bptc.txt

// Copyright (c) 2014-2019 The Khronos Group Inc.
// Copyright notice at https://www.khronos.org/registry/speccopyright.html
[[BPTC]]
== BPTC Compressed Texture Image Formats

_This description is derived from the ``BPTC Compressed Texture Image Formats''
section of the OpenGL 4.4 specification._
More information on
link:https://docs.microsoft.com/en-us/windows/desktop/direct3d11/bc7-format[BC7],
link:https://docs.microsoft.com/en-us/windows/desktop/direct3d11/bc7-format-mode-reference[BC7 modes]
and link:https://docs.microsoft.com/en-us/windows/desktop/direct3d11/bc6h-format[BC6h]
can be found in Microsoft's online documentation.

Compressed texture images stored using the BPTC compressed image formats are
represented as a collection of 4{times}4 texel blocks, each of which
contains 128 bits of texel data stored in little-endian order.
The image is encoded as a normal 2D raster image in which each 4{times}4 block
is treated as a single pixel.
If a BPTC image has a width or height that is not a multiple of four, the
data corresponding to texels outside the image are irrelevant and undefined.
When a BPTC image with width _w_, height _h_, and block size
_blocksize_ (16 bytes) is decoded, the corresponding image size (in
bytes) is:

[latexmath]
++++++++++++++++
\begin{align*}
\left\lceil { w \over 4 } \right\rceil \times
\left\lceil { h \over 4 } \right\rceil \times
blocksize
\end{align*}
++++++++++++++++

When decoding a BPTC image, the block containing the texel at offset (_x_, _y_)
begins at an offset (in bytes) relative to the base of the image of:

[latexmath]
++++++++++++++
\begin{align*}
blocksize \times
 \left( { \left\lceil  { w \over 4 } \right\rceil \times
          \left\lfloor { y \over 4 } \right\rfloor +
          \left\lfloor { x \over 4 } \right\rfloor } \right)
\end{align*}
++++++++++++++

The data corresponding to a specific texel (_x_, _y_) are extracted from a
4{times}4 texel block using a relative (_x_, _y_) value of:

[latexmath]
++++++++++++++
\begin{align*}
(x \bmod 4,y \bmod 4)
\end{align*}
++++++++++++++

There are two distinct BPTC image formats each of which has two variants.
BC7 with or without an sRGB transform function used in the encoding of the
_RGB_ channels compresses 8-bit unsigned, normalized fixed-point data.
BC6H in signed or unsigned form compresses high dynamic range
floating-point values. The formats are similar, so the description of the
BC6H format will reference significant sections of the BC7 description.

[[bptc_bc7]]
=== BC7

Each 4{times}4 block of texels consists of 128 bits of _RGBA_
image data, of which the _RGB_ channels may be encoded linearly or with the
<<TRANSFER_SRGB,sRGB transfer function>>.

Each block contains enough information to select and decode a number of
colors called endpoints, pairs of which forms subsets, then to
interpolate between those endpoints in a variety of ways, and finally to
remap the result into the final output by indexing into these interpolated
values according to a partition layout which maps each relative coordinate
to a subset.

Each block can contain data in one of eight modes. The mode is identified by
the lowest bits of the lowest byte. It is encoded as zero or more zeros
followed by a one. For example, using `x' to indicate a bit not included in
the mode number, mode 0 is encoded as xxxxxxx1 in the low byte in binary,
mode 5 is xx100000, and mode 7 is 10000000. Encoding the low byte as zero is
reserved and should not be used when encoding a BPTC texture; hardware
decoders processing a texel block with a low byte of 0 should return 0 for
all channels of all texels.

All further decoding is driven by the values derived from the mode listed in
<<table-bptcmodes>> and <<table-bptcmodedescriptions>>.
The fields in the block are always in the same order for all modes.
In increasing bit order after the mode, these fields are:
partition pattern selection, rotation, index selection, color, alpha,
per-endpoint P-bit, shared P-bit, primary indices, and secondary indices.
The number of bits to be read in each field is determined directly from
these tables, as shown in <<table-bptcmodebits>>.
[NOTE]
====
Per texel block, _CB_ = 3(each of _R_, _G_,
_B_){times}2(endpoints){times}NS(#subsets){times}CB(bits/channel/endpoint).

_AB_ = 2(endpoints){times}NS(#subsets){times}AB(bits/endpoint).
{_IB_,_IB~2~_} = 16(texels){times}{IB,IB~2~}(#index bits/texel)
- NS(1bit/subset).
====
[[table-bptcmodes]]
.Mode-dependent BPTC parameters
[width="97%",cols="7%,4%,4%,4%,4%,9%,9%,11%,9%,5%,4%,1%,3%,4%,4%,5%,5%,4%,4%"]
|============
^| *Mode* ^| *NS* ^| *PB* ^| *RB* ^| *ISB* ^| *CB* ^| *AB* ^| *EPB* ^| *SPB* ^| *IB* ^| *IB~2~* 1.10+^| ^| *M* ^| *_CB_* ^| *_AB_* ^| *_EPB_* ^| *_SPB_* ^| *_IB_* ^| *_IB~2~_*
2+^| *Bits per...* 3+^| ...texel block 2+^| ...channel/endpoint ^| ...endpoint ^| ...subset 2+^| ...texel 7+^| Bits per texel block (total)
^| *0* ^| 3 ^| 4 ^| 0 ^| 0 ^| 4 ^| 0 ^| 1 ^| 0 ^| 3 ^| 0 ^| 1 ^| 72 ^| 0  ^| 6 ^| 0 ^| 45 ^| 0
^| *1* ^| 2 ^| 6 ^| 0 ^| 0 ^| 6 ^| 0 ^| 0 ^| 1 ^| 3 ^| 0 ^| 2 ^| 72 ^| 0  ^| 0 ^| 2 ^| 46 ^| 0
^| *2* ^| 3 ^| 6 ^| 0 ^| 0 ^| 5 ^| 0 ^| 0 ^| 0 ^| 2 ^| 0 ^| 3 ^| 90 ^| 0  ^| 0 ^| 0 ^| 29 ^| 0
^| *3* ^| 2 ^| 6 ^| 0 ^| 0 ^| 7 ^| 0 ^| 1 ^| 0 ^| 2 ^| 0 ^| 4 ^| 84 ^| 0  ^| 4 ^| 0 ^| 30 ^| 0
^| *4* ^| 1 ^| 0 ^| 2 ^| 1 ^| 5 ^| 6 ^| 0 ^| 0 ^| 2 ^| 3 ^| 5 ^| 30 ^| 12 ^| 0 ^| 0 ^| 31 ^| 47
^| *5* ^| 1 ^| 0 ^| 2 ^| 0 ^| 7 ^| 8 ^| 0 ^| 0 ^| 2 ^| 2 ^| 6 ^| 42 ^| 16 ^| 0 ^| 0 ^| 31 ^| 31
^| *6* ^| 1 ^| 0 ^| 0 ^| 0 ^| 7 ^| 7 ^| 1 ^| 0 ^| 4 ^| 0 ^| 7 ^| 42 ^| 14 ^| 2 ^| 0 ^| 63 ^| 0
^| *7* ^| 2 ^| 6 ^| 0 ^| 0 ^| 5 ^| 5 ^| 1 ^| 0 ^| 2 ^| 0 ^| 8 ^| 60 ^| 20 ^| 4 ^| 0 ^| 30 ^| 0
|============

[[table-bptcmodedescriptions]]
.Full descriptions of the BPTC mode columns
[cols="1,6",width="40%"]
|============
^| *M* | &nbsp; Mode identifier bits
^| *NS* | &nbsp; Number of subsets
^| *PB* | &nbsp; Partition selection bits
^| *RB* | &nbsp; Rotation bits
^| *ISB* | &nbsp; Index selection bit
^| *CB* | &nbsp; Color bits
^| *AB* | &nbsp; Alpha bits
^| *EPB* | &nbsp; Endpoint P-bits (all channels)
^| *SPB* | &nbsp; Shared P-bits
^| *IB* | &nbsp; Index bits
^| *IB~2~* | &nbsp; Secondary index bits
|============
Each block can be divided into between 1 and 3 groups of pixels called _subsets_,
which have different endpoints.
There are two endpoint colors per subset, grouped first by endpoint,
then by subset, then by channel.
For example, mode 1, with two subsets and six color bits, would have six
bits of red for endpoint 0 of the first subset, then six bits of red for
endpoint 1, then the two ends of the second subset, then green and blue stored
similarly.
If a block has any alpha bits, the alpha data follows the color data with
the same organization.
If not, alpha is overridden to 255.
These bits are treated as the high bits of a fixed-point value in a byte
for each color channel of the endpoints: {_E_~_R_~^7..0^, _E_~_G_~^7..0^, _E_~_B_~^7..0^,
_E_~_A_~^7..0^} per endpoint.
If the mode has shared P-bits, there are two endpoint bits, the lower of
which applies to both endpoints of subset 0 and the upper of which applies
to both endpoints of subset 1.
If the mode has per-endpoint P-bits, then there are 2 {times} _subsets_
P-bits stored in the same order as color and alpha.
Both kinds of P-bits are added as a bit below the color data stored in the
byte.
So, for mode 1 with six red bits, the P-bit ends up in bit 1.
For final scaling, the top bits of the value are replicated into any
remaining bits in the byte.
For the example of mode 1, bit 7 (which originated as bit 5 of the 6-bit
encoded channel) would be replicated to bit 0.
<<table-bptcsourcebits>> and <<table-bptcsourcebits2>> show the origin of
each endpoint color bit for each mode.

[[table-bptcmodebits]]
.Bit layout for BC7 modes (LSB..MSB)
[cols="7*1"]
|============
1.6+^.^| Mode

{nbsp}0 2+^| ~_0:_~ *M^0^ = 1* 4+^| ~_1..4:_~ PB^0..3^
^| ~_5..8:_~ _R_~0~^0..3^ ^| ~_9..12:_~ _R_~1~^0..3^ ^| ~_13..16:_~ _R_~2~^0..3^ ^| ~_17..20:_~ _R_~3~^0..3^ ^| ~_21..24:_~ _R_~4~^0..3^ ^| ~_25..28:_~ _R_~5~^0..3^
^| ~_29..32:_~ _G_~0~^0..3^ ^| ~_33..36:_~ _G_~1~^0..3^ ^| ~_37..40:_~ _G_~2~^0..3^ ^| ~_41..44:_~ _G_~3~^0..3^ ^| ~_45..48:_~ _G_~4~^0..3^ ^| ~_49..52:_~ _G_~5~^0..3^
^| ~_53..56:_~ _B_~0~^0..3^ ^| ~_57..60:_~ _B_~1~^0..3^ ^| ~_61..64:_~ _B_~2~^0..3^ ^| ~_65..68:_~ _B_~3~^0..3^ ^| ~_69..72:_~ _B_~4~^0..3^ ^| ~_73..76:_~ _B_~5~^0..3^
^| ~_77:_~ EPB~0~^0^ ^| ~_78:_~ EPB~1~^0^ ^| ~_79:_~ EPB~2~^0^ ^| ~_80:_~ EPB~3~^0^ ^| ~_81:_~ EPB~4~^0^ ^| ~_82:_~ EPB~5~^0^
6+^| ~_83..127:_~ IB^0..44^
1.5+^.^| Mode

