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FFV1 Video Coding Format Version 0, 1, and 3
draft-ietf-cellar-ffv1-18

The information below is for an old version of the document.
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This is an older version of an Internet-Draft that was ultimately published as RFC 9043.
Authors Michael Niedermayer , Dave Rice , Jérôme Martinez
Last updated 2020-10-08 (Latest revision 2020-10-07)
Replaces draft-niedermayer-cellar-ffv1
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Sep 2019
Submit informational specification for FFV1 video codec versions 0, 1 and 3 to IESG for publication
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draft-ietf-cellar-ffv1-18
cellar                                                    M. Niedermayer
Internet-Draft                                                          
Intended status: Informational                                   D. Rice
Expires: 10 April 2021                                                  
                                                             J. Martinez
                                                          7 October 2020

              FFV1 Video Coding Format Version 0, 1, and 3
                       draft-ietf-cellar-ffv1-18

Abstract

   This document defines FFV1, a lossless intra-frame video encoding
   format.  FFV1 is designed to efficiently compress video data in a
   variety of pixel formats.  Compared to uncompressed video, FFV1
   offers storage compression, frame fixity, and self-description, which
   makes FFV1 useful as a preservation or intermediate video format.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 10 April 2021.

Copyright Notice

   Copyright (c) 2020 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
   and restrictions with respect to this document.  Code Components
   extracted from this document must include Simplified BSD License text
   as described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Notation and Conventions  . . . . . . . . . . . . . . . . . .   5
     2.1.  Definitions . . . . . . . . . . . . . . . . . . . . . . .   5
     2.2.  Conventions . . . . . . . . . . . . . . . . . . . . . . .   6
       2.2.1.  Pseudo-code . . . . . . . . . . . . . . . . . . . . .   6
       2.2.2.  Arithmetic Operators  . . . . . . . . . . . . . . . .   6
       2.2.3.  Assignment Operators  . . . . . . . . . . . . . . . .   7
       2.2.4.  Comparison Operators  . . . . . . . . . . . . . . . .   7
       2.2.5.  Mathematical Functions  . . . . . . . . . . . . . . .   8
       2.2.6.  Order of Operation Precedence . . . . . . . . . . . .   8
       2.2.7.  Range . . . . . . . . . . . . . . . . . . . . . . . .   9
       2.2.8.  NumBytes  . . . . . . . . . . . . . . . . . . . . . .   9
       2.2.9.  Bitstream Functions . . . . . . . . . . . . . . . . .   9
   3.  Sample Coding . . . . . . . . . . . . . . . . . . . . . . . .  10
     3.1.  Border  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     3.2.  Samples . . . . . . . . . . . . . . . . . . . . . . . . .  11
     3.3.  Median Predictor  . . . . . . . . . . . . . . . . . . . .  11
     3.4.  Quantization Table Sets . . . . . . . . . . . . . . . . .  12
     3.5.  Context . . . . . . . . . . . . . . . . . . . . . . . . .  13
     3.6.  Quantization Table Set Indexes  . . . . . . . . . . . . .  13
     3.7.  Color spaces  . . . . . . . . . . . . . . . . . . . . . .  13
       3.7.1.  YCbCr . . . . . . . . . . . . . . . . . . . . . . . .  14
       3.7.2.  RGB . . . . . . . . . . . . . . . . . . . . . . . . .  14
     3.8.  Coding of the Sample Difference . . . . . . . . . . . . .  16
       3.8.1.  Range Coding Mode . . . . . . . . . . . . . . . . . .  16
       3.8.2.  Golomb Rice Mode  . . . . . . . . . . . . . . . . . .  22
   4.  Bitstream . . . . . . . . . . . . . . . . . . . . . . . . . .  28
     4.1.  Quantization Table Set  . . . . . . . . . . . . . . . . .  29
       4.1.1.  quant_tables  . . . . . . . . . . . . . . . . . . . .  30
       4.1.2.  context_count . . . . . . . . . . . . . . . . . . . .  31
     4.2.  Parameters  . . . . . . . . . . . . . . . . . . . . . . .  31
       4.2.1.  version . . . . . . . . . . . . . . . . . . . . . . .  33
       4.2.2.  micro_version . . . . . . . . . . . . . . . . . . . .  33
       4.2.3.  coder_type  . . . . . . . . . . . . . . . . . . . . .  34
       4.2.4.  state_transition_delta  . . . . . . . . . . . . . . .  34
       4.2.5.  colorspace_type . . . . . . . . . . . . . . . . . . .  35
       4.2.6.  chroma_planes . . . . . . . . . . . . . . . . . . . .  35

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       4.2.7.  bits_per_raw_sample . . . . . . . . . . . . . . . . .  36
       4.2.8.  log2_h_chroma_subsample . . . . . . . . . . . . . . .  36
       4.2.9.  log2_v_chroma_subsample . . . . . . . . . . . . . . .  36
       4.2.10. extra_plane . . . . . . . . . . . . . . . . . . . . .  36
       4.2.11. num_h_slices  . . . . . . . . . . . . . . . . . . . .  37
       4.2.12. num_v_slices  . . . . . . . . . . . . . . . . . . . .  37
       4.2.13. quant_table_set_count . . . . . . . . . . . . . . . .  37
       4.2.14. states_coded  . . . . . . . . . . . . . . . . . . . .  37
       4.2.15. initial_state_delta . . . . . . . . . . . . . . . . .  37
       4.2.16. ec  . . . . . . . . . . . . . . . . . . . . . . . . .  38
       4.2.17. intra . . . . . . . . . . . . . . . . . . . . . . . .  38
     4.3.  Configuration Record  . . . . . . . . . . . . . . . . . .  39
       4.3.1.  reserved_for_future_use . . . . . . . . . . . . . . .  39
       4.3.2.  configuration_record_crc_parity . . . . . . . . . . .  39
       4.3.3.  Mapping FFV1 into Containers  . . . . . . . . . . . .  39
     4.4.  Frame . . . . . . . . . . . . . . . . . . . . . . . . . .  40
     4.5.  Slice . . . . . . . . . . . . . . . . . . . . . . . . . .  42
     4.6.  Slice Header  . . . . . . . . . . . . . . . . . . . . . .  43
       4.6.1.  slice_x . . . . . . . . . . . . . . . . . . . . . . .  44
       4.6.2.  slice_y . . . . . . . . . . . . . . . . . . . . . . .  44
       4.6.3.  slice_width . . . . . . . . . . . . . . . . . . . . .  44
       4.6.4.  slice_height  . . . . . . . . . . . . . . . . . . . .  44
       4.6.5.  quant_table_set_index_count . . . . . . . . . . . . .  44
       4.6.6.  quant_table_set_index . . . . . . . . . . . . . . . .  45
       4.6.7.  picture_structure . . . . . . . . . . . . . . . . . .  45
       4.6.8.  sar_num . . . . . . . . . . . . . . . . . . . . . . .  45
       4.6.9.  sar_den . . . . . . . . . . . . . . . . . . . . . . .  46
     4.7.  Slice Content . . . . . . . . . . . . . . . . . . . . . .  46
       4.7.1.  primary_color_count . . . . . . . . . . . . . . . . .  46
       4.7.2.  plane_pixel_height  . . . . . . . . . . . . . . . . .  46
       4.7.3.  slice_pixel_height  . . . . . . . . . . . . . . . . .  47
       4.7.4.  slice_pixel_y . . . . . . . . . . . . . . . . . . . .  47
     4.8.  Line  . . . . . . . . . . . . . . . . . . . . . . . . . .  47
       4.8.1.  plane_pixel_width . . . . . . . . . . . . . . . . . .  47
       4.8.2.  slice_pixel_width . . . . . . . . . . . . . . . . . .  48
       4.8.3.  slice_pixel_x . . . . . . . . . . . . . . . . . . . .  48
       4.8.4.  sample_difference . . . . . . . . . . . . . . . . . .  48
     4.9.  Slice Footer  . . . . . . . . . . . . . . . . . . . . . .  48
       4.9.1.  slice_size  . . . . . . . . . . . . . . . . . . . . .  49
       4.9.2.  error_status  . . . . . . . . . . . . . . . . . . . .  49
       4.9.3.  slice_crc_parity  . . . . . . . . . . . . . . . . . .  49
   5.  Restrictions  . . . . . . . . . . . . . . . . . . . . . . . .  49
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  50
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  51
     7.1.  Media Type Definition . . . . . . . . . . . . . . . . . .  51
   8.  Changelog . . . . . . . . . . . . . . . . . . . . . . . . . .  52
   9.  Normative References  . . . . . . . . . . . . . . . . . . . .  52
   10. Informative References  . . . . . . . . . . . . . . . . . . .  53

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   Appendix A.  Multi-theaded decoder implementation suggestions . .  55
   Appendix B.  Future handling of some streams created by non
           conforming encoders . . . . . . . . . . . . . . . . . . .  55
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  55

1.  Introduction

   This document describes FFV1, a lossless video encoding format.  The
   design of FFV1 considers the storage of image characteristics, data
   fixity, and the optimized use of encoding time and storage
   requirements.  FFV1 is designed to support a wide range of lossless
   video applications such as long-term audiovisual preservation,
   scientific imaging, screen recording, and other video encoding
   scenarios that seek to avoid the generational loss of lossy video
   encodings.

   This document defines version 0, 1 and 3 of FFV1.  The distinctions
   of the versions are provided throughout the document, but in summary:

   *  Version 0 of FFV1 was the original implementation of FFV1 and has
      been flagged as stable on April 14, 2006 [FFV1_V0].

