.. Licensed to the Apache Software Foundation (ASF) under one
.. or more contributor license agreements.  See the NOTICE file
.. distributed with this work for additional information
.. regarding copyright ownership.  The ASF licenses this file
.. to you under the Apache License, Version 2.0 (the
.. "License"); you may not use this file except in compliance
.. with the License.  You may obtain a copy of the License at

..   http://www.apache.org/licenses/LICENSE-2.0

.. Unless required by applicable law or agreed to in writing,
.. software distributed under the License is distributed on an
.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
.. KIND, either express or implied.  See the License for the
.. specific language governing permissions and limitations
.. under the License.

.. _format_columnar:

*********************
Arrow Columnar Format
*********************

*Version: 1.3*

The "Arrow Columnar Format" includes a language-agnostic in-memory
data structure specification, metadata serialization, and a protocol
for serialization and generic data transport.

This document is intended to provide adequate detail to create a new
implementation of the columnar format without the aid of an existing
implementation. We utilize Google's `Flatbuffers`_ project for
metadata serialization, so it will be necessary to refer to the
project's `Flatbuffers protocol definition files`_
while reading this document.

The columnar format has some key features:

* Data adjacency for sequential access (scans)
* O(1) (constant-time) random access
* SIMD and vectorization-friendly
* Relocatable without "pointer swizzling", allowing for true zero-copy
  access in shared memory

The Arrow columnar format provides analytical performance and data
locality guarantees in exchange for comparatively more expensive
mutation operations. This document is concerned only with in-memory
data representation and serialization details; issues such as
coordinating mutation of data structures are left to be handled by
implementations.

Terminology
===========

Since different projects have used different words to describe various
concepts, here is a small glossary to help disambiguate.

* **Array** or **Vector**: a sequence of values with known length all
  having the same type. These terms are used interchangeably in
  different Arrow implementations, but we use "array" in this
  document.
* **Slot**: a single logical value in an array of some particular data type
* **Buffer** or **Contiguous memory region**: a sequential virtual
  address space with a given length. Any byte can be reached via a
  single pointer offset less than the region's length.
* **Physical Layout**: The underlying memory layout for an array
  without taking into account any value semantics. For example, a
  32-bit signed integer array and 32-bit floating point array have the
  same layout.
* **Parent** and **child arrays**: names to express relationships
  between physical value arrays in a nested type structure. For
  example, a ``List<T>``-type parent array has a T-type array as its
  child (see more on lists below).
* **Primitive type**: a data type having no child types. This includes
  such types as fixed bit-width, variable-size binary, and null types.
* **Nested type**: a data type whose full structure depends on one or
  more other child types. Two fully-specified nested types are equal
  if and only if their child types are equal. For example, ``List<U>``
  is distinct from ``List<V>`` iff U and V are different types.
* **Logical type**: An application-facing semantic value type that is
  implemented using some physical layout. For example, Decimal
  values are stored as 16 bytes in a fixed-size binary
  layout. Similarly, strings can be stored as ``List<1-byte>``. A
  timestamp may be stored as 64-bit fixed-size layout.

.. _format_layout:

Physical Memory Layout
======================

Arrays are defined by a few pieces of metadata and data:

* A logical data type.
* A sequence of buffers.
* A length as a 64-bit signed integer. Implementations are permitted
  to be limited to 32-bit lengths, see more on this below.
* A null count as a 64-bit signed integer.
* An optional **dictionary**, for dictionary-encoded arrays.

Nested arrays additionally have a sequence of one or more sets of
these items, called the **child arrays**.

Each logical data type has a well-defined physical layout. Here are
the different physical layouts defined by Arrow:

* **Primitive (fixed-size)**: a sequence of values each having the
  same byte or bit width
* **Variable-size Binary**: a sequence of values each having a variable
  byte length. Two variants of this layout are supported using 32-bit
  and 64-bit length encoding.
* **Fixed-size List**: a nested layout where each value has the same
  number of elements taken from a child data type.
* **Variable-size List**: a nested layout where each value is a
  variable-length sequence of values taken from a child data type. Two
  variants of this layout are supported using 32-bit and 64-bit length
  encoding.
* **Struct**: a nested layout consisting of a collection of named
  child **fields** each having the same length but possibly different
  types.
* **Sparse** and **Dense Union**: a nested layout representing a
  sequence of values, each of which can have type chosen from a
  collection of child array types.
* **Dictionary-Encoded**: a layout consisting of a sequence of
  integers (any bit-width) which represent indexes into a dictionary
  which could be of any type.
* **Run-End Encoded (REE)**: a nested layout consisting of two child arrays,
  one representing values, and one representing the logical index where
  the run of a corresponding value ends.
* **Null**: a sequence of all null values, having null logical type

The Arrow columnar memory layout only applies to *data* and not
*metadata*. Implementations are free to represent metadata in-memory
in whichever form is convenient for them. We handle metadata
**serialization** in an implementation-independent way using
`Flatbuffers`_, detailed below.

