1 Introduction

The FFV1 video codec is a simple and efficient lossless intra-frame only codec.

The latest version of this document is available at https://raw.github.com/FFmpeg/FFV1/master/ffv1.md

This document assumes familiarity with mathematical and coding concepts such as Range coding and YCbCr colorspaces.

2 Terms and Definitions

2.1 Terms

The key words MUST, MUST NOT, SHOULD, and SHOULD NOT in this document are to be interpreted as described in RFC 2119.

For reference, below is an excerpt of RFC 2119:

2.2 Definitions

3 Conventions

Note: the operators and the order of precedence are the same as used in the C programming language ISO/IEC 9899.

3.1 Arithmetic operators

3.2 Assignment operators

3.3 Comparison operators

3.4 Order of operation precedence

When order of precedence is not indicated explicitly by use of parentheses, operations are evaluated in the following order (from top to bottom, operations of same precedence being evaluated from left to right). This order of operations is based on the order of operations used in Standard C.

a++, a–
!a, -a
a * b, a / b, a % b
a + b, a - b
a << b, a >> b
a < b, a <= b, a > b, a >= b
a == b, a != b
a & b
a | b
a && b
a || b
a ? b : c
a = b, a += b, a -= b

3.5 Range

a...b means any value starting from a to b, inclusive.

3.6 Bitstream functions

remaining_bits_in_bitstream( ) means the count of remaining bits after the current position in the bitstream. It is computed from the NumBytes value multiplied by 8 minus the count of bits already read by the bitstream parser.

4 General Description

Each frame is split in 1 to 4 planes (Y, Cb, Cr, Alpha). In the case of the normal YCbCr colorspace the Y plane is coded first followed by the Cb and Cr planes, if an Alpha/transparency plane exists, it is coded last. In the case of the JPEG2000-RCT colorspace the lines are interleaved to improve caching efficiency since it is most likely that the RCT will immediately be converted to RGB during decoding; the interleaved coding order is also Y, Cb, Cr, Alpha.

Samples within a plane are coded in raster scan order (left->right, top->bottom). Each sample is predicted by the median predictor from samples in the same plane and the difference is stored see Coding of the Sample Difference.

4.1 Border

For the purpose of the predictior and context, samples above the coded slice are assumed to be 0; samples to the right of the coded slice are identical to the closest left sample; samples to the left of the coded slice are identical to the top right sample (if there is one), otherwise 0.

4.2 Median predictor

median(left, top, left + top - diag)

left, top, diag are the left, top and left-top samples

Note, this is also used in JPEG-LS and HuffYuv.

4.3 Context

The quantized sample differences L-l, l-tl, tl-t, t-T, t-tr are used as context:

$context=Q_{0}[l-tl]+\left|Q_{0}\right|(Q_{1}[tl-t]+\left|Q_{1}\right|(Q_{2}[t-tr]+\left|Q_{2}\right|(Q_{3}[L-l]+\left|Q_{3}\right|Q_{4}[T-t])))$

If the context is smaller than 0 then -context is used and the difference between the sample and its predicted value is encoded with a flipped sign.

4.4 Quantization

There are 5 quantization tables for the 5 sample differences, both the number of quantization steps and their distribution are stored in the bitstream. Each quantization table has exactly 256 entries, and the 8 least significant bits of the sample difference are used as index:

$Q_{i}[a-b]=Table_{i}[(a-b)\&255]$

4.5 Colorspace

4.5.1 JPEG2000-RCT

$Cb=b-g$

$Cr=r-g$

$Y=g+(Cb+Cr)>>2$

$g=Y-(Cb+Cr)>>2$

$r=Cr+g$

$b=Cb+g$

JPEG2000

4.6 Coding of the sample difference

Instead of coding the n+1 bits of the sample difference with Huffman-, or Range coding (or n+2 bits, in the case of RCT), only the n (or n+1) least significant bits are used, since this is sufficient to recover the original sample. In the equation below, the term "bits" represents bits_per_raw_sample+1 for RCT or bits_per_raw_sample otherwise:

$coder\_input=\left[\left(sample\_difference+2^{bits-1}\right)\&\left(2^{bits}-1\right)\right]-2^{bits-1}$

4.6.1 Range coding mode

Early experimental versions of FFV1 used the CABAC Arithmetic coder from H.264 but due to the uncertain patent/royality situation, as well as its slightly worse performance, CABAC was replaced by a range coder based on an algorithm defined by G. Nigel N. Martin in 1979 RangeCoder.

