Internet-Draft FLAC September 2023
van Beurden & Weaver Expires 15 March 2024 [Page]
Workgroup:
cellar
Internet-Draft:
draft-ietf-cellar-flac-11
Published:
Intended Status:
Standards Track
Expires:
Authors:
M.Q.C. van Beurden
A. Weaver

Free Lossless Audio Codec

Abstract

This document defines the Free Lossless Audio Codec (FLAC) format and its streamable subset. FLAC is designed to reduce the amount of computer storage space needed to store digital audio signals without losing information in doing so (i.e., lossless). FLAC is free in the sense that its specification is open and its reference implementation is open-source. Compared to other lossless (audio) coding formats, FLAC is a format with low complexity and can be coded to and from with little computing resources. Decoding of FLAC has seen many independent implementations on many different platforms, and both encoding and decoding can be implemented without needing floating-point arithmetic.

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 15 March 2024.

Table of Contents

1. Introduction

This document defines the FLAC format and its streamable subset. FLAC files and streams can code for pulse-code modulated (PCM) audio with 1 to 8 channels, sample rates from 1 up to 1048575 hertz and bit depths from 4 up to 32 bits. Most tools for coding to and decoding from the FLAC format have been optimized for CD-audio, which is PCM audio with 2 channels, a sample rate of 44.1 kHz, and a bit depth of 16 bits.

FLAC is able to achieve lossless compression because samples in audio signals tend to be highly correlated with their close neighbors. In contrast with general-purpose compressors, which often use dictionaries, do run-length coding, or exploit long-term repetition, FLAC removes redundancy solely in the very short term, looking back at at most 32 samples.

The coding methods provided by the FLAC format work best on PCM audio signals, of which the samples have a signed representation and are centered around zero. Audio signals in which samples have an unsigned representation must be transformed to a signed representation as described in this document in order to achieve reasonable compression. The FLAC format is not suited for compressing audio that is not PCM.

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.

Values expressed as u(n) represent unsigned big-endian integer using n bits. Values expressed as s(n) represent signed big-endian integer using n bits, signed two's complement. Where necessary n is expressed as an equation using * (multiplication), / (division), + (addition), or - (subtraction). An inclusive range of the number of bits expressed is represented with an ellipsis, such as u(m...n).

While the FLAC format can store digital audio as well as other digital signals, this document uses terminology specific to digital audio. The use of more generic terminology was deemed less clear, so a reader interested in non-audio use of the FLAC format is expected to make the translation from audio-specific terms to more generic terminology.

3. Definitions

4. Conceptual overview

Similar to many other audio coders, a FLAC file is encoded following the steps below. On decoding a FLAC file, these steps are undone in reverse order, i.e., from bottom to top.

In addition, FLAC specifies a metadata system (see Section 8), which allows arbitrary information about the stream to be included at the beginning of the stream.

4.1. Blocking

The block size used for audio data has a direct effect on the compression ratio. If the block size is too small, the resulting large number of frames means that a disproportionate amount of bytes will be spent on frame headers. If the block size is too large, the characteristics of the signal may vary so much that the encoder will be unable to find a good predictor. In order to simplify encoder/decoder design, FLAC imposes a minimum block size of 16 samples, except for the last block, and a maximum block size of 65535 samples. The last block is allowed to be smaller than 16 samples to be able to match the length of the encoded audio without using padding.

While the block size does not have to be constant in a FLAC file, it is often difficult to find the optimal arrangement of block sizes for maximum compression. Because of this, the FLAC format explicitly stores whether a file has a constant or a variable block size throughout the stream, and stores a block number instead of a sample number to slightly improve compression if a stream has a constant block size.

4.2. Interchannel Decorrelation

In many audio files, channels are correlated. The FLAC format can exploit this correlation in stereo files by not directly coding subblocks into subframes, but instead coding an average of all samples in both subblocks (a mid channel) or the difference between all samples in both subblocks (a side channel). The following combinations are possible:

  • Independent. All channels are coded independently. All non-stereo files MUST be encoded this way.

  • Mid-side. A left and right subblock are converted to mid and side subframes. To calculate a sample for a mid subframe, the corresponding left and right samples are summed and the result is shifted right by 1 bit. To calculate a sample for a side subframe, the corresponding right sample is subtracted from the corresponding left sample. On decoding, all mid channel samples have to be shifted left by 1 bit. Also, if a side channel sample is odd, 1 has to be added to the corresponding mid channel sample after it has been shifted left by one bit. To reconstruct the left channel, the corresponding samples in the mid and side subframes are added and the result shifted right by 1 bit, while for the right channel the side channel has to be subtracted from the mid channel and the result shifted right by 1 bit.

  • Left-side. The left subblock is coded and the left and right subblocks are used to code a side subframe. The side subframe is constructed in the same way as for mid-side. To decode, the right subblock is restored by subtracting the samples in the side subframe from the corresponding samples in the the left subframe.

  • Right-side. The right subblock is coded and the left and right subblocks are used to code a side subframe. Note that the actual coded subframe order is side-right. The side subframe is constructed in the same way as for mid-side. To decode, the left subblock is restored by adding the samples in the side subframe to the corresponding samples in the right subframe.

The side channel needs one extra bit of bit depth as the subtraction can produce sample values twice as large as the maximum possible in any given bit depth. The mid channel in mid-side stereo does not need one extra bit, as it is shifted right one bit. The right shift of the mid channel does not lead to non-lossless behavior, because an odd sample in the mid subframe must always be accompanied by a corresponding odd sample in the side subframe, which means the lost least-significant bit can be restored by taking it from the sample in the side subframe.

4.3. Prediction

The FLAC format has four methods for modeling the input signal:

  1. Verbatim. Samples are stored directly, without any modeling. This method is used for inputs with little correlation, like white noise. Since the raw signal is not actually passed through the residual coding stage (it is added to the stream 'verbatim'), this method is different from using a zero-order fixed predictor.

  2. Constant. A single sample value is stored. This method is used whenever a signal is pure DC ("digital silence"), i.e., a constant value throughout.

  3. Fixed predictor. Samples are predicted with one of five fixed (i.e., predefined) predictors, and the error of this prediction is processed by the residual coder. These fixed predictors are well suited for predicting simple waveforms. Since the predictors are fixed, no predictor coefficients are stored. From a mathematical point of view, the predictors work by extrapolating the signal from the previous samples. The number of previous samples used is equal to the predictor order. For more information, see Section 9.2.5.

  4. Linear predictor. Samples are predicted using past samples and a set of predictor coefficients, and the error of this prediction is processed by the residual coder. Compared to a fixed predictor, using a generic linear predictor adds overhead as predictor coefficients need to be stored. Therefore, this method of prediction is best suited for predicting more complex waveforms, where the added overhead is offset by space savings in the residual coding stage resulting from more accurate prediction. A linear predictor in FLAC has two parameters besides the predictor coefficients and the predictor order: the number of bits with which each coefficient is stored (the coefficient precision) and a prediction right shift. A prediction is formed by taking the sum of multiplying each predictor coefficient with the corresponding past sample, and dividing that sum by applying the specified right shift. For more information, see Section 9.2.6.

A FLAC encoder is free to select any of the above methods to model the input. However, to ensure lossless coding, the following exceptions apply:

  • When the samples that need to be stored do not all have the same value (i.e., the signal is not constant), a constant subframe cannot be used.
  • When an encoder is unable to find a fixed or linear predictor for which all residual samples are representable in 32-bit signed integers as stated in Section 9.2.7, a verbatim subframe is used.

For more information on fixed and linear predictors, see [HPL-1999-144] and [robinson-tr156].

4.4. Residual Coding

If a subframe uses a predictor to approximate the audio signal, a residual is stored to 'correct' the approximation to the exact value. When an effective predictor is used, the average numerical value of the residual samples is smaller than that of the samples before prediction. While having smaller values on average, it is possible that a few 'outlier' residual samples are much larger than any of the original samples. Sometimes these outliers even exceed the range the bit depth of the original audio offers.

To be able to efficiently code such a stream of relatively small numbers with an occasional outlier, Rice coding (a subset of Golomb coding) is used. Depending on how small the numbers are that have to be coded, a Rice parameter is chosen. The numerical value of each residual sample is split into two parts by dividing it by 2^(Rice parameter), creating a quotient and a remainder. The quotient is stored in unary form, the remainder in binary form. If indeed most residual samples are close to zero and a suitable Rice parameter is chosen, this form of coding, a so-called variable-length code, fewer less bits to store than storing the residual in unencoded form.

As Rice codes can only handle unsigned numbers, signed numbers are zigzag encoded to a so-called folded residual. See Section 9.2.7 for a more thorough explanation.

Quite often, the optimal Rice parameter varies over the course of a subframe. To accommodate this, the residual can be split up into partitions, where each partition has its own Rice parameter. To keep overhead and complexity low, the number of partitions used in a subframe is limited to powers of two.

The FLAC format uses two forms of Rice coding, which only differ in the number of bits used for encoding the Rice parameter, either 4 or 5 bits.

5. Format principles

FLAC has no format version information, but it does contain reserved space in several places. Future versions of the format MAY use this reserved space safely without breaking the format of older streams. Older decoders MAY choose to abort decoding when encountering data encoded using methods they do not recognize. Apart from reserved patterns, the format specifies forbidden patterns in certain places, meaning that the patterns MUST NOT appear in any bitstream. They are listed in the following table.

Table 1
Description Reference
Metadata block type 127 Section 8.1
Minimum and maximum block sizes smaller than 16 in streaminfo metadata block Section 8.2
Sample rate bits 0b1111 Section 9.1.2
Uncommon blocksize 65536 Section 9.1.6
Predictor coefficient precision bits 0b1111 Section 9.2.6
Negative predictor right shift Section 9.2.6

All numbers used in a FLAC bitstream are integers, there are no floating-point representations. All numbers are big-endian coded, except the field lengths used in Vorbis comments (see Section 8.6), which are little-endian coded. All numbers are unsigned except linear predictor coefficients, the linear prediction shift (see Section 9.2.6), and numbers that directly represent samples, which are signed. None of these restrictions apply to application metadata blocks or to Vorbis comment field contents.

All samples encoded to and decoded from the FLAC format MUST be in a signed representation.

There are several ways to convert unsigned sample representations to signed sample representations, but the coding methods provided by the FLAC format work best on audio signals of which the numerical values of the samples are centered around zero, i.e., have no DC offset. In most unsigned audio formats, signals are centered around halfway the range of the unsigned integer type used. If that is the case, converting sample representations by first copying the number to a signed integer with sufficient range and then subtracting half of the range of the unsigned integer type, results in a signal with samples centered around 0.

Unary coding in a FLAC bitstream is done with zero bits terminated with a one bit, e.g., the number 5 is coded unary as 0b000001. This prevents the frame sync code from appearing in unary coded numbers.

When a FLAC file contains data that is forbidden or otherwise not valid, decoder behavior is left unspecified. A decoder MAY choose to stop decoding upon encountering such data. Examples of such data are

6. Format layout

Before the formal description of the stream, an overview of the layout of the FLAC format might be helpful.

A FLAC bitstream consists of the fLaC (i.e., 0x664C6143) marker at the beginning of the stream, followed by a mandatory metadata block (called the STREAMINFO block), any number of other metadata blocks, and then the audio frames.

FLAC supports up to 127 kinds of metadata blocks; currently, 7 kinds are defined in Section 8.

The audio data is composed of one or more audio frames. Each frame consists of a frame header, which contains a sync code, information about the frame like the block size, sample rate, number of channels, et cetera, and an 8-bit CRC. The frame header also contains either the sample number of the first sample in the frame (for variable block size streams), or the frame number (for fixed block size streams). This allows for fast, sample-accurate seeking to be performed. Following the frame header are encoded subframes, one for each channel. The frame is then zero-padded to a byte boundary and finished with a frame footer containing a checksum for the frame. Each subframe has its own header that specifies how the subframe is encoded.

In order to allow a decoder to start decoding at any place in the stream, each frame starts with a byte-aligned 15-bit sync code. However, since it is not guaranteed that the sync code does not appear elsewhere in the frame, the decoder can check that it synced correctly by parsing the rest of the frame header and validating the frame header CRC.

Furthermore, to allow a decoder to start decoding at any place in the stream even without having received a streaminfo metadata block, each frame header contains some basic information about the stream. This information includes sample rate, bits per sample, number of channels, etc. Since the frame header is pure overhead, it has a direct effect on the compression ratio. To keep the frame header as small as possible, FLAC uses lookup tables for the most commonly used values for frame properties. When a certain property has a value that is not covered by the lookup table, the decoder is directed to find the value of that property (for example, the sample rate) at the end of the frame header or in the streaminfo metadata block. If a frame header refers to the streaminfo metadata block, the file is not 'streamable', see Section 7 for details. In this way, the file is streamable and the frame header size small for all of the most common forms of audio data.

Individual subframes (one for each channel) are coded separately within a frame, and appear serially in the stream. In other words, the encoded audio data is NOT channel-interleaved. This reduces decoder complexity at the cost of requiring larger decode buffers. Each subframe has its own header specifying the attributes of the subframe, like prediction method and order, residual coding parameters, etc. Each subframe header is followed by the encoded audio data for that channel.

7. Streamable subset

The FLAC format specifies a subset of itself as the FLAC streamable subset. The purpose of this is to ensure that any streams encoded according to this subset are truly "streamable", meaning that a decoder that cannot seek within the stream can still pick up in the middle of the stream and start decoding. It also makes hardware decoder implementations more practical by limiting the encoding parameters in such a way that decoder buffer sizes and other resource requirements can be easily determined. The flac command-line tool, part of the FLAC reference implementation (see Section 11), generates streamable subset files by default unless the --lax command-line option is used. The streamable subset makes the following limitations on what MAY be used in the stream:

8. File-level metadata

At the start of a FLAC file or stream, following the fLaC ASCII file signature, one or more metadata blocks MUST be present before any audio frames appear. The first metadata block MUST be a streaminfo block.

8.1. Metadata block header

Each metadata block starts with a 4 byte header. The first bit in this header flags whether a metadata block is the last one: it is a 0 when other metadata blocks follow, otherwise it is a 1. The 7 remaining bits of the first header byte contain the type of the metadata block as an unsigned number between 0 and 126 according to the following table. A value of 127 (i.e., 0b1111111) is forbidden. The three bytes that follow code for the size of the metadata block in bytes, excluding the 4 header bytes, as an unsigned number coded big-endian.

Table 2
Value Metadata block type
0 Streaminfo
1 Padding
2 Application
3 Seektable
4 Vorbis comment
5 Cuesheet
6 Picture
7 - 126 reserved
127 forbidden, to avoid confusion with a frame sync code

8.2. Streaminfo

The streaminfo metadata block has information about the whole stream, like sample rate, number of channels, total number of samples, etc. It MUST be present as the first metadata block in the stream. Other metadata blocks MAY follow. There MUST be no more than one streaminfo metadata block per FLAC stream.