{nbsp}1 2+^| ~_0..1:_~ *M^0..1^ = 01* 4+^| ~_2..7:_~ PB^0..5^
^| ~_8..13:_~ _R_~0~^0..5^ ^| ~_14..19:_~ _R_~1~^0..5^ ^| ~_20..25:_~ _R_~2~^0..5^ ^| ~_26..31:_~ _R_~3~^0..5^ 2.3+^|
^| ~_32..37:_~ _G_~0~^0..5^ ^| ~_38..43:_~ _G_~1~^0..5^ ^| ~_44..49:_~ _G_~2~^0..5^ ^| ~_50..55:_~ _G_~3~^0..5^
^| ~_56..61:_~ _B_~0~^0..5^ ^| ~_62..67:_~ _B_~1~^0..5^ ^| ~_68..73:_~ _B_~2~^0..5^ ^| ~_74..79:_~ _B_~3~^0..5^
^| ~_80:_~ SPB~0~^0^ ^| ~_81:_~ SPB~1~^0^ 4+^| ~_82..127:_~ IB^0..45^
1.5+^.^| Mode

{nbsp}2 2+^| ~_0..2:_~ *M^0..2^ = 001* 4+^| ~_3..8:_~ PB^0..5^
^| ~_9..13:_~ _R_~0~^0..4^ ^| ~_14..18:_~ _R_~1~^0..4^ ^| ~_19..23:_~ _R_~2~^0..4^ ^| ~_24..28:_~ _R_~4~^0..4^ ^| ~_29..33:_~ _R_~4~^0..4^ ^| ~_34..38:_~ _R_~5~^0..4^
^| ~_39..43:_~ _G_~0~^0..4^ ^| ~_44..48:_~ _G_~1~^0..4^ ^| ~_49..53:_~ _G_~2~^0..4^ ^| ~_54..58:_~ _G_~4~^0..4^ ^| ~_59..63:_~ _G_~4~^0..4^ ^| ~_64..68:_~ _G_~5~^0..4^
^| ~_69..73:_~ _B_~0~^0..4^ ^| ~_74..78:_~ _B_~1~^0..4^ ^| ~_79..83:_~ _B_~2~^0..4^ ^| ~_84..88:_~ _B_~4~^0..4^ ^| ~_89..93:_~ _B_~4~^0..4^ ^| ~_94..98:_~ _B_~5~^0..4^
6+^| ~_99..127:_~ IB^0..28^
1.5+^.^| Mode

{nbsp}3 2+^| ~_0..3:_~ *M^0..3^ = 0001* 4+^| ~_4..9:_~ PB^0..5^
^| ~_10..16:_~ _R_~0~^0..6^ ^| ~_17..23:_~ _R_~1~^0..6^ ^| ~_24..30:_~ _R_~2~^0..6^ ^| ~_31..37:_~ _R_~3~^0..6^ 2.3+^|
^| ~_38..44:_~ _G_~0~^0..6^ ^| ~_45..51:_~ _G_~1~^0..6^ ^| ~_52..58:_~ _G_~2~^0..6^ ^| ~_59..65:_~ _G_~3~^0..6^
^| ~_66..72:_~ _B_~0~^0..6^ ^| ~_73..79:_~ _B_~1~^0..6^ ^| ~_80..86:_~ _B_~2~^0..6^ ^| ~_87..93:_~ _B_~3~^0..6^
^| ~_94:_~ EPB~0~^0^ ^| ~_95:_~ EPB~1~^0^ ^| ~_96:_~ EPB~2~^0^ ^| ~_97:_~ EPB~3~^0^ 2+^| ~_98..127:_~ IB^0..29^
1.3+^.^| Mode

{nbsp}4 2+^| ~_0..4:_~ *M^0..4^ = 00001* 2+^| ~_5..6:_~ RB^0..1^ 2+^| ~_7:_~ ISB^0^
^| ~_8..12:_~ _R_~0~^0..4^ ^| ~_13..17:_~ _R_~1~^0..4^ ^| ~_18..22:_~ _G_~0~^0..4^ ^| ~_23..27:_~ _G_~1~^0..4^ ^| ~_28..32:_~ _B_~0~^0..4^ ^| ~_33..37:_~ _B_~1~^0..4^
^| ~_38..43:_~ _A_~0~^0..5^ ^| ~_44..49:_~ _A_~1~^0..5^ 2+^| ~_50..80:_~ IB^0..30^ 2+^| ~_81..127:_~ IB~2~^0..46^
1.3+^.^| Mode

{nbsp}5 2+^| ~_0..5:_~ *M^0..5^ = 000001* 4+^| ~_6..7:_~ RB^0..1^
^| ~_8..14:_~ _R_~0~^0..6^ ^| ~_15..21:_~ _R_~1~^0..6^ ^| ~_22..28:_~ _G_~0~^0..6^ ^| ~_29..35:_~ _G_~1~^0..6^ ^| ~_36..42:_~ _B_~0~^0..6^ ^| ~_43..49:_~ _B_~1~^0..6^
^| ~_50..57:_~ _A_~0~^0..7^ ^| ~_58..65:_~ _A_~1~^0..7^ 2+^| ~_66..96:_~ IB^0..30^ 2+^| ~_97..127:_~ IB~2~^0..30^
1.3+^.^| Mode

{nbsp}6 2+^| ~_0..6:_~ *M^0..6^ = 0000001* 4+^|
^| ~_7..13:_~ _R_~0~^0..6^ ^| ~_14..20:_~ _R_~1~^0..6^ ^| ~_21..27:_~ _G_~0~^0..6^ ^| ~_28..34:_~ _G_~1~^0..6^ ^| ~_35..41:_~ _B_~0~^0..6^ ^| ~_42..48:_~ _B_~1~^0..6^
^| ~_49..55:_~ _A_~0~^0..6^ ^| ~_56..62:_~ _A_~1~^0..6^ ^| ~_63:_~ EPB~0~^0^ ^| ~_64:_~ EPB~1~^0^ 2+^| ~_65..127:_~ IB^0..62^
1.6+^.^| Mode

{nbsp}7 2+^| ~_0..7:_~ *M^0..7^ = 00000001* 4+^| ~_8..13:_~ PB^0..5^
^| ~_14..18:_~ _R_~0~^0..4^ ^| ~_19..23:_~ _R_~1~^0..4^ ^| ~_24..28:_~ _R_~2~^0..4^ ^| ~_29..33:_~ _R_~3~^0..4^ 2.4+^|
^| ~_34..38:_~ _G_~0~^0..4^ ^| ~_39..43:_~ _G_~1~^0..4^ ^| ~_44..48:_~ _G_~2~^0..4^ ^| ~_49..53:_~ _G_~3~^0..4^
^| ~_54..58:_~ _B_~0~^0..4^ ^| ~_59..63:_~ _B_~1~^0..4^ ^| ~_64..68:_~ _B_~2~^0..4^ ^| ~_69..73:_~ _B_~3~^0..4^
^| ~_74..78:_~ _A_~0~^0..4^ ^| ~_79..83:_~ _A_~1~^0..4^ ^| ~_84..88:_~ _A_~2~^0..4^ ^| ~_89..93:_~ _A_~3~^0..4^
^| ~_94:_~ EPB~0~^0^ ^| ~_95:_~ EPB~1~^0^ ^| ~_96:_~ EPB~2~^0^ ^| ~_97:_~ EPB~3~^0^ 2+^| ~_98..127:_~ IB^0..29^
|============

ifndef::a2xhtml[]
&nbsp;
endif::[]

[[table-bptcsourcebits]]
.Bit sources for BC7 endpoints (modes 0..2, MSB..LSB per channel)
[cols="32*1",width="97%"]
|============
32+^| *Mode 0*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 8 ^| 7 ^| 6 ^| 5 ^| 77 ^| 8 ^| 7 ^| 6
^| 32 ^| 31 ^| 30 ^| 29 ^| 77 ^| 32 ^| 31 ^| 30
^| 56 ^| 55 ^| 54 ^| 53 ^| 77 ^| 56 ^| 55 ^| 54
8+^| _255_
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 12 ^| 11 ^| 10 ^| 9 ^| 78 ^| 12 ^| 11 ^| 10
^| 36 ^| 35 ^| 34 ^| 33 ^| 78 ^| 36 ^| 35 ^| 34
^| 60 ^| 59 ^| 58 ^| 57 ^| 78 ^| 60 ^| 59 ^| 58
8+^| _255_
8+^| _E_~_R2_~^7..0^ 8+^| _E_~_G2_~^7..0^ 8+^| _E_~_B2_~^7..0^ 8+^| _E_~_A2_~^7..0^
^| 16 ^| 15 ^| 14 ^| 13 ^| 79 ^| 16 ^| 15 ^| 14
^| 40 ^| 39 ^| 38 ^| 37 ^| 79 ^| 40 ^| 39 ^| 38
^| 64 ^| 63 ^| 62 ^| 61 ^| 79 ^| 64 ^| 63 ^| 62
8+^| _255_
8+^| _E_~_R3_~^7..0^ 8+^| _E_~_G3_~^7..0^ 8+^| _E_~_B3_~^7..0^ 8+^| _E_~_A3_~^7..0^
^| 20 ^| 19 ^| 18 ^| 17 ^| 80 ^| 20 ^| 19 ^| 18
^| 44 ^| 43 ^| 42 ^| 41 ^| 80 ^| 44 ^| 43 ^| 42
^| 68 ^| 67 ^| 66 ^| 65 ^| 80 ^| 68 ^| 67 ^| 66
8+^| _255_
8+^| _E_~_R4_~^7..0^ 8+^| _E_~_G4_~^7..0^ 8+^| _E_~_B4_~^7..0^ 8+^| _E_~_A4_~^7..0^
^| 24 ^| 23 ^| 22 ^| 21 ^| 81 ^| 24 ^| 23 ^| 22
^| 48 ^| 47 ^| 46 ^| 45 ^| 81 ^| 48 ^| 47 ^| 46
^| 72 ^| 71 ^| 70 ^| 69 ^| 81 ^| 72 ^| 71 ^| 70
8+^| _255_
8+^| _E_~_R5_~^7..0^ 8+^| _E_~_G5_~^7..0^ 8+^| _E_~_B5_~^7..0^ 8+^| _E_~_A5_~^7..0^
^| 28 ^| 27 ^| 26 ^| 25 ^| 82 ^| 28 ^| 27 ^| 26
^| 52 ^| 51 ^| 50 ^| 49 ^| 82 ^| 52 ^| 51 ^| 50
^| 76 ^| 75 ^| 74 ^| 73 ^| 82 ^| 76 ^| 75 ^| 74
8+^| _255_
32+^| *Mode 1*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 13 ^| 12 ^| 11 ^| 10 ^| 9 ^| 8 ^| 80 ^| 13
^| 37 ^| 36 ^| 35 ^| 34 ^| 33 ^| 32 ^| 80 ^| 37
^| 61 ^| 60 ^| 59 ^| 58 ^| 57 ^| 56 ^| 80 ^| 61
8+^| _255_
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 19 ^| 18 ^| 17 ^| 16 ^| 15 ^| 14 ^| 80 ^| 19
^| 43 ^| 42 ^| 41 ^| 40 ^| 39 ^| 38 ^| 80 ^| 43
^| 67 ^| 66 ^| 65 ^| 64 ^| 63 ^| 62 ^| 80 ^| 67
8+^| _255_
8+^| _E_~_R2_~^7..0^ 8+^| _E_~_G2_~^7..0^ 8+^| _E_~_B2_~^7..0^ 8+^| _E_~_A2_~^7..0^
^| 25 ^| 24 ^| 23 ^| 22 ^| 21 ^| 20 ^| 81 ^| 25
^| 49 ^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 81 ^| 49
^| 73 ^| 72 ^| 71 ^| 70 ^| 69 ^| 68 ^| 81 ^| 73
8+^| _255_
8+^| _E_~_R3_~^7..0^ 8+^| _E_~_G3_~^7..0^ 8+^| _E_~_B3_~^7..0^ 8+^| _E_~_A3_~^7..0^
^| 31 ^| 30 ^| 29 ^| 28 ^| 27 ^| 26 ^| 81 ^| 31
^| 55 ^| 54 ^| 53 ^| 52 ^| 51 ^| 50 ^| 81 ^| 55
^| 79 ^| 78 ^| 77 ^| 76 ^| 75 ^| 74 ^| 81 ^| 79
8+^| _255_
32+^| *Mode 2*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 13 ^| 12 ^| 11 ^| 10 ^| 9 ^| 13 ^| 12 ^| 11
^| 43 ^| 42 ^| 41 ^| 40 ^| 39 ^| 43 ^| 42 ^| 41
^| 73 ^| 72 ^| 71 ^| 70 ^| 69 ^| 73 ^| 72 ^| 71
8+^| _255_
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 18 ^| 17 ^| 16 ^| 15 ^| 14 ^| 18 ^| 17 ^| 16
^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 48 ^| 47 ^| 46
^| 78 ^| 77 ^| 76 ^| 75 ^| 74 ^| 78 ^| 77 ^| 76
8+^| _255_
8+^| _E_~_R2_~^7..0^ 8+^| _E_~_G2_~^7..0^ 8+^| _E_~_B2_~^7..0^ 8+^| _E_~_A2_~^7..0^
^| 23 ^| 22 ^| 21 ^| 20 ^| 19 ^| 23 ^| 22 ^| 21
^| 53 ^| 52 ^| 51 ^| 50 ^| 49 ^| 53 ^| 52 ^| 51
^| 83 ^| 82 ^| 81 ^| 80 ^| 79 ^| 83 ^| 82 ^| 81
8+^| _255_
8+^| _E_~_R3_~^7..0^ 8+^| _E_~_G3_~^7..0^ 8+^| _E_~_B3_~^7..0^ 8+^| _E_~_A3_~^7..0^
^| 28 ^| 27 ^| 26 ^| 25 ^| 24 ^| 28 ^| 27 ^| 26
^| 58 ^| 57 ^| 56 ^| 55 ^| 54 ^| 58 ^| 57 ^| 56
^| 88 ^| 87 ^| 86 ^| 85 ^| 84 ^| 88 ^| 87 ^| 86
8+^| _255_
8+^| _E_~_R4_~^7..0^ 8+^| _E_~_G4_~^7..0^ 8+^| _E_~_B4_~^7..0^ 8+^| _E_~_A4_~^7..0^
^| 33 ^| 32 ^| 31 ^| 30 ^| 29 ^| 33 ^| 32 ^| 31
^| 63 ^| 62 ^| 61 ^| 60 ^| 59 ^| 63 ^| 62 ^| 61
^| 93 ^| 92 ^| 91 ^| 90 ^| 89 ^| 93 ^| 92 ^| 91
8+^| _255_
8+^| _E_~_R5_~^7..0^ 8+^| _E_~_G5_~^7..0^ 8+^| _E_~_B5_~^7..0^ 8+^| _E_~_A5_~^7..0^
^| 38 ^| 37 ^| 36 ^| 35 ^| 34 ^| 38 ^| 37 ^| 36
^| 68 ^| 67 ^| 66 ^| 65 ^| 64 ^| 68 ^| 67 ^| 66
^| 98 ^| 97 ^| 96 ^| 95 ^| 94 ^| 98 ^| 97 ^| 96
8+^| _255_
|============