   *  Version 1 of FFV1 adds support of more video bit depths and has
      been has been flagged as stable on April 24, 2009 [FFV1_V1].

   *  Version 2 of FFV1 only existed in experimental form and is not
      described by this document, but is available as a LyX file at
      https://github.com/FFmpeg/FFV1/
      blob/8ad772b6d61c3dd8b0171979a2cd9f11924d5532/ffv1.lyx
      (https://github.com/FFmpeg/FFV1/
      blob/8ad772b6d61c3dd8b0171979a2cd9f11924d5532/ffv1.lyx).

   *  Version 3 of FFV1 adds several features such as increased
      description of the characteristics of the encoding images and
      embedded CRC data to support fixity verification of the encoding.
      Version 3 has been flagged as stable on August 17, 2013 [FFV1_V3].

   This document assumes familiarity with mathematical and coding
   concepts such as Range coding [range-coding] and YCbCr color spaces
   [YCbCr].

   This specification describes the valid bitstream and how to decode
   such valid bitstream.  Bitstreams not conforming to this
   specification or how they are handled is outside this specification.
   A decoder could reject every invalid bitstream or attempt to perform
   error concealment or re-download or use a redundant copy of the
   invalid part or any other action it deems appropriate.

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2.  Notation and Conventions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.1.  Definitions

   "FFV1": choosen name of this video encoding format, short version of
   "FF Video 1", the letters "FF" coming from "FFmpeg", the name of the
   reference decoder, whose the first letters originaly means "Fast
   Forward".

   "Container": Format that encapsulates Frames (see Section 4.4) and
   (when required) a "Configuration Record" into a bitstream.

   "Sample": The smallest addressable representation of a color
   component or a luma component in a Frame.  Examples of Sample are
   Luma (Y), Blue-difference Chroma (Cb), Red-difference Chroma (Cr),
   Transparency, Red, Green, and Blue.

   "Symbol": A value stored in the bitstream, which is defined and
   decoded through one of the methods described in Table 4.

   "Line": A discrete component of a static image composed of Samples
   that represent a specific quantification of Samples of that image.

   "Plane": A discrete component of a static image composed of Lines
   that represent a specific quantification of Lines of that image.

   "Pixel": The smallest addressable representation of a color in a
   Frame.  It is composed of one or more Samples.

   "ESC": An ESCape Symbol to indicate that the Symbol to be stored is
   too large for normal storage and that an alternate storage method is
   used.

   "MSB": Most Significant Bit, the bit that can cause the largest
   change in magnitude of the Symbol.

   "VLC": Variable Length Code, a code that maps source symbols to a
   variable number of bits.

   "RGB": A reference to the method of storing the value of a Pixel by
   using three numeric values that represent Red, Green, and Blue.

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   "YCbCr": A reference to the method of storing the value of a Pixel by
   using three numeric values that represent the luma of the Pixel (Y)
   and the chroma of the Pixel (Cb and Cr).  YCbCr word is used for
   historical reasons and currently references any color space relying
   on 1 luma Sample and 2 chroma Samples, e.g.  YCbCr, YCgCo or ICtCp.
   The exact meaning of the three numeric values is unspecified.

2.2.  Conventions

2.2.1.  Pseudo-code

   The FFV1 bitstream is described in this document using pseudo-code.
   Note that the pseudo-code is used for clarity in order to illustrate
   the structure of FFV1 and not intended to specify any particular
   implementation.  The pseudo-code used is based upon the C programming
   language [ISO.9899.2018] and uses its "if/else", "while" and "for"
   keywords as well as functions defined within this document.

   In some instances, pseudo-code is presented in a two-column format
   such as shown in Figure 1.  In this form the "type" column provides a
   Symbol as defined in Table 4 that defines the storage of the data
   referenced in that same line of pseudo-code.

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   ExamplePseudoCode( ) {                                        |
       value                                                     | ur
   }                                                             |

       Figure 1: A depiction of type-labelled pseudo-code used within
                               this document.

2.2.2.  Arithmetic Operators

   Note: the operators and the order of precedence are the same as used
   in the C programming language [ISO.9899.2018], with the exception of
   ">>" (removal of implementation defined behavior) and "^" (power
   instead of XOR) operators which are re-defined within this section.

   "a + b" means a plus b.

   "a - b" means a minus b.

   "-a" means negation of a.

   "a * b" means a multiplied by b.

   "a / b" means a divided by b.

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   "a ^ b" means a raised to the b-th power.

   "a & b" means bit-wise "and" of a and b.

   "a | b" means bit-wise "or" of a and b.

   "a >> b" means arithmetic right shift of two's complement integer
   representation of a by b binary digits.  This is equivalent to
   dividing a by 2, b times, with rounding toward negative infinity.

   "a << b" means arithmetic left shift of two's complement integer
   representation of a by b binary digits.

2.2.3.  Assignment Operators

   "a = b" means a is assigned b.

   "a++" is equivalent to a is assigned a + 1.

   "a--" is equivalent to a is assigned a - 1.

   "a += b" is equivalent to a is assigned a + b.

   "a -= b" is equivalent to a is assigned a - b.

   "a *= b" is equivalent to a is assigned a * b.

2.2.4.  Comparison Operators

   "a > b" is true when a is greater than b.

   "a >= b" is true when a is greater than or equal to b.

   "a < b" is true when a is less than b.

   "a <= b" is true when a is less than or equal b.

   "a == b" is true when a is equal to b.

   "a != b" is true when a is not equal to b.

   "a && b" is true when both a is true and b is true.

   "a || b" is true when either a is true or b is true.

   "!a" is true when a is not true.

   "a ? b : c" if a is true, then b, otherwise c.

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2.2.5.  Mathematical Functions

   "floor(a)" means the largest integer less than or equal to a.

   "ceil(a)" means the smallest integer greater than or equal to a.

   "sign(a)" extracts the sign of a number, i.e. if a < 0 then -1, else
   if a > 0 then 1, else 0.

   "abs(a)" means the absolute value of a, i.e. "abs(a)" = "sign(a) *
   a".

   "log2(a)" means the base-two logarithm of a.

   "min(a,b)" means the smaller of two values a and b.

   "max(a,b)" means the larger of two values a and b.

   "median(a,b,c)" means the numerical middle value in a data set of a,
   b, and c, i.e. a+b+c-min(a,b,c)-max(a,b,c).

   "A <== B" means B implies A.

   "A <==> B" means A <== B , B <== A.

   a_(b) means the b-th value of a sequence of a

   a_(b,c) means the 'b,c'-th value of a sequence of a

2.2.6.  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.

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   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, a *= b

2.2.7.  Range

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

2.2.8.  NumBytes

   "NumBytes" is a non-negative integer that expresses the size in 8-bit
   octets of a particular FFV1 "Configuration Record" or "Frame".  FFV1
   relies on its Container to store the "NumBytes" values; see
   Section 4.3.3.

2.2.9.  Bitstream Functions

2.2.9.1.  remaining_bits_in_bitstream

   "remaining_bits_in_bitstream( NumBytes )" means the count of
   remaining bits after the pointer in that "Configuration Record" or
   "Frame".  It is computed from the "NumBytes" value multiplied by 8
   minus the count of bits of that "Configuration Record" or "Frame"
   already read by the bitstream parser.

2.2.9.2.  remaining_symbols_in_syntax

   "remaining_symbols_in_syntax( )" is true as long as the RangeCoder
   has not consumed all the given input bytes.

2.2.9.3.  byte_aligned

   "byte_aligned( )" is true if "remaining_bits_in_bitstream( NumBytes
   )" is a multiple of 8, otherwise false.

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2.2.9.4.  get_bits

   "get_bits( i )" is the action to read the next "i" bits in the
   bitstream, from most significant bit to least significant bit, and to
   return the corresponding value.  The pointer is increased by "i".

3.  Sample Coding

   For each "Slice" (as described in Section 4.5) of a Frame, the
   Planes, Lines, and Samples are coded in an order determined by the
   color space (see Section 3.7).  Each Sample is predicted by the
   median predictor as described in Section 3.3 from other Samples
   within the same Plane and the difference is stored using the method
   described in Section 3.8.

3.1.  Border

   A border is assumed for each coded "Slice" for the purpose of the
   median predictor and context according to the following rules:

   *  one column of Samples to the left of the coded slice is assumed as
      identical to the Samples of the leftmost column of the coded slice
      shifted down by one row.  The value of the topmost Sample of the
      column of Samples to the left of the coded slice is assumed to be
      "0"

   *  one column of Samples to the right of the coded slice is assumed
      as identical to the Samples of the rightmost column of the coded
      slice

   *  an additional column of Samples to the left of the coded slice and
      two rows of Samples above the coded slice are assumed to be "0"

   Figure 2 depicts a slice of 9 Samples "a,b,c,d,e,f,g,h,i" in a 3x3
   arrangement along with its assumed border.

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   +---+---+---+---+---+---+---+---+
   | 0 | 0 |   | 0 | 0 | 0 |   | 0 |
   +---+---+---+---+---+---+---+---+
   | 0 | 0 |   | 0 | 0 | 0 |   | 0 |
   +---+---+---+---+---+---+---+---+
   |   |   |   |   |   |   |   |   |
   +---+---+---+---+---+---+---+---+
   | 0 | 0 |   | a | b | c |   | c |
   +---+---+---+---+---+---+---+---+
   | 0 | a |   | d | e | f |   | f |
   +---+---+---+---+---+---+---+---+
   | 0 | d |   | g | h | i |   | i |
   +---+---+---+---+---+---+---+---+

      Figure 2: A depiction of FFV1's assumed border for a set example
                                  Samples.