If the streaminfo metadata block contains incorrect or incomplete information, decoder behavior is left unspecified (i.e., up to the decoder implementation). A decoder MAY choose to stop further decoding when the information supplied by the streaminfo metadata block turns out to be incorrect or contains forbidden values. A decoder accepting information from the streaminfo block (most-significantly the maximum frame size, maximum block size, number of audio channels, number of bits per sample, and total number of samples) without doing further checks during decoding of audio frames could be vulnerable to buffer overflows. See also Section 12.

Table 3
Data Description
u(16) The minimum block size (in samples) used in the stream, excluding the last block.
u(16) The maximum block size (in samples) used in the stream.
u(24) The minimum frame size (in bytes) used in the stream. A value of 0 signifies that the value is not known.
u(24) The maximum frame size (in bytes) used in the stream. A value of 0 signifies that the value is not known.
u(20) Sample rate in Hz.
u(3) (number of channels)-1. FLAC supports from 1 to 8 channels.
u(5) (bits per sample)-1. FLAC supports from 4 to 32 bits per sample.
u(36) Total number of interchannel samples in the stream. A value of zero here means the number of total samples is unknown.
u(128) MD5 signature of the unencoded audio data. This allows the decoder to determine if an error exists in the audio data even when, despite the error, the bitstream itself is valid. A value of 0 signifies that the value is not known.

The minimum block size and the maximum block size MUST be in the 16-65535 range. The minimum block size MUST be equal to or less than the maximum block size.

Any frame but the last one MUST have a block size equal to or greater than the minimum block size and MUST have a block size equal to or lesser than the maximum block size. The last frame MUST have a block size equal to or lesser than the maximum block size, it does not have to comply to the minimum block size because the block size of that frame must be able to accommodate the length of the audio data the stream contains.

If the minimum block size is equal to the maximum block size, the file contains a fixed block size stream, as the minimum block size excludes the last block. Note that in the case of a stream with a variable block size, the actual maximum block size MAY be smaller than the maximum block size listed in the streaminfo block, and the actual smallest block size excluding the last block MAY be larger than the minimum block size listed in the streaminfo block. This is because the encoder has to write these fields before receiving any input audio data, and cannot know beforehand what block sizes it will use, only between what bounds these will be chosen.

The sample rate MUST NOT be 0 when the FLAC file contains audio. A sample rate of 0 MAY be used when non-audio is represented. This is useful if data is encoded that is not along a time axis, or when the sample rate of the data lies outside the range that FLAC can represent in the streaminfo metadata block. If a sample rate of 0 is used it is recommended to store the meaning of the encoded content in a Vorbis comment field (see Section 8.6) or an application metadata block (see Section 8.4). This document does not define such metadata.

The MD5 signature is made by performing an MD5 transformation on the samples of all channels interleaved, represented in signed, little-endian form. This interleaving is on a per-sample basis, so for a stereo file this means first the first sample of the first channel, then the first sample of the second channel, then the second sample of the first channel etc. Before performing the MD5 transformation, all samples must be byte-aligned. If the bit depth is not a whole number of bytes, the value of each sample is sign extended to the next whole number of bytes.

So, in the case of a 2-channel stream with 6-bit samples, bits will be lined up as follows.

SSAAAAAASSBBBBBBSSCCCCCC
^   ^   ^   ^   ^   ^
|   |   |   |   |  Bits of 2nd sample of 1st channel
|   |   |   |  Sign extension bits of 2nd sample of 2nd channel
|   |   |  Bits of 1st sample of 2nd channel
|   |  Sign extension bits of 1st sample of 2nd channel
|  Bits of 1st sample of 1st channel
Sign extention bits of 1st sample of 1st channel


As another example, in the case of a 1-channel with 12-bit samples, bits are lined up as follows, showing the little-endian byte order

AAAAAAAASSSSAAAABBBBBBBBSSSSBBBB
   ^     ^   ^   ^       ^   ^
   |     |   |   |       |  Most-significant 4 bits of 2nd sample
   |     |   |   | Sign extension bits of 2nd sample
   |     |   |  Least-significant 8 bits of 2nd sample
   |     |  Most-significant 4 bits of 1st sample
   |    Sign extension bits of 1st sample
  Least-significant 8 bits of 1st sample


8.3. Padding

The padding metadata block allows for an arbitrary amount of padding. This block is useful when it is known that metadata will be edited after encoding; the user can instruct the encoder to reserve a padding block of sufficient size so that when metadata is added, it will simply overwrite the padding (which is relatively quick) instead of having to insert it into the existing file (which would normally require rewriting the entire file). There MAY be one or more padding metadata blocks per FLAC stream.

Table 4
Data Description
u(n) n '0' bits (n MUST be a multiple of 8, i.e., a whole number of bytes, and MAY be zero)

8.4. Application

The application metadata block is for use by third-party applications. The only mandatory field is a 32-bit identifier. An ID registry is being maintained at https://xiph.org/flac/id.html.

Table 5
Data Description
u(32) Registered application ID. (Visit the registration page to register an ID with FLAC.)
u(n) Application data (n MUST be a multiple of 8, i.e., a whole number of bytes)

8.5. Seektable

The seektable metadata block can be used to store seek points. It is possible to seek to any given sample in a FLAC stream without a seek table, but the delay can be unpredictable since the bitrate may vary widely within a stream. By adding seek points to a stream, this delay can be significantly reduced. There MUST NOT be more than one seektable metadata block in a stream, but the table can have any number of seek points.

Each seek point takes 18 bytes, so a seek table with 1% resolution within a stream adds less than 2 kilobyte of data. The number of seek points is implied by the metadata header 'length' field, i.e., equal to length / 18. There is also a special 'placeholder' seekpoint that will be ignored by decoders but can be used to reserve space for future seek point insertion.

Table 6
Data Description
Seekpoints Zero or more seek points as defined in Section 8.5.1.

A seektable is generally not usable for seeking in a FLAC file embedded in a container (see Section 10), as such containers usually interleave FLAC data with other data and the offsets used in seekpoints are those of an unmuxed FLAC stream. Also, containers often provide their own seeking methods. It is, however, possible to store the seektable in the container along with other metadata when muxing a FLAC file, so this stored seektable can be restored when demuxing the FLAC stream into a standalone FLAC file.

8.5.1. Seekpoint

Table 7
Data Description
u(64) Sample number of the first sample in the target frame, or 0xFFFFFFFFFFFFFFFF for a placeholder point.
u(64) Offset (in bytes) from the first byte of the first frame header to the first byte of the target frame's header.
u(16) Number of samples in the target frame.

NOTES

  • For placeholder points, the second and third field values are undefined.
  • Seek points within a table MUST be sorted in ascending order by sample number.
  • Seek points within a table MUST be unique by sample number, with the exception of placeholder points.
  • The previous two notes imply that there MAY be any number of placeholder points, but they MUST all occur at the end of the table.
  • The sample offsets are those of an unmuxed FLAC stream. The offsets MUST NOT be updated on muxing to reflect the new offsets of FLAC frames in a container.

8.6. Vorbis comment

A Vorbis comment metadata block contains human-readable information coded in UTF-8. The name Vorbis comment points to the fact that the Vorbis codec stores such metadata in almost the same way, see [Vorbis]. A Vorbis comment metadata block consists of a vendor string optionally followed by a number of fields, which are pairs of field names and field contents. Many users refer to these fields as FLAC tags or simply as tags. A FLAC file MUST NOT contain more than one Vorbis comment metadata block.

In a Vorbis comment metadata block, the metadata block header is directly followed by 4 bytes containing the length in bytes of the vendor string as an unsigned number coded little-endian. The vendor string follows UTF-8 coded, and is not terminated in any way.

Following the vendor string are 4 bytes containing the number of fields that are in the Vorbis comment block, stored as an unsigned number, coded little-endian. If this number is non-zero, it is followed by the fields themselves, each of which is stored with a 4 byte length. First, the 4 byte field length in bytes is stored as an unsigned number, coded little-endian. The field itself is, like the vendor string, UTF-8 coded, not terminated in any way.

Each field consists of a field name and a field content, separated by an = character. The field name MUST only consist of UTF-8 code points U+0020 through U+007E, excluding U+003D, which is the = character. In other words, the field name can contain all printable ASCII characters except the equals sign. The evaluation of the field names MUST be case insensitive, so U+0041 through 0+005A (A-Z) MUST be considered equivalent to U+0061 through U+007A (a-z) respectively. The field contents can contain any UTF-8 character.

Note that the Vorbis comment as used in Vorbis allows for on the order of 2^64 bytes of data whereas the FLAC metadata block is limited to 2^24 bytes. Given the stated purpose of Vorbis comments, i.e., human-readable textual information, the FLAC metadata block limit is unlikely to be restrictive. Also note that the 32-bit field lengths are coded little-endian, as opposed to the usual big-endian coding of fixed-length integers in the rest of the FLAC format.

8.6.1. Standard field names

Only one standard field name is defined; the channel mask field, in Section 8.6.2. In general, most FLAC playback devices and software recognize the following field names:

  • Title: name of the current work.
  • Artist: name of the artist generally responsible for the current work. For orchestral works, this is usually the composer; otherwise, it is often the performer.
  • Album: name of the collection the current work belongs to.

For a more comprehensive list of possible field names, the list of tags used in the MusicBrainz project is recommended.

8.6.2. Channel mask

Besides fields containing information about the work itself, one field is defined for technical reasons, of which the field name is WAVEFORMATEXTENSIBLE_CHANNEL_MASK. This field is used to communicate that the channels in a file differ from the default channels defined in Section 9.1.3. For example, by default, a FLAC file containing two channels is interpreted to contain a left and right channel, but with this field, it is possible to describe different channel contents.

The channel mask consists of flag bits indicating which channels are present, stored in a hexadecimal representation preceded by 0x. The flags only signal which channels are present, not in which order, so if a file has to be encoded in which channels are ordered differently, they have to be reordered. Please note that a file in which the channel order is defined through the WAVEFORMATEXTENSIBLE_CHANNEL_MASK is not streamable (see Section 7), as the field is not found in each frame header. The mask bits can be found in the following table.

Table 8
Bit number Channel description
0 Front left
1 Front right
2 Front center
3 Low-frequency effects (LFE)
4 Back left
5 Back right
6 Front left of center
7 Front right of center
8 Back center
9 Side left
10 Side right
11 Top center
12 Top front left
13 Top front center
14 Top front right
15 Top rear left
16 Top rear center
17 Top rear right

Following are three examples:

  • If a file has a single channel, being a LFE channel, the Vorbis comment field is WAVEFORMATEXTENSIBLE_CHANNEL_MASK=0x8.
  • If a file has four channels, being front left, front right, top front left, and top front right, the Vorbis comment field is WAVEFORMATEXTENSIBLE_CHANNEL_MASK=0x5003.
  • If an input has four channels, being back center, top front center, front center, and top rear center in that order, they have to be reordered to front center, back center, top front center and top rear center. The Vorbis comment field added is WAVEFORMATEXTENSIBLE_CHANNEL_MASK=0x12104.

WAVEFORMATEXTENSIBLE_CHANNEL_MASK fields MAY be padded with zeros, for example, 0x0008 for a single LFE channel. Parsing of WAVEFORMATEXTENSIBLE_CHANNEL_MASK fields MUST be case-insensitive for both the field name and the field contents.

A WAVEFORMATEXTENSIBLE_CHANNEL_MASK field of 0x0 can be used to indicate that none of the audio channels of a file correlate with speaker positions. This is the case when audio needs to be decoded into speaker positions (e.g., Ambisonics B-format audio) or when a multitrack recording is contained.

It is possible for a WAVEFORMATEXTENSIBLE_CHANNEL_MASK field to code for fewer channels than are present in the audio. If that is the case, the remaining channels SHOULD NOT be rendered by a playback application unfamiliar with their purpose. For example, the Ambisonics UHJ format is compatible with stereo playback: its first two channels can be played back on stereo equipment, but all four channels together can be decoded into surround sound. For that example, the Vorbis comment field WAVEFORMATEXTENSIBLE_CHANNEL_MASK=0x3 would be set, indicating the first two channels are front left and front right, and other channels do not correlate with speaker positions directly.

If audio channels not assigned to any speaker are contained and decoding to speaker positions is possible, it is recommended to provide metadata on how this decoding should take place in another Vorbis comment field or an application metadata block. This document does not define such metadata.

8.7. Cuesheet

To either store the track and index point structure of a Compact Disc Digital Audio (CD-DA) along with its audio or to provide a mechanism to store locations of interest within a FLAC file, a cuesheet metadata block can be used. Certain aspects of this metadata block follow directly from the CD-DA specification, called Red Book, which is standardized as [IEC.60908.1999]. The description below is complete and further reference to [IEC.60908.1999] is not needed to implement this metadata block.

The structure of a cuesheet metadata block is enumerated in the following table.

Table 9
Data Description
u(128*8) Media catalog number, in ASCII printable characters 0x20-0x7E.
u(64) Number of lead-in samples.
u(1) 1 if the cuesheet corresponds to a CD-DA, else 0.
u(7+258*8) Reserved. All bits MUST be set to zero.
u(8) Number of tracks in this cuesheet.
Cuesheet tracks A number of structures as specified in Section 8.7.1 equal to the number of tracks specified previously.

If the media catalog number is less than 128 bytes long, it is right-padded with NUL characters. For CD-DA, this is a thirteen digit number, followed by 115 NUL bytes.

The number of lead-in samples has meaning only for CD-DA cuesheets; for other uses, it should be 0. For CD-DA, the lead-in is the TRACK 00 area where the table of contents is stored; more precisely, it is the number of samples from the first sample of the media to the first sample of the first index point of the first track. According to [IEC.60908.1999], the lead-in MUST be silence and CD grabbing software does not usually store it; additionally, the lead-in MUST be at least two seconds but MAY be longer. For these reasons, the lead-in length is stored here so that the absolute position of the first track can be computed. Note that the lead-in stored here is the number of samples up to the first index point of the first track, not necessarily to INDEX 01 of the first track; even the first track MAY have INDEX 00 data.

The number of tracks MUST be at least 1, as a cuesheet block MUST have a lead-out track. For CD-DA, this number MUST be no more than 100 (99 regular tracks and one lead-out track). The lead-out track is always the last track in the cuesheet. For CD-DA, the lead-out track number MUST be 170 as specified by [IEC.60908.1999], otherwise it MUST be 255.