ifndef::a2xhtml[]
&nbsp;
endif::[]

[[table-bptcsourcebits2]]
.Bit sources for BC7 endpoints (modes 3..7, MSB..LSB per channel)
[cols="32*1",width="97%"]
|============
32+^| *Mode 3*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 16 ^| 15 ^| 14 ^| 13 ^| 12 ^| 11 ^| 10 ^| 94
^| 44 ^| 43 ^| 42 ^| 41 ^| 40 ^| 39 ^| 38 ^| 94
^| 72 ^| 71 ^| 70 ^| 69 ^| 68 ^| 67 ^| 66 ^| 94
8+^| _255_
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 23 ^| 22 ^| 21 ^| 20 ^| 19 ^| 18 ^| 17 ^| 95
^| 51 ^| 50 ^| 49 ^| 48 ^| 47 ^| 46 ^| 45 ^| 95
^| 79 ^| 78 ^| 77 ^| 76 ^| 75 ^| 74 ^| 73 ^| 95
8+^| _255_
8+^| _E_~_R2_~^7..0^ 8+^| _E_~_G2_~^7..0^ 8+^| _E_~_B2_~^7..0^ 8+^| _E_~_A2_~^7..0^
^| 30 ^| 29 ^| 28 ^| 27 ^| 26 ^| 25 ^| 24 ^| 96
^| 58 ^| 57 ^| 56 ^| 55 ^| 54 ^| 53 ^| 52 ^| 96
^| 86 ^| 85 ^| 84 ^| 83 ^| 82 ^| 81 ^| 80 ^| 96
8+^| _255_
8+^| _E_~_R3_~^7..0^ 8+^| _E_~_G3_~^7..0^ 8+^| _E_~_B3_~^7..0^ 8+^| _E_~_A3_~^7..0^
^| 37 ^| 36 ^| 35 ^| 34 ^| 33 ^| 32 ^| 31 ^| 97
^| 65 ^| 64 ^| 63 ^| 62 ^| 61 ^| 60 ^| 59 ^| 97
^| 93 ^| 92 ^| 91 ^| 90 ^| 89 ^| 88 ^| 87 ^| 97
8+^| _255_
32+^| *Mode 4*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 12 ^| 11 ^| 10 ^| 9 ^| 8 ^| 12 ^| 11 ^| 10
^| 22 ^| 21 ^| 20 ^| 19 ^| 18 ^| 22 ^| 21 ^| 20
^| 32 ^| 31 ^| 30 ^| 29 ^| 28 ^| 32 ^| 31 ^| 30
^| 43 ^| 42 ^| 41 ^| 40 ^| 39 ^| 38 ^| 43 ^| 42
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 17 ^| 16 ^| 15 ^| 14 ^| 13 ^| 17 ^| 16 ^| 15
^| 27 ^| 26 ^| 25 ^| 24 ^| 23 ^| 27 ^| 26 ^| 25
^| 37 ^| 36 ^| 35 ^| 34 ^| 33 ^| 37 ^| 36 ^| 35
^| 49 ^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 49 ^| 48
32+^| *Mode 5*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 14 ^| 13 ^| 12 ^| 11 ^| 10 ^| 9 ^| 8 ^| 14
^| 28 ^| 27 ^| 26 ^| 25 ^| 24 ^| 23 ^| 22 ^| 28
^| 42 ^| 41 ^| 40 ^| 39 ^| 38 ^| 37 ^| 36 ^| 42
^| 57 ^| 56 ^| 55 ^| 54 ^| 53 ^| 52 ^| 51 ^| 50
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 21 ^| 20 ^| 19 ^| 18 ^| 17 ^| 16 ^| 15 ^| 21
^| 35 ^| 34 ^| 33 ^| 32 ^| 31 ^| 30 ^| 29 ^| 35
^| 49 ^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 43 ^| 49
^| 65 ^| 64 ^| 63 ^| 62 ^| 61 ^| 60 ^| 59 ^| 58
32+^| *Mode 6*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 13 ^| 12 ^| 11 ^| 10 ^| 9 ^| 8 ^| 7 ^| 63
^| 27 ^| 26 ^| 25 ^| 24 ^| 23 ^| 22 ^| 21 ^| 63
^| 41 ^| 40 ^| 39 ^| 38 ^| 37 ^| 36 ^| 35 ^| 63
^| 55 ^| 54 ^| 53 ^| 52 ^| 51 ^| 50 ^| 49 ^| 63
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 20 ^| 19 ^| 18 ^| 17 ^| 16 ^| 15 ^| 14 ^| 64
^| 34 ^| 33 ^| 32 ^| 31 ^| 30 ^| 29 ^| 28 ^| 64
^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 43 ^| 42 ^| 64
^| 62 ^| 61 ^| 60 ^| 59 ^| 58 ^| 57 ^| 56 ^| 64
32+^| *Mode 7*
8+^| _E_~_R0_~^7..0^ 8+^| _E_~_G0_~^7..0^ 8+^| _E_~_B0_~^7..0^ 8+^| _E_~_A0_~^7..0^
^| 18 ^| 17 ^| 16 ^| 15 ^| 14 ^| 94 ^| 18 ^| 17
^| 38 ^| 37 ^| 36 ^| 35 ^| 34 ^| 94 ^| 38 ^| 37
^| 58 ^| 57 ^| 56 ^| 55 ^| 54 ^| 94 ^| 58 ^| 57
^| 78 ^| 77 ^| 76 ^| 75 ^| 74 ^| 94 ^| 78 ^| 77
8+^| _E_~_R1_~^7..0^ 8+^| _E_~_G1_~^7..0^ 8+^| _E_~_B1_~^7..0^ 8+^| _E_~_A1_~^7..0^
^| 23 ^| 22 ^| 21 ^| 20 ^| 19 ^| 95 ^| 23 ^| 22
^| 43 ^| 42 ^| 41 ^| 40 ^| 39 ^| 95 ^| 43 ^| 42
^| 63 ^| 62 ^| 61 ^| 60 ^| 59 ^| 95 ^| 63 ^| 62
^| 83 ^| 82 ^| 81 ^| 80 ^| 79 ^| 95 ^| 83 ^| 82
8+^| _E_~_R2_~^7..0^ 8+^| _E_~_G2_~^7..0^ 8+^| _E_~_B2_~^7..0^ 8+^| _E_~_A2_~^7..0^
^| 28 ^| 27 ^| 26 ^| 25 ^| 24 ^| 96 ^| 28 ^| 27
^| 48 ^| 47 ^| 46 ^| 45 ^| 44 ^| 96 ^| 48 ^| 47
^| 68 ^| 67 ^| 66 ^| 65 ^| 64 ^| 96 ^| 68 ^| 67
^| 88 ^| 87 ^| 86 ^| 85 ^| 84 ^| 96 ^| 88 ^| 87
8+^| _E_~_R3_~^7..0^ 8+^| _E_~_G3_~^7..0^ 8+^| _E_~_B3_~^7..0^ 8+^| _E_~_A3_~^7..0^
^| 33 ^| 32 ^| 31 ^| 30 ^| 29 ^| 97 ^| 33 ^| 32
^| 53 ^| 52 ^| 51 ^| 50 ^| 49 ^| 97 ^| 53 ^| 52
^| 73 ^| 72 ^| 71 ^| 70 ^| 69 ^| 97 ^| 73 ^| 72
^| 93 ^| 92 ^| 91 ^| 90 ^| 89 ^| 97 ^| 93 ^| 92
|============

ifndef::a2xhtml[]

<<<

&nbsp;

<<<

&nbsp;

<<<

&nbsp;

<<<

endif::[]

A texel in a block with one subset is always considered to be in subset zero.
Otherwise, a number encoded in the partition bits is used to look up a
partition pattern in <<bptcP2subset>> or <<bptcP3subset>> for 2 subsets and
3 subsets respectively.
This partition pattern is accessed by the relative _x_ and _y_ offsets within
the block to determine the subset which defines the pixel at these coordinates.

The endpoint colors are interpolated using index values stored in the block.
The index bits are stored in y-major order. That is, the bits for the index
value corresponding to a relative (_x_, _y_) position of (0, 0) are stored
in increasing order in the lowest index bits of the block (but see the next
paragraph about anchor indices), the next bits of the block in increasing
order store the index bits of (1, 0), followed by (2, 0) and (3, 0), then
(0, 1) etc.

Each index has the number of bits indicated by the mode except for one
special index per subset called the anchor index.
Since the interpolation scheme between endpoints is symmetrical, we can
save one bit on one index per subset by ordering the endpoints such that
the highest bit for that index is guaranteed to be zero -- and not storing
that bit.

Each anchor index corresponds to an index in the corresponding partition
number in <<bptcP2subset>> or <<bptcP3subset>>, and are indicated in bold
italics in those tables.
In partition zero, the anchor index is always index zero -- that is, at
a relative position of (0,0) (as can be seen in <<bptcP2subset>> and
<<bptcP3subset>>, index 0 always corresponds to partition zero).
In other partitions, the anchor index is specified by <<bptcA2index>>,
<<bptcA32index>>, and <<bptcA33index>>.