3.2.  Samples

   Relative to any Sample "X", six other relatively positioned Samples
   from the coded Samples and presumed border are identified according
   to the labels used in Figure 3.  The labels for these relatively
   positioned Samples are used within the median predictor and context.

   +---+---+---+---+
   |   |   | T |   |
   +---+---+---+---+
   |   |tl | t |tr |
   +---+---+---+---+
   | L | l | X |   |
   +---+---+---+---+

       Figure 3: A depiction of how relatively positioned Samples are
                      referenced within this document.

   The labels for these relative Samples are made of the first letters
   of the words Top, Left and Right.

3.3.  Median Predictor

   The prediction for any Sample value at position "X" may be computed
   based upon the relative neighboring values of "l", "t", and "tl" via
   this equation:

   median(l, t, l + t - tl)

   Note, this prediction template is also used in [ISO.14495-1.1999] and
   [HuffYUV].

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   Exception for the median predictor: if "colorspace_type == 0 &&
   bits_per_raw_sample == 16 && ( coder_type == 1 || coder_type == 2 )"
   (see Section 4.2.5, Section 4.2.7 and Section 4.2.5), the following
   median predictor MUST be used:

   median(left16s, top16s, left16s + top16s - diag16s)

   where:

   left16s = l  >= 32768 ? ( l  - 65536 ) : l
   top16s  = t  >= 32768 ? ( t  - 65536 ) : t
   diag16s = tl >= 32768 ? ( tl - 65536 ) : tl

   Background: a two's complement 16-bit signed integer was used for
   storing Sample values in all known implementations of FFV1 bitstream.
   So in some circumstances, the most significant bit was wrongly
   interpreted (used as a sign bit instead of the 16th bit of an
   unsigned integer).  Note that when the issue was discovered, the only
   configuration of all known implementations being impacted is 16-bit
   YCbCr with no Pixel transformation with Range Coder coder, as other
   potentially impacted configurations (e.g. 15/16-bit JPEG2000-RCT with
   Range Coder coder, or 16-bit content with Golomb Rice coder) were
   implemented nowhere [ISO.15444-1.2016].  In the meanwhile, 16-bit
   JPEG2000-RCT with Range Coder coder was implemented without this
   issue in one implementation and validated by one conformance checker.
   It is expected (to be confirmed) to remove this exception for the
   median predictor in the next version of the FFV1 bitstream.

3.4.  Quantization Table Sets

   The FFV1 bitstream contains one or more Quantization Table Sets.
   Each Quantization Table Set contains exactly 5 Quantization Tables
   with each Quantization Table corresponding to one of the five
   Quantized Sample Differences.  For each Quantization Table, both the
   number of quantization steps and their distribution are stored in the
   FFV1 bitstream; each Quantization Table has exactly 256 entries, and
   the 8 least significant bits of the Quantized Sample Difference are
   used as index:

   Q_(j)[k] = quant_tables[i][j][k&255]

                                  Figure 4

   In this formula, "i" is the Quantization Table Set index, "j" is the
   Quantized Table index, "k" the Quantized Sample Difference.

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3.5.  Context

   Relative to any Sample "X", the Quantized Sample Differences "L-l",
   "l-tl", "tl-t", "T-t", and "t-tr" are used as context:

   context = Q_(0)[l - tl] +
             Q_(1)[tl - t] +
             Q_(2)[t - tr] +
             Q_(3)[L - l]  +
             Q_(4)[T - t]

                                  Figure 5

   If "context >= 0" then "context" is used and the difference between
   the Sample and its predicted value is encoded as is, else "-context"
   is used and the difference between the Sample and its predicted value
   is encoded with a flipped sign.

3.6.  Quantization Table Set Indexes

   For each Plane of each slice, a Quantization Table Set is selected
   from an index:

   *  For Y Plane, "quant_table_set_index[ 0 ]" index is used

   *  For Cb and Cr Planes, "quant_table_set_index[ 1 ]" index is used

   *  For extra Plane, "quant_table_set_index[ (version <= 3 ||
      chroma_planes) ? 2 : 1 ]" index is used

   Background: in first implementations of FFV1 bitstream, the index for
   Cb and Cr Planes was stored even if it is not used (chroma_planes set
   to 0), this index is kept for "version" <= 3 in order to keep
   compatibility with FFV1 bitstreams in the wild.

3.7.  Color spaces

   FFV1 supports several color spaces.  The count of allowed coded
   planes and the meaning of the extra Plane are determined by the
   selected color space.

   The FFV1 bitstream interleaves data in an order determined by the
   color space.  In YCbCr for each Plane, each Line is coded from top to
   bottom and for each Line, each Sample is coded from left to right.
   In JPEG2000-RCT for each Line from top to bottom, each Plane is coded
   and for each Plane, each Sample is encoded from left to right.

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3.7.1.  YCbCr

   This color space allows 1 to 4 Planes.

   The Cb and Cr Planes are optional, but if used then MUST be used
   together.  Omitting the Cb and Cr Planes codes the frames in
   grayscale without color data.

   An optional transparency Plane can be used to code transparency data.

   An FFV1 Frame using YCbCr MUST use one of the following arrangements:

   *  Y

   *  Y, Transparency

   *  Y, Cb, Cr

   *  Y, Cb, Cr, Transparency

   The Y Plane MUST be coded first.  If the Cb and Cr Planes are used
   then they MUST be coded after the Y Plane.  If a transparency Plane
   is used, then it MUST be coded last.

3.7.2.  RGB

   This color space allows 3 or 4 Planes.

   An optional transparency Plane can be used to code transparency data.

   JPEG2000-RCT is a Reversible Color Transform that codes RGB (red,
   green, blue) Planes losslessly in a modified YCbCr color space
   [ISO.15444-1.2016].  Reversible Pixel transformations between YCbCr
   and RGB use the following formulae.

   Cb = b - g
   Cr = r - g
   Y = g + (Cb + Cr) >> 2
   g = Y - (Cb + Cr) >> 2
   r = Cr + g
   b = Cb + g

                                  Figure 6

   Exception for the JPEG2000-RCT conversion: if "bits_per_raw_sample"
   is between 9 and 15 inclusive and "extra_plane" is 0, the following
   formulae for reversible conversions between YCbCr and RGB MUST be
   used instead of the ones above:

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   Cb = g - b
   Cr = r - b
   Y = b +(Cb + Cr) >> 2
   b = Y -(Cb + Cr) >> 2
   r = Cr + b
   g = Cb + b

                                  Figure 7

   Background: At the time of this writing, in all known implementations
   of FFV1 bitstream, when "bits_per_raw_sample" was between 9 and 15
   inclusive and "extra_plane" is 0, GBR Planes were used as BGR Planes
   during both encoding and decoding.  In the meanwhile, 16-bit
   JPEG2000-RCT was implemented without this issue in one implementation
   and validated by one conformance checker.  Methods to address this
   exception for the transform are under consideration for the next
   version of the FFV1 bitstream.

   Cb and Cr are positively offset by "1 << bits_per_raw_sample" after
   the conversion from RGB to the modified YCbCr and are negatively
   offseted by the same value before the conversion from the modified
   YCbCr to RGB, in order to have only non-negative values after the
   conversion.

   When FFV1 uses the JPEG2000-RCT, the horizontal Lines are interleaved
   to improve caching efficiency since it is most likely that the
   JPEG2000-RCT will immediately be converted to RGB during decoding.
   The interleaved coding order is also Y, then Cb, then Cr, and then,
   if used, transparency.

   As an example, a Frame that is two Pixels wide and two Pixels high,
   could comprise the following structure:

   +------------------------+------------------------+
   | Pixel(1,1)             | Pixel(2,1)             |
   | Y(1,1) Cb(1,1) Cr(1,1) | Y(2,1) Cb(2,1) Cr(2,1) |
   +------------------------+------------------------+
   | Pixel(1,2)             | Pixel(2,2)             |
   | Y(1,2) Cb(1,2) Cr(1,2) | Y(2,2) Cb(2,2) Cr(2,2) |
   +------------------------+------------------------+

   In JPEG2000-RCT, the coding order would be left to right and then top
   to bottom, with values interleaved by Lines and stored in this order:

   Y(1,1) Y(2,1) Cb(1,1) Cb(2,1) Cr(1,1) Cr(2,1) Y(1,2) Y(2,2) Cb(1,2)
   Cb(2,2) Cr(1,2) Cr(2,2)

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3.8.  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 JPEG2000-RCT), only the
   n (or n+1, in the case of JPEG2000-RCT) 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 JPEG2000-RCT or "bits_per_raw_sample" otherwise:

   coder_input = [(sample_difference + 2 ^ (bits - 1)) &
                 (2 ^ bits - 1)] - 2 ^ (bits - 1)

      Figure 8: Description of the coding of the Sample Difference in
                               the bitstream.

3.8.1.  Range Coding Mode

   Early experimental versions of FFV1 used the CABAC Arithmetic coder
   from H.264 as defined in [ISO.14496-10.2014] but due to the uncertain
   patent/royalty 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 [range-coding].

3.8.1.1.  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.  The length of the bytestream encoding n binary symbols is
   j_(n) bytes.

   r_(i) = floor( ( R_(i) * S_(i, C_(i)) ) / 2 ^ 8 )

     Figure 9: A formula of the read of a binary value in Range Binary
                                   mode.