Buffer Alignment and Padding
----------------------------

Implementations are recommended to allocate memory on aligned
addresses (multiple of 8- or 64-bytes) and pad (overallocate) to a
length that is a multiple of 8 or 64 bytes. When serializing Arrow
data for interprocess communication, these alignment and padding
requirements are enforced. If possible, we suggest that you prefer
using 64-byte alignment and padding. Unless otherwise noted, padded
bytes do not need to have a specific value.

The alignment requirement follows best practices for optimized memory
access:

* Elements in numeric arrays will be guaranteed to be retrieved via aligned access.
* On some architectures alignment can help limit partially used cache lines.

The recommendation for 64 byte alignment comes from the `Intel
performance guide`_ that recommends alignment of memory to match SIMD
register width.  The specific padding length was chosen because it
matches the largest SIMD instruction registers available on widely
deployed x86 architecture (Intel AVX-512).

The recommended padding of 64 bytes allows for using `SIMD`_
instructions consistently in loops without additional conditional
checks.  This should allow for simpler, efficient and CPU
cache-friendly code.  In other words, we can load the entire 64-byte
buffer into a 512-bit wide SIMD register and get data-level
parallelism on all the columnar values packed into the 64-byte
buffer. Guaranteed padding can also allow certain compilers to
generate more optimized code directly (e.g. One can safely use Intel's
``-qopt-assume-safe-padding``).

Array lengths
-------------

Array lengths are represented in the Arrow metadata as a 64-bit signed
integer. An implementation of Arrow is considered valid even if it only
supports lengths up to the maximum 32-bit signed integer, though. If using
Arrow in a multi-language environment, we recommend limiting lengths to
2 :sup:`31` - 1 elements or less. Larger data sets can be represented using
multiple array chunks.

Null count
----------

The number of null value slots is a property of the physical array and
considered part of the data structure. The null count is represented
in the Arrow metadata as a 64-bit signed integer, as it may be as
large as the array length.

Validity bitmaps
----------------

Any value in an array may be semantically null, whether primitive or nested
type.

All array types, with the exception of union types (more on these later),
utilize a dedicated memory buffer, known as the validity (or "null") bitmap, to
encode the nullness or non-nullness of each value slot. The validity bitmap
must be large enough to have at least 1 bit for each array slot.

Whether any array slot is valid (non-null) is encoded in the respective bits of
this bitmap. A 1 (set bit) for index ``j`` indicates that the value is not null,
while a 0 (bit not set) indicates that it is null. Bitmaps are to be
initialized to be all unset at allocation time (this includes padding): ::

    is_valid[j] -> bitmap[j / 8] & (1 << (j % 8))

We use `least-significant bit (LSB) numbering`_ (also known as
bit-endianness). This means that within a group of 8 bits, we read
right-to-left: ::

    values = [0, 1, null, 2, null, 3]

    bitmap
    j mod 8   7  6  5  4  3  2  1  0
              0  0  1  0  1  0  1  1

Arrays having a 0 null count may choose to not allocate the validity
bitmap; how this is represented depends on the implementation (for
example, a C++ implementation may represent such an "absent" validity
bitmap using a NULL pointer). Implementations may choose to always allocate
a validity bitmap anyway as a matter of convenience. Consumers of Arrow
arrays should be ready to handle those two possibilities.

Nested type arrays (except for union types as noted above) have their own
top-level validity bitmap and null count, regardless of the null count and
valid bits of their child arrays.

Array slots which are null are not required to have a particular value;
any "masked" memory can have any value and need not be zeroed, though
implementations frequently choose to zero memory for null values.

Fixed-size Primitive Layout
---------------------------

A primitive value array represents an array of values each having the
same physical slot width typically measured in bytes, though the spec
also provides for bit-packed types (e.g. boolean values encoded in
bits).

Internally, the array contains a contiguous memory buffer whose total
size is at least as large as the slot width multiplied by the array
length. For bit-packed types, the size is rounded up to the nearest
byte.

The associated validity bitmap is contiguously allocated (as described
above) but does not need to be adjacent in memory to the values
buffer.

**Example Layout: Int32 Array**

For example a primitive array of int32s: ::

    [1, null, 2, 4, 8]

Would look like: ::

    * Length: 5, Null count: 1
    * Validity bitmap buffer:

      |Byte 0 (validity bitmap) | Bytes 1-63            |
      |-------------------------|-----------------------|
      | 00011101                | 0 (padding)           |

    * Value Buffer:

      |Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-19 | Bytes 20-63 |
      |------------|-------------|-------------|-------------|-------------|-------------|
      | 1          | unspecified | 2           | 4           | 8           | unspecified |

**Example Layout: Non-null int32 Array**

``[1, 2, 3, 4, 8]`` has two possible layouts: ::

    * Length: 5, Null count: 0
    * Validity bitmap buffer:

      | Byte 0 (validity bitmap) | Bytes 1-63            |
      |--------------------------|-----------------------|
      | 00011111                 | 0 (padding)           |

    * Value Buffer:

      |Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | bytes 12-15 | bytes 16-19 | Bytes 20-63 |
      |------------|-------------|-------------|-------------|-------------|-------------|
      | 1          | 2           | 3           | 4           | 8           | unspecified |

or with the bitmap elided: ::

    * Length 5, Null count: 0
    * Validity bitmap buffer: Not required
    * Value Buffer:

      |Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | bytes 12-15 | bytes 16-19 | Bytes 20-63 |
      |------------|-------------|-------------|-------------|-------------|-------------|
      | 1          | 2           | 3           | 4           | 8           | unspecified |

Variable-size Binary Layout
---------------------------

Each value in this layout consists of 0 or more bytes. While primitive
arrays have a single values buffer, variable-size binary have an
**offsets** buffer and **data** buffer.