4.6.1.1 Range binary values

To encode binary digits efficiently a range coder is used. $C_{i}$ is the i-th Context. $B_{i}$ is the i-th byte of the bytestream. $b_{i}$ is the i-th range coded binary value, $S_{0,i}$ is the i-th initial state, which is 128. The length of the bytestream encoding n binary symbols is $j_{n}$ bytes.

$r_{i}=\left\lfloor \frac{R_{i}S_{i,C_{i}}}{2^{8}}\right\rfloor$

$\begin{array}{ccccccccc} S_{i+1,C_{i}}=zero\_state_{S_{i,C_{i}}} & \wedge & l{}_{i}=L_{i} & \wedge & t_{i}=R_{i}-r_{i} & \Longleftarrow & b_{i}=0 & \Longleftrightarrow & L_{i}<R_{i}-r_{i}\\ S_{i+1,C_{i}}=one\_state_{S_{i,C_{i}}} & \wedge & l_{i}=L_{i}-R_{i}+r_{i} & \wedge & t_{i}=r_{i} & \Longleftarrow & b_{i}=1 & \Longleftrightarrow & L_{i}\geq R_{i}-r_{i} \end{array}$

$\begin{array}{ccc} S_{i+1,k}=S_{i,k} & \Longleftarrow & C_{i}\neq k \end{array}$

$\begin{array}{ccccccc} R_{i+1}=2^{8}t_{i} & \wedge & L_{i+1}=2^{8}l_{i}+B_{j_{i}} & \wedge & j_{i+1}=j_{i}+1 & \Longleftarrow & t_{i}<2^{8}\\ R_{i+1}=t_{i} & \wedge & L_{i+1}=l_{i} & \wedge & j_{i+1}=j_{i} & \Longleftarrow & t_{i}\geq2^{8} \end{array}$

$R_{0}=65280$

$L_{0}=2^{8}B_{0}+B_{1}$

$j_{0}=2$

4.6.1.2 Range non binary values

To encode scalar integers it would be possible to encode each bit separately and use the past bits as context. However that would mean 255 contexts per 8-bit symbol which is not only a waste of memory but also requires more past data to reach a reasonably good estimate of the probabilities. Alternatively assuming a Laplacian distribution and only dealing with its variance and mean (as in Huffman coding) would also be possible, however, for maximum flexibility and simplicity, the chosen method uses a single symbol to encode if a number is 0 and if not encodes the number using its exponent, mantissa and sign. The exact contexts used are best described by the following code, followed by some comments.

void put_symbol(RangeCoder *c, uint8_t *state, int v, int is_signed) {
    int i;
    put_rac(c, state+0, !v);
    if (v) {
        int a= ABS(v);
        int e= log2(a); 

        for (i=0; i<e; i++)
            put_rac(c, state+1+MIN(i,9), 1);  //1..10

        put_rac(c, state+1+MIN(i,9), 0);
        for (i=e-1; i>=0; i--)
            put_rac(c, state+22+MIN(i,9), (a>>i)&1); //22..31

        if (is_signed)
            put_rac(c, state+11 + MIN(e, 10), v < 0); //11..21
    }
}

4.6.1.3 Initial values for the context model

At keyframes all range coder state variables are set to their initial state.

4.6.1.4 State transition table

$one\_state_{i}=default\_state\_transition_{i}+state\_transition\_delta_{i}$

$zero\_state_{i}=256-one\_state_{256-i}$

4.6.1.5 default_state_transition

  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,

4.6.1.6 alternative state transition table

The alternative state transition table has been build using iterative minimization of frame sizes and generally performs better than the default. To use it, the coder_type has to be set to 2 and the difference to the default has to be stored in the parameters. The reference implemenation of FFV1 in FFmpeg uses this table by default at the time of this writing when Range coding is used.