[NOTE]
====
In summary, the bit offset for index data with relative _x,y_ coordinates within the texel
block is:

[latexmath]
++++++++++++++
\begin{align*}
\textrm{index offset}_{x,y} &= \begin{cases}
      0, & x = y = 0 \\
      \textrm{IB} \times (x + 4\times y) - 1, & \textrm{NS} = 1,\ 0 < x + 4\times y \\
      \textrm{IB} \times (x + 4\times y) - 1, & \textrm{NS} = 2,\ 0 < x + 4\times y \leq \textrm{anchor}_2[\mathit{part}] \\
      \textrm{IB} \times (x + 4\times y) - 2, & \textrm{NS} = 2,\ \textrm{anchor}_2[\mathit{part}] < x + 4\times y \\
      \textrm{IB} \times (x + 4\times y) - 1, & \textrm{NS} = 3,\ 0 < x + 4\times y \leq \textrm{anchor}_{3,2}[\mathit{part}],\ x + 4\times y \leq \textrm{anchor}_{3,2}[\mathit{part}]\\
      \textrm{IB} \times (x + 4\times y) - 3, & \textrm{NS} = 3,\ x + 4\times y > \textrm{anchor}_{3,2}[\mathit{part}],\ x + 4\times y > \textrm{anchor}_{3,3}[\mathit{part}] \\
      \textrm{IB} \times (x + 4\times y) - 2, & \textrm{NS} = 3,\ \textrm{otherwise} \\
  \end{cases} \\
\end{align*}
++++++++++++++

where anchor~2~ is <<bptcA2index>>, anchor~3,2~ is <<bptcA32index>>,
anchor~3,3~ is <<bptcA33index>>, and _part_ is encoded in the partition
selection bits PB.
====

If secondary index bits are present, they follow the primary index bits and
are read in the same manner.
The anchor index information is only used to determine the number of bits each
index has when read from the block data.

The endpoint color and alpha values used for final interpolation are the
decoded values corresponding to the applicable subset as selected above.
The index value for interpolating color comes from the secondary index bits
for the texel if the mode has an index selection bit and its value is one,
and from the primary index bits otherwise.
The alpha index comes from the secondary index bits if the block has a
secondary index and the block either doesn't have an index selection bit or
that bit is zero, and from the primary index bits otherwise.

[NOTE]
====
As an example of the texel decode process, consider a block encoded with
mode 2 -- that is, M^0^ = 0, M^1^ = 0, M^2^ = 1.
This mode has three subsets, so <<bptcP3subset>> is used to determine which
subset applies to each texel.
Let us assume that this block has partition pattern 6 encoded in the
partition selection bits, and that we wish to decode the texel at relative
(_x_, _y_) offset (1, 2) -- that is, index 9 in y-major order.
We can see from <<bptcP3subset>> that this texel is partitioned into
subset 1 (the second of three), and therefore by endpoints 2 and 3.
Mode 2 stores two index bits per texel, except for index 0 (which is
the anchor index for subset 0), index 15 (for subset 1, as indicated
in <<bptcA32index>>) and index 3 (for subset 2, as indicated in
<<bptcA33index>>).
Index 9 is therefore stored in two bits starting at index bits offset
14 (for indices 1..2 and 4..8) plus 2 (for indices 0 and 3) -- a total
of 16 bit offset into the index bits or, as seen in
<<table-bptcmodebits>>, bits 115 and 116 of the block.
These two bits are used to interpolate between endpoints 2 and 3
using <<BPTCinterpolation>> with weights from the two-bit index row of
<<BPTCInterpolation>>, as described below.
====

[[bptcP2subset]]
.Partition table for 2-subset BPTC, with the 4×4 block of values for each partition number
[cols="5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5",width="97%"]
|==================
4+^| ~0~ 1.40+| 4+^| ~1~ 1.40+| 4+^| ~2~ 1.40+| 4+^| ~3~ 1.40+| 4+^| ~4~ 1.40+| 4+^| ~5~ 1.40+| 4+^| ~6~ 1.40+| 4+^| ~7~
^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 1 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1
^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1
^| 0 ^| 0 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_*

4+^| ~8~ 4+^| ~9~ 4+^| ~10~ 4+^| ~11~ 4+^| ~12~ 4+^| ~13~ 4+^| ~14~ 4+^| ~15~
^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_*

4+^| ~16~ 4+^| ~17~ 4+^| ~18~ 4+^| ~19~ 4+^| ~20~ 4+^| ~21~ 4+^| ~22~ 4+^| ~23~
^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| *_1_* ^| 1
^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1
^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1
^| 1 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| *_1_*

4+^| ~24~ 4+^| ~25~ 4+^| ~26~ 4+^| ~27~ 4+^| ~28~ 4+^| ~29~ 4+^| ~30~ 4+^| ~31~
^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| *_1_* ^| 0 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1
^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1
^| 0 ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1
^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0

4+^| ~32~ 4+^| ~33~ 4+^| ~34~ 4+^| ~35~ 4+^| ~36~ 4+^| ~37~ 4+^| ~38~ 4+^| ~39~
^| *_0_* ^| 1 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 1 ^| 0 ^| 1 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 1 ^| 0 ^| 1
^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 1 ^| 0
^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 1 ^| 0 ^| 1 ^| 0
^| 0 ^| 1 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 1 ^| 0 ^| *_1_*

4+^| ~40~ 4+^| ~41~ 4+^| ~42~ 4+^| ~43~ 4+^| ~44~ 4+^| ~45~ 4+^| ~46~ 4+^| ~47~
^| *_0_* ^| 1 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 1 ^| *_1_* ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 0
^| 1 ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 0
^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0

4+^| ~48~ 4+^| ~49~ 4+^| ~50~ 4+^| ~51~ 4+^| ~52~ 4+^| ~53~ 4+^| ~54~ 4+^| ~55~
^| *_0_* ^| 1 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| *_1_* ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 1 ^| *_1_* ^| 0 ^| *_0_* ^| 0 ^| *_1_* ^| 1
^| 1 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1
^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0
^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0

4+^| ~56~ 4+^| ~57~ 4+^| ~58~ 4+^| ~59~ 4+^| ~60~ 4+^| ~61~ 4+^| ~62~ 4+^| ~63~
^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 1 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| *_1_* ^| 1 ^| *_0_* ^| 0 ^| *_1_* ^| 0 ^| *_0_* ^| 1 ^| 0 ^| 0
^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0
^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1
^| 1 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| *_1_*
|==================

[[bptcP3subset]]
.Partition table for 3-subset BPTC, with the 4×4 block of values for each partition number
[cols="5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5",width="97%"]
|===============
4+^| ~0~ 1.40+| 4+^| ~1~ 1.40+| 4+^| ~2~ 1.40+| 4+^| ~3~ 1.40+| 4+^| ~4~ 1.40+| 4+^| ~5~ 1.40+| 4+^| ~6~ 1.40+| 4+^| ~7~
^| *_0_* ^| 0 ^| 1 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 2 ^| 2 ^| *_2_* ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| *_1_* ^| *_0_* ^| 0 ^| 2 ^| *_2_* ^| *_0_* ^| 0 ^| 1 ^| 1
^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 2 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 1
^| 0 ^| 2 ^| 2 ^| 1 ^| *_2_* ^| 2 ^| 1 ^| 1 ^| *_2_* ^| 2 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 1 ^| 1 ^| 1 ^| 1 ^| *_2_* ^| 2 ^| 1 ^| 1
^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_1_* ^| 2 ^| 2 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 2 ^| *_2_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 2 ^| 2 ^| 1 ^| *_1_*

4+^| ~8~ 4+^| ~9~ 4+^| ~10~ 4+^| ~11~ 4+^| ~12~ 4+^| ~13~ 4+^| ~14~ 4+^| ~15~
^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 2 ^| *_0_* ^| 1 ^| 1 ^| 2 ^| *_0_* ^| 1 ^| 2 ^| 2 ^| *_0_* ^| 0 ^| 1 ^| *_1_* ^| *_0_* ^| 0 ^| 1 ^| *_1_*
^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 2 ^| 0 ^| 1 ^| *_1_* ^| 2 ^| 0 ^| *_1_* ^| 2 ^| 2 ^| 0 ^| 1 ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 1
^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| 2 ^| 2 ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 2 ^| 0 ^| 1 ^| 1 ^| 2 ^| 0 ^| 1 ^| 2 ^| 2 ^| 1 ^| 1 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 0 ^| 0
^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 1 ^| *_2_* ^| 0 ^| 1 ^| 1 ^| *_2_* ^| 0 ^| 1 ^| 2 ^| *_2_* ^| 1 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| 0

4+^| ~16~ 4+^| ~17~ 4+^| ~18~ 4+^| ~19~ 4+^| ~20~ 4+^| ~21~ 4+^| ~22~ 4+^| ~23~
^| *_0_* ^| 0 ^| 0 ^| *_1_* ^| *_0_* ^| 1 ^| 1 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 2 ^| *_2_* ^| *_0_* ^| 1 ^| 1 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 1 ^| 1 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 1 ^| 1 ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| 0 ^| 0
^| 0 ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 1 ^| 0 ^| 1 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| *_1_* ^| 0
^| 1 ^| 1 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 0 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| 1 ^| 0 ^| 1 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 1 ^| 0

4+^| ~24~ 4+^| ~25~ 4+^| ~26~ 4+^| ~27~ 4+^| ~28~ 4+^| ~29~ 4+^| ~30~ 4+^| ~31~
^| *_0_* ^| 1 ^| 2 ^| *_2_* ^| *_0_* ^| 0 ^| 1 ^| 2 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 2 ^| 2 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| *_1_* ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 2 ^| 1 ^| 2 ^| *_2_* ^| 1 ^| 0 ^| 1 ^| *_1_* ^| 0 ^| 1 ^| 1 ^| 0 ^| 2 ^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| 1 ^| 2 ^| 2 ^| 2 ^| 0 ^| 0 ^| 0
^| 0 ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| *_1_* ^| 2 ^| 2 ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 1 ^| *_1_* ^| 1 ^| 0 ^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 0 ^| 1 ^| *_2_* ^| 2 ^| *_2_* ^| 2 ^| 1 ^| 1
^| 0 ^| 0 ^| 0 ^| 0 ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 1 ^| 1 ^| 0 ^| 1 ^| 2 ^| 2 ^| 1 ^| 0 ^| 0 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 2 ^| 2 ^| 2 ^| *_1_*

4+^| ~32~ 4+^| ~33~ 4+^| ~34~ 4+^| ~35~ 4+^| ~36~ 4+^| ~37~ 4+^| ~38~ 4+^| ~39~
^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 2 ^| 2 ^| *_2_* ^| *_0_* ^| 0 ^| 1 ^| *_1_* ^| *_0_* ^| 1 ^| 2 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 1 ^| 2 ^| 0 ^| *_0_* ^| 1 ^| 2 ^| 0 ^| *_0_* ^| 0 ^| 1 ^| 1
^| 0 ^| 0 ^| 0 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 2 ^| 0 ^| *_1_* ^| 2 ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 2 ^| 0 ^| 1 ^| 2 ^| 0 ^| 1 ^| 2 ^| 2 ^| 2 ^| 0 ^| 0
^| *_1_* ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 1 ^| *_2_* ^| 0 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| *_2_* ^| 0 ^| *_1_* ^| 2 ^| *_1_* ^| *_2_* ^| 0 ^| 1 ^| 1 ^| 1 ^| *_2_* ^| 2
^| 1 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 0 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 1 ^| 2 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 2 ^| 0 ^| 0 ^| 1 ^| 2 ^| 0 ^| 0 ^| 0 ^| 1 ^| *_1_*