8.7.1. Cuesheet track

Table 10
Data Description
u(64) Track offset of the first index point in samples, relative to the beginning of the FLAC audio stream.
u(8) Track number.
u(12*8) Track ISRC.
u(1) The track type: 0 for audio, 1 for non-audio. This corresponds to the CD-DA Q-channel control bit 3.
u(1) The pre-emphasis flag: 0 for no pre-emphasis, 1 for pre-emphasis. This corresponds to the CD-DA Q-channel control bit 5.
u(6+13*8) Reserved. All bits MUST be set to zero.
u(8) The number of track index points.
Cuesheet track index points For all tracks except the lead-out track, a number of structures as specified in Section 8.7.1.1 equal to the number of index points specified previously.

Note that the track offset differs from the one in CD-DA, where the track's offset in the TOC is that of the track's INDEX 01 even if there is an INDEX 00. For CD-DA, the track offset MUST be evenly divisible by 588 samples (588 samples = 44100 samples/s * 1/75 s).

A track number of 0 is not allowed, because the CD-DA specification reserves this for the lead-in. For CD-DA the number MUST be 1-99, or 170 for the lead-out; for non-CD-DA, the track number MUST be 255 for the lead-out. It is recommended to start with track 1 and increase sequentially. Track numbers MUST be unique within a cuesheet.

The track ISRC (International Standard Recording Code) is a 12-digit alphanumeric code; see [ISRC-handbook]. A value of 12 ASCII NUL characters MAY be used to denote the absence of an ISRC.

There MUST be at least one index point in every track in a cuesheet except for the lead-out track, which MUST have zero. For CD-DA, the number of index points MUST NOT be more than 100.

8.7.1.1. Cuesheet track index point
Table 11
Data Description
u(64) Offset in samples, relative to the track offset, of the index point.
u(8) The track index point number.
u(3*8) Reserved. All bits MUST be set to zero.

For CD-DA, the track index point offset MUST be evenly divisible by 588 samples (588 samples = 44100 samples/s * 1/75 s). Note that the offset is from the beginning of the track, not the beginning of the audio data.

For CD-DA, a track index point number of 0 corresponds to the track pre-gap. The first index point in a track MUST have a number of 0 or 1, and subsequently, index point numbers MUST increase by 1. Index point numbers MUST be unique within a track.

8.8. Picture

The picture metadata block contains image data of a picture in some way belonging to the audio contained in the FLAC file. Its format is derived from the APIC frame in the ID3v2 specification. However, contrary to the APIC frame in ID3v2, the media type and description are prepended with a 4-byte length field instead of being null delimited strings. A FLAC file MAY contain one or more picture metadata blocks.

Note that while the length fields for media type, description, and picture data are 4 bytes in length and could in theory code for a size up to 4 GiB, the total metadata block size cannot exceed what can be described by the metadata block header, i.e., 16 MiB.

The structure of a picture metadata block is enumerated in the following table.

Table 12
Data Description
u(32) The picture type according to next table
u(32) The length of the media type string in bytes.
u(n*8) The media type string, in printable ASCII characters 0x20-0x7E. The media type MAY also be --> to signify that the data part is a URI of the picture instead of the picture data itself.
u(32) The length of the description string in bytes.
u(n*8) The description of the picture, in UTF-8.
u(32) The width of the picture in pixels.
u(32) The height of the picture in pixels.
u(32) The color depth of the picture in bits per pixel.
u(32) For indexed-color pictures (e.g., GIF), the number of colors used, or 0 for non-indexed pictures.
u(32) The length of the picture data in bytes.
u(n*8) The binary picture data.

The height, width, color depth, and 'number of colors' fields are for informational purposes only. Applications MUST NOT use them in decoding the picture or deciding how to display it, but MAY use them to decide whether to process a block or not (e.g., when selecting between different picture blocks) and MAY show them to the user. If a picture has no concept for any of these fields (e.g., vector images may not have a height or width in pixels) or the content of any field is unknown, the affected fields MUST be set to zero.

The following table contains all the defined picture types. Values other than those listed in the table are reserved. There MAY only be one each of picture types 1 and 2 in a file. In general practice, many FLAC playback devices and software display the contents of a picture metadata block with picture type 3 (front cover) during playback, if present.

Table 13
Value Picture type
0 Other
1 PNG file icon of 32x32 pixels
2 General file icon
3 Front cover
4 Back cover
5 Liner notes page
6 Media label (e.g., CD, Vinyl or Cassette label)
7 Lead artist, lead performer, or soloist
8 Artist or performer
9 Conductor
10 Band or orchestra
11 Composer
12 Lyricist or text writer
13 Recording location
14 During recording
15 During performance
16 Movie or video screen capture
17 A bright colored fish
18 Illustration
19 Band or artist logotype
20 Publisher or studio logotype

If not a picture but a URI is contained in this block, the following points apply:

  • The URI can be either in absolute or relative form. If an URI is in relative form, it is related to the URI of the FLAC content processed.
  • Applications MUST obtain explicit user approval to retrieve images via remote protocols and to retrieve local images not located in the same directory as the FLAC file being processed.
  • Applications supporting linked images MUST handle unavailability of URIs gracefully. They MAY report unavailability to the user.
  • Applications MAY reject processing URIs for any reason, in particular for security or privacy reasons.

9. Frame structure

Directly after the last metadata block, one or more frames follow. Each frame consists of a frame header, one or more subframes, padding zero bits to achieve byte-alignment, and a frame footer. The number of subframes in each frame is equal to the number of audio channels.

Each frame header stores the audio sample rate, number of bits per sample, and number of channels independently of the streaminfo metadata block and other frame headers. This was done to permit multicasting of FLAC files, but it also allows these properties to change mid-stream. Because not all environments in which FLAC decoders are used are able to cope with changes to these properties during playback, a decoder MAY choose to stop decoding on such a change. A decoder that does not check for such a change could be vulnerable to buffer overflows. See also Section 12.

Note that storing audio with changing audio properties in FLAC results in various practical problems. For example, these changes of audio properties must happen on a frame boundary, or the process will not be lossless. When a variable block size is chosen to accommodate this, note that blocks smaller than 16 samples are not allowed and it is therefore not possible to store an audio stream in which these properties change within 16 samples of the last change or the start of the file. Also, since the streaminfo metadata block can only accommodate a single set of properties, it is only valid for part of such an audio stream. Instead, it is RECOMMENDED to store an audio stream with changing properties in FLAC encapsulated in a container capable of handling such changes, as these do not suffer from the mentioned limitations. See Section 10 for details.

9.1. Frame header

Each frame MUST start on a byte boundary and starts with the 15-bit frame sync code 0b111111111111100. Following the sync code is the blocking strategy bit, which MUST NOT change during the audio stream. The blocking strategy bit is 0 for a fixed block size stream or 1 for a variable block size stream. If the blocking strategy is known, a decoder can include this bit when searching for the start of a frame to reduce the possibility of encountering a false positive, as the first two bytes of a frame are either 0xFFF8 for a fixed block size stream or 0xFFF9 for a variable block size stream.

9.1.1. Block size bits

Following the frame sync code and blocking strategy bit are 4 bits (the first 4 bits of the third byte of each frame) referred to as the block size bits. Their value relates to the block size according to the following table, where v is the value of the 4 bits as an unsigned number. If the block size bits code for an uncommon block size, this is stored after the coded number, see Section 9.1.6.

Table 14
Value Block size
0b0000 reserved
0b0001 192
0b0010 - 0b0101 144 * (2^v), i.e., 576, 1152, 2304, or 4608
0b0110 uncommon block size minus 1 stored as an 8-bit number
0b0111 uncommon block size minus 1 stored as a 16-bit number
0b1000 - 0b1111 2^v, i.e., 256, 512, 1024, 2048, 4096, 8192, 16384, or 32768

9.1.2. Sample rate bits

The next 4 bits (the last 4 bits of the third byte of each frame), referred to as the sample rate bits, contain the sample rate of the audio according to the following table. If the sample rate bits code for an uncommon sample rate, this is stored after the uncommon block size or after the coded number if no uncommon block size was used. See Section 9.1.7.

Table 15
Value Sample rate
0b0000 sample rate only stored in the streaminfo metadata block
0b0001 88.2 kHz
0b0010 176.4 kHz
0b0011 192 kHz
0b0100 8 kHz
0b0101 16 kHz
0b0110 22.05 kHz
0b0111 24 kHz
0b1000 32 kHz
0b1001 44.1 kHz
0b1010 48 kHz
0b1011 96 kHz
0b1100 uncommon sample rate in kHz stored as an 8-bit number
0b1101 uncommon sample rate in Hz stored as a 16-bit number
0b1110 uncommon sample rate in Hz divided by 10, stored as a 16-bit number
0b1111 forbidden

9.1.3. Channels bits

The next 4 bits (the first 4 bits of the fourth byte of each frame), referred to as the channels bits, contain both the number of channels of the audio as well as any stereo decorrelation used according to the following table.

If a channel layout different than the ones listed in the following table is used, this can be signaled with a WAVEFORMATEXTENSIBLE_CHANNEL_MASK tag in a Vorbis comment metadata block, see Section 8.6.2 for details. Note that even when such a different channel layout is specified with a WAVEFORMATEXTENSIBLE_CHANNEL_MASK and the channel ordering in the following table is overridden, the channels bits still contain the actual number of channels coded in the frame. For details on the way left/side, right/side, and mid/side stereo are coded, see Section 4.2.

Table 16
Value Channels
0b0000 1 channel: mono
0b0001 2 channels: left, right
0b0010 3 channels: left, right, center
0b0011 4 channels: front left, front right, back left, back right
0b0100 5 channels: front left, front right, front center, back/surround left, back/surround right
0b0101 6 channels: front left, front right, front center, LFE, back/surround left, back/surround right
0b0110 7 channels: front left, front right, front center, LFE, back center, side left, side right
0b0111 8 channels: front left, front right, front center, LFE, back left, back right, side left, side right
0b1000 2 channels, left, right, stored as left/side stereo
0b1001 2 channels, left, right, stored as right/side stereo
0b1010 2 channels, left, right, stored as mid/side stereo
0b1011 - 0b1111 reserved

9.1.4. Bit depth bits

The next 3 bits (bits 5, 6 and 7 of each fourth byte of each frame) contain the bit depth of the audio according to the following table.

Table 17
Value Bit depth
0b000 bit depth only stored in the streaminfo metadata block
0b001 8 bits per sample
0b010 12 bits per sample
0b011 reserved
0b100 16 bits per sample
0b101 20 bits per sample
0b110 24 bits per sample
0b111 32 bits per sample

The next bit is reserved and MUST be zero.

9.1.5. Coded number

Following the reserved bit (starting at the fifth byte of the frame) is either a sample or a frame number, which will be referred to as the coded number. When dealing with variable block size streams, the sample number of the first sample in the frame is encoded. When the file contains a fixed block size stream, the frame number is encoded. See Section 9.1 on the blocking strategy bit which signals whether a stream is a fixed block size stream or a variable block size stream. Also see Appendix B.1.

The coded number is stored in a variable length code like UTF-8 as defined in [RFC3629], but extended to a maximum of 36 bits unencoded, 7 bytes encoded.

When a frame number is encoded, the value MUST NOT be larger than what fits a value of 31 bits unencoded or 6 bytes encoded. Please note that as most general purpose UTF-8 encoders and decoders follow [RFC3629], they will not be able to handle these extended codes. Furthermore, while UTF-8 is specifically used to encode characters, FLAC uses it to encode numbers instead. To encode or decode a coded number, follow the procedures of Section 3 of [RFC3629], but instead of using a character number, use a frame or sample number, and instead of the table in Section 3 of [RFC3629], use the extended table below.

Table 18
Number range (hexadecimal) Octet sequence (binary)
0000 0000 0000 -
0000 0000 007F
0xxxxxxx
0000 0000 0080 -
0000 0000 07FF
110xxxxx 10xxxxxx
0000 0000 0800 -
0000 0000 FFFF
1110xxxx 10xxxxxx 10xxxxxx
0000 0001 0000 -
0000 001F FFFF
11110xxx 10xxxxxx 10xxxxxx 10xxxxxx
0000 0020 0000 -
0000 03FF FFFF
111110xx 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx
0000 0400 0000 -
0000 7FFF FFFF
1111110x 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx
0000 8000 0000 -
000F FFFF FFFF
11111110 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx

If the coded number is a frame number, it MUST be equal to the number of frames preceding the current frame. If the coded number is a sample number, it MUST be equal to the number of samples preceding the current frame. In a stream where these requirements are not met, seeking is not (reliably) possible.

For example, a frame that belongs to a variable block size stream and has exactly 51 billion samples preceding it, has its coded number constructed as follows.

Octets 1-5
0b11111110 0b10101111 0b10011111 0b10110101 0b10100011
               ^^^^^^     ^^^^^^     ^^^^^^     ^^^^^^
                 |          |          |      Bits 18-13
                 |          |      Bits 24-19
                 |      Bits 30-25
             Bits 36-31

Octets 6-7
0b10111000 0b10000000
    ^^^^^^     ^^^^^^
      |       Bits 6-1
  Bits 12-7

A decoder that relies on the coded number during seeking could be vulnerable to buffer overflows or getting stuck in an infinite loop if it seeks in a stream where the coded numbers are non-consecutive or otherwise not valid. See also Section 12.

9.1.6. Uncommon block size

If the block size bits defined earlier in this section were 0b0110 or 0b0111 (uncommon block size minus 1 stored), this follows the coded number as either an 8-bit or a 16-bit unsigned number coded big-endian. A value of 65535 (corresponding to a block size of 65536) is forbidden and MUST NOT be used, because such a block size cannot be represented in the streaminfo metadata block. A value from 0 up to (and including) 14, which corresponds to a block size from 1 to 15, is only valid for the last frame in a stream and MUST NOT be used for any other frame. See also Section 8.2.

9.1.7. Uncommon sample rate

Following the uncommon block size (or the coded number if no uncommon block size is stored) is the sample rate, if the sample rate bits were 0b1100, 0b1101, or 0b1110 (uncommon sample rate stored), as either an 8-bit or a 16-bit unsigned number coded big-endian.

The sample rate MUST NOT be 0 when the subframe contains audio. A sample rate of 0 MAY be used when non-audio is represented. See Section 8.2 for details.

9.1.8. Frame header CRC

Finally, after either the frame/sample number, an uncommon block size, or an uncommon sample rate, depending on whether the latter two are stored, is an 8-bit CRC. This CRC is initialized with 0 and has the polynomial x^8 + x^2 + x^1 + x^0. This CRC covers the whole frame header before the CRC, including the sync code.

9.2. Subframes

Following the frame header are a number of subframes equal to the number of audio channels. Note that as subframes contain a bitstream that does not necessarily has to be a whole number of bytes, only the first subframe always starts at a byte boundary.

