Data Formats

Android uses a wide variety of audio data formats internally, and exposes a subset of these in public APIs, file formats, and the Hardware Abstraction Layer (HAL).

Properties

The audio data formats are classified by their properties:

Compression
Uncompressed, lossless compressed, or lossy compressed. PCM is the most common uncompressed audio format. FLAC is a lossless compressed format, while MP3 and AAC are lossy compressed formats.
Bit depth
Number of significant bits per audio sample.
Container size
Number of bits used to store or transmit a sample. Usually this is the same as the bit depth, but sometimes additional padding bits are allocated for alignment. For example, a 24-bit sample could be contained within a 32-bit word.
Alignment
If the container size is exactly equal to the bit depth, the representation is called packed. Otherwise the representation is unpacked. The significant bits of the sample are typically aligned with either the leftmost (most significant) or rightmost (least significant) bit of the container. It is conventional to use the terms packed and unpacked only when the bit depth is not a power of two.
Signedness
Whether samples are signed or unsigned.
Representation
Either fixed point or floating point; see below.

Fixed point representation

Fixed point is the most common representation for uncompressed PCM audio data, especially at hardware interfaces.

A fixed-point number has a fixed (constant) number of digits before and after the radix point. All of our representations use base 2, so we substitute bit for digit, and binary point or simply point for radix point. The bits to the left of the point are the integer part, and the bits to the right of the point are the fractional part.

We speak of integer PCM, because fixed-point values are usually stored and manipulated as integer values. The interpretation as fixed-point is implicit.

We use two's complement for all signed fixed-point representations, so the following holds where all values are in units of one LSB:

|largest negative value| = |largest positive value| + 1

Q and U notation

There are various notations for fixed-point representation in an integer. We use Q notation: Qm.n means m integer bits and n fractional bits. The "Q" counts as one bit, though the value is expressed in two's complement. The total number of bits is m + n + 1.

Um.n is for unsigned numbers: m integer bits and n fractional bits, and the "U" counts as zero bits. The total number of bits is m + n.

The integer part may be used in the final result, or be temporary. In the latter case, the bits that make up the integer part are called guard bits. The guard bits permit an intermediate calculation to overflow, as long as the final value is within range or can be clamped to be within range. Note that fixed-point guard bits are at the left, while floating-point unit guard digits are used to reduce roundoff error and are on the right.

Floating point representation

Floating point is an alternative to fixed point, in which the location of the point can vary. The primary advantages of floating-point include:

  • Greater headroom and dynamic range; floating-point arithmetic tolerates exceeeding nominal ranges during intermediate computation, and only clamps values at the end
  • Support for special values such as infinities and NaN
  • Easier to use in many cases

Historically, floating-point arithmetic was slower than integer or fixed-point arithmetic, but now it is common for floating-point to be faster, provided control flow decisions aren't based on the value of a computation.

Android formats for audio

The major Android formats for audio are listed in the table below:

Notation
Property Q0.15 Q0.7 1 Q0.23 Q0.31 float
Container
bits
16 8 24 or 32 2 32 32
Significant bits
including sign
16 8 24 24 or 32 2 25 3
Headroom
in dB
0 0 0 0 126 4
Dynamic range
in dB
90 42 138 138 to 186 900 5

All fixed-point formats above have a nominal range of -1.0 to +1.0 minus one LSB. There is one more negative value than positive value due to the two's complement representation.

Footnotes:

  1. All formats above express signed sample values. The 8-bit format is commonly called "unsigned", but it is actually a signed value with bias of 0.10000000.
  2. Q0.23 may be packed into 24 bits (three 8-bit bytes), or unpacked in 32 bits. If unpacked, the significant bits are either right-justified towards the LSB with sign extension padding towards the MSB (Q8.23), or left-justified towards the MSB with zero fill towards the LSB (Q0.31). Q0.31 theoretically permits up to 32 significant bits, but hardware interfaces that accept Q0.31 rarely use all the bits.
  3. Single-precision floating point has 23 explicit bits plus one hidden bit and sign bit, resulting in 25 significant bits total. Denormal numbers have fewer significant bits.
  4. Single-precision floating point can express values up to ±1.7e+38, which explains the large headroom.
  5. The dynamic range shown is for denormals up to the nominal maximum value ±1.0. Note that some architecture-specific floating point implementations such as NEON don't support denormals.

Conversions

This section discusses data conversions between various representations.

Floating point conversions

To convert a value from Qm.n format to floating point:

  1. Convert the value to floating point as if it were an integer (by ignoring the point).
  2. Multiply by 2-n.

For example, to convert a Q4.27 internal value to floating point, use:

float = integer * (2 ^ -27)

Conversions from floating point to fixed point follow these rules:

  • Single-precision floating point has a nominal range of ±1.0, but the full range for intermediate values is ±1.7e+38. Conversion between floating point and fixed point for external representation (such as output to audio devices) will consider only the nominal range, with clamping for values that exceed that range. In particular, when +1.0 is converted to a fixed-point format, it is clamped to +1.0 minus one LSB.
  • Denormals (subnormals) and both +/- 0.0 are allowed in representation, but may be silently converted to 0.0 during processing.
  • Infinities will either pass through operations or will be silently hard-limited to +/- 1.0. Generally the latter is for conversion to a fixed-point format.
  • NaN behavior is undefined: a NaN may propagate as an identical NaN, or may be converted to a Default NaN, may be silently hard limited to +/- 1.0, or silently converted to 0.0, or result in an error.

Fixed point conversions

Conversions between different Qm.n formats follow these rules:

  • When m is increased, sign extend the integer part at left.
  • When m is decreased, clamp the integer part.
  • When n is increased, zero extend the fractional part at right.
  • When n is decreased, either dither, round, or truncate the excess fractional bits at right.

For example, to convert a Q4.27 value to Q0.15 (without dither or rounding), right shift the Q4.27 value by 12 bits, and clamp any results that exceed the 16-bit signed range. This aligns the point of the Q representation.

To convert Q7.24 to Q7.23, do a signed divide by 2, or equivalently add the sign bit to the Q7.24 integer quantity, and then signed right shift by 1. Note that a simple signed right shift is not equivalent to a signed divide by 2.

Lossy and lossless conversions

A conversion is lossless if it is invertible: a conversion from A to B to C results in A = C. Otherwise the conversion is lossy.

Lossless conversions permit round-trip format conversion.

Conversions from fixed point representation with 25 or fewer significant bits to floating point are lossless. Conversions from floating point to any common fixed point representation are lossy.