=============================================
Snow Video Codec Specification Draft 20080110
=============================================

Introduction:
=============
This specification describes the Snow bitstream syntax and semantics as
well as the formal Snow decoding process.

The decoding process is described precisely and any compliant decoder
MUST produce the exact same output for a spec-conformant Snow stream.
For encoding, though, any process which generates a stream compliant to
the syntactical and semantic requirements and which is decodable by
the process described in this spec shall be considered a conformant
Snow encoder.

Definitions:
============

MUST    the specific part must be done to conform to this standard
SHOULD  it is recommended to be done that way, but not strictly required

ilog2(x) is the rounded down logarithm of x with basis 2
ilog2(0) = 0

Type definitions:
=================

b   1-bit range coded
u   unsigned scalar value range coded
s   signed scalar value range coded


Bitstream syntax:
=================

frame:
    header
    prediction
    residual

header:
    keyframe                            b   MID_STATE
    if(keyframe || always_reset)
        reset_contexts
    if(keyframe){
        version                         u   header_state
        always_reset                    b   header_state
        temporal_decomposition_type     u   header_state
        temporal_decomposition_count    u   header_state
        spatial_decomposition_count     u   header_state
        colorspace_type                 u   header_state
        if (nb_planes > 2) {
            chroma_h_shift              u   header_state
            chroma_v_shift              u   header_state
        }
        spatial_scalability             b   header_state
        max_ref_frames-1                u   header_state
        qlogs
    }
    if(!keyframe){
        update_mc                       b   header_state
        if(update_mc){
            for(plane=0; plane<nb_plane_types; plane++){
                diag_mc                 b   header_state
                htaps/2-1               u   header_state
                for(i= p->htaps/2; i; i--)
                    |hcoeff[i]|         u   header_state
            }
        }
        update_qlogs                    b   header_state
        if(update_qlogs){
            spatial_decomposition_count u   header_state
            qlogs
        }
    }

    spatial_decomposition_type          s   header_state
    qlog                                s   header_state
    mv_scale                            s   header_state
    qbias                               s   header_state
    block_max_depth                     s   header_state

qlogs:
    for(plane=0; plane<nb_plane_types; plane++){
        quant_table[plane][0][0]        s   header_state
        for(level=0; level < spatial_decomposition_count; level++){
            quant_table[plane][level][1]s   header_state
            quant_table[plane][level][3]s   header_state
        }
    }

reset_contexts
    *_state[*]= MID_STATE

prediction:
    for(y=0; y<block_count_vertical; y++)
        for(x=0; x<block_count_horizontal; x++)
            block(0)

block(level):
    mvx_diff=mvy_diff=y_diff=cb_diff=cr_diff=0
    if(keyframe){
        intra=1
    }else{
        if(level!=max_block_depth){
            s_context= 2*left->level + 2*top->level + topleft->level + topright->level
            leaf                        b   block_state[4 + s_context]
        }
        if(level==max_block_depth || leaf){
            intra                       b   block_state[1 + left->intra + top->intra]
            if(intra){
                y_diff                  s   block_state[32]
                cb_diff                 s   block_state[64]
                cr_diff                 s   block_state[96]
            }else{
                ref_context= ilog2(2*left->ref) + ilog2(2*top->ref)
                if(ref_frames > 1)
                    ref                 u   block_state[128 + 1024 + 32*ref_context]
                mx_context= ilog2(2*abs(left->mx - top->mx))
                my_context= ilog2(2*abs(left->my - top->my))
                mvx_diff                s   block_state[128 + 32*(mx_context + 16*!!ref)]
                mvy_diff                s   block_state[128 + 32*(my_context + 16*!!ref)]
            }
        }else{
            block(level+1)
            block(level+1)
            block(level+1)
            block(level+1)
        }
    }


residual:
    residual2(luma)
    if (nb_planes > 2) {
        residual2(chroma_cr)
        residual2(chroma_cb)
    }

residual2:
    for(level=0; level<spatial_decomposition_count; level++){
        if(level==0)
            subband(LL, 0)
        subband(HL, level)
        subband(LH, level)
        subband(HH, level)
    }

subband:
    FIXME

nb_plane_types = gray ? 1 : 2;