  0, 10, 10, 10, 10, 16, 16, 16, 28, 16, 16, 29, 42, 49, 20, 49,

 59, 25, 26, 26, 27, 31, 33, 33, 33, 34, 34, 37, 67, 38, 39, 39,

 40, 40, 41, 79, 43, 44, 45, 45, 48, 48, 64, 50, 51, 52, 88, 52,

 53, 74, 55, 57, 58, 58, 74, 60,101, 61, 62, 84, 66, 66, 68, 69,

 87, 82, 71, 97, 73, 73, 82, 75,111, 77, 94, 78, 87, 81, 83, 97,

 85, 83, 94, 86, 99, 89, 90, 99,111, 92, 93,134, 95, 98,105, 98,

105,110,102,108,102,118,103,106,106,113,109,112,114,112,116,125,

115,116,117,117,126,119,125,121,121,123,145,124,126,131,127,129,

165,130,132,138,133,135,145,136,137,139,146,141,143,142,144,148,

147,155,151,149,151,150,152,157,153,154,156,168,158,162,161,160,

172,163,169,164,166,184,167,170,177,174,171,173,182,176,180,178,

175,189,179,181,186,183,192,185,200,187,191,188,190,197,193,196,

197,194,195,196,198,202,199,201,210,203,207,204,205,206,208,214,

209,211,221,212,213,215,224,216,217,218,219,220,222,228,223,225,

226,224,227,229,240,230,231,232,233,234,235,236,238,239,237,242,

241,243,242,244,245,246,247,248,249,250,251,252,252,253,254,255,

4.6.2 Huffman coding mode

This coding mode uses golomb rice codes. The VLC code is split into 2 parts, the prefix stores the most significant bits, the suffix stores the k least significant bits or stores the whole number in the ESC case. The end of the bitstream (of the frame) is filled with 0-bits so that the bitstream contains a multiple of 8 bits.

4.6.2.1 Prefix

4.6.2.2 Suffix

4.6.2.3 Examples

4.6.2.4 Run mode

Run mode is entered when the context is 0, and left as soon as a non-0 difference is found, the level is identical to the predicted one, the run and the first different level is coded.

4.6.2.5 Run length coding

The run value is encoded in 2 parts, the prefix part stores the more significant part of the run as well as adjusting the run_index which determines the number of bits in the less significant part of the run. The 2nd part of the value stores the less significant part of the run as it is. The run_index is reset for each plane and slice to 0.

log2_run[41]={
 0, 0, 0, 0, 1, 1, 1, 1,
 2, 2, 2, 2, 3, 3, 3, 3,
 4, 4, 5, 5, 6, 6, 7, 7,
 8, 9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,
24,
};

if (run_count == 0 && run_mode == 1) {
    if (get_bits1()) {
        run_count = 1 << log2_run[run_index];
        if (x + run_count <= w)
            run_index++;
    } else {
        if (log2_run[run_index])
            run_count = get_bits(log2_run[run_index]);
        else
            run_count = 0;
        if (run_index)
            run_index--;
        run_mode = 2;
    }
}

The log2_run function is also used within JPEGLS.

4.6.2.6 Level coding

Level coding is identical to the normal difference coding with the exception that the 0 value is removed as it cannot occur:

    if(diff>0) diff--;
    encode(diff);

Note, this is different from JPEG-LS, which doesn’t use prediction in run mode and uses a different encoding and context model for the last difference On a small set of test samples the use of prediction slightly improved the compression rate.

5 Bitstream

The same context which is initialized to 128 is used for all fields in the header.

Default values at the decoder initialization phase:

ConfigurationRecordIsPresent is set to 0.

5.1 Configuration Record

In the case of a bitstream with version >= 2, a configuration record is stored in the the underlying container, at the track header level. It contains the parameters used for all frames. The size of the configuration record, NumBytes, is supplied by the underlying container.

ConfigurationRecord( NumBytes ) {
    ConfigurationRecordIsPresent = 1
    Parameters( )
    while( remaining_bits_in_bitstream( ) > 32 )
        reserved_for_future_use                     // u(1)
    configuration_record_crc_parity                 // u(32)

reserved_for_future_use has semantics that are reserved for future use. Encoders conforming to this version of this specification SHALL NOT write this value. Decoders conforming to this version of this specification SHALL ignore its value.

configuration_record_crc_parity 32 bits that are choosen so that the configuration record as a whole has a crc remainder of 0. This is equivalent to storing the crc remainder in the 32-bit parity. The CRC generator polynom used is the standard IEEE CRC polynom (0x104C11DB7) with initial value 0.