The offsets buffer contains `length + 1` signed integers (either
32-bit or 64-bit, depending on the logical type), which encode the
start position of each slot in the data buffer. The length of the
value in each slot is computed using the difference between the offset
at that slot's index and the subsequent offset. For example, the
position and length of slot j is computed as:

::

    slot_position = offsets[j]
    slot_length = offsets[j + 1] - offsets[j]  // (for 0 <= j < length)

It should be noted that a null value may have a positive slot length.
That is, a null value may occupy a **non-empty** memory space in the data
buffer. When this is true, the content of the corresponding memory space
is undefined.

Offsets must be monotonically increasing, that is ``offsets[j+1] >= offsets[j]``
for ``0 <= j < length``, even for null slots. This property ensures the
location for all values is valid and well defined.

Generally the first slot in the offsets array is 0, and the last slot
is the length of the values array. When serializing this layout, we
recommend normalizing the offsets to start at 0.

.. _variable-size-list-layout:

Variable-size List Layout
-------------------------

List is a nested type which is semantically similar to variable-size
binary. It is defined by two buffers, a validity bitmap and an offsets
buffer, and a child array. The offsets are the same as in the
variable-size binary case, and both 32-bit and 64-bit signed integer
offsets are supported options for the offsets. Rather than referencing
an additional data buffer, instead these offsets reference the child
array.

Similar to the layout of variable-size binary, a null value may
correspond to a **non-empty** segment in the child array. When this is
true, the content of the corresponding segment can be arbitrary.

A list type is specified like ``List<T>``, where ``T`` is any type
(primitive or nested). In these examples we use 32-bit offsets where
the 64-bit offset version would be denoted by ``LargeList<T>``.

**Example Layout: ``List<Int8>`` Array**

We illustrate an example of ``List<Int8>`` with length 4 having values::

    [[12, -7, 25], null, [0, -127, 127, 50], []]

will have the following representation: ::

    * Length: 4, Null count: 1
    * Validity bitmap buffer:

      | Byte 0 (validity bitmap) | Bytes 1-63            |
      |--------------------------|-----------------------|
      | 00001101                 | 0 (padding)           |

    * Offsets buffer (int32)

      | Bytes 0-3  | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-19 | Bytes 20-63 |
      |------------|-------------|-------------|-------------|-------------|-------------|
      | 0          | 3           | 3           | 7           | 7           | unspecified |

    * Values array (Int8array):
      * Length: 7,  Null count: 0
      * Validity bitmap buffer: Not required
      * Values buffer (int8)

        | Bytes 0-6                    | Bytes 7-63  |
        |------------------------------|-------------|
        | 12, -7, 25, 0, -127, 127, 50 | unspecified |

**Example Layout: ``List<List<Int8>>``**

``[[[1, 2], [3, 4]], [[5, 6, 7], null, [8]], [[9, 10]]]``

will be represented as follows: ::

    * Length 3
    * Nulls count: 0
    * Validity bitmap buffer: Not required
    * Offsets buffer (int32)

      | Bytes 0-3  | Bytes 4-7  | Bytes 8-11 | Bytes 12-15 | Bytes 16-63 |
      |------------|------------|------------|-------------|-------------|
      | 0          |  2         |  5         |  6          | unspecified |

    * Values array (`List<Int8>`)
      * Length: 6, Null count: 1
      * Validity bitmap buffer:

        | Byte 0 (validity bitmap) | Bytes 1-63  |
        |--------------------------|-------------|
        | 00110111                 | 0 (padding) |

      * Offsets buffer (int32)

        | Bytes 0-27           | Bytes 28-63 |
        |----------------------|-------------|
        | 0, 2, 4, 7, 7, 8, 10 | unspecified |

      * Values array (Int8):
        * Length: 10, Null count: 0
        * Validity bitmap buffer: Not required

          | Bytes 0-9                     | Bytes 10-63 |
          |-------------------------------|-------------|
          | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | unspecified |

Fixed-Size List Layout
----------------------

Fixed-Size List is a nested type in which each array slot contains a
fixed-size sequence of values all having the same type.

A fixed size list type is specified like ``FixedSizeList<T>[N]``,
where ``T`` is any type (primitive or nested) and ``N`` is a 32-bit
signed integer representing the length of the lists.

A fixed size list array is represented by a values array, which is a
child array of type T. T may also be a nested type. The value in slot
``j`` of a fixed size list array is stored in an ``N``-long slice of
the values array, starting at an offset of ``j * N``.

**Example Layout: ``FixedSizeList<byte>[4]`` Array**

Here we illustrate ``FixedSizeList<byte>[4]``.