9.2.1. Subframe header

Each subframe starts with a header. The first bit of the header MUST be 0, followed by 6 bits describing which subframe type is used according to the following table, where v is the value of the 6 bits as an unsigned number.

Table 19
Value Subframe type
0b000000 Constant subframe
0b000001 Verbatim subframe
0b000010 - 0b000111 reserved
0b001000 - 0b001100 Subframe with a fixed predictor of order v-8, i.e., 0, 1, 2, 3 or 4
0b001101 - 0b011111 reserved
0b100000 - 0b111111 Subframe with a linear predictor of order v-31, i.e., 1 through 32 (inclusive)

Following the subframe type bits is a bit that flags whether the subframe uses any wasted bits (see Section 9.2.2). If it is 0, the subframe doesn't use any wasted bits and the subframe header is complete. If it is 1, the subframe does use wasted bits and the number of used wasted bits follows unary coded.

9.2.2. Wasted bits per sample

Most uncompressed audio file formats can only store audio samples with a bit depth that is an integer number of bytes. Samples of which the bit depth is not an integer number of bytes are usually stored in such formats by padding them with least-significant zero bits to a bit depth that is an integer number of bytes. For example, shifting a 14-bit sample right by 2 pads it to a 16-bit sample, which then has two zero least-significant bits. In this specification, these least-significant zero bits are referred to as wasted bits per sample or simply wasted bits. They are wasted in the sense that they contain no information, but are stored anyway.

The FLAC format can optionally take advantage of these wasted bits by signaling their presence and coding the subframe without them. To do this, the wasted bits per sample flag in a subframe header is set to 0 and the number of wasted bits per sample (k) minus 1 follows the flag in an unary encoding. For example, if k is 3, 0b001 follows. If k = 0, the wasted bits per sample flag is 0 and no unary coded k follows. In this document, if a subframe header signals a certain number of wasted bits, it is said it 'uses' these wasted bits.

If a subframe uses wasted bits (i.e., k is not equal to 0), samples are coded ignoring k least-significant bits. For example, if a frame not employing stereo decorrelation specifies a sample size of 16 bits per sample in the frame header and k of a subframe is 3, samples in the subframe are coded as 13 bits per sample. For more details, see Section 9.2.3 on how the bit depth of a subframe is calculated. A decoder MUST add k least-significant zero bits by shifting left (padding) after decoding a subframe sample. If the frame has left/side, right/side, or mid/side stereo, a decoder MUST perform padding on the subframes before restoring the channels to left and right. The number of wasted bits per sample MUST be such that the resulting number of bits per sample (of which the calculation is explained in Section 9.2.3) is larger than zero.

Besides audio files that have a certain number of wasted bits for the whole file, there exist audio files in which the number of wasted bits varies. There are DVD-Audio discs in which blocks of samples have had their least-significant bits selectively zeroed to slightly improve the compression of their otherwise lossless Meridian Lossless Packing codec. There are also audio processors like lossyWAV that enable users to improve compression of their files by a lossless audio codec in a non-lossless way. Because of this, the number of wasted bits k MAY change between frames and MAY differ between subframes. If the number of wasted bits changes halfway through a subframe (e.g., the first part has 2 wasted bits and the second part has 4 wasted bits) the subframe uses the lowest number of wasted bits, as otherwise non-zero bits would be discarded and the process would not be lossless.

9.2.3. Constant subframe

In a constant subframe, only a single sample is stored. This sample is stored as an integer number coded big-endian, signed two's complement. The number of bits used to store this sample depends on the bit depth of the current subframe. The bit depth of a subframe is equal to the bit depth as coded in the frame header (see Section 9.1.4), minus the number of used wasted bits coded in the subframe header (see Section 9.2.2). If a subframe is a side subframe (see Section 4.2), the bit depth of that subframe is increased by 1 bit.

9.2.4. Verbatim subframe

A verbatim subframe stores all samples unencoded in sequential order. See Section 9.2.3 on how a sample is stored unencoded. The number of samples that need to be stored in a subframe is given by the block size in the frame header.

9.2.5. Fixed predictor subframe

Five different fixed predictors are defined in the following table, one for each prediction order 0 through 4. In the table is also a derivation, which explains the rationale for choosing these fixed predictors.

Table 20
Order Prediction Derivation
0 0 N/A
1 a(n-1) N/A
2 2 * a(n-1) - a(n-2) a(n-1) + a'(n-1)
3 3 * a(n-1) - 3 * a(n-2) + a(n-3) a(n-1) + a'(n-1) + a''(n-1)
4 4 * a(n-1) - 6 * a(n-2) + 4 * a(n-3) - a(n-4) a(n-1) + a'(n-1) + a''(n-1) + a'''(n-1)

Where

  • n is the number of the sample being predicted.
  • a(n) is the sample being predicted.
  • a(n-1) is the sample before the one being predicted.
  • a'(n-1) is the difference between the previous sample and the sample before that, i.e., a(n-1) - a(n-2). This is the closest available first-order discrete derivative.
  • a''(n-1) is a'(n-1) - a'(n-2) or the closest available second-order discrete derivative.
  • a'''(n-1) is a''(n-1) - a''(n-2) or the closest available third-order discrete derivative.

As a predictor makes use of samples preceding the sample that is predicted, it can only be used when enough samples are known. As each subframe in FLAC is coded completely independently, the first few samples in each subframe cannot be predicted. Therefore, a number of so-called warm-up samples equal to the predictor order is stored. These are stored unencoded, bypassing the predictor and residual coding stages. See Section 9.2.3 on how samples are stored unencoded. The table below defines how a fixed predictor subframe appears in the bitstream.

Table 21
Data Description
s(n) Unencoded warm-up samples (n = subframe's bits per sample * predictor order).
Coded residual Coded residual as defined in Section 9.2.7

As the fixed predictors are specified, they do not have to be stored. The fixed predictor order, which is stored in the subframe header, specifies which predictor is used.

To encode a signal with a fixed predictor, each sample has the corresponding prediction subtracted and sent to the residual coder. To decode a signal with a fixed predictor, the residual is decoded, and then the prediction can be added for each sample. This means that decoding MUST be a sequential process within a subframe, as for each sample, enough fully decoded previous samples are needed to calculate the prediction.

For fixed predictor order 0, the prediction is always 0, thus each residual sample is equal to its corresponding input or decoded sample. The difference between a fixed predictor with order 0 and a verbatim subframe, is that a verbatim subframe stores all samples unencoded, while a fixed predictor with order 0 has all its samples processed by the residual coder.

The first order fixed predictor is comparable to how DPCM encoding works, as the resulting residual sample is the difference between the corresponding sample and the sample before it. The higher order fixed predictors can be understood as polynomials fitted to the previous samples.

9.2.6. Linear predictor subframe

Whereas fixed predictors are well suited for simple signals, using a (non-fixed) linear predictor on more complex signals can improve compression by making the residual samples even smaller. There is a certain trade-off however, as storing the predictor coefficients takes up space as well.

In the FLAC format, a predictor is defined by up to 32 predictor coefficients and a shift. To form a prediction, each coefficient is multiplied by its corresponding past sample, the results are summed, and this sum is then shifted. To encode a signal with a linear predictor, each sample has the corresponding prediction subtracted and sent to the residual coder. To decode a signal with a linear predictor, the residual is decoded, and then the prediction can be added for each sample. This means that decoding MUST be a sequential process within a subframe, as for each sample, enough decoded samples are needed to calculate the prediction.

The table below defines how a linear predictor subframe appears in the bitstream.

Table 22
Data Description
s(n) Unencoded warm-up samples (n = subframe's bits per sample * lpc order).
u(4) (Predictor coefficient precision in bits)-1 (NOTE: 0b1111 is forbidden).
s(5) Prediction right shift needed in bits.
s(n) Unencoded predictor coefficients (n = predictor coefficient precision * lpc order).
Coded residual Coded residual as defined in Section 9.2.7

See Section 9.2.3 on how the warm-up samples are stored unencoded. The unencoded predictor coefficients are stored the same way as the warm-up samples, but the number of bits needed for each coefficient is defined by the predictor coefficient precision. While the prediction right shift is signed two's complement, this number MUST NOT be negative, see Appendix B.4 for an explanation why this is.

Please note that the order in which the predictor coefficients appear in the bitstream corresponds to which past sample they belong to. In other words, the order of the predictor coefficients is opposite to the chronological order of the samples. So, the first predictor coefficient has to be multiplied with the sample directly before the sample that is being predicted, the second predictor coefficient has to be multiplied with the sample before that, etc.

9.2.7. Coded residual

The first two bits in a coded residual indicate which coding method is used. See the table below`.

Table 23
Value Description
0b00 partitioned Rice code with 4-bit parameters
0b01 partitioned Rice code with 5-bit parameters
0b10 - 0b11 reserved

Both defined coding methods work the same way, but differ in the number of bits used for Rice parameters. The 4 bits that directly follow the coding method bits form the partition order, which is an unsigned number. The rest of the coded residual consists of 2^(partition order) partitions. For example, if the 4 bits are 0b1000, the partition order is 8 and the residual is split up into 2^8 = 256 partitions.

Each partition contains a certain number of residual samples. The number of residual samples in the first partition is equal to (block size >> partition order) - predictor order, i.e., the block size divided by the number of partitions minus the predictor order. In all other partitions, the number of residual samples is equal to (block size >> partition order).

The partition order MUST be such that the block size is evenly divisible by the number of partitions. This means, for example, that for all odd block sizes, only partition order 0 is allowed. The partition order also MUST be such that the (block size >> partition order) is larger than the predictor order. This means, for example, that with a block size of 4096 and a predictor order of 4, the partition order cannot be larger than 9.

Each partition starts with a parameter. If the coded residual of a subframe is one with 4-bit Rice parameters (see the table at the start of this section), the first 4 bits of each partition are either a Rice parameter or an escape code. These 4 bits indicate an escape code if they are 0b1111, otherwise they contain the Rice parameter as an unsigned number. If the coded residual of the current subframe is one with 5-bit Rice parameters, the first 5 bits of each partition indicate an escape code if they are 0b11111, otherwise, they contain the Rice parameter as an unsigned number as well.

9.2.7.1. Escaped partition

If an escape code was used, the partition does not contain a variable-length Rice coded residual, but a fixed-length unencoded residual. Directly following the escape code are 5 bits containing the number of bits with which each residual sample is stored, as an unsigned number. The residual samples themselves are stored signed two's complement. For example, when a partition is escaped and each residual sample is stored with 3 bits, the number -1 is represented as 0b111.

Note that it is possible that the number of bits with which each sample is stored is 0, which means all residual samples in that partition have a value of 0 and that no bits are used to store the samples. In that case, the partition contains nothing except the escape code and 0b00000.

9.2.7.2. Rice code

If a Rice parameter was provided for a certain partition, that partition contains a Rice coded residual. The residual samples, which are signed numbers, are represented by unsigned numbers in the Rice code. For positive numbers, the representation is the number doubled, for negative numbers, the representation is the number multiplied by -2 and has 1 subtracted. This representation of signed numbers is also known as zigzag encoding. The zigzag encoded residual is called the folded residual.

Each folded residual sample is then split into two parts, a most-significant part and a least-significant part. The Rice parameter at the start of each partition determines where that split lies: it is the number of bits in the least-significant part. Each residual sample is then stored by coding the most-significant part as unary, followed by the least-significant part as binary.

For example, take a partition with Rice parameter 3 containing a folded residual sample with 38 as its value, which is 0b100110 in binary. The most-significant part is 0b100 (4) and is stored unary as 0b00001. The least-significant part is 0b110 (6) and is stored as is. The Rice code word is thus 0b00001110. The Rice code words for all residual samples in a partition are stored consecutively.

To decode a Rice code word, zero bits must be counted until encountering a one bit, after which a number of bits given by the Rice parameter must be read. The count of zero bits is shifted left by the Rice parameter (i.e., multiplied by 2 raised to the power Rice parameter) and bitwise ORed with (i.e., added to) the read value. This is the folded residual value. An even folded residual value is shifted right 1 bit (i.e., divided by two) to get the (unfolded) residual value. An odd folded residual value is shifted right 1 bit and then has all bits flipped (1 added to and divided by -2) to get the (unfolded) residual value, subject to negative numbers being signed two's complement on the decoding machine.

Appendix D shows decoding of a complete coded residual.

9.2.7.3. Residual sample value limit

All residual sample values MUST be representable in the range offered by a 32-bit integer, signed one's complement. Equivalently, all residual sample values MUST fall in the range offered by a 32-bit integer signed two's complement excluding the most negative possible value of that range. This means residual sample values MUST NOT have an absolute value equal to, or larger than, 2 to the power 31. A FLAC encoder MUST make sure of this. If a FLAC encoder is, for a certain subframe, unable to find a suitable predictor for which all residual samples fall within said range, it MUST default to writing a verbatim subframe. Appendix A explains in which circumstances residual samples are already implicitly representable in said range and thus an additional check is not needed.

The reason for this limit is to ensure that decoders can use 32-bit integers when processing residuals, simplifying decoding. The reason the most negative value of a 32-bit int signed two's complement is specifically excluded is to prevent decoders from having to implement specific handling of that value, as it cannot be negated within a 32-bit signed int, and most library routines calculating an absolute value have undefined behavior on processing that value.

10. Container mappings

The FLAC format can be used without any container, as it already provides for a very thin transport layer. However, the functionality of this transport is rather limited, and to be able to combine FLAC audio with video, it needs to be encapsulated by a more capable container. This presents a problem: the transport layer provided by the FLAC format mixes data that belongs to the encoded data (like block size and sample rate) with data that belongs to the transport (like checksum and timecode). The choice was made to encapsulate FLAC frames as they are, which means some data will be duplicated and potentially deviating between the FLAC frames and the encapsulating container.

As FLAC frames are completely independent of each other, container format features handling dependencies do not need to be used. For example, all FLAC frames embedded in Matroska are marked as keyframes when they are stored in a SimpleBlock, and tracks in an MP4 file containing only FLAC frames do not need a sync sample box.

10.1. Ogg mapping

The Ogg container format is defined in [RFC3533]. The first packet of a logical bitstream carrying FLAC data is structured according to the following table.

Table 24
Data Description
5 bytes Bytes 0x7F 0x46 0x4C 0x41 0x43 (as also defined by [RFC5334])
2 bytes Version number of the FLAC-in-Ogg mapping. These bytes are 0x01 0x00, meaning version 1.0 of the mapping.
2 bytes Number of header packets (excluding the first header packet) as an unsigned number coded big-endian.
4 bytes The fLaC signature
4 bytes A metadata block header for the streaminfo block
34 bytes A streaminfo metadata block

The number of header packets MAY be 0, which means the number of packets that follow is unknown. This first packet MUST NOT share a Ogg page with any other packets. This means the first page of a logical stream of FLAC-in-Ogg is always 79 bytes.

