[6] d0[5] d1[5]
4 11 8 6 5 b0[6] b1[6] b0[7] b1[7] a[9] a[10]
5 11 6 7 6 a[9] a[10] c[7] c[6] d0[5] d1[5]
6 12 7 7 5 b0[6] b1[6] a[11] c[6] a[9] a[10]
7 12 6 7 6 a[9] a[10] a[11] c[6] d0[5] d1[5]
-------------------------------------------------------------------------
Table C.2.23 - Endpoint Bit Mode
The complete decoding procedure is as follows:
// Find major component
int majcomp = ((v4 & 0x80) >> 7) | ((v5 & 0x80) >> 6);
// Deal with simple case first
if( majcomp == 3 )
{
e0 = (v0 << 4, v2 << 4, (v4 & 0x7f) << 5, 0x780);
e1 = (v1 << 4, v3 << 4, (v5 & 0x7f) << 5, 0x780);
return;
}
// Decode mode, parameters.
int mode = ((v1&0x80)>>7) | ((v2&0x80)>>6) | ((v3&0x80)>>5);
int va = v0 | ((v1 & 0x40) << 2);
int vb0 = v2 & 0x3f;
int vb1 = v3 & 0x3f;
int vc = v1 & 0x3f;
int vd0 = v4 & 0x7f;
int vd1 = v5 & 0x7f;
// Assign top bits of vd0, vd1.
static const int dbitstab[8] = {7,6,7,6,5,6,5,6};
vd0 = signextend( vd0, dbitstab[mode] );
vd1 = signextend( vd1, dbitstab[mode] );
// Extract and place extra bits
int x0 = (v2 >> 6) & 1;
int x1 = (v3 >> 6) & 1;
int x2 = (v4 >> 6) & 1;
int x3 = (v5 >> 6) & 1;
int x4 = (v4 >> 5) & 1;
int x5 = (v5 >> 5) & 1;
int ohm = 1 << mode;
if( ohm & 0xA4 ) va |= x0 << 9;
if( ohm & 0x08 ) va |= x2 << 9;
if( ohm & 0x50 ) va |= x4 << 9;
if( ohm & 0x50 ) va |= x5 << 10;
if( ohm & 0xA0 ) va |= x1 << 10;
if( ohm & 0xC0 ) va |= x2 << 11;
if( ohm & 0x04 ) vc |= x1 << 6;
if( ohm & 0xE8 ) vc |= x3 << 6;
if( ohm & 0x20 ) vc |= x2 << 7;
if( ohm & 0x5B ) vb0 |= x0 << 6;
if( ohm & 0x5B ) vb1 |= x1 << 6;
if( ohm & 0x12 ) vb0 |= x2 << 7;
if( ohm & 0x12 ) vb1 |= x3 << 7;
// Now shift up so that major component is at top of 12-bit value
int shamt = (modeval >> 1) ^ 3;
va <<= shamt; vb0 <<= shamt; vb1 <<= shamt;
vc <<= shamt; vd0 <<= shamt; vd1 <<= shamt;
e1.r = clamp( va, 0, 0xFFF );
e1.g = clamp( va - vb0, 0, 0xFFF );
e1.b = clamp( va - vb1, 0, 0xFFF );
e1.alpha = 0x780;
e0.r = clamp( va - vc, 0, 0xFFF );
e0.g = clamp( va - vb0 - vc - vd0, 0, 0xFFF );
e0.b = clamp( va - vb1 - vc - vd1, 0, 0xFFF );
e0.alpha = 0x780;
if( majcomp == 1 ) { swap( e0.r, e0.g ); swap( e1.r, e1.g ); }
else if( majcomp == 2 ) { swap( e0.r, e0.b ); swap( e1.r, e1.b ); }
HDR Endpoint Mode 14
Mode 14 specifies two RGBA values, using the eight values (v0, v1, v2,
v3, v4, v5, v6, v7). First, the RGB values are decoded from (v0..v5)
using the method from Mode 11, then the alpha values are filled in
from v6 and v7:
// Decode RGB as for mode 11
(e0,e1) = decode_mode_11(v0,v1,v2,v3,v4,v5)
// Now fill in the alphas
e0.alpha = v6;
e1.alpha = v7;
Note that in this mode, the alpha values are interpreted (and
interpolated) as 8-bit unsigned normalized values, as in the LDR modes.