   S_(i + 1, C_(i)) =  zero_state_(S_(i, C_(i)))  AND
              l_(i) =  L_(i)                      AND
              t_(i) =  R_(i) - r_(i)              <==
              b_(i) =  0                          <==>
              L_(i) <  R_(i) - r_(i)

   S_(i + 1, C_(i)) =  one_state_(S_(i, C_(i)))   AND
              l_(i) =  L_(i) - R_(i) + r_(i)      AND
              t_(i) =  r_(i)                      <==
              b_(i) =  1                          <==>
              L_(i) >= R_(i) - r_(i)

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                                 Figure 10

   S_(i + 1, k) = S_(i, k) <== C_(i) != k

                                 Figure 11

   R_(i + 1) =  2 ^ 8 * t_(i)                     AND
   L_(i + 1) =  2 ^ 8 * l_(i) + B_(j_(i))         AND
   j_(i + 1) =  j_(i) + 1                         <==
   t_(i)     <  2 ^ 8

   R_(i + 1) =  t_(i)                             AND
   L_(i + 1) =  l_(i)                             AND
   j_(i + 1) =  j_(i)                             <==
   t_(i)     >= 2 ^ 8

                                 Figure 12

   R_(0) = 65280

                                 Figure 13

   L_(0) = 2 ^ 8 * B_(0) + B_(1)

                                 Figure 14

   j_(0) = 2

                                 Figure 15

       range = 0xFF00;
       end   = 0;
       low   = get_bits(16);
       if (low >= range) {
           low = range;
           end = 1;
       }

       Figure 16: A pseudo-code description of the initial states in
                             Range Binary mode.

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   refill() {
       if (range < 256) {
           range = range * 256;
           low   = low * 256;
           if (!end) {
               c.low += get_bits(8);
               if (remaining_bits_in_bitstream( NumBytes ) == 0) {
                   end = 1;
               }
           }
       }
   }

        Figure 17: A pseudo-code description of refilling the Range
                         Binary Value coder buffer.

   get_rac(state) {
       rangeoff  = (range * state) / 256;
       range    -= rangeoff;
       if (low < range) {
           state = zero_state[state];
           refill();
           return 0;
       } else {
           low   -= range;
           state  = one_state[state];
           range  = rangeoff;
           refill();
           return 1;
       }
   }

        Figure 18: A pseudo-code description of the read of a binary
                        value in Range Binary mode.

3.8.1.1.1.  Termination

   The range coder can be used in three modes.

   *  In "Open mode" when decoding, every Symbol the reader attempts to
      read is available.  In this mode arbitrary data can have been
      appended without affecting the range coder output.  This mode is
      not used in FFV1.

   *  In "Closed mode" the length in bytes of the bytestream is provided
      to the range decoder.  Bytes beyond the length are read as 0 by
      the range decoder.  This is generally one byte shorter than the
      open mode.

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   *  In "Sentinel mode" the exact length in bytes is not known and thus
      the range decoder MAY read into the data that follows the range
      coded bytestream by one byte.  In "Sentinel mode", the end of the
      range coded bytestream is a binary Symbol with state 129, which
      value SHALL be discarded.  After reading this Symbol, the range
      decoder will have read one byte beyond the end of the range coded
      bytestream.  This way the byte position of the end can be
      determined.  Bytestreams written in "Sentinel mode" can be read in
      "Closed mode" if the length can be determined, in this case the
      last (sentinel) Symbol will be read non-corrupted and be of value
      0.

   Above describes the range decoding.  Encoding is defined as any
   process which produces a decodable bytestream.

   There are three places where range coder termination is needed in
   FFV1.  First is in the "Configuration Record", in this case the size
   of the range coded bytestream is known and handled as "Closed mode".
   Second is the switch from the "Slice Header" which is range coded to
   Golomb coded slices as "Sentinel mode".  Third is the end of range
   coded Slices which need to terminate before the CRC at their end.
   This can be handled as "Sentinel mode" or as "Closed mode" if the CRC
   position has been determined.

3.8.1.2.  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 that 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
   Figure 19.

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   int get_symbol(RangeCoder *c, uint8_t *state, int is_signed) {
       if (get_rac(c, state + 0) {
           return 0;
       }

       int e = 0;
       while (get_rac(c, state + 1 + min(e, 9)) { //1..10
           e++;
       }

       int a = 1;
       for (int i = e - 1; i >= 0; i--) {
           a = a * 2 + get_rac(c, state + 22 + min(i, 9));  // 22..31
       }

       if (!is_signed) {
           return a;
       }

       if (get_rac(c, state + 11 + min(e, 10))) { //11..21
           return -a;
       } else {
           return a;
       }
   }

     Figure 19: A pseudo-code description of the contexts of Range Non
                               Binary Values.

   "get_symbol" is used for the read out of "sample_difference"
   indicated in Figure 8.

   "get_rac" returns a boolean, computed from the bytestream as
   described in Figure 9 as a formula and in Figure 18 as pseudo-code.

3.8.1.3.  Initial Values for the Context Model

   When "keyframe" (see Section 4.4) value is 1, all Range coder state
   variables are set to their initial state.

3.8.1.4.  State Transition Table

   one_state_(i) =
          default_state_transition_(i) + state_transition_delta_(i)

                                 Figure 20

   zero_state_(i) = 256 - one_state_(256-i)

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                                 Figure 21

3.8.1.5.  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,

3.8.1.6.  Alternative State Transition Table

   The alternative state transition table has been built using iterative
   minimization of frame sizes and generally performs better than the
   default.  To use it, the "coder_type" (see Section 4.2.3) MUST be set
   to 2 and the difference to the default MUST be stored in the
   "Parameters", see Section 4.2.  The reference implementation of FFV1
   in FFmpeg uses Figure 22 by default at the time of this writing when
   Range coding is used.

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     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,

      Figure 22: Alternative state transition table for Range coding.

3.8.2.  Golomb Rice Mode

   The end of the bitstream of the Frame is padded with 0-bits until the
   bitstream contains a multiple of 8 bits.

3.8.2.1.  Signed Golomb Rice Codes

   This coding mode uses Golomb Rice codes.  The VLC is split into two
   parts.  The prefix stores the most significant bits and the suffix
   stores the k least significant bits or stores the whole number in the
   ESC case.

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   int get_ur_golomb(k) {
       for (prefix = 0; prefix < 12; prefix++) {
           if (get_bits(1)) {
               return get_bits(k) + (prefix << k);
           }
       }
       return get_bits(bits) + 11;
   }

      Figure 23: A pseudo-code description of the read of an unsigned
                        integer in Golomb Rice mode.

   int get_sr_golomb(k) {
       v = get_ur_golomb(k);
       if (v & 1) return - (v >> 1) - 1;
       else       return   (v >> 1);
   }

        Figure 24: A pseudo-code description of the read of a signed
                        integer in Golomb Rice mode.

3.8.2.1.1.  Prefix

                        +================+=======+
                        | bits           | value |
                        +================+=======+
                        | 1              | 0     |
                        +----------------+-------+
                        | 01             | 1     |
                        +----------------+-------+
                        | ...            | ...   |
                        +----------------+-------+
                        | 0000 0000 01   | 9     |
                        +----------------+-------+
                        | 0000 0000 001  | 10    |
                        +----------------+-------+
                        | 0000 0000 0001 | 11    |
                        +----------------+-------+
                        | 0000 0000 0000 | ESC   |
                        +----------------+-------+

                                 Table 1

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3.8.2.1.2.  Suffix

           +=========+========================================+
           +=========+========================================+
           | non ESC | the k least significant bits MSB first |
           +---------+----------------------------------------+
           | ESC     | the value - 11, in MSB first order     |
           +---------+----------------------------------------+

                                 Table 2

   ESC MUST NOT be used if the value can be coded as non ESC.

3.8.2.1.3.  Examples

   Table 3 shows practical examples of how Signed Golomb Rice Codes are
   decoded based on the series of bits extracted from the bitstream as
   described by the method above:

                  +=====+=======================+=======+
                  |  k  | bits                  | value |
                  +=====+=======================+=======+
                  |  0  | 1                     |     0 |
                  +-----+-----------------------+-------+
                  |  0  | 001                   |     2 |
                  +-----+-----------------------+-------+
                  |  2  | 1 00                  |     0 |
                  +-----+-----------------------+-------+
                  |  2  | 1 10                  |     2 |
                  +-----+-----------------------+-------+
                  |  2  | 01 01                 |     5 |
                  +-----+-----------------------+-------+
                  | any | 000000000000 10000000 |   139 |
                  +-----+-----------------------+-------+

                    Table 3: Examples of decoded Signed
                             Golomb Rice Codes.

3.8.2.2.  Run Mode

   Run mode is entered when the context is 0 and left as soon as a non-0
   difference is found.  The sample difference is identical to the
   predicted one.  The run and the first different sample difference are
   coded as defined in Section 3.8.2.4.1.

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3.8.2.2.1.  Run Length Coding

   The run value is encoded in two parts.  The prefix part stores the
   more significant part of the run as well as adjusting the "run_index"
   that determines the number of bits in the less significant part of
   the run.  The second 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_bits(1)) {
           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" array is also used within [ISO.14495-1.1999].

3.8.2.3.  Sign extension

   "sign_extend" is the function of increasing the number of bits of an
   input binary number in twos complement signed number representation
   while preserving the input number's sign (positive/negative) and
   value, in order to fit in the output bit width.  It MAY be computed
   with:

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   sign_extend(input_number, input_bits) {
       negative_bias = 1 << (input_bits - 1);
       bits_mask = negative_bias - 1;
       output_number = input_number & bits_mask; // Remove negative bit
       is_negative = input_number & negative_bias; // Test negative bit
       if (is_negative)
           output_number -= negative_bias;
       return output_number
   }

3.8.2.4.  Scalar Mode

   Each difference is coded with the per context mean prediction removed
   and a per context value for k.