4+^| ~40~ 4+^| ~41~ 4+^| ~42~ 4+^| ~43~ 4+^| ~44~ 4+^| ~45~ 4+^| ~46~ 4+^| ~47~
^| *_0_* ^| 0 ^| 1 ^| 1 ^| *_0_* ^| 1 ^| 0 ^| *_1_* ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 2 ^| 2 ^| *_0_* ^| 0 ^| 2 ^| *_2_* ^| *_0_* ^| 2 ^| 2 ^| 0 ^| *_0_* ^| 1 ^| 0 ^| 1 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 1 ^| 1 ^| *_2_* ^| 2 ^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 2 ^| 2 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 1 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 1 ^| 2 ^| 1
^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 1 ^| 2 ^| 1 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 0 ^| 2 ^| 2 ^| 0 ^| 2 ^| 2 ^| 0 ^| 2 ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 1 ^| 2 ^| 1
^| 0 ^| 0 ^| 1 ^| *_1_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 1 ^| 2 ^| *_1_* ^| 1 ^| 1 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| *_1_* ^| 0 ^| 1 ^| 0 ^| *_1_* ^| 2 ^| 1 ^| 2 ^| *_1_*

4+^| ~48~ 4+^| ~49~ 4+^| ~50~ 4+^| ~51~ 4+^| ~52~ 4+^| ~53~ 4+^| ~54~ 4+^| ~55~
^| *_0_* ^| 1 ^| 0 ^| *_1_* ^| *_0_* ^| 2 ^| 2 ^| *_2_* ^| *_0_* ^| 0 ^| 0 ^| 2 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 2 ^| 2 ^| 2 ^| *_0_* ^| 0 ^| 0 ^| 2 ^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| 0
^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| *_1_* ^| 1 ^| 2 ^| 0 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| 1 ^| 1 ^| 2 ^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0
^| 0 ^| 1 ^| 0 ^| 1 ^| 0 ^| 2 ^| 2 ^| 2 ^| 0 ^| 0 ^| 0 ^| 2 ^| 2 ^| 1 ^| 1 ^| 2 ^| 0 ^| 1 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 2 ^| 0 ^| 1 ^| 1 ^| 0 ^| 2 ^| 1 ^| *_1_* ^| 2
^| 2 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 1 ^| 1 ^| *_1_* ^| 1 ^| 1 ^| 1 ^| *_2_* ^| 2 ^| 1 ^| 1 ^| *_2_* ^| 0 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 0 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 1 ^| 1 ^| *_2_*

4+^| ~56~ 4+^| ~57~ 4+^| ~58~ 4+^| ~59~ 4+^| ~60~ 4+^| ~61~ 4+^| ~62~ 4+^| ~63~
^| *_0_* ^| 1 ^| 1 ^| 0 ^| *_0_* ^| 0 ^| 2 ^| 2 ^| *_0_* ^| 0 ^| 2 ^| 2 ^| *_0_* ^| 0 ^| 0 ^| 0 ^| *_0_* ^| 0 ^| 0 ^| *_2_* ^| *_0_* ^| 2 ^| 2 ^| 2 ^| *_0_* ^| 1 ^| 0 ^| *_1_* ^| *_0_* ^| 1 ^| 1 ^| *_1_*
^| 0 ^| *_1_* ^| 1 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 1 ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 1 ^| 1 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 0 ^| 1 ^| 1
^| 2 ^| 2 ^| 2 ^| 2 ^| 0 ^| 0 ^| *_1_* ^| 1 ^| *_1_* ^| 1 ^| 2 ^| 2 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 0 ^| 2 ^| 0 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 0 ^| 1
^| 2 ^| 2 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 2 ^| *_2_* ^| 0 ^| 0 ^| 2 ^| *_2_* ^| 2 ^| *_1_* ^| 1 ^| *_2_* ^| 0 ^| 0 ^| 0 ^| *_1_* ^| *_1_* ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| *_2_* ^| 2 ^| 2 ^| 2 ^| 0
|==========

[[bptcA32index]]
.BPTC anchor index values for the second subset of three-subset partitioning, by partition number
[width="40%"]
|================
^| ~0~ ^| ~1~ ^| ~2~ ^| ~3~ ^| ~4~ ^| ~5~ ^| ~6~ ^| ~7~
^|  3 ^|  3 ^| 15 ^| 15 ^|  8 ^|  3 ^| 15 ^| 15
^| ~8~ ^| ~9~ ^| ~10~ ^| ~11~ ^| ~12~ ^| ~13~ ^| ~14~ ^| ~15~
^|  8 ^|  8 ^|  6 ^|  6 ^|  6 ^|  5 ^|  3 ^|  3
^| ~16~ ^| ~17~ ^| ~18~ ^| ~19~ ^| ~20~ ^| ~21~ ^| ~22~ ^| ~23~
^|  3 ^|  3 ^|  8 ^| 15 ^|  3 ^|  3 ^|  6 ^| 10
^| ~24~ ^| ~25~ ^| ~26~ ^| ~27~ ^| ~28~ ^| ~29~ ^| ~30~ ^| ~31~
^|  5 ^|  8 ^|  8 ^|  6 ^|  8 ^|  5 ^| 15 ^| 15
^| ~32~ ^| ~33~ ^| ~34~ ^| ~35~ ^| ~36~ ^| ~37~ ^| ~38~ ^| ~39~
^|  8 ^| 15 ^|  3 ^|  5 ^|  6 ^| 10 ^|  8 ^| 15
^| ~40~ ^| ~41~ ^| ~42~ ^| ~43~ ^| ~44~ ^| ~45~ ^| ~46~ ^| ~47~
^| 15 ^|  3 ^| 15 ^|  5 ^| 15 ^| 15 ^| 15 ^| 15
^| ~48~ ^| ~49~ ^| ~50~ ^| ~51~ ^| ~52~ ^| ~53~ ^| ~54~ ^| ~55~
^|  3 ^| 15 ^|  5 ^|  5 ^|  5 ^|  8 ^|  5 ^| 10
^| ~56~ ^| ~57~ ^| ~58~ ^| ~59~ ^| ~60~ ^| ~61~ ^| ~62~ ^| ~63~
^|  5 ^| 10 ^|  8 ^| 13 ^| 15 ^| 12 ^|  3 ^|  3
|================

[[bptcA33index]]
.BPTC anchor index values for the third subset of three-subset partitioning, by partition number
[width="40%"]
|===============
^| ~0~ ^| ~1~ ^| ~2~ ^| ~3~ ^| ~4~ ^| ~5~ ^| ~6~ ^| ~7~
^| 15 ^|  8 ^|  8 ^|  3 ^| 15 ^| 15 ^|  3 ^|  8
^| ~8~ ^| ~9~ ^| ~10~ ^| ~11~ ^| ~12~ ^| ~13~ ^| ~14~ ^| ~15~
^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^|  8
^| ~16~ ^| ~17~ ^| ~18~ ^| ~19~ ^| ~20~ ^| ~21~ ^| ~22~ ^| ~23~
^| 15 ^|  8 ^| 15 ^|  3 ^| 15 ^|  8 ^| 15 ^|  8
^| ~24~ ^| ~25~ ^| ~26~ ^| ~27~ ^| ~28~ ^| ~29~ ^| ~30~ ^| ~31~
^|  3 ^| 15 ^|  6 ^| 10 ^| 15 ^| 15 ^| 10 ^|  8
^| ~32~ ^| ~33~ ^| ~34~ ^| ~35~ ^| ~36~ ^| ~37~ ^| ~38~ ^| ~39~
^| 15 ^|  3 ^| 15 ^| 10 ^| 10 ^|  8 ^|  9 ^| 10
^| ~40~ ^| ~41~ ^| ~42~ ^| ~43~ ^| ~44~ ^| ~45~ ^| ~46~ ^| ~47~
^|  6 ^| 15 ^|  8 ^| 15 ^|  3 ^|  6 ^|  6 ^|  8
^| ~48~ ^| ~49~ ^| ~50~ ^| ~51~ ^| ~52~ ^| ~53~ ^| ~54~ ^| ~55~
^| 15 ^|  3 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15
^| ~56~ ^| ~57~ ^| ~58~ ^| ~59~ ^| ~60~ ^| ~61~ ^| ~62~ ^| ~63~
^| 15 ^| 15 ^| 15 ^| 15 ^|  3 ^| 15 ^| 15 ^|  8
|===============


ifndef::a2xhtml[]
<<<

&nbsp;

<<<
endif::[]

[[bptcA2index]]
.BPTC anchor index values for the second subset of two-subset partitioning, by partition number
[width="40%"]
|==============
^| ~0~ ^| ~1~ ^| ~2~ ^| ~3~ ^| ~4~ ^| ~5~ ^| ~6~ ^| ~7~
^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15
^| ~8~ ^| ~9~ ^| ~10~ ^| ~11~ ^| ~12~ ^| ~13~ ^| ~14~ ^| ~15~
^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^| 15
^| ~16~ ^| ~17~ ^| ~18~ ^| ~19~ ^| ~20~ ^| ~21~ ^| ~22~ ^| ~23~
^| 15 ^|  2 ^|  8 ^|  2 ^|  2 ^|  8 ^|  8 ^| 15
^| ~24~ ^| ~25~ ^| ~26~ ^| ~27~ ^| ~28~ ^| ~29~ ^| ~30~ ^| ~31~
^|  2 ^|  8 ^|  2 ^|  2 ^|  8 ^|  8 ^|  2 ^|  2
^| ~32~ ^| ~33~ ^| ~34~ ^| ~35~ ^| ~36~ ^| ~37~ ^| ~38~ ^| ~39~
^| 15 ^| 15 ^|  6 ^|  8 ^|  2 ^|  8 ^| 15 ^| 15
^| ~40~ ^| ~41~ ^| ~42~ ^| ~43~ ^| ~44~ ^| ~45~ ^| ~46~ ^| ~47~
^|  2 ^|  8 ^|  2 ^|  2 ^|  2 ^| 15 ^| 15 ^|  6
^| ~48~ ^| ~49~ ^| ~50~ ^| ~51~ ^| ~52~ ^| ~53~ ^| ~54~ ^| ~55~
^|  6 ^|  2 ^|  6 ^|  8 ^| 15 ^| 15 ^|  2 ^|  2
^| ~56~ ^| ~57~ ^| ~58~ ^| ~59~ ^| ~60~ ^| ~61~ ^| ~62~ ^| ~63~
^| 15 ^| 15 ^| 15 ^| 15 ^| 15 ^|  2 ^|  2 ^| 15
|==============

ifndef::a2xhtml[]
<<<

&nbsp;

<<<

&nbsp;

<<<
endif::[]

Interpolation is always performed using a 6-bit interpolation factor.
The effective interpolation factors for 2-, 3-, and 4-bit indices are
given in <<BPTCInterpolation>>.