For an array of length 4 with respective values: ::

    [[192, 168, 0, 12], null, [192, 168, 0, 25], [192, 168, 0, 1]]

will have the following representation: ::

    * Length: 4, Null count: 1
    * Validity bitmap buffer:

      | Byte 0 (validity bitmap) | Bytes 1-63            |
      |--------------------------|-----------------------|
      | 00001101                 | 0 (padding)           |

    * Values array (byte array):
      * Length: 16,  Null count: 0
      * validity bitmap buffer: Not required

        | Bytes 0-3       | Bytes 4-7   | Bytes 8-15                      |
        |-----------------|-------------|---------------------------------|
        | 192, 168, 0, 12 | unspecified | 192, 168, 0, 25, 192, 168, 0, 1 |


Struct Layout
-------------

A struct is a nested type parameterized by an ordered sequence of
types (which can all be distinct), called its fields. Each field must
have a UTF8-encoded name, and these field names are part of the type
metadata.

Physically, a struct array has one child array for each field. The
child arrays are independent and need not be adjacent to each other in
memory. A struct array also has a validity bitmap to encode top-level
validity information.

For example, the struct (field names shown here as strings for illustration
purposes)::

    Struct <
      name: VarBinary
      age: Int32
    >

has two child arrays, one ``VarBinary`` array (using variable-size binary
layout) and one 4-byte primitive value array having ``Int32`` logical
type.

**Example Layout: ``Struct<VarBinary, Int32>``**

The layout for ``[{'joe', 1}, {null, 2}, null, {'mark', 4}]`` would be: ::

    * Length: 4, Null count: 1
    * Validity bitmap buffer:

      |Byte 0 (validity bitmap) | Bytes 1-63            |
      |-------------------------|-----------------------|
      | 00001011                | 0 (padding)           |

    * Children arrays:
      * field-0 array (`VarBinary`):
        * Length: 4, Null count: 2
        * Validity bitmap buffer:

          | Byte 0 (validity bitmap) | Bytes 1-63            |
          |--------------------------|-----------------------|
          | 00001001                 | 0 (padding)           |

        * Offsets buffer:

          | Bytes 0-19     |
          |----------------|
          | 0, 3, 3, 3, 7  |

         * Values array:
            * Length: 7, Null count: 0
            * Validity bitmap buffer: Not required

            * Value buffer:

              | Bytes 0-6      |
              |----------------|
              | joemark        |

      * field-1 array (int32 array):
        * Length: 4, Null count: 1
        * Validity bitmap buffer:

          | Byte 0 (validity bitmap) | Bytes 1-63            |
          |--------------------------|-----------------------|
          | 00001011                 | 0 (padding)           |

        * Value Buffer:

          |Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-63 |
          |------------|-------------|-------------|-------------|-------------|
          | 1          | 2           | unspecified | 4           | unspecified |

Struct Validity
~~~~~~~~~~~~~~~

A struct array has its own validity bitmap that is independent of its
child arrays' validity bitmaps. The validity bitmap for the struct
array might indicate a null when one or more of its child arrays has
a non-null value in its corresponding slot; or conversely, a child
array might have a null in its validity bitmap while the struct array's
validity bitmap shows a non-null value.

Therefore, to know whether a particular child entry is valid, one must
take the logical AND of the corresponding bits in the two validity bitmaps
(the struct array's and the child array's).

This is illustrated in the example above, the child arrays have valid entries
for the null struct but they are "hidden" by the struct array's validity
bitmap. However, when treated independently, corresponding entries of the
children array will be non-null.

Union Layout
------------

A union is defined by an ordered sequence of types; each slot in the
union can have a value chosen from these types. The types are named
like a struct's fields, and the names are part of the type metadata.

Unlike other data types, unions do not have their own validity bitmap. Instead,
the nullness of each slot is determined exclusively by the child arrays which
are composed to create the union.

We define two distinct union types, "dense" and "sparse", that are
optimized for different use cases.

Dense Union
~~~~~~~~~~~

Dense union represents a mixed-type array with 5 bytes of overhead for
each value. Its physical layout is as follows:

* One child array for each type
* Types buffer: A buffer of 8-bit signed integers. Each type in the
  union has a corresponding type id whose values are found in this
  buffer. A union with more than 127 possible types can be modeled as
  a union of unions.
* Offsets buffer: A buffer of signed Int32 values indicating the
  relative offset into the respective child array for the type in a
  given slot. The respective offsets for each child value array must
  be in order / increasing.

**Example Layout: ``DenseUnion<f: Float32, i: Int32>``**

For the union array: ::

    [{f=1.2}, null, {f=3.4}, {i=5}]

will have the following layout: ::

    * Length: 4, Null count: 0
    * Types buffer:

      |Byte 0   | Byte 1      | Byte 2   | Byte 3   | Bytes 4-63  |
      |---------|-------------|----------|----------|-------------|
      | 0       | 0           | 0        | 1        | unspecified |

    * Offset buffer:

      |Bytes 0-3 | Bytes 4-7   | Bytes 8-11 | Bytes 12-15 | Bytes 16-63 |
      |----------|-------------|------------|-------------|-------------|
      | 0        | 1           | 2          | 0           | unspecified |

    * Children arrays:
      * Field-0 array (f: Float32):
        * Length: 2, Null count: 1
        * Validity bitmap buffer: 00000101