This configuration record can be placed in any file format supporting configuration records, fitting as much as possible with how the file format uses to store configuration records. The configuration record storage place and NumBytes are currently defined and supported by this version of this specification for the following container formats:

5.1.1 In AVI File Format

The Configuration Record extends the stream format chunk ("AVI ", "hdlr", "strl", "strf") with the ConfigurationRecord bistream. See AVI for more information about chunks.

NumBytes is defined as the size, in bytes, of the strf chunk indicated in the chunk header minus the size of the stream format structure.

5.1.2 In ISO/IEC 14496-12 (MP4 File Format)

The Configuration Record extends the sample description box ("moov", "trak", "mdia", "minf", "stbl", "stsd") with a "glbl" box which contains the ConfigurationRecord bitstream. See ISO14496_12 for more information about boxes.

NumBytes is defined as the size, in bytes, of the "glbl" box indicated in the box header minus the size of the box header.

5.1.3 In NUT File Format

The codec_specific_data element (in "stream_header" packet) contains the ConfigurationRecord bitstream. See NUT for more information about elements.

NumBytes is defined as the size, in bytes, of the codec_specific_data element as indicated in the "length" field of codec_specific_data

5.2 Frame

5.3 Slice

primary_color_count is defined as 1 + ( chroma_planes ? 2 : 0 ) + ( alpha_plane ? 1 : 0 ).

slice_size indicates the size of the slice in bytes. Note: this allows finding the start of slices before previous slices have been fully decoded. And allows this way parallel decoding as well as error resilience.

error_status specifies the error status.

slice_crc_parity 32 bits that are choosen so that the slice as a whole has a crc remainder of 0. This is equivalent to storing the crc remainder in the 32-bit parity. The CRC generator polynom used is the standard IEEE CRC polynom (0x104C11DB7) with initial value 0.

5.4 Slice Header

slice_x indicates the x position on the slice raster formed by num_h_slices. Inferred to be 0 if not present.

slice_y indicates the y position on the slice raster formed by num_v_slices. Inferred to be 0 if not present.

slice_width indicates the width on the slice raster. Inferred to be 1 if not present.

slice_height indicates the height on the slice raster. Inferred to be 1 if not present.

quant_table_index_count is defined as 1 + ( ( chroma_planes || version < 4 ) ? 1 : 0 ) + ( alpha_plane ? 1 : 0 ).

quant_table_index indicates the index to select the quantization table set and the initial states for the slice. Inferred to be 0 if not present.

picture_structure specifies the picture structure. Inferred to be 0 if not present.

sar_num specifies the sample aspect ratio numerator. Inferred to be 0 if not present. MUST be 0 if sample aspect ratio is unknown.

sar_den specifies the sample aspect ratio numerator. Inferred to be 0 if not present. MUST be 0 if sample aspect ratio is unknown.

reset_contexts indicates if slice contexts must be reset. Inferred to be 0 if not present.

slice_coding_mode indicates the slice coding mode. Inferred to be 0 if not present.

5.5 Parameters

version specifies the version of the bitstream. Each version is incompatible with others versions: decoders SHOULD reject a file due to unknown version. Decoders SHOULD reject a file with version < 2 && ConfigurationRecordIsPresent == 1. Decoders SHOULD reject a file with version >= 2 && ConfigurationRecordIsPresent == 0.

* Version 2 was never enabled in the encoder thus version 2 files SHOULD NOT exist, and this document does not describe them to keep the text simpler.

micro_version specifies the micro-version of the bitstream. After a version is considered stable (a micro-version value is assigned to be the first stable variant of a specific version), each new micro-version after this first stable variant is compatible with the previous micro-version: decoders SHOULD NOT reject a file due to an unknown micro-version equal or above the micro-version considered as stable.

Meaning of micro_version for version 3:

* were development versions which may be incompatible with the stable variants.