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   get_vlc_symbol(state) {
       i = state->count;
       k = 0;
       while (i < state->error_sum) {
           k++;
           i += i;
       }

       v = get_sr_golomb(k);

       if (2 * state->drift < -state->count) {
           v = -1 - v;
       }

       ret = sign_extend(v + state->bias, bits);

       state->error_sum += abs(v);
       state->drift     += v;

       if (state->count == 128) {
           state->count     >>= 1;
           state->drift     >>= 1;
           state->error_sum >>= 1;
       }
       state->count++;
       if (state->drift <= -state->count) {
           state->bias = max(state->bias - 1, -128);

           state->drift = max(state->drift + state->count,
                              -state->count + 1);
       } else if (state->drift > 0) {
           state->bias = min(state->bias + 1, 127);

           state->drift = min(state->drift - state->count, 0);
       }

       return ret;
   }

3.8.2.4.1.  Golomb Rice Sample Difference Coding

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

       diff = get_vlc_symbol(context_state);
       if (diff >= 0) {
           diff++;
       }

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   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.

3.8.2.5.  Initial Values for the VLC context state

   When "keyframe" (see Section 4.4) value is 1, all coder state
   variables are set to their initial state.

       drift     = 0;
       error_sum = 4;
       bias      = 0;
       count     = 1;

4.  Bitstream

   An FFV1 bitstream is composed of a series of one or more Frames and
   (when required) a "Configuration Record".

   Within the following sub-sections, pseudo-code is used, as described
   in Section 2.2.1, to explain the structure of each FFV1 bitstream
   component.  Table 4 lists symbols used to annotate that pseudo-code
   in order to define the storage of the data referenced in that line of
   pseudo-code.

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       +========+=================================================+
       | Symbol | Definition                                      |
       +========+=================================================+
       | u(n)   | unsigned big endian integer Symbol using n bits |
       +--------+-------------------------------------------------+
       | sg     | Golomb Rice coded signed scalar Symbol coded    |
       |        | with the method described in Section 3.8.2      |
       +--------+-------------------------------------------------+
       | br     | Range coded Boolean (1-bit) Symbol with the     |
       |        | method described in Section 3.8.1.1             |
       +--------+-------------------------------------------------+
       | ur     | Range coded unsigned scalar Symbol coded with   |
       |        | the method described in Section 3.8.1.2         |
       +--------+-------------------------------------------------+
       | sr     | Range coded signed scalar Symbol coded with the |
       |        | method described in Section 3.8.1.2             |
       +--------+-------------------------------------------------+
       | sd     | Sample difference Symbol coded with the method  |
       |        | described in Section 3.8                        |
       +--------+-------------------------------------------------+

           Table 4: Definition of pseudo-code symbols for this
                                document.

   The following MUST be provided by external means during
   initialization of the decoder:

   "frame_pixel_width" is defined as Frame width in Pixels.

   "frame_pixel_height" is defined as Frame height in Pixels.

   Default values at the decoder initialization phase:

   "ConfigurationRecordIsPresent" is set to 0.

4.1.  Quantization Table Set

   The Quantization Table Sets are stored by storing the number of equal
   entries -1 of the first half of the table (represented as "len - 1"
   in the pseudo-code below) using the method described in
   Section 3.8.1.2.  The second half doesn't need to be stored as it is
   identical to the first with flipped sign. "scale" and "len_count[ i
   ][ j ]" are temporary values used for the computing of
   "context_count[ i ]" and are not used outside Quantization Table Set
   pseudo-code.

   Example:

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

   Stored values: 1, 3, 1

   "QuantizationTableSet" has its own initial states, all set to 128.

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

   "MAX_CONTEXT_INPUTS" is 5.

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   QuantizationTable(i, j, scale) {                              |
       v = 0                                                     |
       for (k = 0; k < 128;) {                                   |
           len - 1                                               | ur
           for (n = 0; n < len; n++) {                           |
               quant_tables[ i ][ j ][ k ] = scale * v           |
               k++                                               |
           }                                                     |
           v++                                                   |
       }                                                         |
       for (k = 1; k < 128; k++) {                               |
           quant_tables[ i ][ j ][ 256 - k ] = \                 |
           -quant_tables[ i ][ j ][ k ]                          |
       }                                                         |
       quant_tables[ i ][ j ][ 128 ] = \                         |
       -quant_tables[ i ][ j ][ 127 ]                            |
       len_count[ i ][ j ] = v                                   |
   }                                                             |

4.1.1.  quant_tables

   "quant_tables[ i ][ j ][ k ]" indicates the quantification table
   value of the Quantized Sample Difference "k" of the Quantization
   Table "j" of the Set Quantization Table Set "i".

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4.1.2.  context_count

   "context_count[ i ]" indicates the count of contexts for Quantization
   Table Set "i". "context_count[ i ]" MUST be less than or equal to
   32768.

4.2.  Parameters

   The "Parameters" section contains significant characteristics about
   the decoding configuration used for all instances of Frame (in FFV1
   version 0 and 1) or the whole FFV1 bitstream (other versions),
   including the stream version, color configuration, and quantization
   tables.  Figure 25 describes the contents of the bitstream.

   "Parameters" has its own initial states, all set to 128.

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   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   Parameters( ) {                                               |
       version                                                   | ur
       if (version >= 3) {                                       |
           micro_version                                         | ur
       }                                                         |
       coder_type                                                | ur
       if (coder_type > 1) {                                     |
           for (i = 1; i < 256; i++) {                           |
               state_transition_delta[ i ]                       | sr
           }                                                     |
       }                                                         |
       colorspace_type                                           | ur
       if (version >= 1) {                                       |
           bits_per_raw_sample                                   | ur
       }                                                         |
       chroma_planes                                             | br
       log2_h_chroma_subsample                                   | ur
       log2_v_chroma_subsample                                   | ur
       extra_plane                                               | br
       if (version >= 3) {                                       |
           num_h_slices - 1                                      | ur
           num_v_slices - 1                                      | ur
           quant_table_set_count                                 | ur
       }                                                         |
       for (i = 0; i < quant_table_set_count; i++) {             |
           QuantizationTableSet( i )                             |
       }                                                         |
       if (version >= 3) {                                       |
           for (i = 0; i < quant_table_set_count; i++) {         |
               states_coded                                      | br
               if (states_coded) {                               |
                   for (j = 0; j < context_count[ i ]; j++) {    |
                       for (k = 0; k < CONTEXT_SIZE; k++) {      |
                           initial_state_delta[ i ][ j ][ k ]    | sr
                       }                                         |
                   }                                             |
               }                                                 |
           }                                                     |
           ec                                                    | ur
           intra                                                 | ur
       }                                                         |
   }                                                             |

      Figure 25: A pseudo-code description of the bitstream contents.

   CONTEXT_SIZE is 32.

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4.2.1.  version

   "version" specifies the version of the FFV1 bitstream.

   Each version is incompatible with other versions: decoders SHOULD
   reject FFV1 bitstreams due to an unknown version.

   Decoders SHOULD reject FFV1 bitstreams with version <= 1 &&
   ConfigurationRecordIsPresent == 1.

   Decoders SHOULD reject FFV1 bitstreams with version >= 3 &&
   ConfigurationRecordIsPresent == 0.

                    +=======+=========================+
                    | value | version                 |
                    +=======+=========================+
                    | 0     | FFV1 version 0          |
                    +-------+-------------------------+
                    | 1     | FFV1 version 1          |
                    +-------+-------------------------+
                    | 2     | reserved*               |
                    +-------+-------------------------+
                    | 3     | FFV1 version 3          |
                    +-------+-------------------------+
                    | Other | reserved for future use |
                    +-------+-------------------------+

                                  Table 5

   * Version 2 was experimental and this document does not describe it.

4.2.2.  micro_version

   "micro_version" specifies the micro-version of the FFV1 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 FFV1
   bitstreams due to an unknown micro-version equal or above the micro-
   version considered as stable.

   Meaning of "micro_version" for "version" 3:

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                    +=======+=========================+
                    | value | micro_version           |
                    +=======+=========================+
                    | 0...3 | reserved*               |
                    +-------+-------------------------+
                    | 4     | first stable variant    |
                    +-------+-------------------------+
                    | Other | reserved for future use |
                    +-------+-------------------------+

                        Table 6: The definitions for
                      "micro_version" values for FFV1
                                 version 3.

   * development versions may be incompatible with the stable variants.

4.2.3.  coder_type

   "coder_type" specifies the coder used.

        +=======+=================================================+
        | value | coder used                                      |
        +=======+=================================================+
        | 0     | Golomb Rice                                     |
        +-------+-------------------------------------------------+
        | 1     | Range Coder with default state transition table |
        +-------+-------------------------------------------------+
        | 2     | Range Coder with custom state transition table  |
        +-------+-------------------------------------------------+
        | Other | reserved for future use                         |
        +-------+-------------------------------------------------+

                                  Table 7

   Restrictions:

   If "coder_type" is 0, then "bits_per_raw_sample" SHOULD NOT be > 8.

   Background: At the time of this writing, there is no known
   implementation of FFV1 bitstream supporting Golomb Rice algorithm
   with "bits_per_raw_sample" greater than 8, and Range Coder is
   prefered.

4.2.4.  state_transition_delta

   "state_transition_delta" specifies the Range coder custom state
   transition table.

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   If "state_transition_delta" is not present in the FFV1 bitstream, all
   Range coder custom state transition table elements are assumed to be
   0.