Tag description:
----------------

version
    0
    this MUST NOT change within a bitstream

always_reset
    if 1 then the range coder contexts will be reset after each frame

temporal_decomposition_type
    0

temporal_decomposition_count
    0

spatial_decomposition_count
    FIXME

colorspace_type
    0   unspecified YcbCr
    1   Gray
    2   Gray + Alpha
    3   GBR
    4   GBRA
    this MUST NOT change within a bitstream

chroma_h_shift
    log2(luma.width / chroma.width)
    this MUST NOT change within a bitstream

chroma_v_shift
    log2(luma.height / chroma.height)
    this MUST NOT change within a bitstream

spatial_scalability
    0

max_ref_frames
    maximum number of reference frames
    this MUST NOT change within a bitstream

update_mc
    indicates that motion compensation filter parameters are stored in the
    header

diag_mc
    flag to enable faster diagonal interpolation
    this SHOULD be 1 unless it turns out to be covered by a valid patent

htaps
    number of half pel interpolation filter taps, MUST be even, >0 and <10

hcoeff
    half pel interpolation filter coefficients, hcoeff[0] are the 2 middle
    coefficients [1] are the next outer ones and so on, resulting in a filter
    like: ...eff[2], hcoeff[1], hcoeff[0], hcoeff[0], hcoeff[1], hcoeff[2] ...
    the sign of the coefficients is not explicitly stored but alternates
    after each coeff and coeff[0] is positive, so ...,+,-,+,-,+,+,-,+,-,+,...
    hcoeff[0] is not explicitly stored but found by subtracting the sum
    of all stored coefficients with signs from 32
    hcoeff[0]= 32 - hcoeff[1] - hcoeff[2] - ...
    a good choice for hcoeff and htaps is
    htaps= 6
    hcoeff={40,-10,2}
    an alternative which requires more computations at both encoder and
    decoder side and may or may not be better is
    htaps= 8
    hcoeff={42,-14,6,-2}


ref_frames
    minimum of the number of available reference frames and max_ref_frames
    for example the first frame after a key frame always has ref_frames=1

spatial_decomposition_type
    wavelet type
    0 is a 9/7 symmetric compact integer wavelet
    1 is a 5/3 symmetric compact integer wavelet
    others are reserved
    stored as delta from last, last is reset to 0 if always_reset || keyframe

qlog
    quality (logarthmic quantizer scale)
    stored as delta from last, last is reset to 0 if always_reset || keyframe

mv_scale
    stored as delta from last, last is reset to 0 if always_reset || keyframe
    FIXME check that everything works fine if this changes between frames

qbias
    dequantization bias
    stored as delta from last, last is reset to 0 if always_reset || keyframe

block_max_depth
    maximum depth of the block tree
    stored as delta from last, last is reset to 0 if always_reset || keyframe

quant_table
    quantiztation table


Highlevel bitstream structure:
=============================
 --------------------------------------------
|                   Header                   |
 --------------------------------------------
|    ------------------------------------    |
|   |               Block0               |   |
|   |             split?                 |   |
|   |     yes              no            |   |
|   |  .........         intra?          |   |
|   | : Block01 :    yes         no      |   |
|   | : Block02 :  .......   ..........  |   |
|   | : Block03 : :  y DC : : ref index: |   |
|   | : Block04 : : cb DC : : motion x : |   |
|   |  .........  : cr DC : : motion y : |   |
|   |              .......   ..........  |   |
|    ------------------------------------    |
|    ------------------------------------    |
|   |               Block1               |   |
|                    ...                     |
 --------------------------------------------
| ------------   ------------   ------------ |
|| Y subbands | | Cb subbands| | Cr subbands||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
|| |LL0||HL0| | | |LL0||HL0| | | |LL0||HL0| ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
|| |LH0||HH0| | | |LH0||HH0| | | |LH0||HH0| ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
|| |HL1||LH1| | | |HL1||LH1| | | |HL1||LH1| ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
||  ---  ---  | |  ---  ---  | |  ---  ---  ||
|| |HH1||HL2| | | |HH1||HL2| | | |HH1||HL2| ||
||    ...     | |    ...     | |    ...     ||
| ------------   ------------   ------------ |
 --------------------------------------------