This is the only mode that exhibits this behaviour.
HDR Endpoint Mode 15
Mode 15 specifies two RGBA values, using the eight values (v0, v1, v2,
v3, v4, v5, v6, v7). First, the RGB values are decoded from (v0..v5)
using the method from Mode 11. The alpha values are stored in values
v6 and v7 as a mode and two values which are interpreted according
to the mode:
Value 7 6 5 4 3 2 1 0
----- ------------------------------
v6 |M0 | A[6:0] |
----- ------------------------------
v7 |M1 | B[6:0] |
----- ------------------------------
Table C.2.24 - HDR Mode 15 Alpha Value Layout
The alpha values are decoded from v6 and v7 as follows:
// Decode RGB as for mode 11
(e0,e1) = decode_mode_11(v0,v1,v2,v3,v4,v5)
// Extract mode bits
mode = ((v6 >> 7) & 1) | ((v7 >> 6) & 2);
v6 &= 0x7F;
v7 &= 0x7F;
if(mode==3)
{
// Directly specify alphas
e0.alpha = v6 << 5;
e1.alpha = v7 << 5;
}
else
{
// Transfer bits from v7 to v6 and sign extend v7.
v6 |= (v7 << (mode+1))) & 0x780;
v7 &= (0x3F >> mode);
v7 ^= 0x20 >> mode;
v7 -= 0x20 >> mode;
v6 <<= (4-mode);
v7 <<= (4-mode);
// Add delta and clamp
v7 += v6;
v7 = clamp(v7, 0, 0xFFF);
e0.alpha = v6;
e1.alpha = v7;
}
Note that in this mode, the alpha values are interpreted (and
interpolated) as 12-bit HDR values, and are interpolated as
for any other HDR component.
C.2.16 Weight Decoding
-----------------------
The weight information is stored as a stream of bits, growing downwards
from the most significant bit in the block. Bit n in the stream is thus
bit 127-n in the block.
For each location in the weight grid, a value (in the specified range)
is packed into the stream. These are ordered in a raster pattern
starting from location (0,0,0), with the X dimension increasing fastest,
and the Z dimension increasing slowest. If dual-plane mode is selected,
both weights are emitted together for each location, plane 0 first,
then plane 1.
C.2.17 Weight Unquantization
-----------------------------
Each weight plane is specified as a sequence of integers in a given
range. These values are packed using integer sequence encoding.
Once unpacked, the values must be unquantized from their storage
range, returning them to a standard range of 0..64. The procedure
for doing so is similar to the color endpoint unquantization.
First, we unquantize the actual stored weight values to the range 0..63.
For bit-only representations, this is simple bit replication from the
most significant bit of the value.
For trit or quint-based representations, this involves a set of bit
manipulations and adjustments to avoid the expense of full-width
multipliers.
For representations with no additional bits, the results are as follows:
Range 0 1 2 3 4
--------------------------
0..2 0 32 63 - -
0..4 0 16 32 47 63
--------------------------
Table C.2.25 - Weight Unquantization Values
For other values, we calculate the initial inputs to a bit manipulation
procedure. These are denoted A (7 bits), B (7 bits), C (7 bits), and
D (3 bits) and are decoded using the range as follows:
Range T Q B Bits A B C D
-------------------------------------------------------
0..5 1 1 a aaaaaaa 0000000 50 Trit value
0..9 1 1 a aaaaaaa 0000000 28 Quint value
0..11 1 2 ba aaaaaaa b000b0b 23 Trit value
0..19 1 2 ba aaaaaaa b0000b0 13 Quint value
0..23 1 3 cba aaaaaaa cb000cb 11 Trit value
-------------------------------------------------------
Table C.2.26 - Weight Unquantization Parameters
These are then processed as follows:
T = D * C + B;
T = T ^ A;
T = (A & 0x20) | (T >> 2);
Note that the multiply in the first line is nearly trivial as it only
needs to multiply by 0, 1, 2, 3 or 4.