Meaning of micro_version for version 4 (note: at the time of writting of this specification, version 4 is not considered stable so the first stable version value is to be annonced in the future):

* were development versions which may be incompatible with the stable variants.

coder_type specifies the coder used

state_transition_delta specifies the range coder custom state transition table. If state_transition_delta is not present in the bitstream, all range coder custom state transition table elements are assumed to be 0.

colorspace_type specifies the color space.

chroma_planes indicates if chroma (color) planes are present.

bits_per_raw_sample indicates the number of bits for each luma and chroma sample. Inferred to be 8 if not present.

* Encoders MUST not store bits_per_raw_sample = 0 Decoders SHOULD accept and interpret bits_per_raw_sample = 0 as 8.

h_chroma_subsample indicates the subsample factor between luma and chroma width ($chroma\_width=2^{-log2\_h\_chroma\_subsample}luma\_width$)

v_chroma_subsample indicates the subsample factor between luma and chroma height ($chroma\_height=2^{-log2\_v\_chroma\_subsample}luma\_height$)

alpha_plane

indicates if a transparency plane is present.

num_h_slices indicates the number of horizontal elements of the slice raster. Inferred to be 1 if not present.

num_v_slices indicates the number of vertical elements of the slice raster. Inferred to be 1 if not present.

quant_table_count indicates the number of quantization table sets. Inferred to be 1 if not present.

states_coded indicates if the respective quantization table set has the initial states coded. Inferred to be 0 if not present.

initial_state_delta [ i ][ j ][ k ] indicates the initial range coder state, it is encoded using k as context index and pred = j ? initial_states[ i ][j - 1][ k ] : 128 initial_state[ i ][ j ][ k ] = ( pred + initial_state_delta[ i ][ j ][ k ] ) & 255

slice_count indicates the number of slices in the current frame, slice_count is 1 if it is not explicitly coded.

ec indicates the error detection/correction type.

intra indicates the relationship between frames. Inferred to be 0 if not present.

5.6 Quantization Tables

The quantization tables are stored by storing the number of equal entries -1 of the first half of the table using the method described in Range Non Binary Values. The second half doesn’t need to be stored as it is identical to the first with flipped sign.

example:

Table: 0 0 1 1 1 1 2 2-2-2-2-1-1-1-1 0

Stored values: 1, 3, 1

QuantizationTable( i ) {                          // type
    scale = 1
    for( j = 0; j < MAX_CONTEXT_INPUTS; j++ ) {
        QuantizationTablePerContext( i, j, scale )
        scale *= 2 * len_count[ i ][ j ] - 1
    }
    context_count[ i ] = ( scale + 1 ) / 2

MAX_CONTEXT_INPUTS is 5.

quant_tables indicates the quantification table values.

context_count indicates the count of contexts.

5.6.1 Restrictions

In version 2 and later the maximum slice size in pixels is $\frac{width\centerdot height}{4}$, unless the frame is smaller or equal 352x288 this is to ensure that fast multithreaded decoding is possible.

6 Changelog

See https://github.com/FFmpeg/FFV1/commits/master

7 ToDo

• mean,k estimation for the golomb rice codes

8 Bibliography

8.1 References

RFC 2119 - Key words for use in RFCs to Indicate Requirement Levels https://www.ietf.org/rfc/rfc2119.txt

ISO/IEC 9899 - Programming languages - C http://www.open-std.org/JTC1/SC22/WG14/www/standards

JPEG-LS FCD 14495 http://www.jpeg.org/public/fcd14495p.pdf

H.264 Draft http://bs.hhi.de/~wiegand/JVT-G050.pdf

HuffYuv http://cultact-server.novi.dk/kpo/huffyuv/huffyuv.html

FFmpeg http://ffmpeg.org

JPEG2000 http://www.jpeg.org/jpeg2000/

Range encoding: an algorithm for removing redundancy from a digitised message. Presented by G. Nigel N. Martin at the Video & Data Recording Conference, IBM UK Scientific Center held in Southampton July 24-27 1979.

AVI RIFF File Format https://msdn.microsoft.com/en-us/library/windows/desktop/dd318189%28v=vs.85%29.aspx

Information technology Coding of audio-visual objects Part 12: ISO base media file format http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=61988

NUT Open Container Format http://www.ffmpeg.org/~michael/nut.txt

9 Copyright

Copyright 2003-2013 Michael Niedermayer <michaelni@gmx.at> This text can be used under the GNU Free Documentation License or GNU General Public License. See http://www.gnu.org/licenses/fdl.txt.