4.2.5.  colorspace_type

   "colorspace_type" specifies the color space encoded, the pixel
   transformation used by the encoder, the extra plane content, as well
   as interleave method.

   +=======+==============+================+==============+============+
   | value | color space  | pixel          | extra plane  | interleave |
   |       | encoded      | transformation | content      | method     |
   +=======+==============+================+==============+============+
   | 0     | YCbCr        | None           | Transparency | Plane then |
   |       |              |                |              | Line       |
   +-------+--------------+----------------+--------------+------------+
   | 1     | RGB          | JPEG2000-RCT   | Transparency | Line then  |
   |       |              |                |              | Plane      |
   +-------+--------------+----------------+--------------+------------+
   | Other | reserved     | reserved for   | reserved for | reserved   |
   |       | for future   | future use     | future use   | for future |
   |       | use          |                |              | use        |
   +-------+--------------+----------------+--------------+------------+

                                  Table 8

   FFV1 bitstreams with "colorspace_type" == 1 && ("chroma_planes" !=
   1 || "log2_h_chroma_subsample" != 0 || "log2_v_chroma_subsample" !=
   0) are not part of this specification.

4.2.6.  chroma_planes

   "chroma_planes" indicates if chroma (color) Planes are present.

                 +=======+===============================+
                 | value | presence                      |
                 +=======+===============================+
                 | 0     | chroma Planes are not present |
                 +-------+-------------------------------+
                 | 1     | chroma Planes are present     |
                 +-------+-------------------------------+

                                  Table 9

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4.2.7.  bits_per_raw_sample

   "bits_per_raw_sample" indicates the number of bits for each Sample.
   Inferred to be 8 if not present.

                +=======+=================================+
                | value | bits for each sample            |
                +=======+=================================+
                | 0     | reserved*                       |
                +-------+---------------------------------+
                | Other | the actual bits for each Sample |
                +-------+---------------------------------+

                                  Table 10

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

4.2.8.  log2_h_chroma_subsample

   "log2_h_chroma_subsample" indicates the subsample factor, stored in
   powers to which the number 2 is raised, between luma and chroma width
   ("chroma_width = 2 ^ -log2_h_chroma_subsample * luma_width").

4.2.9.  log2_v_chroma_subsample

   "log2_v_chroma_subsample" indicates the subsample factor, stored in
   powers to which the number 2 is raised, between luma and chroma
   height ("chroma_height = 2 ^ -log2_v_chroma_subsample *
   luma_height").

4.2.10.  extra_plane

   "extra_plane" indicates if an extra Plane is present.

                  +=======+============================+
                  | value | presence                   |
                  +=======+============================+
                  | 0     | extra Plane is not present |
                  +-------+----------------------------+
                  | 1     | extra Plane is present     |
                  +-------+----------------------------+

                                 Table 11

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4.2.11.  num_h_slices

   "num_h_slices" indicates the number of horizontal elements of the
   slice raster.

   Inferred to be 1 if not present.

4.2.12.  num_v_slices

   "num_v_slices" indicates the number of vertical elements of the slice
   raster.

   Inferred to be 1 if not present.

4.2.13.  quant_table_set_count

   "quant_table_set_count" indicates the number of Quantization
   Table Sets. "quant_table_set_count" MUST be less than or equal to 8.

   Inferred to be 1 if not present.

   MUST NOT be 0.

4.2.14.  states_coded

   "states_coded" indicates if the respective Quantization Table Set has
   the initial states coded.

   Inferred to be 0 if not present.

                +=======+================================+
                | value | initial states                 |
                +=======+================================+
                | 0     | initial states are not present |
                |       | and are assumed to be all 128  |
                +-------+--------------------------------+
                | 1     | initial states are present     |
                +-------+--------------------------------+

                                 Table 12

4.2.15.  initial_state_delta

   "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

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                                 Figure 26

   initial_state[ i ][ j ][ k ] =
          ( pred + initial_state_delta[ i ][ j ][ k ] ) & 255

                                 Figure 27

4.2.16.  ec

   "ec" indicates the error detection/correction type.

        +=======+=================================================+
        | value | error detection/correction type                 |
        +=======+=================================================+
        | 0     | 32-bit CRC in "ConfigurationRecord"             |
        +-------+-------------------------------------------------+
        | 1     | 32-bit CRC in "Slice" and "ConfigurationRecord" |
        +-------+-------------------------------------------------+
        | Other | reserved for future use                         |
        +-------+-------------------------------------------------+

                                  Table 13

4.2.17.  intra

   "intra" indicates the constraint on "keyframe" in each instance of
   Frame.

   Inferred to be 0 if not present.

     +=======+=======================================================+
     | value | relationship                                          |
     +=======+=======================================================+
     | 0     | "keyframe" can be 0 or 1 (non keyframes or keyframes) |
     +-------+-------------------------------------------------------+
     | 1     | "keyframe" MUST be 1 (keyframes only)                 |
     +-------+-------------------------------------------------------+
     | Other | reserved for future use                               |
     +-------+-------------------------------------------------------+

                                  Table 14

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4.3.  Configuration Record

   In the case of a FFV1 bitstream with "version >= 3", a "Configuration
   Record" is stored in the underlying Container as described in
   Section 4.3.3.  It contains the "Parameters" used for all instances
   of Frame.  The size of the "Configuration Record", "NumBytes", is
   supplied by the underlying Container.

   pseudo-code                                                | type
   -----------------------------------------------------------|-----
   ConfigurationRecord( NumBytes ) {                          |
       ConfigurationRecordIsPresent = 1                       |
       Parameters( )                                          |
       while (remaining_symbols_in_syntax(NumBytes - 4)) {    |
           reserved_for_future_use                            | br/ur/sr
       }                                                      |
       configuration_record_crc_parity                        | u(32)
   }                                                          |

4.3.1.  reserved_for_future_use

   "reserved_for_future_use" is a placeholder for future updates of this
   specification.

   Encoders conforming to this version of this specification SHALL NOT
   write "reserved_for_future_use".

   Decoders conforming to this version of this specification SHALL
   ignore "reserved_for_future_use".

4.3.2.  configuration_record_crc_parity

   "configuration_record_crc_parity" 32 bits that are chosen 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 polynomial used is described in Section 4.9.3.

4.3.3.  Mapping FFV1 into Containers

   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 formats:

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4.3.3.1.  AVI File Format

   The "Configuration Record" extends the stream format chunk ("AVI ",
   "hdlr", "strl", "strf") with the ConfigurationRecord bitstream.

   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.

4.3.3.2.  ISO Base Media File Format

   The "Configuration Record" extends the sample description box
   ("moov", "trak", "mdia", "minf", "stbl", "stsd") with a "glbl" box
   that contains the ConfigurationRecord bitstream.  See
   [ISO.14496-12.2015] 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.

4.3.3.3.  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".

4.3.3.4.  Matroska File Format

   FFV1 SHOULD use "V_FFV1" as the Matroska "Codec ID".  For FFV1
   versions 2 or less, the Matroska "CodecPrivate" Element SHOULD NOT be
   used.  For FFV1 versions 3 or greater, the Matroska "CodecPrivate"
   Element MUST contain the FFV1 "Configuration Record" structure and no
   other data.  See [Matroska] for more information about elements.

   "NumBytes" is defined as the "Element Data Size" of the
   "CodecPrivate" Element.

4.4.  Frame

   A Frame is an encoded representation of a complete static image.  The
   whole Frame is provided by the underlaying container.

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   A Frame consists of the "keyframe" field, "Parameters" (if "version"
   <= 1), and a sequence of independent slices.  The pseudo-code below
   describes the contents of a Frame.

   "keyframe" field has its own initial state, set to 128.

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   Frame( NumBytes ) {                                           |
       keyframe                                                  | br
       if (keyframe && !ConfigurationRecordIsPresent {           |
           Parameters( )                                         |
       }                                                         |
       while (remaining_bits_in_bitstream( NumBytes )) {         |
           Slice( )                                              |
       }                                                         |
   }                                                             |

   Architecture overview of slices in a Frame:

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    +=================================================================+
    +=================================================================+
    | first slice header                                              |
    +-----------------------------------------------------------------+
    | first slice content                                             |
    +-----------------------------------------------------------------+
    | first slice footer                                              |
    +-----------------------------------------------------------------+
    | --------------------------------------------------------------- |
    +-----------------------------------------------------------------+
    | second slice header                                             |
    +-----------------------------------------------------------------+
    | second slice content                                            |
    +-----------------------------------------------------------------+
    | second slice footer                                             |
    +-----------------------------------------------------------------+
    | --------------------------------------------------------------- |
    +-----------------------------------------------------------------+
    | ...                                                             |
    +-----------------------------------------------------------------+
    | --------------------------------------------------------------- |
    +-----------------------------------------------------------------+
    | last slice header                                               |
    +-----------------------------------------------------------------+
    | last slice content                                              |
    +-----------------------------------------------------------------+
    | last slice footer                                               |
    +-----------------------------------------------------------------+

                                  Table 15

4.5.  Slice

   A "Slice" is an independent spatial sub-section of a Frame that is
   encoded separately from another region of the same Frame.  The use of
   more than one "Slice" per Frame can be useful for taking advantage of
   the opportunities of multithreaded encoding and decoding.

   A "Slice" consists of a "Slice Header" (when relevant), a "Slice
   Content", and a "Slice Footer" (when relevant).  The pseudo-code
   below describes the contents of a "Slice".