As a final step, for all types of value, the range is expanded from
0..63 up to 0..64 as follows:
if (T > 32) { T += 1; }
This allows the implementation to use 64 as a divisor during inter-
polation, which is much easier than using 63.
C.2.18 Weight Infill
---------------------
After unquantization, the weights are subject to weight selection and
infill. The infill method is used to calculate the weight for a texel
position, based on the weights in the stored weight grid array (which
may be a different size).
The procedure below must be followed exactly, to ensure bit exact
results.
The block size is specified as three dimensions along the s, t and r
axes (Bs, Bt, Br). Texel coordinates within the block (s,t,r) can
have values from 0 to one less than the block dimension in that axis.
For each block dimension, we compute scale factors (Ds, Dt, Dr)
Ds = floor( (1024 + floor(Bs/2)) / (Bs-1) );
Dt = floor( (1024 + floor(Bt/2)) / (Bt-1) );
Dr = floor( (1024 + floor(Br/2)) / (Br-1) );
Since the block dimensions are constrained, these are easily looked up
in a table. These scale factors are then used to scale the (s,t,r)
coordinates to a homogeneous coordinate (cs, ct, cr):
cs = Ds * s;
ct = Dt * t;
cr = Dr * r;
This homogeneous coordinate (cs, ct, cr) is then scaled again to give
a coordinate (gs, gt, gr) in the weight-grid space . The weight-grid is
of size (N, M, Q), as specified in the block mode field:
gs = (cs*(N-1)+32) >> 6;
gt = (ct*(M-1)+32) >> 6;
gr = (cr*(Q-1)+32) >> 6;
The resulting coordinates may be in the range 0..176. These are inter-
preted as 4:4 unsigned fixed point numbers in the range 0.0 .. 11.0.
If we label the integral parts of these (js, jt, jr) and the fractional
parts (fs, ft, fr), then:
js = gs >> 4; fs = gs & 0x0F;
jt = gt >> 4; ft = gt & 0x0F;
jr = gr >> 4; fr = gr & 0x0F;
These values are then used to interpolate between the stored weights.
This process differs for 2D and 3D.
For 2D, bilinear interpolation is used:
v0 = js + jt*N;
p00 = decode_weight(v0);
p01 = decode_weight(v0 + 1);
p10 = decode_weight(v0 + N);
p11 = decode_weight(v0 + N + 1);
The function decode_weight(n) decodes the nth weight in the stored weight
stream. The values p00 to p11 are the weights at the corner of the square
in which the texel position resides. These are then weighted using the
fractional position to produce the effective weight i as follows:
w11 = (fs*ft+8) >> 4;
w10 = ft - w11;
w01 = fs - w11;
w00 = 16 - fs - ft + w11;
i = (p00*w00 + p01*w01 + p10*w10 + p11*w11 + 8) >> 4;
For 3D, simplex interpolation is used as it is cheaper than a naïve
trilinear interpolation. First, we pick some parameters for the inter-
polation based on comparisons of the fractional parts of the texel
position:
fs>ft ft>fr fs>fr s1 s2 w0 w1 w2 w3
----------------------------------------------------------
True True True 1 N 16-fs fs-ft ft-fr fr
False True True N 1 16-ft ft-fs fs-fr fr
True False True 1 N*M 16-fs fs-fr fr-ft ft
True False False N*M 1 16-fr fr-fs fs-ft ft
False True False N N*M 16-ft ft-fr fr-fs fs
False False False N*M N 16-fr fr-ft ft-fs fs
----------------------------------------------------------
Table C.2.27 -Simplex Interpolation Parameters
Some test results are implied by the others. The effective
weight i is then calculated as:
v0 = js + jt*N + jr*N*M;
p0 = decode_index(v0);
p1 = decode_index(v0 + s1);
p2 = decode_index(v0 + s1 + s2);
p3 = decode_index(v0 + N*M + N + 1);
i = (p0*w0 + p1*w1 + p2*w2 + p3*w3 + 8) >> 4;
C.2.19 Weight Application
--------------------------
Once the effective weight i for the texel has been calculated, the color
endpoints are interpolated and expanded.