        * Value Buffer:

          | Bytes 0-11     | Bytes 12-63  |
          |----------------|-------------|
          | 1.2, null, 3.4 | unspecified |


      * Field-1 array (i: Int32):
        * Length: 1, Null count: 0
        * Validity bitmap buffer: Not required

        * Value Buffer:

          | Bytes 0-3 | Bytes 4-63  |
          |-----------|-------------|
          | 5         | unspecified |

Sparse Union
~~~~~~~~~~~~

A sparse union has the same structure as a dense union, with the omission of
the offsets array. In this case, the child arrays are each equal in length to
the length of the union.

While a sparse union may use significantly more space compared with a
dense union, it has some advantages that may be desirable in certain
use cases:

* A sparse union is more amenable to vectorized expression evaluation in some use cases.
* Equal-length arrays can be interpreted as a union by only defining the types array.

**Example layout: ``SparseUnion<i: Int32, f: Float32, s: VarBinary>``**

For the union array: ::

    [{i=5}, {f=1.2}, {s='joe'}, {f=3.4}, {i=4}, {s='mark'}]

will have the following layout: ::

    * Length: 6, Null count: 0
    * Types buffer:

     | Byte 0     | Byte 1      | Byte 2      | Byte 3      | Byte 4      | Byte 5       | Bytes  6-63           |
     |------------|-------------|-------------|-------------|-------------|--------------|-----------------------|
     | 0          | 1           | 2           | 1           | 0           | 2            | unspecified (padding) |

    * Children arrays:

      * i (Int32):
        * Length: 6, Null count: 4
        * Validity bitmap buffer:

          |Byte 0 (validity bitmap) | Bytes 1-63            |
          |-------------------------|-----------------------|
          |00010001                 | 0 (padding)           |

        * Value buffer:

          |Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-19 | Bytes 20-23  | Bytes 24-63           |
          |------------|-------------|-------------|-------------|-------------|--------------|-----------------------|
          | 5          | unspecified | unspecified | unspecified | 4           |  unspecified | unspecified (padding) |

      * f (Float32):
        * Length: 6, Null count: 4
        * Validity bitmap buffer:

          |Byte 0 (validity bitmap) | Bytes 1-63            |
          |-------------------------|-----------------------|
          | 00001010                | 0 (padding)           |

        * Value buffer:

          |Bytes 0-3    | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-19 | Bytes 20-23  | Bytes 24-63           |
          |-------------|-------------|-------------|-------------|-------------|--------------|-----------------------|
          | unspecified |  1.2        | unspecified | 3.4         | unspecified |  unspecified | unspecified (padding) |

      * s (`VarBinary`)
        * Length: 6, Null count: 4
        * Validity bitmap buffer:

          | Byte 0 (validity bitmap) | Bytes 1-63            |
          |--------------------------|-----------------------|
          | 00100100                 | 0 (padding)           |

        * Offsets buffer (Int32)

          | Bytes 0-3  | Bytes 4-7   | Bytes 8-11  | Bytes 12-15 | Bytes 16-19 | Bytes 20-23 | Bytes 24-27 | Bytes 28-63 |
          |------------|-------------|-------------|-------------|-------------|-------------|-------------|-------------|
          | 0          | 0           | 0           | 3           | 3           | 3           | 7           | unspecified |

        * Values array (VarBinary):
          * Length: 7,  Null count: 0
          * Validity bitmap buffer: Not required

            | Bytes 0-6  | Bytes 7-63            |
            |------------|-----------------------|
            | joemark    | unspecified (padding) |

Only the slot in the array corresponding to the type index is considered. All
"unselected" values are ignored and could be any semantically correct array
value.

Null Layout
-----------

We provide a simplified memory-efficient layout for the Null data type
where all values are null. In this case no memory buffers are
allocated.

.. _dictionary-encoded-layout:

Dictionary-encoded Layout
-------------------------

Dictionary encoding is a data representation technique to represent
values by integers referencing a **dictionary** usually consisting of
unique values. It can be effective when you have data with many
repeated values.

Any array can be dictionary-encoded. The dictionary is stored as an optional
property of an array. When a field is dictionary encoded, the values are
represented by an array of non-negative integers representing the index of the
value in the dictionary. The memory layout for a dictionary-encoded array is
the same as that of a primitive integer layout. The dictionary is handled as a
separate columnar array with its own respective layout.

As an example, you could have the following data: ::

    type: VarBinary

    ['foo', 'bar', 'foo', 'bar', null, 'baz']

In dictionary-encoded form, this could appear as:

::

    data VarBinary (dictionary-encoded)
       index_type: Int32
       values: [0, 1, 0, 1, null, 2]

    dictionary
       type: VarBinary
       values: ['foo', 'bar', 'baz']

Note that a dictionary is permitted to contain duplicate values or
nulls:

::

    data VarBinary (dictionary-encoded)
       index_type: Int32
       values: [0, 1, 3, 1, 4, 2]

    dictionary
       type: VarBinary
       values: ['foo', 'bar', 'baz', 'foo', null]

The null count of such arrays is dictated only by the validity bitmap
of its indices, irrespective of any null values in the dictionary.

Since unsigned integers can be more difficult to work with in some cases