[[BPTCInterpolation]]
.BPTC interpolation factors
[cols="h,18*",width="85%"]
|==========
.2+^.^| 2 2+^| Index 4+^| ~0~ 4+^| ~1~ 4+^| ~2~ 4+^| ~3~
2+^| _Weight_ 4+^| 0 4+^| 21 4+^| 43 4+^| 64
.2+^.^| 3 2+^| Index 2+^| ~0~ 2+^| ~1~ 2+^| ~2~ 2+^| ~3~ 2+^| ~4~ 2+^| ~5~ 2+^| ~6~ 2+^| ~7~
2+^| _Weight_ 2+^| 0 2+^| 9 2+^| 18 2+^| 27 2+^| 37 2+^| 46 2+^| 55 2+^| 64
.2+^.^| 4 2+^| Index ^| ~0~ ^| ~1~ ^| ~2~ ^| ~3~ ^| ~4~ ^| ~5~ ^| ~6~ ^| ~7~ ^| ~8~ ^| ~9~ ^| ~10~ ^| ~11~ ^| ~12~ ^| ~13~ ^| ~14~ ^| ~15~
2+^| _Weight_ ^| 0 ^| 4 ^| 9 ^| 13 ^| 17 ^| 21 ^| 26 ^| 30 ^| 34 ^| 38 ^| 43 ^| 47 ^| 51 ^| 55 ^| 60 ^| 64
|==========

// Note: The interpolation formula is not explicitly present in the OpenGL Specification.
// Since bit-exact interpolation is mandated by some implementations, the following formula is
// provided, as described in https://docs.microsoft.com/en-us/windows/desktop/direct3d11/bc7-format

Given _E_~0~ and _E_~1~, unsigned integer endpoints [0 .. 255] for each channel and _weight_
as an unsigned integer interpolation factor from <<BPTCInterpolation>>:

[[BPTCinterpolation]]
.BPTC endpoint interpolation formula
[latexmath]
++++++++++++++
\begin{align*}
\mathit{interpolated\ value} & = ((64 - \mathit{weight}) \times \textit{E}_0 + \mathit{weight} \times \textit{E}_1 + 32) \gg 6
\end{align*}
++++++++++++++

where latexmath:[$\gg$] performs a (truncating) bitwise right-shift, and
_interpolated value_ is an (unsigned) integer in the range [0..255].
The interpolation results in an _RGBA_ color. If rotation bits are present,
this interpolated color is remapped according to <<BPTCRotation>>.

[[BPTCRotation]]
.BPTC Rotation bits
[cols="h,3",width="20%"]
|============
^| 0 ^| no change
^| 1 ^| _swap_(_A_, _R_)
^| 2 ^| _swap_(_A_, _G_)
^| 3 ^| _swap_(_A_, _B_)
|============

These 8-bit values should be interpreted as _RGBA_ 8-bit normalized channels,
either linearly encoded (by multiplying by latexmath:[$1\over 255$]) or
with the <<TRANSFER_SRGB,sRGB transfer function>>.

<<<

[[bptc_bc6h]]
=== BC6H

Each 4{times}4 block of texels consists of 128 bits of _RGB_ data. The
signed and unsigned formats are very similar and will be described together.
In the description and pseudocode below, _signed_ will be used as a condition which is true
for the signed version of the format and false for the unsigned version of the format.
Both formats only contain _RGB_ data, so the returned alpha value is 1.0. If a
block uses a reserved or invalid encoding, the return value is
(0.0,&nbsp;0.0,&nbsp;0.0,&nbsp;1.0).

[NOTE]
====
Where BC7 encodes a fixed-point 8-bit value, BC6H encodes a 16-bit integer
which will be interpreted as a 16-bit half float.
Interpolation in BC6H is therefore nonlinear, but monotonic.
====

Each block can contain data in one of 14 modes. The mode number is encoded
in either the low two bits or the low five bits. If the low two bits are
less than two, that is the mode number, otherwise the low five bits is the mode
number. Mode numbers not listed in <<table-bptcblockmodes>>
(19,&nbsp;23,&nbsp;27,&nbsp;and&nbsp;31) are reserved.

[[table-bptcblockmodes]]
.Endpoint and partition parameters for BPTC block modes
[width="100%",cols="10%,15%,20%,20%,10%,1%,7%,10%,7%"]
|==============
.2+^.^| *Mode number* .2+^.^| *Transformed endpoints* ^.^| *Partition bits (PB)* ^.^| *Endpoint bits (EPB)* ^.^| *Delta bits* 1.16+| ^.^| *Mode* ^.^| *Endpoint* ^.^| *Delta*
^| Bits per texel block 2+^| {_R_,_G_,_B_} bits per endpoint 3+^| Bits per texel block (total)
^| *0*  ^| {check} ^| 5 ^| {10, 10, 10} ^| {5, 5, 5} ^| 2 ^| 30 ^| 45
^| *1*  ^| {check} ^| 5 ^| {7, 7, 7}  ^| {6, 6, 6} ^| 2 ^| 21 ^| 54
^| *2*  ^| {check} ^| 5 ^| {11, 11, 11} ^| {5, 4, 4} ^| 5 ^| 33 ^| 39
^| *6*  ^| {check} ^| 5 ^| {11, 11, 11} ^| {4, 5, 4} ^| 5 ^| 33 ^| 39
^| *10* ^| {check} ^| 5 ^| {11, 11, 11} ^| {4, 4, 5} ^| 5 ^| 33 ^| 39
^| *14* ^| {check} ^| 5 ^| {9, 9, 9}  ^| {5, 5, 5} ^| 5 ^| 27 ^| 45
^| *18* ^| {check} ^| 5 ^| {8, 8, 8}  ^| {6, 5, 5} ^| 5 ^| 24 ^| 48
^| *22* ^| {check} ^| 5 ^| {8, 8, 8}  ^| {5, 6, 5} ^| 5 ^| 24 ^| 48
^| *26* ^| {check} ^| 5 ^| {8, 8, 8}  ^| {5, 5, 6} ^| 5 ^| 24 ^| 48
^| *30* ^|         ^| 5 ^| {6, 6, 6}  ^| -         ^| 5 ^| 72 ^| 0
^| *3*  ^|         ^| 0 ^| {10, 10, 10} ^| -         ^| 5 ^| 60 ^| 0
^| *7*  ^| {check} ^| 0 ^| {11, 11, 11} ^| {9, 9, 9} ^| 5 ^| 33 ^| 27
^| *11* ^| {check} ^| 0 ^| {12, 12, 12} ^| {8, 8, 8} ^| 5 ^| 36 ^| 24
^| *15* ^| {check} ^| 0 ^| {16, 16, 16} ^| {4, 4, 4} ^| 5 ^| 48 ^| 12
|==============

The data for the compressed blocks is stored in a different manner for each
mode.
The interpretation of bits for each mode are specified in <<table-bptcblockformat>>.
The descriptions are intended to be read from left to right with the LSB on the left.
Each element is of the form _v_^_a_.._b_^. If _a_ {geq} _b_, this indicates
extracting _b_ - _a_ {plus} 1 bits from the block at that location and put them in
the corresponding bits of the variable _v_.
If _a_ < _b_, then the bits are reversed.
_v_^_a_^ is used as a shorthand for the one bit _v_^_a_.._a_^.
As an example, M^1..0^, _G_~2~^4^ would move the low two bits from the block into the
low two bits of mode number M, then the next bit of the block into bit 4 of _G_~2~.
The resultant bit interpretations are shown explicitly in <<table-bptcbc6hbits>>
and <<table-bptcbc6hbits2>>.
The variable names given in the table will be referred to in the language below.

Subsets and indices work in much the same way as described for the
BC7 formats above.
If a float block has no partition bits, then it is a single-subset block.
If it has partition bits, then it is a two-subset block.
The partition number references the first half of <<bptcP2subset>>.

<<<

[[table-bptcblockformat]]
.Block descriptions for BC6H block modes (LSB..MSB)
[options="header",cols="3,13",width="85%"]
|===========================
^| Mode Number  ^| Block description
^.^|  0     ^.^| M^1..0^, _G_~2~^4^, _B_~2~^4^, _B_~3~^4^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^4..0^,
         _G_~3~^4^, _G_~2~^3..0^, _G_~1~^4..0^, _B_~3~^0^, _G_~3~^3..0^, _B_~1~^4..0^, _B_~3~^1^, _B_~2~^3..0^,
         _R_~2~^4..0^, _B_~3~^2^, _R_~3~^4..0^, _B_~3~^3^, PB^4..0^
^.^|  1     ^.^| M^1..0^, _G_~2~^5^, _G_~3~^4^, _G_~3~^5^, _R_~0~^6..0^, _B_~3~^0^, _B_~3~^1^, _B_~2~^4^,
         _G_~0~^6..0^, _B_~2~^5^, _B_~3~^2^, _G_~2~^4^, _B_~0~^6..0^, _B_~3~^3^, _B_~3~^5^, _B_~3~^4^,
         _R_~1~^5..0^, _G_~2~^3..0^, _G_~1~^5..0^, _G_~3~^3..0^, _B_~1~^5..0^, _B_~2~^3..0^, _R_~2~^5..0^,
         _R_~3~^5..0^, PB^4..0^
^.^|  2     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^4..0^, _R_~0~^10^, _G_~2~^3..0^,
         _G_~1~^3..0^, _G_~0~^10^, _B_~3~^0^, _G_~3~^3..0^, _B_~1~^3..0^, _B_~0~^10^, _B_~3~^1^, _B_~2~^3..0^,
         _R_~2~^4..0^, _B_~3~^2^, _R_~3~^4..0^, _B_~3~^3^, PB^4..0^
^.^|  6     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^3..0^, _R_~0~^10^, _G_~3~^4^,
         _G_~2~^3..0^, _G_~1~^4..0^, _G_~0~^10^, _G_~3~^3..0^, _B_~1~^3..0^, _B_~0~^10^, _B_~3~^1^,
         _B_~2~^3..0^, _R_~2~^3..0^, _B_~3~^0^, _B_~3~^2^, _R_~3~^3..0^, _G_~2~^4^, _B_~3~^3^, PB^4..0^
^.^| 10     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^3..0^, _R_~0~^10^, _B_~2~^4^,
         _G_~2~^3..0^, _G_~1~^3..0^, _G_~0~^10^, _B_~3~^0^, _G_~3~^3..0^, _B_~1~^4..0^, _B_~0~^10^,
         _B_~2~^3..0^, _R_~2~^3..0^, _B_~3~^1^, _B_~3~^2^, _R_~3~^3..0^, _B_~3~^4^, _B_~3~^3^, PB^4..0^
^.^| 14     ^.^| M^4..0^, _R_~0~^8..0^, _B_~2~^4^, _G_~0~^8..0^, _G_~2~^4^, _B_~0~^8..0^, _B_~3~^4^, _R_~1~^4..0^,
         _G_~3~^4^, _G_~2~^3..0^, _G_~1~^4..0^, _B_~3~^0^, _G_~3~^3..0^, _B_~1~^4..0^, _B_~3~^1^, _B_~2~^3..0^,
         _R_~2~^4..0^, _B_~3~^2^, _R_~3~^4..0^, _B_~3~^3^, PB^4..0^
^.^| 18     ^.^| M^4..0^, _R_~0~^7..0^, _G_~3~^4^, _B_~2~^4^, _G_~0~^7..0^, _B_~3~^2^, _G_~2~^4^, _B_~0~^7..0^,
         _B_~3~^3^, _B_~3~^4^, _R_~1~^5..0^, _G_~2~^3..0^, _G_~1~^4..0^, _B_~3~^0^, _G_~3~^3..0^, _B_~1~^4..0^,
         _B_~3~^1^, _B_~2~^3..0^, _R_~2~^5..0^, _R_~3~^5..0^, PB^4..0^
^.^| 22     ^.^| M^4..0^, _R_~0~^7..0^, _B_~3~^0^, _B_~2~^4^, _G_~0~^7..0^, _G_~2~^5^, _G_~2~^4^, _B_~0~^7..0^,
         _G_~3~^5^, _B_~3~^4^, _R_~1~^4..0^, _G_~3~^4^, _G_~2~^3..0^, _G_~1~^5..0^, _G_~3~^3..0^, _B_~1~^4..0^,
         _B_~3~^1^, _B_~2~^3..0^, _R_~2~^4..0^, _B_~3~^2^, _R_~3~^4..0^, _B_~3~^3^, PB^4..0^
^.^| 26     ^.^| M^4..0^, _R_~0~^7..0^, _B_~3~^1^, _B_~2~^4^, _G_~0~^7..0^, _B_~2~^5^, _G_~2~^4^, _B_~0~^7..0^,
         _B_~3~^5^, _B_~3~^4^, _R_~1~^4..0^, _G_~3~^4^, _G_~2~^3..0^, _G_~1~^4..0^, _B_~3~^0^, _G_~3~^3..0^,
         _B_~1~^5..0^, _B_~2~^3..0^, _R_~2~^4..0^, _B_~3~^2^, _R_~3~^4..0^, _B_~3~^3^, PB^4..0^
^.^| 30     ^.^| M^4..0^, _R_~0~^5..0^, _G_~3~^4^, _B_~3~^0^, _B_~3~^1^, _B_~2~^4^, _G_~0~^5..0^, _G_~2~^5^,
         _B_~2~^5^, _B_~3~^2^, _G_~2~^4^, _B_~0~^5..0^, _G_~3~^5^, _B_~3~^3^, _B_~3~^5^, _B_~3~^4^,
         _R_~1~^5..0^, _G_~2~^3..0^, _G_~1~^5..0^, _G_~3~^3..0^, _B_~1~^5..0^, _B_~2~^3..0^, _R_~2~^5..0^,
         _R_~3~^5..0^, PB^4..0^
^.^|  3     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^9..0^, _G_~1~^9..0^, _B_~1~^9..0^
^.^|  7     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^8..0^, _R_~0~^10^, _G_~1~^8..0^,
         _G_~0~^10^, _B_~1~^8..0^, _B_~0~^10^
^.^| 11     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^7..0^, _R_~0~^10..11^, _G_~1~^7..0^,
         _G_~0~^10..11^, _B_~1~^7..0^, _B_~0~^10..11^
^.^| 15     ^.^| M^4..0^, _R_~0~^9..0^, _G_~0~^9..0^, _B_~0~^9..0^, _R_~1~^3..0^, _R_~0~^10..15^, _G_~1~^3..0^,
         _G_~0~^10..15^, _B_~1~^3..0^, _B_~0~^10..15^
|==========================