For LDR endpoint modes, each color component C is calculated from the
corresponding 8-bit endpoint components C0 and C1 as follows:
If sRGB conversion is not enabled, C0 and C1 are first expanded to
16 bits by bit replication:
C0 = (C0 << 8) | C0; C1 = (C1 << 8) | C1;
If sRGB conversion is enabled, C0 and C1 are expanded to 16 bits
differently, as follows:
C0 = (C0 << 8) | 0x80; C1 = (C1 << 8) | 0x80;
C0 and C1 are then interpolated to produce a UNORM16 result C:
C = floor( (C0*(64-i) + C1*i + 32)/64 )
If sRGB conversion is enabled, the top 8 bits of the interpolation
result are passed to the external sRGB conversion block. Otherwise, if
C = 65535, then the final result is 1.0 (0x3C00) otherwise C is divided
by 65536 and the infinite-precision result of the division is converted
to FP16 with round-to-zero semantics.
For HDR endpoint modes, color values are represented in a 12-bit
pseudo-logarithmic representation, and interpolation occurs in a
piecewise-approximate logarithmic manner as follows:
In LDR mode, the error result is returned.
In HDR mode, the color components from each endpoint, C0 and C1, are
initially shifted left 4 bits to become 16-bit integer values and these
are interpolated in the same way as LDR. The 16-bit value C is then
decomposed into the top five bits, E, and the bottom 11 bits M, which
are then processed and recombined with E to form the final value Cf:
C = floor( (C0*(64-i) + C1*i + 32)/64 )
E = (C&0xF800) >> 11; M = C&0x7FF;
if (M < 512) { Mt = 3*M; }
else if (M >= 1536) { Mt = 5*M - 2048; }
else { Mt = 4*M - 512; }
Cf = (E<<10) + (Mt>>3)
This interpolation is a considerably closer approximation to a
logarithmic space than simple 16-bit interpolation.
This final value Cf is interpreted as an IEEE FP16 value. If the result
is +Inf or NaN, it is converted to the bit pattern 0x7BFF, which is the
largest representable finite value.
C.2.20 Dual-Plane Decoding
---------------------------
If dual-plane mode is disabled, all of the endpoint components are inter-
polated using the same weight value.
If dual-plane mode is enabled, two weights are stored with each texel.
One component is then selected to use the second weight for interpolation,
instead of the first weight. The first weight is then used for all other
components.
The component to treat specially is indicated using the 2-bit Color
Component Selector (CCS) field as follows:
Value Weight 0 Weight 1
--------------------------
0 GBA R
1 RBA G
2 RGA B
3 RGB A
--------------------------
Table C.2.28 -Dual Plane Color Component Selector Values
The CCS bits are stored at a variable position directly below the weight
bits and any additional CEM bits.
C.2.21 Partition Pattern Generation
------------------------------------
When multiple partitions are active, each texel position is assigned a
partition index. This partition index is calculated using a seed (the
partition pattern index), the texel's x,y,z position within the block,
and the number of partitions. An additional argument, small_block, is
set to 1 if the number of texels in the block is less than 31,
otherwise it is set to 0.
This function is specified in terms of x, y and z in order to support
3D textures. For 2D textures and texture slices, z will always be 0.