Following the first packet are one or more header packets, each of which contains a single metadata block. The first of these packets SHOULD be a Vorbis comment metadata block, for historic reasons. This is contrary to unencapsulated FLAC streams, where the order of metadata blocks is not important except for the streaminfo block and where a Vorbis comment metadata block is optional.

Following the header packets are audio packets. Each audio packet contains a single FLAC frame. The first audio packet MUST start on a new Ogg page, i.e., the last metadata block MUST finish its page before any audio packets are encapsulated.

The granule position of all pages containing header packets MUST be 0. For pages containing audio packets, the granule position is the number of the last sample contained in the last completed packet in the frame. The sample numbering considers interchannel samples. If a page contains no packet end (e.g., when it only contains the start of a large packet, which continues on the next page), then the granule position is set to the maximum value possible, i.e., 0xFF 0xFF 0xFF 0xFF 0xFF 0xFF 0xFF 0xFF.

The granule position of the first audio data page with a completed packet MAY be larger than the number of samples contained in packets that complete on that page. In other words, the apparent sample number of the first sample in the stream following from the granule position and the audio data MAY be larger than 0. This allows, for example, a server to cast a live stream to several clients that joined at different moments, without rewriting the granule position for each client.

If an audio stream is encoded where audio properties (sample rate, number of channels, or bit depth) change at some point in the stream, this should be dealt with by finishing encoding of the current Ogg stream and starting a new Ogg stream, concatenated to the previous one. This is called chaining in Ogg. See the Ogg specification [RFC3533] for details.

10.2. Matroska mapping

The Matroska container format is defined in [I-D.ietf-cellar-matroska]. The codec ID (EBML path \Segment\Tracks\TrackEntry\CodecID) assigned to signal tracks carrying FLAC data is A_FLAC in ASCII. All FLAC data before the first audio frame (i.e., the fLaC ASCII signature and all metadata blocks) is stored as CodecPrivate data (EBML path \Segment\Tracks\TrackEntry\CodecPrivate).

Each FLAC frame (including all of its subframes) is treated as a single frame in the Matroska context.

If an audio stream is encoded where audio properties (sample rate, number of channels, or bit depth) change at some point in the stream, this should be dealt with by finishing the current Matroska segment and starting a new one with the new properties.

10.3. ISO Base Media File Format (MP4) mapping

The full encapsulation definition of FLAC audio in MP4 files was deemed too extensive to include in this document. A definition document can be found at [FLAC-in-MP4-specification]. The definition document is summarized here.

The sample entry code is 'fLaC'. The channelcount and samplesize fields in the sample entry follow the values found in the FLAC stream. The samplerate field can be different, because FLAC can carry audio with much higher sample rates than can be coded for in the sample entry. When possible, the samplerate field should contain the sample rate as found in the FLAC stream, shifted left by 16 bits to get the 16.16 fixed point representation of the samplerate field. When the FLAC stream contains a sample rate higher than can be coded, the samplerate field contains the greatest expressible regular division of the sample rate, e.g., 48000 for sample rates of 96 kHz and 192 kHz or 44100 for a sample rate of 88200 Hz. When the FLAC stream contains audio with an unusual sample rate that has no regular division, the maximum value of 65535.0 Hz is used. As FLAC streams with a high sample rate are common, a parser or decoder MUST read the value from the FLAC streaminfo metadata block or a frame header to determine the actual sample rate. The sample entry contains one 'FLAC specific box' with code 'dfLa'.

The FLAC specific box extends FullBox, with version number 0 and all flags set to 0, and contains all FLAC data before the first audio frame but fLaC ASCII signature (i.e., all metadata blocks).

If an audio stream is encoded where audio properties (sample rate, number of channels or bit depth) change at some point in the stream, this MUST be dealt with in a MP4 generic manner, e.g., with several stsd atoms and different sample-description-index values in the stsc atom.

Each FLAC frame is a single sample in the context of MP4 files.

11. Implementation status

Note to RFC Editor - please remove this entire section before publication, as well as the reference to RFC 7942.

This section records the status of known implementations of the FLAC format, and is based on a proposal described in [RFC7942]. Please note that the listing of any individual implementation here does not imply endorsement by the IETF. Furthermore, no effort has been spent to verify the information presented here that was supplied by IETF contributors. This is not intended as, and must not be construed to be, a catalog of available implementations or their features. Readers are advised to note that other implementations may exist.

A reference encoder and decoder implementation of the FLAC format exists, known as libFLAC, maintained by Xiph.Org. It can be found at https://xiph.org/flac/ Note that while all libFLAC components are licensed under 3-clause BSD, the flac and metaflac command line tools often supplied together with libFLAC are licensed under GPL.

Another completely independent implementation of both encoder and decoder of the FLAC format is available in libavcodec, maintained by FFmpeg, licensed under LGPL 2.1 or later. It can be found at https://ffmpeg.org/

A list of other implementations and an overview of which parts of the format they implement can be found at [FLAC-wiki-implementations].

12. Security Considerations

Like any other codec (such as [RFC6716]), FLAC 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 FLAC codec need to take appropriate security considerations into account, as outlined in [RFC4732]. It is extremely important for the decoder to be robust against malformed payloads. Payloads that do not conform to this specification MUST NOT cause the decoder to overrun its allocated memory or take an excessive amount of resources to decode. An overrun in allocated memory could lead to arbitrary code execution by an attacker. The same applies to the encoder, even though problems with encoders are typically rarer. Malformed audio streams MUST NOT cause the encoder to misbehave because this would allow an attacker to attack transcoding gateways.

As with all compression algorithms, both encoding and decoding can produce an output much larger than the input. For decoding, the most extreme possible case of this is a frame with eight constant subframes of block size 65535 and coding for 32-bit PCM. This frame is only 49 bytes in size, but codes for more than 2 megabytes of uncompressed PCM data. For encoding, it is possible to have an even larger size increase, although such behavior is generally considered faulty. This happens if the encoder chooses a rice parameter that does not fit with the residual that has to be encoded. In such a case, very long unary coded symbols can appear, in the most extreme case, more than 4 gigabytes per sample. Decoder and encoder implementors are advised to take precautions to prevent excessive resource utilization in such cases.

Where metadata is handled, implementors are advised to either thoroughly test the handling of extreme cases or impose reasonable limits beyond the limits of this specification document. For example, a single Vorbis comment metadata block can contain millions of valid fields. It is unlikely such a limit is ever reached except in a potentially malicious file. Likewise, the media type and description of a picture metadata block can be millions of characters long, despite there being no reasonable use of such contents. One possible use case for very long character strings is in lyrics, which can be stored in Vorbis comment metadata block fields.

Various kinds of metadata blocks contain length fields or field counts. While reading a block following these lengths or counts, a decoder MUST make sure higher-level lengths or counts (most importantly, the length field of the metadata block itself) are not exceeded. As some of these length fields code string lengths, memory for which must be allocated, parsers MUST first verify that a block is valid before allocating memory based on its contents, except when explicitly instructed to salvage data from a malformed file.

Metadata blocks can also contain references, e.g., the picture metadata block can contain a URI. Applications MUST obtain explicit user approval to retrieve resources via remote protocols and to retrieve local resources not located in the same directory as the FLAC file being processed.

Seeking in a FLAC stream that is not in a container relies on the coded number in frame headers and optionally a seektable metadata block. Parsers MUST employ thorough checks on whether a found coded number or seekpoint is at all possible. Without these checks, seeking might get stuck in an infinite loop when numbers in frames are non-consecutive or otherwise not valid, which could be used in denial of service attacks.

Implementors are advised to employ fuzz testing combined with different sanitizers on FLAC decoders to find security problems. Ignoring the results of CRC checks improves the efficiency of decoder fuzz testing.

See [FLAC-decoder-testbench] for a non-exhaustive list of FLAC files with extreme configurations that lead to crashes or reboots on some known implementations. Besides providing a starting point for security testing, this set of files can also be used to test conformance with this specification.

FLAC files may contain executable code, although the FLAC format is not designed for it and it is uncommon. One use case where FLAC is occasionally used to store executable code is when compressing images of mixed mode CDs, which contain both audio and non-audio data, of which the non-audio portion can contain executable code.

13. IANA Considerations

This document registers one new media type, "audio/flac", as defined in the following section.

13.1. Media type registration

The following information serves as the registration form for the "audio/flac" media type. This media type is applicable for FLAC audio that is not packaged in a container as described in Section 10. FLAC audio packaged in such a container will take on the media type of that container, for example, audio/ogg when packaged in an Ogg container, or video/mp4 when packaged in an MP4 container alongside a video track.

Type name: audio

Subtype name: flac

Required parameters: N/A

Optional parameters: N/A

Encoding considerations: as per THISRFC

Security considerations: see the security considerations in Section
12 of THISRFC

Interoperability considerations: see the descriptions of past format
changes in Appendix B of THISRFC

Published specification: THISRFC

Applications that use this media type: ffmpeg, apache, firefox

Fragment identifier considerations: none

Additional information:

  Deprecated alias names for this type: audio/x-flac

  Magic number(s): fLaC

  File extension(s): flac

  Macintosh file type code(s): none

  Uniform Type Identifier: org.xiph.flac conforms to public.audio

  Windows Clipboard Format Name: audio/flac

Person & email address to contact for further information:
IETF CELLAR WG cellar@ietf.org

Intended usage: COMMON

Restrictions on usage: N/A

Author: IETF CELLAR WG

Change controller: Internet Engineering Task Force
(mailto:iesg@ietf.org)

Provisional registration? (standards tree only): NO

14. Acknowledgments

FLAC owes much to the many people who have advanced the audio compression field so freely. For instance:

The FLAC format, the FLAC reference implementation, and this document were originally developed by Josh Coalson. While many others have contributed since, this original effort is deeply appreciated.

15. Normative References

[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC3629]
Yergeau, F., "UTF-8, a transformation format of ISO 10646", STD 63, RFC 3629, DOI 10.17487/RFC3629, , <https://www.rfc-editor.org/info/rfc3629>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/info/rfc8174>.

16. Informative References

[Durbin]
Durbin, J., "The Fitting of Time-Series Models", DOI 10.2307/1401322, , <https://www.jstor.org/stable/1401322>.
[FIR]
"Finite impulse response - Wikipedia", <https://en.wikipedia.org/wiki/Finite_impulse_response>.
[FLAC-decoder-testbench]
"FLAC decoder testbench", commit aa7b0c6, , <https://github.com/ietf-wg-cellar/flac-test-files>.
[FLAC-in-MP4-specification]
Montgomery, C., "Encapsulation of FLAC in ISO Base Media File Format", commit 78d85dd, , <https://github.com/xiph/flac/blob/master/doc/isoflac.txt>.
[FLAC-specification-github]
"FLAC specification github repository", <https://github.com/ietf-wg-cellar/flac-specification>.
[FLAC-wiki-implementations]
"FLAC specification wiki: Implementations", <https://github.com/ietf-wg-cellar/flac-specification/wiki/Implementations>.
[FLAC-wiki-interoperability]
"FLAC specification wiki: Interoperability considerations", <https://github.com/ietf-wg-cellar/flac-specification/wiki/Interoperability-considerations>.
[HPL-1999-144]
Hans, M. and RW. Schafer, "Lossless Compression of Digital Audio", DOI 10.1109/79.939834, , <https://www.hpl.hp.com/techreports/1999/HPL-1999-144.pdf>.
[I-D.ietf-cellar-matroska]
Lhomme, S., Bunkus, M., and D. Rice, "Matroska Media Container Format Specifications", Work in Progress, Internet-Draft, draft-ietf-cellar-matroska-19, , <https://datatracker.ietf.org/doc/html/draft-ietf-cellar-matroska-19>.
[IEC.60908.1999]
International Electrotechnical Commission, "Audio recording - Compact disc digital audio system", IEC International standard 60908 second edition, .
[ISRC-handbook]
International ISRC Registration Authority, "International Standard Recording Code (ISRC) Handbook, 4th edition", , <https://www.ifpi.org/isrc_handbook/>.
[LinearPrediction]
"Linear prediction - Wikipedia", <https://en.wikipedia.org/wiki/Linear_prediction>.
[RFC3533]
Pfeiffer, S., "The Ogg Encapsulation Format Version 0", RFC 3533, DOI 10.17487/RFC3533, , <https://www.rfc-editor.org/info/rfc3533>.
[RFC4732]
Handley, M., Ed., Rescorla, E., Ed., and IAB, "Internet Denial-of-Service Considerations", RFC 4732, DOI 10.17487/RFC4732, , <https://www.rfc-editor.org/info/rfc4732>.
[RFC5334]
Goncalves, I., Pfeiffer, S., and C. Montgomery, "Ogg Media Types", RFC 5334, DOI 10.17487/RFC5334, , <https://www.rfc-editor.org/info/rfc5334>.
[RFC6716]
Valin, JM., Vos, K., and T. Terriberry, "Definition of the Opus Audio Codec", RFC 6716, DOI 10.17487/RFC6716, , <https://www.rfc-editor.org/info/rfc6716>.
[RFC7942]
Sheffer, Y. and A. Farrel, "Improving Awareness of Running Code: The Implementation Status Section", BCP 205, RFC 7942, DOI 10.17487/RFC7942, , <https://www.rfc-editor.org/info/rfc7942>.
[Rice]
Rice, RF. and JR. Plaunt, "Adaptive Variable-Length Coding for Efficient Compression of Spacecraft Television Data", DOI 10.1109/TCOM.1971.1090789, , <https://ieeexplore.ieee.org/document/1090789>.
[Shannon]
Shannon, CE., "Communication in the Presence of Noise", DOI 10.1109/JRPROC.1949.232969, , <https://ieeexplore.ieee.org/document/1697831>.
[VarLengthCode]
"Variable-length code - Wikipedia", <https://en.wikipedia.org/wiki/Variable-length_code>.
[Vorbis]
Xiph.Org, "Ogg Vorbis I format specification: comment field and header specification", <https://xiph.org/vorbis/doc/v-comment.html>.
[robinson-tr156]
Robinson, T., "SHORTEN: Simple lossless and near-lossless waveform compression", , <https://mi.eng.cam.ac.uk/reports/abstracts/robinson_tr156.html>.

Appendix A. Numerical considerations

In order to maintain lossless behavior, all arithmetic used in encoding and decoding sample values MUST be done with integer data types to eliminate the possibility of introducing rounding errors associated with floating-point arithmetic. Use of floating-point representations in analysis (e.g., finding a good predictor or Rice parameter) is not a concern, as long as the process of using the found predictor and Rice parameter to encode audio samples is implemented with only integer math.