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   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   Slice( ) {                                                    |
       if (version >= 3) {                                       |
           SliceHeader( )                                        |
       }                                                         |
       SliceContent( )                                           |
       if (coder_type == 0) {                                    |
           while (!byte_aligned()) {                             |
               padding                                           | u(1)
           }                                                     |
       }                                                         |
       if (version <= 1) {                                       |
           while (remaining_bits_in_bitstream( NumBytes ) != 0) {|
               reserved                                          | u(1)
           }                                                     |
       }                                                         |
       if (version >= 3) {                                       |
           SliceFooter( )                                        |
       }                                                         |
   }                                                             |

   "padding" specifies a bit without any significance and used only for
   byte alignment.  MUST be 0.

   "reserved" specifies a bit without any significance in this revision
   of the specification and may have a significance in a later revision
   of this specification.

   Encoders SHOULD NOT fill "reserved".

   Decoders SHOULD ignore "reserved".

4.6.  Slice Header

   A "Slice Header" provides information about the decoding
   configuration of the "Slice", such as its spatial position, size, and
   aspect ratio.  The pseudo-code below describes the contents of the
   "Slice Header".

   "Slice Header" has its own initial states, all set to 128.

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   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   SliceHeader( ) {                                              |
       slice_x                                                   | ur
       slice_y                                                   | ur
       slice_width - 1                                           | ur
       slice_height - 1                                          | ur
       for (i = 0; i < quant_table_set_index_count; i++) {       |
           quant_table_set_index[ i ]                            | ur
       }                                                         |
       picture_structure                                         | ur
       sar_num                                                   | ur
       sar_den                                                   | ur
   }                                                             |

4.6.1.  slice_x

   "slice_x" indicates the x position on the slice raster formed by
   num_h_slices.

   Inferred to be 0 if not present.

4.6.2.  slice_y

   "slice_y" indicates the y position on the slice raster formed by
   num_v_slices.

   Inferred to be 0 if not present.

4.6.3.  slice_width

   "slice_width" indicates the width on the slice raster formed by
   num_h_slices.

   Inferred to be 1 if not present.

4.6.4.  slice_height

   "slice_height" indicates the height on the slice raster formed by
   num_v_slices.

   Inferred to be 1 if not present.

4.6.5.  quant_table_set_index_count

   "quant_table_set_index_count" is defined as:

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   1 + ( ( chroma_planes || version <= 3 ) ? 1 : 0 )
       + ( extra_plane ? 1 : 0 )

4.6.6.  quant_table_set_index

   "quant_table_set_index" indicates the Quantization Table Set index to
   select the Quantization Table Set and the initial states for the
   "Slice Content".

   Inferred to be 0 if not present.

4.6.7.  picture_structure

   "picture_structure" specifies the temporal and spatial relationship
   of each Line of the Frame.

   Inferred to be 0 if not present.

                    +=======+=========================+
                    | value | picture structure used  |
                    +=======+=========================+
                    | 0     | unknown                 |
                    +-------+-------------------------+
                    | 1     | top field first         |
                    +-------+-------------------------+
                    | 2     | bottom field first      |
                    +-------+-------------------------+
                    | 3     | progressive             |
                    +-------+-------------------------+
                    | Other | reserved for future use |
                    +-------+-------------------------+

                                  Table 16

4.6.8.  sar_num

   "sar_num" specifies the Sample aspect ratio numerator.

   Inferred to be 0 if not present.

   A value of 0 means that aspect ratio is unknown.

   Encoders MUST write 0 if Sample aspect ratio is unknown.

   If "sar_den" is 0, decoders SHOULD ignore the encoded value and
   consider that "sar_num" is 0.

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4.6.9.  sar_den

   "sar_den" specifies the Sample aspect ratio denominator.

   Inferred to be 0 if not present.

   A value of 0 means that aspect ratio is unknown.

   Encoders MUST write 0 if Sample aspect ratio is unknown.

   If "sar_num" is 0, decoders SHOULD ignore the encoded value and
   consider that "sar_den" is 0.

4.7.  Slice Content

   A "Slice Content" contains all Line elements part of the "Slice".

   Depending on the configuration, Line elements are ordered by Plane
   then by row (YCbCr) or by row then by Plane (RGB).

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   SliceContent( ) {                                             |
       if (colorspace_type == 0) {                               |
           for (p = 0; p < primary_color_count; p++) {           |
               for (y = 0; y < plane_pixel_height[ p ]; y++) {   |
                   Line( p, y )                                  |
               }                                                 |
           }                                                     |
       } else if (colorspace_type == 1) {                        |
           for (y = 0; y < slice_pixel_height; y++) {            |
               for (p = 0; p < primary_color_count; p++) {       |
                   Line( p, y )                                  |
               }                                                 |
           }                                                     |
       }                                                         |
   }                                                             |

4.7.1.  primary_color_count

   "primary_color_count" is defined as:

   1 + ( chroma_planes ? 2 : 0 ) + ( extra_plane ? 1 : 0 )

4.7.2.  plane_pixel_height

   "plane_pixel_height[ p ]" is the height in Pixels of Plane p of the
   "Slice".  It is defined as:

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   chroma_planes == 1 && (p == 1 || p == 2)
       ? ceil(slice_pixel_height / (1 << log2_v_chroma_subsample))
       : slice_pixel_height

4.7.3.  slice_pixel_height

   "slice_pixel_height" is the height in pixels of the slice.  It is
   defined as:

   floor(
           ( slice_y + slice_height )
           * slice_pixel_height
           / num_v_slices
       ) - slice_pixel_y.

4.7.4.  slice_pixel_y

   "slice_pixel_y" is the slice vertical position in pixels.  It is
   defined as:

   floor( slice_y * frame_pixel_height / num_v_slices )

4.8.  Line

   A Line is a list of the sample differences (relative to the
   predictor) of primary color components.  The pseudo-code below
   describes the contents of the Line.

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   Line( p, y ) {                                                |
       if (colorspace_type == 0) {                               |
           for (x = 0; x < plane_pixel_width[ p ]; x++) {        |
               sample_difference[ p ][ y ][ x ]                  | sd
           }                                                     |
       } else if (colorspace_type == 1) {                        |
           for (x = 0; x < slice_pixel_width; x++) {             |
               sample_difference[ p ][ y ][ x ]                  | sd
           }                                                     |
       }                                                         |
   }                                                             |

4.8.1.  plane_pixel_width

   "plane_pixel_width[ p ]" is the width in Pixels of Plane p of the
   "Slice".  It is defined as:

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   chroma\_planes == 1 && (p == 1 || p == 2)
       ? ceil( slice_pixel_width / (1 << log2_h_chroma_subsample) )
       : slice_pixel_width.

4.8.2.  slice_pixel_width

   "slice_pixel_width" is the width in Pixels of the slice.  It is
   defined as:

   floor(
           ( slice_x + slice_width )
           * slice_pixel_width
           / num_h_slices
       ) - slice_pixel_x

4.8.3.  slice_pixel_x

   "slice_pixel_x" is the slice horizontal position in Pixels.  It is
   defined as:

   floor( slice_x * frame_pixel_width / num_h_slices )

4.8.4.  sample_difference

   "sample_difference[ p ][ y ][ x ]" is the sample difference for
   Sample at Plane "p", y position "y", and x position "x".  The Sample
   value is computed based on median predictor and context described in
   Section 3.2.

4.9.  Slice Footer

   A "Slice Footer" provides information about slice size and
   (optionally) parity.  The pseudo-code below describes the contents of
   the "Slice Footer".

   Note: "Slice Footer" is always byte aligned.

   pseudo-code                                                   | type
   --------------------------------------------------------------|-----
   SliceFooter( ) {                                              |
       slice_size                                                | u(24)
       if (ec) {                                                 |
           error_status                                          | u(8)
           slice_crc_parity                                      | u(32)
       }                                                         |
   }                                                             |

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4.9.1.  slice_size

   "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 parallel decoding as well as
   error resilience.

4.9.2.  error_status

   "error_status" specifies the error status.

             +=======+======================================+
             | value | error status                         |
             +=======+======================================+
             | 0     | no error                             |
             +-------+--------------------------------------+
             | 1     | slice contains a correctable error   |
             +-------+--------------------------------------+
             | 2     | slice contains a uncorrectable error |
             +-------+--------------------------------------+
             | Other | reserved for future use              |
             +-------+--------------------------------------+

                                 Table 17

4.9.3.  slice_crc_parity

   "slice_crc_parity" 32 bits that are chosen 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 polynomial used is the standard IEEE CRC polynomial
   (0x104C11DB7), with initial value 0, without pre-inversion and
   without post-inversion.

5.  Restrictions

   To ensure that fast multithreaded decoding is possible, starting with
   version 3 and if "frame_pixel_width * frame_pixel_height" is more
   than 101376, "slice_width * slice_height" MUST be less or equal to
   "num_h_slices * num_v_slices / 4".  Note: 101376 is the frame size in
   Pixels of a 352x288 frame also known as CIF ("Common Intermediate
   Format") frame size format.

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   For each Frame, each position in the slice raster MUST be filled by
   one and only one slice of the Frame (no missing slice position, no
   slice overlapping).

   For each Frame with "keyframe" value of 0, each slice MUST have the
   same value of "slice_x", "slice_y", "slice_width", "slice_height" as
   a slice in the previous Frame.

6.  Security Considerations

   Like any other codec, (such as [RFC6716]), FFV1 should not be used
   with insecure ciphers or cipher-modes that are vulnerable to known
   plaintext attacks.  Some of the header bits as well as the padding
   are easily predictable.