The full partition selection algorithm is as follows:
int select_partition(int seed, int x, int y, int z,
int partitioncount, int small_block)
{
if( small_block ){ x <<= 1; y <<= 1; z <<= 1; }
seed += (partitioncount-1) * 1024;
uint32_t rnum = hash52(seed);
uint8_t seed1 = rnum & 0xF;
uint8_t seed2 = (rnum >> 4) & 0xF;
uint8_t seed3 = (rnum >> 8) & 0xF;
uint8_t seed4 = (rnum >> 12) & 0xF;
uint8_t seed5 = (rnum >> 16) & 0xF;
uint8_t seed6 = (rnum >> 20) & 0xF;
uint8_t seed7 = (rnum >> 24) & 0xF;
uint8_t seed8 = (rnum >> 28) & 0xF;
uint8_t seed9 = (rnum >> 18) & 0xF;
uint8_t seed10 = (rnum >> 22) & 0xF;
uint8_t seed11 = (rnum >> 26) & 0xF;
uint8_t seed12 = ((rnum >> 30) | (rnum << 2)) & 0xF;
seed1 *= seed1; seed2 *= seed2;
seed3 *= seed3; seed4 *= seed4;
seed5 *= seed5; seed6 *= seed6;
seed7 *= seed7; seed8 *= seed8;
seed9 *= seed9; seed10 *= seed10;
seed11 *= seed11; seed12 *= seed12;
int sh1, sh2, sh3;
if( seed & 1 )
{ sh1 = (seed&2 ? 4:5); sh2 = (partitioncount==3 ? 6:5); }
else
{ sh1 = (partitioncount==3 ? 6:5); sh2 = (seed&2 ? 4:5); }
sh3 = (seed & 0x10) ? sh1 : sh2:
seed1 >>= sh1; seed2 >>= sh2; seed3 >>= sh1; seed4 >>= sh2;
seed5 >>= sh1; seed6 >>= sh2; seed7 >>= sh1; seed8 >>= sh2;
seed9 >>= sh3; seed10 >>= sh3; seed11 >>= sh3; seed12 >>= sh3;
int a = seed1*x + seed2*y + seed11*z + (rnum >> 14);
int b = seed3*x + seed4*y + seed12*z + (rnum >> 10);
int c = seed5*x + seed6*y + seed9 *z + (rnum >> 6);
int d = seed7*x + seed8*y + seed10*z + (rnum >> 2);
a &= 0x3F; b &= 0x3F; c &= 0x3F; d &= 0x3F;
if( partitioncount < 4 ) d = 0;
if( partitioncount < 3 ) c = 0;
if( a >= b && a >= c && a >= d ) return 0;
else if( b >= c && b >= d ) return 1;
else if( c >= d ) return 2;
else return 3;
}
As has been observed before, the bit selections are much easier to
express in hardware than in C.
The seed is expanded using a hash function hash52, which is defined as
follows:
uint32_t hash52( uint32_t p )
{
p ^= p >> 15; p -= p << 17; p += p << 7; p += p << 4;
p ^= p >> 5; p += p << 16; p ^= p >> 7; p ^= p >> 3;
p ^= p << 6; p ^= p >> 17;
return p;
}
This assumes that all operations act on 32-bit values
C.2.22 Data Size Determination
-------------------------------
The size of the data used to represent color endpoints is not
explicitly specified. Instead, it is determined from the block mode and
number of partitions as follows:
config_bits = 17;
if(num_partitions>1)
if(single_CEM)
config_bits = 29;
else
config_bits = 25 + 3*num_partitions;
num_weights = M * N * Q; // size of weight grid
if(dual_plane)
config_bits += 2;
num_weights *= 2;
weight_bits = ceil(num_weights*8*trits_in_weight_range/5) +
ceil(num_weights*7*quints_in_weight_range/3) +
num_weights*bits_in_weight_range;
remaining_bits = 128 - config_bits - weight_bits;
num_CEM_pairs = base_CEM_class+1 + count_bits(extra_CEM_bits);
The CEM value range is then looked up from a table indexed by remaining
bits and num_CEM_pairs. This table is initialized such that the range
is as large as possible, consistent with the constraint that the number
of bits required to encode num_CEM_pairs pairs of values is not more
than the number of remaining bits.