Furthermore, the possibility of integer overflow can be eliminated by using large enough data types. Choosing a 64-bit signed data type for all arithmetic involving sample values would make sure the possibility for overflow is eliminated, but usually smaller data types are chosen for increased performance, especially in embedded devices. This appendix provides guidelines for choosing the appropriate data type for each step of encoding and decoding FLAC files.

In this appendix, signed data types are signed two's complement.

A.1. Determining the necessary data type size

To find the smallest data type size that is guaranteed not to overflow for a certain sequence of arithmetic operations, the combination of values producing the largest possible result should be considered.

If, for example, two 16-bit signed integers are added, the largest possible result forms if both values are the largest number that can be represented with a 16-bit signed integer. To store the result, a signed integer data type with at least 17 bits is needed. Similarly, when adding 4 of these values, 18 bits are needed; when adding 8, 19 bits are needed, etc. In general, the number of bits necessary when adding numbers together is increased by the log base 2 of the number of values rounded up to the nearest integer. So, when adding 18 unknown values stored in 8 bit signed integers, we need a signed integer data type of at least 13 bits to store the result, as the log base 2 of 18 rounded up is 5.

When multiplying two numbers, the number of bits needed for the result is the size of the first number plus the size of the second number. If, for example, a 16-bit signed integer is multiplied by another 16-bit signed integer, the result needs at least 32 bits to be stored without overflowing. To show this in practice, the largest signed value that can be stored in 4 bits is -8. (-8)*(-8) is 64, which needs at least 8 bits (signed) to store.

A.2. Stereo decorrelation

When stereo decorrelation is used, the side channel will have one extra bit of bit depth, see Section 4.2.

This means that while 16-bit signed integers have sufficient range to store samples from a fully decoded FLAC frame with a bit depth of 16 bits, the decoding of a side subframe in such a file will need a data type with at least 17 bits to store decoded subframe samples before undoing stereo decorrelation.

Most FLAC decoders store decoded (subframe) samples as 32-bit values, which is sufficient for files with bit depths up to (and including) 31 bits.

A.3. Prediction

A prediction (which is used to calculate the residual on encoding or added to the residual to calculate the sample value on decoding) is formed by multiplying and summing preceding sample values. In order to eliminate the possibility of integer overflow, the combination of preceding sample values and predictor coefficients producing the largest possible value should be considered.

To determine the size of the data type needed to calculate either a residual sample (on encoding) or an audio sample value (on decoding) in a fixed predictor subframe, the maximal possible value for these is calculated as described in Appendix A.1 in the following table. For example: if a frame codes for 16-bit audio and has some form of stereo decorrelation, the subframe coding for the side channel would need 16+1+3 bits if a third order fixed predictor is used.

Table 25
Order Calculation of residual Sample values summed Extra bits
0 a(n) 1 0
1 a(n) - a(n-1) 2 1
2 a(n) - 2 * a(n-1) + a(n-2) 4 2
3 a(n) - 3 * a(n-1) + 3 * a(n-2) - a(n-3) 8 3
4 a(n) - 4 * a(n-1) + 6 * a(n-2) - 4 * a(n-3) + a(n-4) 16 4

Where

  • n is the number of the sample being predicted.
  • a(n) is the sample being predicted.
  • a(n-1) is the sample before the one being predicted, a(n-2) is the sample before that, etc.

For subframes with a linear predictor, the calculation is a little more complicated. Each prediction is the sum of several multiplications. Each of these multiply a sample value with a predictor coefficient. The extra bits needed can be calculated by adding the predictor coefficient precision (in bits) to the bit depth of the audio samples. To account for the summing of these multiplications, the log base 2 of the predictor order rounded up is added.

For example, if the sample bit depth of the source is 24, the current subframe encodes a side channel (see Section 4.2), the predictor order is 12, and the predictor coefficient precision is 15 bits, the minimum required size of the used signed integer data type is at least (24 + 1) + 15 + ceil(log2(12)) = 44 bits. As another example, with a side-channel subframe bit depth of 16, a predictor order of 8, and a predictor coefficient precision of 12 bits, the minimum required size of the used signed integer data type is (16 + 1) + 12 + ceil(log2(8)) = 32 bits.

A.4. Residual

As stated in Section 9.2.7, an encoder must make sure residual samples are representable by a 32-bit integer, signed two's complement, excluding the most negative value. Continuing as in the previous section, it is possible to calculate when residual samples already implicitly fit and when an additional check is needed. This implicit fit is achieved when residuals would fit a theoretical 31-bit signed int, as that satisfies both of the mentioned criteria. When this implicit fit is not achieved, all residual values must be calculated and checked individually.

For the residual of a fixed predictor, the maximum residual sample size was already calculated in the previous section. However, for a linear predictor, the prediction is shifted right by a certain amount. The number of bits needed for the residual is the number of bits calculated in the previous section, reduced by the prediction right shift, and increased by one bit to account for the subtraction of the prediction from the current sample on encoding.

Taking the last example of the previous section, where 32 bits were needed for the prediction, the required data type size for the residual samples in case of a right shift of 10 bits would be 32 - 10 + 1 = 23 bits, which means it is not necessary to perform the aforementioned check.

As another example, when encoding 32-bit PCM with fixed predictors, all predictor orders must be checked. While the 0-order fixed predictor is guaranteed to have residual samples that fit a 32-bit signed int, it might produce a residual sample value that is the most negative representable value of that 32-bit signed int.

Note that on decoding, while the residual sample values are limited to the aforementioned range, the predictions are not. This means that while the decoding of the residual samples can happen fully in 32-bit signed integers, decoders must be sure to execute the addition of each residual sample to its accompanying prediction with a wide enough signed integer data type like on encoding.

A.5. Rice coding

When folding (i.e., zig-zag encoding) the residual sample values, no extra bits are needed when the absolute value of each residual sample is first stored in an unsigned data type of the size of the last step, then doubled, and then has one subtracted depending on whether the residual sample was positive or negative. Many implementations, however, choose to require one extra bit of data type size so zig-zag encoding can happen in one step and without a cast instead of the procedure described in the previous sentence.

Appendix B. Past format changes

This informational appendix documents the changes made to the FLAC format over the years. This information might be of use when encountering FLAC files that were made with software following the format as it was before the changes documented in this appendix.

The FLAC format was first specified in December 2000 and the bitstream format was considered frozen with the release of FLAC (the reference encoder/decoder) 1.0 in July 2001. Only changes made since this first stable release are considered in this appendix. Changes made to the FLAC streamable subset definition (see Section 7) are not considered.

B.1. Addition of blocking strategy bit

Perhaps the largest backwards incompatible change to the specification was published in July 2007. Before this change, variable block size streams were not explicitly marked as such by a flag bit in the frame header. A decoder had two ways to detect a variable block size stream, either by comparing the minimum and maximum block size in the STREAMINFO metadata block (which are equal for a fixed block size stream), or, if a decoder did not receive a STREAMINFO metadata block, by detecting a change of block size during a stream, which could in theory not happen at all. As the meaning of the coded number in the frame header depends on whether or not a stream is variable block size, this presented a problem: the meaning of the coded number could not be reliably determined. To fix this problem, one of the reserved bits was changed to be used as a blocking strategy bit. See also Section 9.1.

Along with the addition of a new flag, the meaning of the block size bits (see Section 9.1.1) was subtly changed. Initially, block size bits patterns 0b0001-0b0101 and 0b1000-0b1111 could only be used for fixed block size streams, while 0b0110 and 0b0111 could be used for both fixed block size and variable block size streams. With the change, these restrictions were lifted, and patterns 0b0001-0b1111 are now used for both variable block size and fixed block size streams.

B.2. Restriction of encoded residual samples

Another change to the specification was deemed necessary during standardization by the CELLAR working group of the IETF. As specified in Section 9.2.7 a limit is imposed on residual samples. This limit was not specified prior to the IETF standardization effort. However, as far as was known to the working group, no FLAC encoder at that time produced FLAC files containing residual samples exceeding this limit. This is mostly because it is very unlikely to encounter residual samples exceeding this limit when encoding 24-bit PCM, and encoding of PCM with higher bit depths was not yet implemented in any known encoder. In fact, these FLAC encoders would produce corrupt files upon being triggered to produce such residual samples and it is unlikely any non-experimental encoder would ever do so, even when presented with crafted material. Therefore, it was not expected that existing implementations would be rendered non-compliant by this change.

B.3. Addition of 5-bit Rice parameters

One significant addition to the format was the residual coding method using 5-bit Rice parameters. Prior to publication of this addition in July 2007, there was only one residual coding method specified, a partitioned Rice code with 4-bit Rice parameters. The range offered by this coding method proved too small when encoding 24-bit PCM, therefore, a second residual coding method was specified, identical to the first but with 5-bit Rice parameters.

B.4. Restriction of LPC shift to non-negative values

As stated in Section 9.2.6, the predictor right shift is a number signed two's complement, which MUST NOT be negative. This is because right shifting a number by a negative amount is undefined behavior in the C programming language standard. The intended behavior was that a positive number would be a right shift and a negative number would be a left shift. The FLAC reference encoder was changed in 2007 to not generate LPC subframes with a negative predictor right shift, as it turned out that the use of such subframes would only very rarely provide any benefit, and the decoders that were already widely in use at that point were not able to handle such subframes.

Appendix C. Interoperability considerations

As documented in Appendix B, there have been some changes and additions to the FLAC format. Additionally, implementation of certain features of the FLAC format took many years, meaning early decoder implementations could not be tested against files with these features. Finally, many lower-quality FLAC decoders only implement just enough features required for playback of the most common FLAC files.

This appendix provides some considerations for encoder implementations aiming to create highly compatible files. As this topic is one that might change after this document is finished, consult [FLAC-wiki-interoperability] for more up-to-date information.

C.1. Features outside of the streamable subset

As described in Section 7, FLAC specifies a subset of its capabilities as the FLAC streamable subset. Certain decoders may choose to only decode FLAC files conforming to the limitations imposed by the streamable subset. Therefore, maximum compatibility with decoders is achieved when the limitations of the FLAC streamable subset are followed when creating FLAC files.

C.2. Variable block size

Because it is often difficult to find the optimal arrangement of block sizes for maximum compression, most encoders choose to create files with a fixed block size. Because of this, many decoder implementations receive minimal use when handling variable block size streams, and this can reveal bugs or reveal that implementations do not decode them at all. Furthermore, as explained in Appendix B.1, there have been some changes to the way variable block size streams were encoded. Because of this, maximum compatibility with decoders is achieved when FLAC files are created using fixed block size streams.

C.3. 5-bit Rice parameter

As the addition of the 5-bit Rice parameter, as described in Appendix B.3, occurred quite a few years after the FLAC format was first introduced, some early decoders might not be able to decode files containing such Rice parameters. The introduction of this was specifically aimed at improving compression of 24-bit PCM audio, and compression of 16-bit PCM audio only rarely benefits from using 5-bit Rice parameters. Therefore, maximum compatibility with decoders is achieved when FLAC files containing audio with a bit depth of 16 bits or lower are created without any use of 5-bit Rice parameters.

C.4. Rice escape code

Escaped Rice partitions are seldom used, as it turned out their use provides only a very small compression improvement. As many encoders therefore do not use these by default or are not capable of producing them at all, it is likely that many decoder implementations are not able to decode them correctly. Therefore, maximum compatibility with decoders is achieved when FLAC files are created without any use of escaped Rice partitions.

C.5. Uncommon block size

For unknown reasons, some decoders have chosen to support only common block sizes except for the last block. Therefore, maximum compatibility with decoders is achieved when creating FLAC files using common block sizes, as listed in Section 9.1.1, for all but the last block.

C.6. Uncommon bit depth

Most audio is stored in bit depths that are a whole number of bytes, e.g., 8, 16 or 24 bit. There is however audio with different bit depths. A few examples:

  • DVD-Audio has the possibility to store 20 bit PCM audio.
  • DAT and DV can store 12 bit PCM audio.
  • NICAM-728 samples at 14 bit, which is companded to 10 bit.
  • 8-bit µ-law can be losslessly converted to 14 bit (Linear) PCM.
  • 8-bit A-law can be losslessly converted to 13 bit (Linear) PCM.

The FLAC format can contain these bit depths directly, but because they are uncommon, some decoders are not able to process the resulting files correctly. It is possible to store these formats in a FLAC file with a more common bit depth without sacrificing compression by padding each sample with zero bits to a bit depth that is a whole byte. The FLAC format can efficiently compress these wasted bits. See Section 9.2.2 for details.

Therefore, maximum compatibility with decoders is achieved when FLAC files are created by padding samples of such audio with zero bits to the bit depth that is the next whole number of bytes.

In cases where the original signal is already padded, this operation cannot be reversed losslessly without knowing the original bit depth. To leave no ambiguity, the original bit depth needs to be stored, for example, in a vorbis comment field, by storing the header of the original file, or in a description of the file. The choice of a suitable method is left to the implementer.

Besides audio with a 'non-whole byte' bit depth, some decoder implementations have chosen to only accept FLAC files coding for PCM audio with a bit depth of 16 bit. Many implementations support bit depths up to 24 bit but no higher. Consult [FLAC-wiki-interoperability] for more up-to-date information.

C.7. Multi-channel audio and uncommon sample rates

Many FLAC audio players are unable to render multi-channel audio or audio with an uncommon sample rate. While this is not a concern specific to the FLAC format, it is of note when requiring maximum compatibility with decoders. Unlike the previously mentioned interoperability considerations, this is one that cannot be satisfied without sacrificing the lossless nature of the FLAC format.

From a non-exhaustive inquiry, it seems that a non-negligible amount of players, especially hardware players, do not support audio with 3 or more channels or sample rates other than those considered common, see Section 9.1.2.

For those players that do support and are able to render multi-channel audio, many do not parse and use the WAVEFORMATEXTENSIBLE_CHANNEL_MASK tag (see Section 8.6.2). This too is an interoperability consideration that cannot be satisfied without sacrificing the lossless nature of the FLAC format.

C.8. Changing audio properties mid-stream

Each FLAC frame header stores the audio sample rate, number of bits per sample, and number of channels independently of the streaminfo metadata block and other frame headers. This was done to permit multicasting of FLAC files, but it also allows these properties to change mid-stream. However, many FLAC decoders do not handle such changes, as few other formats are capable of holding such streams and changing playback properties during playback is often not possible without interrupting playback. Also, as explained in Section 9, using this feature of FLAC results in various practical problems.

However, even when storing an audio stream with changing properties in FLAC encapsulated in a container capable of handling such changes, as recommended in Section 9, many decoders are not able to decode such a stream correctly. Therefore, maximum compatibility with decoders is achieved when FLAC files are created with a single set of audio properties, in which the properties coded in the streaminfo metadata block (see Section 8.2) and the properties coded in all frame headers (see Section 9.1) are the same. This can be achieved by splitting up an input stream with changing audio properties at the points where these properties change into separate streams or files.