(e.g. in the JVM), we recommend preferring signed integers over unsigned
integers for representing dictionary indices. Additionally, we recommend
avoiding using 64-bit unsigned integer indices unless they are required by an
application.

We discuss dictionary encoding as it relates to serialization further
below.

.. _run-end-encoded-layout:

Run-End Encoded Layout
----------------------

Run-end encoding (REE) is a variation of run-length encoding (RLE). These
encodings are well-suited for representing data containing sequences of the
same value, called runs. In run-end encoding, each run is represented as a
value and an integer giving the index in the array where the run ends.

Any array can be run-end encoded. A run-end encoded array has no buffers
by itself, but has two child arrays. The first child array, called the run ends array,
holds either 16, 32, or 64-bit signed integers. The actual values of each run
are held in the second child array.
For the purposes of determining field names and schemas, these child arrays
are prescribed the standard names of **run_ends** and **values** respectively.

The values in the first child array represent the accumulated length of all runs 
from the first to the current one, i.e. the logical index where the
current run ends. This allows relatively efficient random access from a logical
index using binary search. The length of an individual run can be determined by
subtracting two adjacent values. (Contrast this with run-length encoding, in
which the lengths of the runs are represented directly, and in which random
access is less efficient.) 

.. note::
   Because the ``run_ends`` child array cannot have nulls, it's reasonable
   to consider why the ``run_ends`` are a child array instead of just a
   buffer, like the offsets for a :ref:`variable-size-list-layout`. This
   layout was considered, but it was decided to use the child arrays. 

   Child arrays allow us to keep the "logical length" (the decoded length)
   associated with the parent array and the "physical length" (the number
   of run ends) associated with the child arrays.  If ``run_ends`` was a
   buffer in the parent array then the size of the buffer would be unrelated
   to the length of the array and this would be confusing.


A run must have have a length of at least 1. This means the values in the
run ends array all are positive and in strictly ascending order. A run end cannot be
null.

The REE parent has no validity bitmap, and it's null count field should always be 0.
Null values are encoded as runs with the value null.

As an example, you could have the following data: ::

    type: Float32
    [1.0, 1.0, 1.0, 1.0, null, null, 2.0]

In Run-end-encoded form, this could appear as:

::

    * Length: 7, Null count: 0
    * Child Arrays:

      * run_ends (Int32):
        * Length: 3, Null count: 0 (Run Ends cannot be null)
        * Validity bitmap buffer: Not required (if it exists, it should be all 1s)
        * Values buffer

          | Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | Bytes 12-63           |
          |-------------|-------------|-------------|-----------------------|
          | 4           | 6           | 7           | unspecified (padding) |

      * values (Float32):
        * Length: 3, Null count: 1
        * Validity bitmap buffer:

          | Byte 0 (validity bitmap) | Bytes 1-63            |
          |--------------------------|-----------------------|
          | 00000101                 | 0 (padding)           |

        * Values buffer

          | Bytes 0-3   | Bytes 4-7   | Bytes 8-11  | Bytes 12-63           |
          |-------------|-------------|-------------|-----------------------|
          | 1.0         | unspecified | 2.0         | unspecified (padding) |


Buffer Listing for Each Layout
------------------------------

For the avoidance of ambiguity, we provide listing the order and type
of memory buffers for each layout.

.. csv-table:: Buffer Layouts
   :header: "Layout Type", "Buffer 0", "Buffer 1", "Buffer 2"
   :widths: 30, 20, 20, 20

   "Primitive",validity,data,
   "Variable Binary",validity,offsets,data
   "List",validity,offsets,
   "Fixed-size List",validity,,
   "Struct",validity,,
   "Sparse Union",type ids,,
   "Dense Union",type ids,offsets,
   "Null",,,
   "Dictionary-encoded",validity,data (indices),
   "Run-end encoded",,,

Logical Types
=============

The `Schema.fbs`_ defines built-in logical types supported by the
Arrow columnar format. Each logical type uses one of the above
physical layouts. Nested logical types may have different physical
layouts depending on the particular realization of the type.

We do not go into detail about the logical types definitions in this
document as we consider `Schema.fbs`_ to be authoritative.

.. _format-ipc:

Serialization and Interprocess Communication (IPC)
==================================================

The primitive unit of serialized data in the columnar format is the
"record batch". Semantically, a record batch is an ordered collection
of arrays, known as its **fields**, each having the same length as one
another but potentially different data types. A record batch's field
names and types collectively form the batch's **schema**.

In this section we define a protocol for serializing record batches
into a stream of binary payloads and reconstructing record batches
from these payloads without need for memory copying.

The columnar IPC protocol utilizes a one-way stream of binary messages
of these types:

* Schema
* RecordBatch
* DictionaryBatch

We specify a so-called *encapsulated IPC message* format which
includes a serialized Flatbuffer type along with an optional message
body. We define this message format before describing how to serialize
each constituent IPC message type.