Indices are read in the same way as the BC7 formats including obeying the
anchor values for index 0 and as needed by <<bptcA2index>>.
That is, for modes with only one partition, the mode and endpoint data are followed
by 63 bits of index data (four index bits IB~_x,y_~^0..3^ per texel, with one implicit
bit for IB~_x,y_~^3^) starting at bit 65 with IB~0,0~^0^.
For modes with two partitions, the mode, endpoint and partition data are followed by
46 bits of index data (three per texel IB~_x,y_~^0..2^, with two implicit bits, one for
partition 0 at IB~0,0~^2^ and one IB~_x,y_~^2^ bit for partition 1 at an offset
determined by the partition pattern selected) starting at bit 82 with IB~0,0~^0^.
In both cases, index bits are stored in y-major offset order by increasing
little-endian bit number, with the bits for each index stored consecutively:

[latexmath]
++++++++++++++
\begin{align*}
{\textrm{Bit offset of IB}_{x,y}}^0 &= \begin{cases}
      65, & 1\ \textrm{subset},\ x = y = 0 \\
      65 + 4 \times (x + 4\times y) - 1, & 1\ \textrm{subset},\ 0 < x + 4\times y \\
      82, & 2\ \textrm{subsets},\ x = y = 0 \\
      82 + 3 \times (x + 4\times y) - 1, & 2\ \textrm{subsets},\ 0 < x + 4\times y \leq \textrm{anchor}_2[\mathit{part}] \\
      82 + 3 \times (x + 4\times y) - 2, & 2\ \textrm{subsets},\ \textrm{anchor}_2[\mathit{part}] < x + 4\times y \\
  \end{cases} \\
\end{align*}
++++++++++++++

[[table-bptcbc6hbits]]
.Interpretation of lower bits for BC6H block modes
[width="85%", cols=">1,14*^1"]
|================
>| 14+^| *Mode*
^| *Bit* | *0* | *1* | *2* | *6* | *10* | *14* | *18* | *22* | *26* | *30* | *3* | *7* | *11* | *15*
>|  *0* &nbsp; | M^0^: *0* | M^0^: *1* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *0* | M^0^: *1* | M^0^: *1* | M^0^: *1* | M^0^: *1*
>|  *1* &nbsp; | M^1^: *0* | M^1^: *0* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1* | M^1^: *1*
>|  *2* &nbsp; | _G_~2~^4^ | _G_~2~^5^ | M^2^: *0* | M^2^: *1* | M^2^: *0* | M^2^: *1* | M^2^: *0* | M^2^: *1* | M^2^: *0* | M^2^: *1* | M^2^: *0* | M^2^: *1* | M^2^: *0* | M^2^: *1*
>|  *3* &nbsp; | _B_~2~^4^ | _G_~3~^4^ | M^3^: *0* | M^3^: *0* | M^3^: *1* | M^3^: *1* | M^3^: *0* | M^3^: *0* | M^3^: *1* | M^3^: *1* | M^3^: *0* | M^3^: *0* | M^3^: *1* | M^3^: *1*
>|  *4* &nbsp; | _B_~3~^4^ | _G_~3~^5^ | M^4^: *0* | M^4^: *0* | M^4^: *0* | M^4^: *0* | M^4^: *1* | M^4^: *1* | M^4^: *1* | M^4^: *1* | M^4^: *0* | M^4^: *0* | M^4^: *0* | M^4^: *0*
>|  *5* &nbsp; | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^ | _R_~0~^0^
>|  *6* &nbsp; | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^ | _R_~0~^1^
>|  *7* &nbsp; | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^ | _R_~0~^2^
>|  *8* &nbsp; | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^ | _R_~0~^3^
>|  *9* &nbsp; | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^ | _R_~0~^4^
>| *10* &nbsp; | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^ | _R_~0~^5^
>| *11* &nbsp; | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _G_~3~^4^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^ | _R_~0~^6^
>| *12* &nbsp; | _R_~0~^7^ | _B_~3~^0^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _B_~3~^0^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^ | _R_~0~^7^
>| *13* &nbsp; | _R_~0~^8^ | _B_~3~^1^ | _R_~0~^8^ | _R_~0~^8^ | _R_~0~^8^ | _R_~0~^8^ | _G_~3~^4^ | _B_~3~^0^ | _B_~3~^1^ | _B_~3~^1^ | _R_~0~^8^ | _R_~0~^8^ | _R_~0~^8^ | _R_~0~^8^
>| *14* &nbsp; | _R_~0~^9^ | _B_~2~^4^ | _R_~0~^9^ | _R_~0~^9^ | _R_~0~^9^ | _B_~2~^4^ | _B_~2~^4^ | _B_~2~^4^ | _B_~2~^4^ | _B_~2~^4^ | _R_~0~^9^ | _R_~0~^9^ | _R_~0~^9^ | _R_~0~^9^
>| *15* &nbsp; | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^ | _G_~0~^0^
>| *16* &nbsp; | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^ | _G_~0~^1^
>| *17* &nbsp; | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^ | _G_~0~^2^
>| *18* &nbsp; | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^ | _G_~0~^3^
>| *19* &nbsp; | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^ | _G_~0~^4^
>| *20* &nbsp; | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^ | _G_~0~^5^
>| *21* &nbsp; | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~2~^5^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^ | _G_~0~^6^
>| *22* &nbsp; | _G_~0~^7^ | _B_~2~^5^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _B_~2~^5^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^ | _G_~0~^7^
>| *23* &nbsp; | _G_~0~^8^ | _B_~3~^2^ | _G_~0~^8^ | _G_~0~^8^ | _G_~0~^8^ | _G_~0~^8^ | _B_~3~^2^ | _G_~2~^5^ | _B_~2~^5^ | _B_~3~^2^ | _G_~0~^8^ | _G_~0~^8^ | _G_~0~^8^ | _G_~0~^8^
>| *24* &nbsp; | _G_~0~^9^ | _G_~2~^4^ | _G_~0~^9^ | _G_~0~^9^ | _G_~0~^9^ | _G_~2~^4^ | _G_~2~^4^ | _G_~2~^4^ | _G_~2~^4^ | _G_~2~^4^ | _G_~0~^9^ | _G_~0~^9^ | _G_~0~^9^ | _G_~0~^9^
>| *25* &nbsp; | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^ | _B_~0~^0^
>| *26* &nbsp; | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^ | _B_~0~^1^
>| *27* &nbsp; | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^ | _B_~0~^2^
>| *28* &nbsp; | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^ | _B_~0~^3^
>| *29* &nbsp; | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^ | _B_~0~^4^
>| *30* &nbsp; | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^ | _B_~0~^5^
>| *31* &nbsp; | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _G_~3~^5^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^ | _B_~0~^6^
>| *32* &nbsp; | _B_~0~^7^ | _B_~3~^3^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~3~^3^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^ | _B_~0~^7^
>| *33* &nbsp; | _B_~0~^8^ | _B_~3~^5^ | _B_~0~^8^ | _B_~0~^8^ | _B_~0~^8^ | _B_~0~^8^ | _B_~3~^3^ | _G_~3~^5^ | _B_~3~^5^ | _B_~3~^5^ | _B_~0~^8^ | _B_~0~^8^ | _B_~0~^8^ | _B_~0~^8^
>| *34* &nbsp; | _B_~0~^9^ | _B_~3~^4^ | _B_~0~^9^ | _B_~0~^9^ | _B_~0~^9^ | _B_~3~^4^ | _B_~3~^4^ | _B_~3~^4^ | _B_~3~^4^ | _B_~3~^4^ | _B_~0~^9^ | _B_~0~^9^ | _B_~0~^9^ | _B_~0~^9^
>| *35* &nbsp; | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^ | _R_~1~^0^
>| *36* &nbsp; | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^ | _R_~1~^1^
>| *37* &nbsp; | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^ | _R_~1~^2^
>| *38* &nbsp; | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^ | _R_~1~^3^
>| *39* &nbsp; | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~0~^10^ | _R_~0~^10^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~1~^4^ | _R_~0~^15^
>| *40* &nbsp; | _G_~3~^4^ | _R_~1~^5^ | _R_~0~^10^ | _G_~3~^4^ | _B_~2~^4^ | _G_~3~^4^ | _R_~1~^5^ | _G_~3~^4^ | _G_~3~^4^ | _R_~1~^5^ | _R_~1~^5^ | _R_~1~^5^ | _R_~1~^5^ | _R_~0~^14^
|================