An equivalent iterative algorithm would be:
num_CEM_values = num_CEM_pairs*2;
for(range = each possible CEM range in descending order of size)
{
CEM_bits = ceil(num_CEM_values*8*trits_in_CEM_range/5) +
ceil(num_CEM_values*7*quints_in_CEM_range/3) +
num_CEM_values*bits_in_CEM_range;
if(CEM_bits <= remaining_bits)
break;
}
return range;
In cases where this procedure results in unallocated bits, these bits
are not read by the decoding process and can have any value.
C.2.23 Void-Extent Blocks
--------------------------
A void-extent block is a block encoded with a single color. It also
specifies some additional information about the extent of the single-
color area beyond this block, which can optionally be used by a
decoder to reduce or prevent redundant block fetches.
The layout of a 2D Void-Extent block is as follows:
127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112
---------------------------------------------------------------
| Block color A component |
---------------------------------------------------------------
111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96
---------------------------------------------------------------
| Block color B component |
---------------------------------------------------------------
95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80
---------------------------------------------------------------
| Block color G component |
---------------------------------------------------------------
79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64
---------------------------------------------------------------
| Block color R component |
---------------------------------------------------------------
63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48
---------------------------------------------------------------
| Void-extent maximum T coordinate | Min T
---------------------------------------------------------------
47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32
---------------------------------------------------------------
Void-extent minimum T coordinate | Void-extent max S
---------------------------------------------------------------
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
---------------------------------------------------------------
Void-extent max S coord | Void-extent minimum S coordinate
---------------------------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
Min S coord | 1 | 1 | D | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
--------------------------------------------------------------
Table C.2.29 - 2D Void-Extent Block Layout Overview
The layout of a 3D Void-Extent block is as follows:
127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112
---------------------------------------------------------------
| Block color A component |
---------------------------------------------------------------
111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96
---------------------------------------------------------------
| Block color B component |
---------------------------------------------------------------
95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80
---------------------------------------------------------------
| Block color G component |
---------------------------------------------------------------
79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64
---------------------------------------------------------------
| Block color R component |
---------------------------------------------------------------
63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48
---------------------------------------------------------------
| Void-extent max R coordinate | Void-extent min R coord
---------------------------------------------------------------
47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32
---------------------------------------------------------------
min R | Void-extent max T coordinate | Void-extent min T
---------------------------------------------------------------
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
---------------------------------------------------------------
min T coord | Void-extent minimum S coordinate | Minimum S
---------------------------------------------------------------
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
--------------------------------------------------------------
Minimum S coord | D | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
--------------------------------------------------------------
Table C.2.30 - 3D Void-Extent Block Layout Overview
Bit 9 is the Dynamic Range flag, which indicates the format in which
colors are stored. A 0 value indicates LDR, in which case the color
components are stored as UNORM16 values. A 1 indicates HDR, in which
case the color components are stored as FP16 values.
The reason for the storage of UNORM16 values in the LDR case is due
to the possibility that the value will need to be passed on to sRGB
conversion. By storing the color value in the format which comes out
of the interpolator, before the conversion to FP16, we avoid having
to have separate versions for sRGB and linear modes.
If a void-extent block with HDR values is decoded in LDR mode, then
the result will be the error color, opaque magenta, for all texels
within the block.
In the HDR case, if the color component values are infinity or NaN, this
will result in undefined behavior. As usual, this must not lead to GL
interruption or termination.
The minimum and maximum coordinate values are treated as unsigned
integers and then normalized into the range 0..1 (by dividing by 2^13-1
or 2^9-1, for 2D and 3D respectively). The maximum values for each
dimension must be greater than the corresponding minimum values,
unless they are all all-1s.
If all the coordinates are all-1s, then the void extent is ignored,
and the block is simply a constant-color block.
The existence of single-color blocks with void extents must not produce
results different from those obtained if these single-color blocks are
defined without void-extents. Any situation in which the results would
differ is invalid. Results from invalid void extents are undefined.
If a void-extent appears in a MIPmap level other than the most detailed
one, then the extent will apply to all of the more detailed levels too.
This allows decoders to avoid sampling more detailed MIPmaps.