Decoding process:
=================

                                         ------------
                                        |            |
                                        |  Subbands  |
                   ------------         |            |
                  |            |         ------------
                  |  Intra DC  |               |
                  |            |    LL0 subband prediction
                   ------------                |
                                \        Dequantizaton
 -------------------             \             |
|  Reference frames |             \           IDWT
| -------   ------- |    Motion    \           |
||Frame 0| |Frame 1|| Compensation  .   OBMC   v      -------
| -------   ------- | --------------. \------> + --->|Frame n|-->output
| -------   ------- |                                 -------
||Frame 2| |Frame 3||<----------------------------------/
|        ...        |
 -------------------


Range Coder:
============

Binary Range Coder:
-------------------
The implemented range coder is an adapted version based upon "Range encoding:
an algorithm for removing redundancy from a digitised message." by G. N. N.
Martin.
The symbols encoded by the Snow range coder are bits (0|1). The
associated probabilities are not fix but change depending on the symbol mix
seen so far.


bit seen | new state
---------+-----------------------------------------------
    0    | 256 - state_transition_table[256 - old_state];
    1    |       state_transition_table[      old_state];

state_transition_table = {
  0,   0,   0,   0,   0,   0,   0,   0,  20,  21,  22,  23,  24,  25,  26,  27,
 28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  37,  38,  39,  40,  41,  42,
 43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,  56,  56,  57,
 58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,  70,  71,  72,  73,
 74,  75,  75,  76,  77,  78,  79,  80,  81,  82,  83,  84,  85,  86,  87,  88,
 89,  90,  91,  92,  93,  94,  94,  95,  96,  97,  98,  99, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 114, 115, 116, 117, 118,
119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 133,
134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149,
150, 151, 152, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 171, 172, 173, 174, 175, 176, 177, 178, 179,
180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 190, 191, 192, 194, 194,
195, 196, 197, 198, 199, 200, 201, 202, 202, 204, 205, 206, 207, 208, 209, 209,
210, 211, 212, 213, 215, 215, 216, 217, 218, 219, 220, 220, 222, 223, 224, 225,
226, 227, 227, 229, 229, 230, 231, 232, 234, 234, 235, 236, 237, 238, 239, 240,
241, 242, 243, 244, 245, 246, 247, 248, 248,   0,   0,   0,   0,   0,   0,   0};

FIXME


Range Coding of integers:
-------------------------
FIXME


Neighboring Blocks:
===================
left and top are set to the respective blocks unless they are outside of
the image in which case they are set to the Null block

top-left is set to the top left block unless it is outside of the image in
which case it is set to the left block

if this block has no larger parent block or it is at the left side of its
parent block and the top right block is not outside of the image then the
top right block is used for top-right else the top-left block is used

Null block
y,cb,cr are 128
level, ref, mx and my are 0


Motion Vector Prediction:
=========================
1. the motion vectors of all the neighboring blocks are scaled to
compensate for the difference of reference frames

scaled_mv= (mv * (256 * (current_reference+1) / (mv.reference+1)) + 128)>>8

2. the median of the scaled left, top and top-right vectors is used as
motion vector prediction

3. the used motion vector is the sum of the predictor and
   (mvx_diff, mvy_diff)*mv_scale


Intra DC Predicton:
======================
the luma and chroma values of the left block are used as predictors

the used luma and chroma is the sum of the predictor and y_diff, cb_diff, cr_diff
to reverse this in the decoder apply the following:
block[y][x].dc[0] = block[y][x-1].dc[0] +  y_diff;
block[y][x].dc[1] = block[y][x-1].dc[1] + cb_diff;
block[y][x].dc[2] = block[y][x-1].dc[2] + cr_diff;
block[*][-1].dc[*]= 128;