Encapsulated message format
---------------------------

For simple streaming and file-based serialization, we define a
"encapsulated" message format for interprocess communication. Such
messages can be "deserialized" into in-memory Arrow array objects by
examining only the message metadata without any need to copy or move
any of the actual data.

The encapsulated binary message format is as follows:

* A 32-bit continuation indicator. The value ``0xFFFFFFFF`` indicates
  a valid message. This component was introduced in version 0.15.0 in
  part to address the 8-byte alignment requirement of Flatbuffers
* A 32-bit little-endian length prefix indicating the metadata size
* The message metadata as using the ``Message`` type defined in
  `Message.fbs`_
* Padding bytes to an 8-byte boundary
* The message body, whose length must be a multiple of 8 bytes

Schematically, we have: ::

    <continuation: 0xFFFFFFFF>
    <metadata_size: int32>
    <metadata_flatbuffer: bytes>
    <padding>
    <message body>

The complete serialized message must be a multiple of 8 bytes so that messages
can be relocated between streams. Otherwise the amount of padding between the
metadata and the message body could be non-deterministic.

The ``metadata_size`` includes the size of the ``Message`` plus
padding. The ``metadata_flatbuffer`` contains a serialized ``Message``
Flatbuffer value, which internally includes:

* A version number
* A particular message value (one of ``Schema``, ``RecordBatch``, or
  ``DictionaryBatch``)
* The size of the message body
* A ``custom_metadata`` field for any application-supplied metadata

When read from an input stream, generally the ``Message`` metadata is
initially parsed and validated to obtain the body size. Then the body
can be read.

Schema message
--------------

The Flatbuffers files `Schema.fbs`_ contains the definitions for all
built-in logical data types and the ``Schema`` metadata type which
represents the schema of a given record batch. A schema consists of
an ordered sequence of fields, each having a name and type. A
serialized ``Schema`` does not contain any data buffers, only type
metadata.

The ``Field`` Flatbuffers type contains the metadata for a single
array. This includes:

* The field's name
* The field's logical type
* Whether the field is semantically nullable. While this has no
  bearing on the array's physical layout, many systems distinguish
  nullable and non-nullable fields and we want to allow them to
  preserve this metadata to enable faithful schema round trips.
* A collection of child ``Field`` values, for nested types
* A ``dictionary`` property indicating whether the field is
  dictionary-encoded or not. If it is, a dictionary "id" is assigned
  to allow matching a subsequent dictionary IPC message with the
  appropriate field.

We additionally provide both schema-level and field-level
``custom_metadata`` attributes allowing for systems to insert their
own application defined metadata to customize behavior.

RecordBatch message
-------------------

A RecordBatch message contains the actual data buffers corresponding
to the physical memory layout determined by a schema. The metadata for
this message provides the location and size of each buffer, permitting
Array data structures to be reconstructed using pointer arithmetic and
thus no memory copying.

The serialized form of the record batch is the following:

* The ``data header``, defined as the ``RecordBatch`` type in
  `Message.fbs`_.
* The ``body``, a flat sequence of memory buffers written end-to-end
  with appropriate padding to ensure a minimum of 8-byte alignment

The data header contains the following:

* The length and null count for each flattened field in the record
  batch
* The memory offset and length of each constituent ``Buffer`` in the
  record batch's body

Fields and buffers are flattened by a pre-order depth-first traversal
of the fields in the record batch. For example, let's consider the
schema ::

    col1: Struct<a: Int32, b: List<item: Int64>, c: Float64>
    col2: Utf8

The flattened version of this is: ::

    FieldNode 0: Struct name='col1'
    FieldNode 1: Int32 name='a'
    FieldNode 2: List name='b'
    FieldNode 3: Int64 name='item'
    FieldNode 4: Float64 name='c'
    FieldNode 5: Utf8 name='col2'

For the buffers produced, we would have the following (refer to the
table above): ::

    buffer 0: field 0 validity
    buffer 1: field 1 validity
    buffer 2: field 1 values
    buffer 3: field 2 validity
    buffer 4: field 2 offsets
    buffer 5: field 3 validity
    buffer 6: field 3 values
    buffer 7: field 4 validity
    buffer 8: field 4 values
    buffer 9: field 5 validity
    buffer 10: field 5 offsets
    buffer 11: field 5 data

The ``Buffer`` Flatbuffers value describes the location and size of a
piece of memory. Generally these are interpreted relative to the
**encapsulated message format** defined below.

The ``size`` field of ``Buffer`` is not required to account for padding
bytes. Since this metadata can be used to communicate in-memory pointer
addresses between libraries, it is recommended to set ``size`` to the actual
memory size rather than the padded size.

Byte Order (`Endianness`_)
---------------------------

The Arrow format is little endian by default.

Serialized Schema metadata has an endianness field indicating
endianness of RecordBatches. Typically this is the endianness of the
system where the RecordBatch was generated. The main use case is
exchanging RecordBatches between systems with the same Endianness.  At
first we will return an error when trying to read a Schema with an
endianness that does not match the underlying system. The reference
implementation is focused on Little Endian and provides tests for