Appendix D. Examples

This informational appendix contains short example FLAC files that are decoded step by step. These examples provide a more engaging way to understand the FLAC format than the formal specification. The text explaining these examples assumes the reader has at least cursorily read the specification and that the reader refers to the specification for explanation of the terminology used. These examples mostly focus on the layout of several metadata blocks and subframe types and the implications of certain aspects (for example, wasted bits and stereo decorrelation) on this layout.

The examples feature files generated by various FLAC encoders. These are presented in hexadecimal or binary format, followed by tables and text referring to various features by their starting bit positions in these representations. Each starting position (shortened to 'start' in the tables) is a hexadecimal byte position and a start bit within that byte, separated by a plus sign. Counts for these start at zero. For example, a feature starting at the 3rd bit of the 17th byte is referred to as starting at 0x10+2. The files that are explored in these examples can be found at [FLAC-specification-github].

All data in this appendix has been thoroughly verified. However, as this appendix is informational, if any information here conflicts with statements in the formal specification, the latter takes precedence.

D.1. Decoding example 1

This very short example FLAC file codes for PCM audio that has two channels, each containing one sample. The focus of this example is on the essential parts of a FLAC file.

D.1.1. Example file 1 in hexadecimal representation

00000000: 664c 6143 8000 0022 1000 1000  fLaC..."....
0000000c: 0000 0f00 000f 0ac4 42f0 0000  ........B...
00000018: 0001 3e84 b418 07dc 6903 0758  ..>.....i..X
00000024: 6a3d ad1a 2e0f fff8 6918 0000  j=......i...
00000030: bf03 58fd 0312 8baa 9a         ..X......

D.1.2. Example file 1 in binary representation

00000000: 01100110 01001100 01100001 01000011  fLaC
00000004: 10000000 00000000 00000000 00100010  ..."
00000008: 00010000 00000000 00010000 00000000  ....
0000000c: 00000000 00000000 00001111 00000000  ....
00000010: 00000000 00001111 00001010 11000100  ....
00000014: 01000010 11110000 00000000 00000000  B...
00000018: 00000000 00000001 00111110 10000100  ..>.
0000001c: 10110100 00011000 00000111 11011100  ....
00000020: 01101001 00000011 00000111 01011000  i..X
00000024: 01101010 00111101 10101101 00011010  j=..
00000028: 00101110 00001111 11111111 11111000  ....
0000002c: 01101001 00011000 00000000 00000000  i...
00000030: 10111111 00000011 01011000 11111101  ..X.
00000034: 00000011 00010010 10001011 10101010  ....
00000038: 10011010

D.1.3. Signature and streaminfo

The first 4 bytes of the file contain the fLaC file signature. Directly following it is a metadata block. The signature and the first metadata block header are broken down in the following table.

Table 26
Start Length Contents Description
0x00+0 4 bytes 0x664C6143 fLaC
0x04+0 1 bit 0b1 Last metadata block
0x04+1 7 bits 0b0000000 Streaminfo metadata block
0x05+0 3 bytes 0x000022 Length 34 byte

As the header indicates that this is the last metadata block, the position of the first audio frame can now be calculated as the position of the first byte after the metadata block header + the length of the block, i.e., 8+34 = 42 or 0x2a. As can be seen, 0x2a indeed contains the frame sync code for fixed block size streams, 0xfff8.

The streaminfo metadata block contents are broken down in the following table.

Table 27
Start Length Contents Description
0x08+0 2 bytes 0x1000 Min. block size 4096
0x0a+0 2 bytes 0x1000 Max. block size 4096
0x0c+0 3 bytes 0x00000f Min. frame size 15 byte
0x0f+0 3 bytes 0x00000f Max. frame size 15 byte
0x12+0 20 bits 0x0ac4, 0b0100 Sample rate 44100 hertz
0x14+4 3 bits 0b001 2 channels
0x14+7 5 bits 0b01111 Sample bit depth 16
0x15+4 36 bits 0b0000, 0x00000001 Total no. of samples 1
0x1a 16 bytes (...) MD5 signature

The minimum and maximum block size are both 4096. This was apparently the block size the encoder planned to use, but as only 1 interchannel sample was provided, no frames with 4096 samples are actually present in this file.

Note that anywhere a number of samples is mentioned (block size, total number of samples, sample rate), interchannel samples are meant.

The MD5 sum (starting at 0x1a) is 0x3e84 b418 07dc 6903 0758 6a3d ad1a 2e0f. This will be validated after decoding the samples.

D.1.4. Audio frames

The frame header starts at position 0x2a and is broken down in the following table.

Table 28
Start Length Contents Description
0x2a+0 15 bits 0xff, 0b1111100 frame sync
0x2b+7 1 bit 0b0 blocking strategy
0x2c+0 4 bits 0b0110 8-bit block size further down
0x2c+4 4 bits 0b1001 sample rate 44.1 kHz
0x2d+0 4 bits 0b0001 stereo, no decorrelation
0x2d+4 3 bits 0b100 bit depth 16 bit
0x2d+7 1 bit 0b0 mandatory 0 bit
0x2e+0 1 byte 0x00 frame number 0
0x2f+0 1 byte 0x00 block size 1
0x30+0 1 byte 0xbf frame header CRC

As the stream is a fixed block size stream, the number at 0x2e contains a frame number. As the value is smaller than 128, only 1 byte is used for the encoding.

At byte 0x31, the first subframe starts, which is broken down in the following table.

Table 29
Start Length Contents Description
0x31+0 1 bit 0b0 mandatory 0 bit
0x31+1 6 bits 0b000001 verbatim subframe
0x31+7 1 bit 0b1 wasted bits used
0x32+0 2 bits 0b01 2 wasted bits used
0x32+2 14 bits 0b011000, 0xfd 14-bit unencoded sample

As the wasted bits flag is 1 in this subframe, an unary coded number follows. Starting at 0x32, we see 0b01, which unary codes for 1, meaning this subframe uses 2 wasted bits.

As this is a verbatim subframe, the subframe only contains unencoded sample values. With a block size of 1, it contains only a single sample. The bit depth of the audio is 16 bits, but as the subframe header signals the use of 2 wasted bits, only 14 bits are stored. As no stereo decorrelation is used, a bit depth increase for the side channel is not applicable. So, the next 14 bits (starting at position 0x32+2) contain the unencoded sample coded big-endian, signed two's complement. The value reads 0b011000 11111101, or 6397. This value needs to be shifted left by 2 bits, to account for the wasted bits. The value is then 0b011000 11111101 00, or 25588.

The second subframe starts at 0x34, and is broken down in the following table.

Table 30
Start Length Contents Description
0x34+0 1 bit 0b0 mandatory 0 bit
0x34+1 6 bits 0b000001 verbatim subframe
0x34+7 1 bit 0b1 wasted bits used
0x35+0 4 bits 0b0001 4 wasted bits used
0x35+4 12 bits 0b0010, 0x8b 12-bit unencoded sample

Here the wasted bits flag is also one, but the unary coded number that follows it is 4 bit long, indicating the use of 4 wasted bits. This means the sample is stored in 12 bits. The sample value is 0b0010 10001011, or 651. This value now has to be shifted left by 4 bits, i.e., 0b0010 10001011 0000 or 10416.

At this point, we would undo stereo decorrelation if that was applicable.

As the last subframe ends byte-aligned, no padding bits follow it. The next 2 bytes, starting at 0x38, contain the frame CRC. As this is the only frame in the file, the file ends with the CRC.

To validate the MD5, we line up the samples interleaved, byte-aligned, little endian, signed two's complement. The first sample, with value 25588, translates to 0xf463, the second sample, with value 10416, translates to 0xb028. When MD5 summing 0xf463b028, we get the MD5 sum found in the header, so decoding was lossless.

D.2. Decoding example 2

This FLAC file is larger than the first example, but still contains very little audio. The focus of this example is on decoding a subframe with a fixed predictor and a coded residual, but it also contains a very short seektable, a Vorbis comment metadata block, and a padding metadata block.

D.2.1. Example file 2 in hexadecimal representation

00000000: 664c 6143 0000 0022 0010 0010  fLaC..."....
0000000c: 0000 1700 0044 0ac4 42f0 0000  .....D..B...
00000018: 0013 d5b0 5649 75e9 8b8d 8b93  ....VIu.....
00000024: 0422 757b 8103 0300 0012 0000  ."u{........
00000030: 0000 0000 0000 0000 0000 0000  ............
0000003c: 0000 0010 0400 003a 2000 0000  .......: ...
00000048: 7265 6665 7265 6e63 6520 6c69  reference li
00000054: 6246 4c41 4320 312e 332e 3320  bFLAC 1.3.3
00000060: 3230 3139 3038 3034 0100 0000  20190804....
0000006c: 0e00 0000 5449 544c 453d d7a9  ....TITLE=..
00000078: d79c d795 d79d 8100 0006 0000  ............
00000084: 0000 0000 fff8 6998 000f 9912  ......i.....
00000090: 0867 0162 3d14 4299 8f5d f70d  .g.b=.B..]..
0000009c: 6fe0 0c17 caeb 2100 0ee7 a77a  o.....!....z
000000a8: 24a1 590c 1217 b603 097b 784f  $.Y......{xO
000000b4: aa9a 33d2 85e0 70ad 5b1b 4851  ..3...p.[.HQ
000000c0: b401 0d99 d2cd 1a68 f1e6 b810  .......h....
000000cc: fff8 6918 0102 a402 c382 c40b  ..i.........
000000d8: c14a 03ee 48dd 03b6 7c13 30    .J..H...|.0

D.2.2. Example file 2 in binary representation (only audio frames)

00000088: 11111111 11111000 01101001 10011000  ..i.
0000008c: 00000000 00001111 10011001 00010010  ....
00000090: 00001000 01100111 00000001 01100010  .g.b
00000094: 00111101 00010100 01000010 10011001  =.B.
00000098: 10001111 01011101 11110111 00001101  .]..
0000009c: 01101111 11100000 00001100 00010111  o...
000000a0: 11001010 11101011 00100001 00000000  ..!.
000000a4: 00001110 11100111 10100111 01111010  ...z
000000a8: 00100100 10100001 01011001 00001100  $.Y.
000000ac: 00010010 00010111 10110110 00000011  ....
000000b0: 00001001 01111011 01111000 01001111  .{xO
000000b4: 10101010 10011010 00110011 11010010  ..3.
000000b8: 10000101 11100000 01110000 10101101  ..p.
000000bc: 01011011 00011011 01001000 01010001  [.HQ
000000c0: 10110100 00000001 00001101 10011001  ....
000000c4: 11010010 11001101 00011010 01101000  ...h
000000c8: 11110001 11100110 10111000 00010000  ....
000000cc: 11111111 11111000 01101001 00011000  ..i.
000000d0: 00000001 00000010 10100100 00000010  ....
000000d4: 11000011 10000010 11000100 00001011  ....
000000d8: 11000001 01001010 00000011 11101110  .J..
000000dc: 01001000 11011101 00000011 10110110  H...
000000e0: 01111100 00010011 00110000           |.0

D.2.3. Streaminfo metadata block

Most of the streaminfo block, including its header, is the same as in example 1, so only parts that are different are listed in the following table.

Table 31
Start Length Contents Description
0x04+0 1 bit 0b0 Not the last metadata block
0x08+0 2 bytes 0x0010 Min. block size 16
0x0a+0 2 bytes 0x0010 Max. block size 16
0x0c+0 3 bytes 0x000017 Min. frame size 23 byte
0x0f+0 3 bytes 0x000044 Max. frame size 68 byte
0x15+4 36 bits 0b0000, 0x00000013 Total no. of samples 19
0x1a 16 bytes (...) MD5 signature

This time, the minimum and maximum block sizes are reflected in the file: there is one block of 16 samples, the last block (which has 3 samples) is not considered for the minimum block size. The MD5 signature is 0xd5b0 5649 75e9 8b8d 8b93 0422 757b 8103, this will be verified at the end of this example.

D.2.4. Seektable

The seektable metadata block only holds one entry. It is not really useful here, as it points to the first frame, but it is enough for this example. The seektable metadata block is broken down in the following table.

Table 32
Start Length Contents Description
0x2a+0 1 bit 0b0 Not the last metadata block
0x2a+1 7 bits 0b0000011 Seektable metadata block
0x2b+0 3 bytes 0x000012 Length 18 byte
0x2e+0 8 bytes 0x0000000000000000 Seekpoint to sample 0
0x36+0 8 bytes 0x0000000000000000 Seekpoint to offset 0
0x3e+0 2 bytes 0x0010 Seekpoint to block size 16

D.2.5. Vorbis comment

The Vorbis comment metadata block contains the vendor string and a single comment. It is broken down in the following table.

Table 33
Start Length Contents Description
0x40+0 1 bit 0b0 Not the last metadata block
0x40+1 7 bits 0b0000100 Vorbis comment metadata block
0x41+0 3 bytes 0x00003a Length 58 byte
0x44+0 4 bytes 0x20000000 Vendor string length 32 byte
0x48+0 32 bytes (...) Vendor string
0x68+0 4 bytes 0x01000000 Number of fields 1
0x6c+0 4 bytes 0x0e000000 Field length 14 byte
0x70+0 14 bytes (...) Field contents

The vendor string is reference libFLAC 1.3.3 20190804, and the field contents of the only field is TITLE=שלום. The Vorbis comment field is 14 bytes but only 10 characters in size, because it contains four 2-byte characters.

D.2.6. Padding

The last metadata block is a (very short) padding block.

Table 34
Start Length Contents Description
0x7e+0 1 bit 0b1 Last metadata block
0x7e+1 7 bits 0b0000001 Padding metadata block
0x7f+0 3 bytes 0x000006 Length 6 byte
0x82+0 6 bytes 0x000000000000 Padding bytes

D.2.7. First audio frame

The frame header starts at position 0x88 and is broken down in the following table.

Table 35
Start Length Contents Description
0x88+0 15 bits 0xff, 0b1111100 frame sync
0x89+7 1 bit 0b0 blocking strategy
0x8a+0 4 bits 0b0110 8-bit block size further down
0x8a+4 4 bits 0b1001 sample rate 44.1 kHz
0x8b+0 4 bits 0b1001 right-side stereo
0x8b+4 3 bits 0b100 bit depth 16 bit
0x8b+7 1 bit 0b0 mandatory 0 bit
0x8c+0 1 byte 0x00 frame number 0
0x8d+0 1 byte 0x0f block size 16
0x8e+0 1 byte 0x99 frame header CRC

The first subframe starts at byte 0x8f, it is broken down in the following table excluding the coded residual. As this subframe codes for a side channel, the bit depth is increased by 1 bit from 16 bit to 17 bit. This is most clearly present in the unencoded warm-up sample.