Motion Compensation:
====================

Halfpel interpolation:
----------------------
halfpel interpolation is done by convolution with the halfpel filter stored
in the header:

horizontal halfpel samples are found by
H1[y][x] =    hcoeff[0]*(F[y][x  ] + F[y][x+1])
            + hcoeff[1]*(F[y][x-1] + F[y][x+2])
            + hcoeff[2]*(F[y][x-2] + F[y][x+3])
            + ...
h1[y][x] = (H1[y][x] + 32)>>6;

vertical halfpel samples are found by
H2[y][x] =    hcoeff[0]*(F[y  ][x] + F[y+1][x])
            + hcoeff[1]*(F[y-1][x] + F[y+2][x])
            + ...
h2[y][x] = (H2[y][x] + 32)>>6;

vertical+horizontal halfpel samples are found by
H3[y][x] =    hcoeff[0]*(H2[y][x  ] + H2[y][x+1])
            + hcoeff[1]*(H2[y][x-1] + H2[y][x+2])
            + ...
H3[y][x] =    hcoeff[0]*(H1[y  ][x] + H1[y+1][x])
            + hcoeff[1]*(H1[y+1][x] + H1[y+2][x])
            + ...
h3[y][x] = (H3[y][x] + 2048)>>12;


                   F   H1  F
                   |   |   |
                   |   |   |
                   |   |   |
                   F   H1  F
                   |   |   |
                   |   |   |
                   |   |   |
   F-------F-------F-> H1<-F-------F-------F
                   v   v   v
                  H2   H3  H2
                   ^   ^   ^
   F-------F-------F-> H1<-F-------F-------F
                   |   |   |
                   |   |   |
                   |   |   |
                   F   H1  F
                   |   |   |
                   |   |   |
                   |   |   |
                   F   H1  F


unavailable fullpel samples (outside the picture for example) shall be equal
to the closest available fullpel sample


Smaller pel interpolation:
--------------------------
if diag_mc is set then points which lie on a line between 2 vertically,
horiziontally or diagonally adjacent halfpel points shall be interpolated
linearls with rounding to nearest and halfway values rounded up.
points which lie on 2 diagonals at the same time should only use the one
diagonal not containing the fullpel point


           F-->O---q---O<--h1->O---q---O<--F
           v \           / v \           / v
           O   O       O   O   O       O   O
           |         /     |     \         |
           q       q       q       q       q
           |     /         |         \     |
           O   O       O   O   O       O   O
           ^ /           \ ^ /           \ ^
          h2-->O---q---O<--h3->O---q---O<--h2
           v \           / v \           / v
           O   O       O   O   O       O   O
           |     \         |         /     |
           q       q       q       q       q
           |         \     |     /         |
           O   O       O   O   O       O   O
           ^ /           \ ^ /           \ ^
           F-->O---q---O<--h1->O---q---O<--F


the remaining points shall be bilinearly interpolated from the
up to 4 surrounding halfpel and fullpel points, again rounding should be to
nearest and halfway values rounded up

compliant Snow decoders MUST support 1-1/8 pel luma and 1/2-1/16 pel chroma
interpolation at least


Overlapped block motion compensation:
-------------------------------------
FIXME

LL band prediction:
===================
Each sample in the LL0 subband is predicted by the median of the left, top and
left+top-topleft samples, samples outside the subband shall be considered to
be 0. To reverse this prediction in the decoder apply the following.
for(y=0; y<height; y++){
    for(x=0; x<width; x++){
        sample[y][x] += median(sample[y-1][x],
                               sample[y][x-1],
                               sample[y-1][x]+sample[y][x-1]-sample[y-1][x-1]);
    }
}
sample[-1][*]=sample[*][-1]= 0;
width,height here are the width and height of the LL0 subband not of the final
video


Dequantizaton:
==============
FIXME

Wavelet Transform:
==================

Snow supports 2 wavelet transforms, the symmetric biorthogonal 5/3 integer
transform and a integer approximation of the symmetric biorthogonal 9/7
daubechies wavelet.