If the more detailed MIPmap level is not a constant color in this region,
then the block may be marked as constant color, but without a void extent,
as detailed above.
If a void-extent extends to the edge of a texture, then filtered texture
colors may not be the same color as that specified in the block, due to
texture border colors, wrapping, or cube face wrapping.
Care must be taken when updating or extracting partial image data that
void-extents in the image do not become invalid.
C.2.24 Illegal Encodings
-------------------------
In ASTC, there is a variety of ways to encode an illegal block. Decoders
are required to recognize all illegal blocks and emit the standard error
color value upon encountering an illegal block.
Here is a comprehensive list of situations that represent illegal block
encodings:
* The block mode specified is one of the modes explicitly listed
as Reserved.
* A block mode has been specified that would require more than
64 weights total.
* A block mode has been specified that would require more than
96 bits for integer sequence encoding of the weight grid.
* A block mode has been specifed that would require fewer than
24 bits for integer sequence encoding of the weight grid.
* The size of the weight grid exceeds the size of the block footprint
in any dimension.
* Color endpoint modes have been specified such that the color
integer sequence encoding would require more than 18 integers.
* The number of bits available for color endpoint encoding after all
the other fields have been counted is less than ceil(13C/5) where C
is the number of color endpoint integers (this would restrict color
integers to a range smaller than 0..5, which is not supported).
* Dual weight mode is enabled for a block with 4 partitions.
* Void-Extent blocks where the low coordinate for some texture axis
is greater than or equal to the high coordinate.
Note also that, in LDR mode, a block which has both HDR and LDR endpoint
modes assigned to different partitions is not an error block. Only those
texels which belong to the HDR partition will result in the error color.
Texels belonging to a LDR partition will be decoded as normal.
C.2.25 LDR PROFILE SUPPORT
---------------------------
In order to ease verification and accelerate adoption, an LDR-only
subset of the full ASTC specification has been made available.
Implementations of this LDR Profile must satisfy the following requirements:
* All textures with valid encodings for LDR Profile must decode
identically using either a LDR Profile, HDR Profile, or Full Profile
decoder.
* All features included only in the HDR Profile or Full Profile must be
treated as reserved in the LDR Profile, and return the error color on
decoding.
* Any sequence of API calls valid for the LDR Profile must also be valid
for the HDR Profile or Full Profile and return identical results when
given a texture encoded for the LDR Profile.
The feature subset for the LDR profile is:
* 2D textures only.
* Only those block sizes listed in Table C.2.2 are supported.
* LDR operation mode only.
* Only LDR endpoint formats must be supported, namely formats
0, 1, 4, 5, 6, 8, 9, 10, 12, 13.
* Decoding from a HDR endpoint results in the error color.
* Interpolation returns UNORM8 results when used in conjunction
with sRGB.
* LDR void extent blocks must be supported, but void extents
may not be checked.
C.2.26 HDR PROFILE SUPPORT
---------------------------
In order to ease verification and accelerate adoption, a second subset
of the full ASTC specification has been made available, known as the
HDR profile.
Implementations of the HDR Profile must satisfy the following requirements:
* The HDR profile is a sueprset of the LDR profile and therefore all
valid LDR encodings must decode identically using a HDR profile
decoder.
* All textures with valid encodings for HDR Profile must decode
identically using either a HDR Profile or Full Profile decoder.
* All features included only in the Full Profile must be treated as
reserved in the HDR Profile, and return the error color on decoding.
* Any sequence of API calls valid for the HDR Profile must also be valid
for the Full Profile and return identical results when given a texture
encoded for the HDR Profile.
The feature subset for the HDR profile is:
* 2D textures only.
* Only those block sizes listed in Table C.2.2 are supported.
* All endpoint formats must be supported.
* 2D void extent blocks must be supported, but void extents
may not be checked.
Additions to Appendix D of the OpenGL ES 3.0 Specification (Shared
Objects and Multiple Contexts)
None
Additions to Appendix E of the OpenGL ES 3.0 Specification (Version 3.0
and before)
None