[[table-bptcbc6hbits2]]
.Interpretation of upper bits for BC6H block modes
[width="80%", cols=">1,14*^1"]
|================
>| 14+^| *Mode*
^| *Bit* | *0* | *1* | *2* | *6* | *10* | *14* | *18* | *22* | *26* | *30* | *3* | *7* | *11* | *15*
>| *41* &nbsp; | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _G_~2~^0^ | _R_~1~^6^ | _R_~1~^6^ | _R_~1~^6^ | _R_~0~^13^
>| *42* &nbsp; | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _G_~2~^1^ | _R_~1~^7^ | _R_~1~^7^ | _R_~1~^7^ | _R_~0~^12^
>| *43* &nbsp; | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _G_~2~^2^ | _R_~1~^8^ | _R_~1~^8^ | _R_~0~^11^ | _R_~0~^11^
>| *44* &nbsp; | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _G_~2~^3^ | _R_~1~^9^ | _R_~0~^10^ | _R_~0~^10^ | _R_~0~^10^
>| *45* &nbsp; | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^ | _G_~1~^0^
>| *46* &nbsp; | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^ | _G_~1~^1^
>| *47* &nbsp; | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^ | _G_~1~^2^
>| *48* &nbsp; | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^ | _G_~1~^3^
>| *49* &nbsp; | _G_~1~^4^ | _G_~1~^4^ | _G_~0~^10^ | _G_~1~^4^ | _G_~0~^10^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~1~^4^ | _G_~0~^15^
>| *50* &nbsp; | _B_~3~^0^ | _G_~1~^5^ | _B_~3~^0^ | _G_~0~^10^ | _B_~3~^0^ | _B_~3~^0^ | _B_~3~^0^ | _G_~1~^5^ | _B_~3~^0^ | _G_~1~^5^ | _G_~1~^5^ | _G_~1~^5^ | _G_~1~^5^ | _G_~0~^14^
>| *51* &nbsp; | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~3~^0^ | _G_~1~^6^ | _G_~1~^6^ | _G_~1~^6^ | _G_~0~^13^
>| *52* &nbsp; | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~3~^1^ | _G_~1~^7^ | _G_~1~^7^ | _G_~1~^7^ | _G_~0~^12^
>| *53* &nbsp; | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~3~^2^ | _G_~1~^8^ | _G_~1~^8^ | _G_~0~^11^ | _G_~0~^11^
>| *54* &nbsp; | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~3~^3^ | _G_~1~^9^ | _G_~0~^10^ | _G_~0~^10^ | _G_~0~^10^
>| *55* &nbsp; | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^ | _B_~1~^0^
>| *56* &nbsp; | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^ | _B_~1~^1^
>| *57* &nbsp; | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^ | _B_~1~^2^
>| *58* &nbsp; | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^ | _B_~1~^3^
>| *59* &nbsp; | _B_~1~^4^ | _B_~1~^4^ | _B_~0~^10^ | _B_~0~^10^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~1~^4^ | _B_~0~^15^
>| *60* &nbsp; | _B_~3~^1^ | _B_~1~^5^ | _B_~3~^1^ | _B_~3~^1^ | _B_~0~^10^ | _B_~3~^1^ | _B_~3~^1^ | _B_~3~^1^ | _B_~1~^5^ | _B_~1~^5^ | _B_~1~^5^ | _B_~1~^5^ | _B_~1~^5^ | _B_~0~^14^
>| *61* &nbsp; | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~2~^0^ | _B_~1~^6^ | _B_~1~^6^ | _B_~1~^6^ | _B_~0~^13^
>| *62* &nbsp; | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~2~^1^ | _B_~1~^7^ | _B_~1~^7^ | _B_~1~^7^ | _B_~0~^12^
>| *63* &nbsp; | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~2~^2^ | _B_~1~^8^ | _B_~1~^8^ | _B_~0~^11^ | _B_~0~^11^
>| *64* &nbsp; | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~2~^3^ | _B_~1~^9^ | _B_~0~^10^ | _B_~0~^10^ | _B_~0~^10^
>| *65* &nbsp; | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | _R_~2~^0^ | IB~0,0~^0^ | IB~0,0~^0^ | IB~0,0~^0^ | IB~0,0~^0^
>| *66* &nbsp; | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | _R_~2~^1^ | IB~0,0~^1^ | IB~0,0~^1^ | IB~0,0~^1^ | IB~0,0~^1^
>| *67* &nbsp; | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | _R_~2~^2^ | IB~0,0~^2^ | IB~0,0~^2^ | IB~0,0~^2^ | IB~0,0~^2^
>| *68* &nbsp; | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | _R_~2~^3^ | IB~1,0~^0^ | IB~1,0~^0^ | IB~1,0~^0^ | IB~1,0~^0^
>| *69* &nbsp; | _R_~2~^4^ | _R_~2~^4^ | _R_~2~^4^ | _B_~3~^0^ | _B_~3~^1^ | _R_~2~^4^ | _R_~2~^4^ | _R_~2~^4^ | _R_~2~^4^ | _R_~2~^4^ | IB~1,0~^1^ | IB~1,0~^1^ | IB~1,0~^1^ | IB~1,0~^1^
>| *70* &nbsp; | _B_~3~^2^ | _R_~2~^5^ | _B_~3~^2^ | _B_~3~^2^ | _B_~3~^2^ | _B_~3~^2^ | _R_~2~^5^ | _B_~3~^2^ | _B_~3~^2^ | _R_~2~^5^ | IB~1,0~^2^ | IB~1,0~^2^ | IB~1,0~^2^ | IB~1,0~^2^
>| *71* &nbsp; | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | _R_~3~^0^ | IB~1,0~^3^ | IB~1,0~^3^ | IB~1,0~^3^ | IB~1,0~^3^
>| *72* &nbsp; | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | _R_~3~^1^ | IB~2,0~^0^ | IB~2,0~^0^ | IB~2,0~^0^ | IB~2,0~^0^
>| *73* &nbsp; | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | _R_~3~^2^ | IB~2,0~^1^ | IB~2,0~^1^ | IB~2,0~^1^ | IB~2,0~^1^
>| *74* &nbsp; | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | _R_~3~^3^ | IB~2,0~^2^ | IB~2,0~^2^ | IB~2,0~^2^ | IB~2,0~^2^
>| *75* &nbsp; | _R_~3~^4^ | _R_~3~^4^ | _R_~3~^4^ | _G_~2~^4^ | _B_~3~^4^ | _R_~3~^4^ | _R_~3~^4^ | _R_~3~^4^ | _R_~3~^4^ | _R_~3~^4^ | IB~2,0~^3^ | IB~2,0~^3^ | IB~2,0~^3^ | IB~2,0~^3^
>| *76* &nbsp; | _B_~3~^3^ | _R_~3~^5^ | _B_~3~^3^ | _B_~3~^3^ | _B_~3~^3^ | _B_~3~^3^ | _R_~3~^5^ | _B_~3~^3^ | _B_~3~^3^ | _R_~3~^5^ | IB~3,0~^0^ | IB~3,0~^0^ | IB~3,0~^0^ | IB~3,0~^0^
>| *77* &nbsp; | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | PB^0^ | IB~3,0~^1^ | IB~3,0~^1^ | IB~3,0~^1^ | IB~3,0~^1^
>| *78* &nbsp; | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | PB^1^ | IB~3,0~^2^ | IB~3,0~^2^ | IB~3,0~^2^ | IB~3,0~^2^
>| *79* &nbsp; | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | PB^2^ | IB~3,0~^3^ | IB~3,0~^3^ | IB~3,0~^3^ | IB~3,0~^3^
>| *80* &nbsp; | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | PB^3^ | IB~0,1~^0^ | IB~0,1~^0^ | IB~0,1~^0^ | IB~0,1~^0^
>| *81* &nbsp; | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | PB^4^ | IB~0,1~^1^ | IB~0,1~^1^ | IB~0,1~^1^ | IB~0,1~^1^
|================

[NOTE]
====
<<table-bptcbc6hbits>> and <<table-bptcbc6hbits2>> show bits 0..81 for each mode.
Since modes 3, 7, 11 and 15 each have only one partition, only the first
index is an anchor index, and there is a fixed mapping between texels and
index bits.
These modes also have four index bits IB~_x,y_~^0..3^ per texel (except for the
anchor index), and these pixel indices start at bit 65 with IB~0,0~^0^.
The interpretation of bits 82 and later is not tabulated.
For modes with two partitions, the mapping from index bits IB~_x,y_~ to
coordinates depends on the choice of anchor index for the secondary
partition (determined by the pattern selected by the partition bits
PB^4..0^), and is therefore not uniquely defined by the mode -- and not
useful to tabulate in this form.
====

<<<

In a single-subset blocks, the two endpoints are contained in _R_~0~, _G_~0~, _B_~0~
(collectively referred to as _E_~0~) and _R_~1~, _G_~1~, _B_~1~ (collectively _E_~1~).
In a two-subset block, the endpoints for the second subset are in _R_~2~, _G_~2~,
_B_~2~ and _R_~3~, _G_~3~, _B_~3~ (collectively _E_~2~ and _E_~3~ respectively).
The values in _E_~0~ are sign-extended to the implementation's internal integer
representation if the format of the texture is signed.
The values in _E_~1~ (and _E_~2~ and _E_~3~ if the block has two subsets) are
sign-extended if the format of the texture is signed or if the block mode
has transformed endpoints.
If the mode has transformed endpoints, the values from _E_~0~ are used as a
base to offset all other endpoints, wrapped at the number of endpoint bits.
For example, _R_~1~ = (_R_~0~ {plus} _R_~1~) & latexmath:[$((1 \ll \mathrm{EPB})-1)$].

[NOTE]
====
In BC7, all modes represent endpoint values independently.
This means it is always possible to represent the endpoints nearest to the
anchor indices by choosing the endpoint order appropriately.
Since in BC6H transformed endpoints are represented as two's complement
offsets relative to the first endpoint, there is an asymmetry: it is
possible to represent larger negative values in two's complement than
positive values, so _E_~1~, _E_~2~ and _E_~3~ can be more distant from _E_~0~ in
a negative direction than positive in modes with transformed endpoints.
This means that endpoints cannot necessarily be chosen independently
of the anchor index in BC6H, since the order of endpoints cannot
necessarily be reversed.
In addition, _E_~2~ and _E_~3~ always depends on _E_~0~, so swapping _E_~0~ and
_E_~1~ to suit the anchor bit for the first subset may make make the
relative offsets of _E_~2~ and _E_~3~ unrepresentable in a given mode if
they fall out of range.
====

Next, the endpoints are unquantized to maximize the usage of the bits and
to ensure that the negative ranges are oriented properly to interpolate as
a two's complement value.
The following pseudocode assumes the computation uses sufficiently large
intermediate values to avoid overflow.
For the unsigned float format, we unquantize a value _x_ to _unq_ by:

-----
if (EPB >= 15)
    unq = x;
else if (x == 0)
    unq = 0;
else if (x == ((1 << EPB)-1))
    unq = 0xFFFF;
else
    unq = ((x << 15) + 0x4000) >> (EPB-1);
-----

The signed float unquantization is similar, but needs to worry about
orienting the negative range:

-----
s = 0;
if (EPB >= 16) {
    unq = x;
} else {
    if (x < 0) {
        s = 1;
        x = -x;
    }

    if (x == 0)
        unq = 0;
    else if (x >= ((1 << (EPB-1))-1))
        unq = 0x7FFF;
    else
        unq = ((x << 15) + 0x4000) >> (EPB-1);

    if (s)
        unq = -unq;
}
-----

After the endpoints are unquantized, interpolation proceeds as in the
fixed-point formats above using <<BPTCinterpolation>>, including the interpolation
weight table, <<BPTCInterpolation>>.

<<<

The interpolated values are passed through a final unquantization step.
For the unsigned format, this limits the range of the integer representation
to those bit sequences which, when interpreted as a 16-bit half float,
represent [0.0..65504.0], where 65504.0 is the largest finite value
representable in a half float.
The bit pattern that represents 65504.0 is integer 0x7BFF, so the integer
input range 0..0xFFFF can be mapped to this range by scaling the
interpolated integer i by latexmath:[$31\over 64$]:

-----
out = (i * 31) >> 6;
-----

For the signed format, the final unquantization step limits the range of
the integer representation to the bit sequences which, when interpreted as
a 16-bit half float, represent the range [latexmath:[$-\infty$]..65504.0],
where latexmath:[$-\infty$] is represented in half float as the bit
pattern 0xFC00.
The signed 16-bit integer range [-0x8000..0x7FFF] is remapped to this
float representation by taking the absolute value of the interpolated
value i, scaling it by latexmath:[$31\over 32$], and restoring the sign bit:

-----
out = i < 0 ? (((-i) * 31) >> 5) | 0x8000 : (i * 31) >> 5;
-----

The resultant bit pattern should be interpreted as a 16-bit half float.

[NOTE]
====
The ability to support latexmath:[$-\infty$] is considered ``accidental''
due to the asymmetry of two's complement representation: in order to
map integer 0x7FFF to 65504.0 and 0x0000 to 0.0, -0x7FFF maps to the
largest finite negative value, -65504.0, represented as 0xFBFF.
A two's complement signed integer can also represent -0x8000; it
happens that the same unquantization formula maps 0x8000 to 0xFC00,
which is the half float bit pattern for latexmath:[$-\infty$].
Although decoders for BC6H should be bit-exact, encoders for this format
are encouraged to map latexmath:[$-\infty$] to -65504.0 (and to map
latexmath:[$\infty$] to 65504.0 and NaN values to 0.0) prior to encoding.
====