   Implementations of the FFV1 codec need to take appropriate security
   considerations into account, as outlined in [RFC4732].  It is
   extremely important for the decoder to be robust against malicious
   payloads.  Malicious payloads MUST NOT cause the decoder to overrun
   its allocated memory or to take an excessive amount of resources to
   decode.  The same applies to the encoder, even though problems in
   encoders are typically rarer.  Malicious video streams MUST NOT cause
   the encoder to misbehave because this would allow an attacker to
   attack transcoding gateways.  A frequent security problem in image
   and video codecs is failure to check for integer overflows.  An
   example is allocating "frame_pixel_width * frame_pixel_height" in
   Pixel count computations without considering that the multiplication
   result may have overflowed the arithmetic types range.  The range
   coder could, if implemented naively, read one byte over the end.  The
   implementation MUST ensure that no read outside allocated and
   initialized memory occurs.

   None of the content carried in FFV1 is intended to be executable.

   The reference implementation [REFIMPL] contains no known buffer
   overflow or cases where a specially crafted packet or video segment
   could cause a significant increase in CPU load.

   The reference implementation [REFIMPL] was validated in the following
   conditions:

   *  Sending the decoder valid packets generated by the reference
      encoder and verifying that the decoder's output matches the
      encoder's input.

   *  Sending the decoder packets generated by the reference encoder and
      then subjected to random corruption.

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   *  Sending the decoder random packets that are not FFV1.

   In all of the conditions above, the decoder and encoder was run
   inside the [VALGRIND] memory debugger as well as clangs address
   sanitizer [Address-Sanitizer], which track reads and writes to
   invalid memory regions as well as the use of uninitialized memory.
   There were no errors reported on any of the tested conditions.

7.  IANA Considerations

   The IANA is requested to register the following values:

7.1.  Media Type Definition

   This registration is done using the template defined in [RFC6838] and
   following [RFC4855].

   Type name: video

   Subtype name: FFV1

   Required parameters: None.

   Optional parameters: These parameters are used to signal the
   capabilities of a receiver implementation.  These parameters MUST NOT
   be used for any other purpose.

   *  "version": The "version" of the FFV1 encoding as defined by
      Section 4.2.1.

   *  "micro_version": The "micro_version" of the FFV1 encoding as
      defined by Section 4.2.2.

   *  "coder_type": The "coder_type" of the FFV1 encoding as defined by
      Section 4.2.3.

   *  "colorspace_type": The "colorspace_type" of the FFV1 encoding as
      defined by Section 4.2.5.

   *  "bits_per_raw_sample": The "bits_per_raw_sample" of the FFV1
      encoding as defined by Section 4.2.7.

   *  "max_slices": The value of "max_slices" is an integer indicating
      the maximum count of slices with a frames of the FFV1 encoding.

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   Encoding considerations: This media type is defined for encapsulation
   in several audiovisual container formats and contains binary data;
   see Section 4.3.3.  This media type is framed binary data; see
   Section 4.8 of [RFC6838].

   Security considerations: See Section 6 of this document.

   Interoperability considerations: None.

   Published specification: RFC XXXX.

   [RFC Editor: Upon publication as an RFC, please replace "XXXX" with
   the number assigned to this document and remove this note.]

   Applications which use this media type: Any application that requires
   the transport of lossless video can use this media type.  Some
   examples are, but not limited to screen recording, scientific
   imaging, and digital video preservation.

   Fragment identifier considerations: N/A.

   Additional information: None.

   Person & email address to contact for further information: Michael
   Niedermayer michael@niedermayer.cc (mailto:michael@niedermayer.cc)

   Intended usage: COMMON

   Restrictions on usage: None.

   Author: Dave Rice dave@dericed.com (mailto:dave@dericed.com)

   Change controller: IETF cellar working group delegated from the IESG.

8.  Changelog

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

   [RFC Editor: Please remove this Changelog section prior to
   publication.]

9.  Normative References

   [ISO.15444-1.2016]
              International Organization for Standardization,
              "Information technology -- JPEG 2000 image coding system:
              Core coding system", October 2016.

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   [ISO.9899.2018]
              International Organization for Standardization,
              "Programming languages - C", ISO Standard 9899, 2018.

   [Matroska] IETF, "Matroska", 2019, <https://datatracker.ietf.org/doc/
              draft-ietf-cellar-matroska/>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC4732]  Handley, M., Ed., Rescorla, E., Ed., and IAB, "Internet
              Denial-of-Service Considerations", RFC 4732,
              DOI 10.17487/RFC4732, December 2006,
              <https://www.rfc-editor.org/info/rfc4732>.

   [RFC4855]  Casner, S., "Media Type Registration of RTP Payload
              Formats", RFC 4855, DOI 10.17487/RFC4855, February 2007,
              <https://www.rfc-editor.org/info/rfc4855>.

   [RFC6716]  Valin, JM., Vos, K., and T. Terriberry, "Definition of the
              Opus Audio Codec", RFC 6716, DOI 10.17487/RFC6716,
              September 2012, <https://www.rfc-editor.org/info/rfc6716>.

   [RFC6838]  Freed, N., Klensin, J., and T. Hansen, "Media Type
              Specifications and Registration Procedures", BCP 13,
              RFC 6838, DOI 10.17487/RFC6838, January 2013,
              <https://www.rfc-editor.org/info/rfc6838>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

10.  Informative References

   [Address-Sanitizer]
              The Clang Team, "ASAN AddressSanitizer website", undated,
              <https://clang.llvm.org/docs/AddressSanitizer.html>.

   [AVI]      Microsoft, "AVI RIFF File Reference", undated,
              <https://msdn.microsoft.com/en-us/library/windows/desktop/
              dd318189%28v=vs.85%29.aspx>.

   [FFV1_V0]  Niedermayer, M., "Commit to mark FFV1 version 0 as non-
              experimental", April 2006, <https://git.videolan.org/?p=ff
              mpeg.git;a=commit;h=b548f2b91b701e1235608ac882ea6df915167c
              7e>.

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   [FFV1_V1]  Niedermayer, M., "Commit to release FFV1 version 1", April
              2009, <https://git.videolan.org/?p=ffmpeg.git;a=commit;h=6
              8f8d33becbd73b4d0aa277f472a6e8e72ea6849>.

   [FFV1_V3]  Niedermayer, M., "Commit to mark FFV1 version 3 as non-
              experimental", August 2013, <https://git.videolan.org/?p=f
              fmpeg.git;a=commit;h=abe76b851c05eea8743f6c899cbe5f7409b0f
              301>.

   [HuffYUV]  Rudiak-Gould, B., "HuffYUV", December 2003,
              <https://web.archive.org/web/20040402121343/
              http://cultact-server.novi.dk/kpo/huffyuv/huffyuv.html>.

   [ISO.14495-1.1999]
              International Organization for Standardization,
              "Information technology -- Lossless and near-lossless
              compression of continuous-tone still images: Baseline",
              December 1999.

   [ISO.14496-10.2014]
              International Organization for Standardization,
              "Information technology -- Coding of audio-visual objects
              -- Part 10: Advanced Video Coding", September 2014.

   [ISO.14496-12.2015]
              International Organization for Standardization,
              "Information technology -- Coding of audio-visual objects
              -- Part 12: ISO base media file format", December 2015.

   [NUT]      Niedermayer, M., "NUT Open Container Format", December
              2013, <https://ffmpeg.org/~michael/nut.txt>.

   [range-coding]
              Martin, G. N. N., "Range encoding: an algorithm for
              removing redundancy from a digitised message", Proceedings
              of the Conference on Video and Data Recording. Institution
              of Electronic and Radio Engineers, Hampshire, England,
              July 1979.

   [REFIMPL]  Niedermayer, M., "The reference FFV1 implementation / the
              FFV1 codec in FFmpeg", undated, <https://ffmpeg.org>.

   [VALGRIND] Valgrind Developers, "Valgrind website", undated,
              <https://valgrind.org/>.

   [YCbCr]    Wikipedia, "YCbCr", undated,
              <https://en.wikipedia.org/w/index.php?title=YCbCr>.

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Appendix A.  Multi-theaded decoder implementation suggestions

   This appendix is informative.

   The FFV1 bitstream is parsable in two ways: in sequential order as
   described in this document or with the pre-analysis of the footer of
   each slice.  Each slice footer contains a "slice_size" field so the
   boundary of each slice is computable without having to parse the
   slice content.  That allows multi-threading as well as independence
   of slice content (a bitstream error in a slice header or slice
   content has no impact on the decoding of the other slices).

   After having checked "keyframe" field, a decoder SHOULD parse
   "slice_size" fields, from "slice_size" of the last slice at the end
   of the "Frame" up to "slice_size" of the first slice at the beginning
   of the "Frame", before parsing slices, in order to have slices
   boundaries.  A decoder MAY fallback on sequential order e.g. in case
   of a corrupted "Frame" (frame size unknown, "slice_size" of slices
   not coherent...) or if there is no possibility of seeking into the
   stream.

Appendix B.  Future handling of some streams created by non conforming
             encoders

   This appendix is informative.

   Some bitstreams were found with 40 extra bits corresponding to
   "error_status" and "slice_crc_parity" in the "reserved" bits of
   "Slice()".  Any revision of this specification SHOULD care about
   avoiding to add 40 bits of content after "SliceContent" if "version"
   == 0 or "version" == 1.  Else a decoder conforming to the revised
   specification could not distinguish between a revised bitstream and
   such buggy bitstream in the wild.

Authors' Addresses

   Michael Niedermayer

   Email: michael@niedermayer.cc

   Dave Rice

   Email: dave@dericed.com

   Jerome Martinez

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   Email: jerome@mediaarea.net

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