2D IDWT (inverse discrete wavelet transform)
--------------------------------------------
The 2D IDWT applies a 2D filter recursively, each time combining the
4 lowest frequency subbands into a single subband until only 1 subband
remains.
The 2D filter is done by first applying a 1D filter in the vertical direction
and then applying it in the horizontal one.
 ---------------    ---------------    ---------------    ---------------
|LL0|HL0|       |  |   |   |       |  |       |       |  |       |       |
|---+---|  HL1  |  | L0|H0 |  HL1  |  |  LL1  |  HL1  |  |       |       |
|LH0|HH0|       |  |   |   |       |  |       |       |  |       |       |
|-------+-------|->|-------+-------|->|-------+-------|->|   L1  |  H1   |->...
|       |       |  |       |       |  |       |       |  |       |       |
|  LH1  |  HH1  |  |  LH1  |  HH1  |  |  LH1  |  HH1  |  |       |       |
|       |       |  |       |       |  |       |       |  |       |       |
 ---------------    ---------------    ---------------    ---------------


1D Filter:
----------
1. interleave the samples of the low and high frequency subbands like
s={L0, H0, L1, H1, L2, H2, L3, H3, ... }
note, this can end with a L or a H, the number of elements shall be w
s[-1] shall be considered equivalent to s[1  ]
s[w ] shall be considered equivalent to s[w-2]

2. perform the lifting steps in order as described below

5/3 Integer filter:
1. s[i] -= (s[i-1] + s[i+1] + 2)>>2; for all even i < w
2. s[i] += (s[i-1] + s[i+1]    )>>1; for all odd  i < w

\ | /|\ | /|\ | /|\ | /|\
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   -1/4
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
  |  +  |  +  |  +  |  +   +1/2


Snow's 9/7 Integer filter:
1. s[i] -= (3*(s[i-1] + s[i+1])         + 4)>>3; for all even i < w
2. s[i] -=     s[i-1] + s[i+1]                 ; for all odd  i < w
3. s[i] += (   s[i-1] + s[i+1] + 4*s[i] + 8)>>4; for all even i < w
4. s[i] += (3*(s[i-1] + s[i+1])            )>>1; for all odd  i < w

\ | /|\ | /|\ | /|\ | /|\
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   -3/8
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
 (|  + (|  + (|  + (|  +   -1
\ + /|\ + /|\ + /|\ + /|\  +1/4
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   +1/16
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
  |  +  |  +  |  +  |  +   +3/2

optimization tips:
following are exactly identical
(3a)>>1 == a + (a>>1)
(a + 4b + 8)>>4 == ((a>>2) + b + 2)>>2

16bit implementation note:
The IDWT can be implemented with 16bits, but this requires some care to
prevent overflows, the following list, lists the minimum number of bits needed
for some terms
1. lifting step
A= s[i-1] + s[i+1]                              16bit
3*A + 4                                         18bit
A + (A>>1) + 2                                  17bit

3. lifting step
s[i-1] + s[i+1]                                 17bit

4. lifiting step
3*(s[i-1] + s[i+1])                             17bit


TODO:
=====
Important:
finetune initial contexts
flip wavelet?
try to use the wavelet transformed predicted image (motion compensated image) as context for coding the residual coefficients
try the MV length as context for coding the residual coefficients
use extradata for stuff which is in the keyframes now?
implement per picture halfpel interpolation
try different range coder state transition tables for different contexts

Not Important:
compare the 6 tap and 8 tap hpel filters (psnr/bitrate and subjective quality)
spatial_scalability b vs u (!= 0 breaks syntax anyway so we can add a u later)


Credits:
========
Michael Niedermayer
Loren Merritt


Copyright:
==========
GPL + GFDL + whatever is needed to make this a RFC