Table 36
Start Length Contents Description
0x8f+0 1 bit 0b0 mandatory 0 bit
0x8f+1 6 bits 0b001001 fixed subframe, 1st order
0x8f+7 1 bit 0b0 no wasted bits used
0x90+0 17 bits 0x0867, 0b0 unencoded warm-up sample

The coded residual is broken down in the following table. All quotients are unary coded, all remainders are stored unencoded with a number of bits specified by the Rice parameter.

Table 37
Start Length Contents Description
0x92+1 2 bits 0b00 Rice code with 4-bit parameter
0x92+3 4 bits 0b0000 Partition order 0
0x92+7 4 bits 0b1011 Rice parameter 11
0x93+3 4 bits 0b0001 Quotient 3
0x93+7 11 bits 0b00011110100 Remainder 244
0x95+2 2 bits 0b01 Quotient 1
0x95+4 11 bits 0b01000100001 Remainder 545
0x96+7 2 bits 0b01 Quotient 1
0x97+1 11 bits 0b00110011000 Remainder 408
0x98+4 1 bit 0b1 Quotient 0
0x98+5 11 bits 0b11101011101 Remainder 1885
0x9a+0 1 bit 0b1 Quotient 0
0x9a+1 11 bits 0b11101110000 Remainder 1904
0x9b+4 1 bit 0b1 Quotient 0
0x9b+5 11 bits 0b10101101111 Remainder 1391
0x9d+0 1 bit 0b1 Quotient 0
0x9d+1 11 bits 0b11000000000 Remainder 1536
0x9e+4 1 bit 0b1 Quotient 0
0x9e+5 11 bits 0b10000010111 Remainder 1047
0xa0+0 1 bit 0b1 Quotient 0
0xa0+1 11 bits 0b10010101110 Remainder 1198
0xa1+4 1 bit 0b1 Quotient 0
0xa1+5 11 bits 0b01100100001 Remainder 801
0xa3+0 13 bits 0b0000000000001 Quotient 12
0xa4+5 11 bits 0b11011100111 Remainder 1767
0xa6+0 1 bit 0b1 Quotient 0
0xa6+1 11 bits 0b01001110111 Remainder 631
0xa7+4 1 bit 0b1 Quotient 0
0xa7+5 11 bits 0b01000100100 Remainder 548
0xa9+0 1 bit 0b1 Quotient 0
0xa9+1 11 bits 0b01000010101 Remainder 533
0xaa+4 1 bit 0b1 Quotient 0
0xaa+5 11 bits 0b00100001100 Remainder 268

At this point, the decoder should know it is done decoding the coded residual, as it received 16 samples: 1 warm-up sample and 15 residual samples. Each residual sample can be calculated from the quotient and remainder, and undoing the zig-zag encoding. For example, the value of the first zig-zag encoded residual sample is 3 * 2^11 + 244 = 6388. As this is an even number, the zig-zag encoding is undone by dividing by 2, the residual sample value is 3194. This is done for all residual samples in the next table.

Table 38
Quotient Remainder Zig-zag encoded Residual sample value
3 244 6388 3194
1 545 2593 -1297
1 408 2456 1228
0 1885 1885 -943
0 1904 1904 952
0 1391 1391 -696
0 1536 1536 768
0 1047 1047 -524
0 1198 1198 599
0 801 801 -401
12 1767 26343 -13172
0 631 631 -316
0 548 548 274
0 533 533 -267
0 268 268 134

It can be calculated that using a Rice code is, in this case, more efficient than storing values unencoded. The Rice code (excluding the partition order and parameter) is 199 bits in length. The largest residual value (-13172) would need 15 bits to be stored unencoded, so storing all 15 samples with 15 bits results in a sequence with a length of 225 bits.

The next step is using the predictor and the residuals to restore the sample values. As this subframe uses a fixed predictor with order 1, this means adding the residual value to the value of the previous sample.

Table 39
Residual Sample value
(warm-up) 4302
3194 7496
-1297 6199
1228 7427
-943 6484
952 7436
-696 6740
768 7508
-524 6984
599 7583
-401 7182
-13172 -5990
-316 -6306
274 -6032
-267 -6299
134 -6165

With this, the decoding of the first subframe is complete. The decoding of the second subframe is very similar, as it also uses a fixed predictor of order 1, so this is left as an exercise for the reader, the results are in the next table. The next step is undoing stereo decorrelation, which is done in the following table. As the stereo decorrelation is right-side, in which the actual ordering of the subframes is side-right, the samples in the right channel come directly from the second subframe, while the samples in the left channel are found by adding the values of both subframes for each sample.

Table 40
Subframe 1 Subframe 2 Left Right
4302 6070 10372 6070
7496 10545 18041 10545
6199 8743 14942 8743
7427 10449 17876 10449
6484 9143 15627 9143
7436 10463 17899 10463
6740 9502 16242 9502
7508 10569 18077 10569
6984 9840 16824 9840
7583 10680 18263 10680
7182 10113 17295 10113
-5990 -8428 -14418 -8428
-6306 -8895 -15201 -8895
-6032 -8476 -14508 -8476
-6299 -8896 -15195 -8896
-6165 -8653 -14818 -8653

As the second subframe ends byte-aligned, no padding bits follow it. Finally, the last 2 bytes of the frame contain the frame CRC.

D.2.8. Second audio frame

The second audio frame is very similar to the frame decoded in the first example, but this time not 1 but 3 samples are present.

The frame header starts at position 0xcc and is broken down in the following table.

Table 41
Start Length Contents Description
0xcc+0 15 bits 0xff, 0b1111100 frame sync
0xcd+7 1 bit 0b0 blocking strategy
0xce+0 4 bits 0b0110 8-bit block size further down
0xce+4 4 bits 0b1001 sample rate 44.1 kHz
0xcf+0 4 bits 0b0001 stereo, no decorrelation
0xcf+4 3 bits 0b100 bit depth 16 bit
0xcf+7 1 bit 0b0 mandatory 0 bit
0xd0+0 1 byte 0x01 frame number 1
0xd1+0 1 byte 0x02 block size 3
0xd2+0 1 byte 0xa4 frame header CRC

The first subframe starts at 0xd3+0 and is broken down in the following table.

Table 42
Start Length Contents Description
0xd3+0 1 bit 0b0 mandatory 0 bit
0xd3+1 6 bits 0b000001 verbatim subframe
0xd3+7 1 bit 0b0 no wasted bits used
0xd4+0 16 bits 0xc382 16-bit unencoded sample
0xd6+0 16 bits 0xc40b 16-bit unencoded sample
0xd8+0 16 bits 0xc14a 16-bit unencoded sample

The second subframe starts at 0xda+0 and is broken down in the following table.

Table 43
Start Length Contents Description
0xda+0 1 bit 0b0 mandatory 0 bit
0xda+1 6 bits 0b000001 verbatim subframe
0xda+7 1 bit 0b1 wasted bits used
0xdb+0 1 bit 0b1 1 wasted bit used
0xdb+1 15 bits 0b110111001001000 15-bit unencoded sample
0xdd+0 15 bits 0b110111010000001 15-bit unencoded sample
0xde+7 15 bits 0b110110110011111 15-bit unencoded sample

As this subframe uses wasted bits, the 15-bit unencoded samples need to be shifted left by 1 bit. For example, sample 1 is stored as -4536 and becomes -9072 after shifting left 1 bit.

As the last subframe does not end on byte alignment, 2 padding bits are added before the 2 byte frame CRC follows at 0xe1+0.

D.2.9. MD5 checksum verification

All samples in the file have been decoded, we can now verify the MD5 sum. All sample values must be interleaved and stored signed, coded little-endian. The result of this follows in groups of 12 samples (i.e., 6 interchannel samples) per line.

0x8428 B617 7946 3129 5E3A 2722 D445 D128 0B3D B723 EB45 DF28
0x723f 1E25 9D46 4929 B841 7026 5747 B829 8F43 8127 AEC7 14DF
0x9FC4 41DD 54C7 E4DE A5C4 40DD 1EC6 33DE 82C3 90DC 0BC4 02DD
0x4AC1 3EDB

The MD5sum of this is indeed the same as the one found in the streaminfo metadata block.

D.3. Decoding example 3

This example is once again a very short FLAC file. The focus of this example is on decoding a subframe with a linear predictor and a coded residual with more than one partition.

D.3.1. Example file 3 in hexadecimal representation

00000000: 664c 6143 8000 0022 1000 1000  fLaC..."....
0000000c: 0000 1f00 001f 07d0 0070 0000  .........p..
00000018: 0018 f8f9 e396 f5cb cfc6 dc80  ............
00000024: 7f99 7790 6b32 fff8 6802 0017  ..w.k2..h...
00000030: e944 004f 6f31 3d10 47d2 27cb  .D.Oo1=.G.'.
0000003c: 6d09 0831 452b dc28 2222 8057  m..1E+.("".W
00000048: a3                             .

D.3.2. Example file 3 in binary representation (only audio frame)

0000002a: 11111111 11111000 01101000 00000010  ..h.
0000002e: 00000000 00010111 11101001 01000100  ...D
00000032: 00000000 01001111 01101111 00110001  .Oo1
00000036: 00111101 00010000 01000111 11010010  =.G.
0000003a: 00100111 11001011 01101101 00001001  '.m.
0000003e: 00001000 00110001 01000101 00101011  .1E+
00000042: 11011100 00101000 00100010 00100010  .(""
00000046: 10000000 01010111 10100011           .W.

D.3.3. Streaminfo metadata block

Most of the streaminfo metadata block, including its header, is the same as in example 1, so only parts that are different are listed in the following table.

Table 44
Start Length Contents Description
0x0c+0 3 bytes 0x00001f Min. frame size 31 byte
0x0f+0 3 bytes 0x00001f Max. frame size 31 byte
0x12+0 20 bits 0x07d0, 0x0000 Sample rate 32000 hertz
0x14+4 3 bits 0b000 1 channel
0x14+7 5 bits 0b00111 Sample bit depth 8 bit
0x15+4 36 bits 0b0000, 0x00000018 Total no. of samples 24
0x1a 16 bytes (...) MD5 signature

D.3.4. Audio frame

The frame header starts at position 0x2a and is broken down in the following table.

Table 45
Start Length Contents Description
0x2a+0 15 bits 0xff, 0b1111100 Frame sync
0x2b+7 1 bit 0b0 blocking strategy
0x2c+0 4 bits 0b0110 8-bit block size further down
0x2c+4 4 bits 0b1000 Sample rate 32 kHz
0x2d+0 4 bits 0b0000 Mono audio (1 channel)
0x2d+4 3 bits 0b001 Bit depth 8 bit
0x2d+7 1 bit 0b0 Mandatory 0 bit
0x2e+0 1 byte 0x00 Frame number 0
0x2f+0 1 byte 0x17 Block size 24
0x30+0 1 byte 0xe9 Frame header CRC

The first and only subframe starts at byte 0x31, it is broken down in the following table, without the coded residual.

Table 46
Start Length Contents Description
0x31+0 1 bit 0b0 Mandatory 0 bit
0x31+1 6 bits 0b100010 Linear prediction subframe, 3rd order
0x31+7 1 bit 0b0 No wasted bits used
0x32+0 8 bits 0x00 Unencoded warm-up sample 0
0x33+0 8 bits 0x4f Unencoded warm-up sample 79
0x34+0 8 bits 0x6f Unencoded warm-up sample 111
0x35+0 4 bits 0b0011 Coefficient precision 4 bit
0x35+4 5 bits 0b00010 Prediction right shift 2
0x36+1 4 bits 0b0111 Predictor coefficient 7
0x36+5 4 bits 0b1010 Predictor coefficient -6
0x37+1 4 bits 0b0010 Predictor coefficient 2

The data stream continues with the coded residual, which is broken down in the following table. Residual partitions 3 and 4 are left as an exercise for the reader.

Table 47
Start Length Contents Description
0x37+5 2 bits 0b00 Rice-coded residual, 4-bit parameter
0x37+7 4 bits 0b0010 Partition order 2
0x38+3 4 bits 0b0011 Rice parameter 3
0x38+7 1 bit 0b1 Quotient 0
0x39+0 3 bits 0b110 Remainder 6
0x39+3 1 bit 0b1 Quotient 0
0x39+4 3 bits 0b001 Remainder 1
0x39+7 4 bits 0b0001 Quotient 3
0x3a+3 3 bits 0b001 Remainder 1
0x3a+6 4 bits 0b1111 No Rice parameter, escape code
0x3b+2 5 bits 0b00101 Partition encoded with 5 bits
0x3b+7 5 bits 0b10110 Residual -10
0x3c+4 5 bits 0b11010 Residual -6
0x3d+1 5 bits 0b00010 Residual 2
0x3d+6 5 bits 0b01000 Residual 8
0x3e+3 5 bits 0b01000 Residual 8
0x3f+0 5 bits 0b00110 Residual 6
0x3f+5 4 bits 0b0010 Rice parameter 2
0x40+1 22 bits (...) Residual partition 3
0x42+7 4 bits 0b0001 Rice parameter 1
0x43+3 23 bits (...) Residual partition 4

The frame ends with 6 padding bits and a 2 byte frame CRC

To decode this subframe, 21 predictions have to be calculated and added to their corresponding residuals. This is a sequential process: as each prediction uses previous samples, it is not possible to start this decoding halfway a subframe or decode a subframe with parallel threads.

The following table breaks down the calculation for each sample. For example, the predictor without shift value of row 4 is found by applying the predictor with the three warm-up samples: 7*111 - 6*79 + 2*0 = 303. This value is then shifted right by 2 bits: 303 >> 2 = 75. Then, the decoded residual sample is added: 75 + 3 = 78.

Table 48
Residual Predictor w/o shift Predictor Sample value
(warm-up) N/A N/A 0
(warm-up) N/A N/A 79
(warm-up) N/A N/A 111
3 303 75 78
-1 38 9 8
-13 -190 -48 -61
-10 -319 -80 -90
-6 -248 -62 -68
2 -58 -15 -13
8 137 34 42
8 236 59 67
6 191 47 53
0 53 13 13
-3 -93 -24 -27
-5 -161 -41 -46
-4 -134 -34 -38
-1 -44 -11 -12
1 52 13 14
1 94 23 24
4 60 15 19
2 17 4 6
2 -24 -6 -4
2 -26 -7 -5
0 1 0 0

By lining all these samples up, we get the following input for the MD5 summing process.

0x004F 6F4E 08C3 A6BC F32A 4335 0DE5 D2DA F40E 1813 06FC FB00

Which indeed results in the MD5 signature found in the streaminfo metadata block.

Authors' Addresses

Martijn van Beurden
Netherlands
Andrew Weaver