it. Eventually we may provide automatic conversion via byte swapping.

IPC Streaming Format
--------------------

We provide a streaming protocol or "format" for record batches. It is
presented as a sequence of encapsulated messages, each of which
follows the format above. The schema comes first in the stream, and it
is the same for all of the record batches that follow. If any fields
in the schema are dictionary-encoded, one or more ``DictionaryBatch``
messages will be included. ``DictionaryBatch`` and ``RecordBatch``
messages may be interleaved, but before any dictionary key is used in
a ``RecordBatch`` it should be defined in a ``DictionaryBatch``. ::

    <SCHEMA>
    <DICTIONARY 0>
    ...
    <DICTIONARY k - 1>
    <RECORD BATCH 0>
    ...
    <DICTIONARY x DELTA>
    ...
    <DICTIONARY y DELTA>
    ...
    <RECORD BATCH n - 1>
    <EOS [optional]: 0xFFFFFFFF 0x00000000>

.. note:: An edge-case for interleaved dictionary and record batches occurs
   when the record batches contain dictionary encoded arrays that are
   completely null. In this case, the dictionary for the encoded column might
   appear after the first record batch.

When a stream reader implementation is reading a stream, after each
message, it may read the next 8 bytes to determine both if the stream
continues and the size of the message metadata that follows. Once the
message flatbuffer is read, you can then read the message body.

The stream writer can signal end-of-stream (EOS) either by writing 8 bytes
containing the 4-byte continuation indicator (``0xFFFFFFFF``) followed by 0
metadata length (``0x00000000``) or closing the stream interface. We
recommend the ".arrows" file extension for the streaming format although
in many cases these streams will not ever be stored as files.

IPC File Format
---------------

We define a "file format" supporting random access that is an extension of
the stream format. The file starts and ends with a magic string ``ARROW1``
(plus padding). What follows in the file is identical to the stream format.
At the end of the file, we write a *footer* containing a redundant copy of
the schema (which is a part of the streaming format) plus memory offsets and
sizes for each of the data blocks in the file. This enables random access to
any record batch in the file. See `File.fbs`_ for the precise details of the
file footer.

Schematically we have: ::

    <magic number "ARROW1">
    <empty padding bytes [to 8 byte boundary]>
    <STREAMING FORMAT with EOS>
    <FOOTER>
    <FOOTER SIZE: int32>
    <magic number "ARROW1">

In the file format, there is no requirement that dictionary keys
should be defined in a ``DictionaryBatch`` before they are used in a
``RecordBatch``, as long as the keys are defined somewhere in the
file. Further more, it is invalid to have more than one **non-delta**
dictionary batch per dictionary ID (i.e. dictionary replacement is not
supported). Delta dictionaries are applied in the order they appear in
the file footer. We recommend the ".arrow" extension for files created with
this format. Note that files created with this format are sometimes called
"Feather V2" or with the ".feather" extension, the name and the extension
derived from "Feather (V1)", which was a proof of concept early in
the Arrow project for language-agnostic fast data frame storage for
Python (pandas) and R.

Dictionary Messages
-------------------

Dictionaries are written in the stream and file formats as a sequence of record
batches, each having a single field. The complete semantic schema for a
sequence of record batches, therefore, consists of the schema along with all of
the dictionaries. The dictionary types are found in the schema, so it is
necessary to read the schema to first determine the dictionary types so that
the dictionaries can be properly interpreted: ::

    table DictionaryBatch {
      id: long;
      data: RecordBatch;
      isDelta: boolean = false;
    }

The dictionary ``id`` in the message metadata can be referenced one or more times
in the schema, so that dictionaries can even be used for multiple fields. See
the :ref:`dictionary-encoded-layout` section for more about the semantics of
dictionary-encoded data.

The dictionary ``isDelta`` flag allows existing dictionaries to be
expanded for future record batch materializations. A dictionary batch
with ``isDelta`` set indicates that its vector should be concatenated
with those of any previous batches with the same ``id``. In a stream
which encodes one column, the list of strings ``["A", "B", "C", "B",
"D", "C", "E", "A"]``, with a delta dictionary batch could take the
form: ::

    <SCHEMA>
    <DICTIONARY 0>
    (0) "A"
    (1) "B"
    (2) "C"

    <RECORD BATCH 0>
    0
    1
    2
    1

    <DICTIONARY 0 DELTA>
    (3) "D"
    (4) "E"

    <RECORD BATCH 1>
    3
    2
    4
    0
    EOS

Alternatively, if ``isDelta`` is set to false, then the dictionary
replaces the existing dictionary for the same ID.  Using the same
example as above, an alternate encoding could be: ::


    <SCHEMA>
    <DICTIONARY 0>
    (0) "A"
    (1) "B"
    (2) "C"

    <RECORD BATCH 0>
    0
    1
    2
    1

    <DICTIONARY 0>
    (0) "A"
    (1) "C"
    (2) "D"
    (3) "E"

    <RECORD BATCH 1>
    2
    1
    3
    0
    EOS


Custom Application Metadata
---------------------------

We provide a ``custom_metadata`` field at three levels to provide a
mechanism for developers to pass application-specific metadata in
Arrow protocol messages. This includes ``Field``, ``Schema``, and
``Message``.

The colon symbol ``:`` is to be used as a namespace separator. It can
be used multiple times in a key.

The ``ARROW`` pattern is a reserved namespace for internal Arrow use
in the ``custom_metadata`` fields. For example,
``ARROW:extension:name``.

.. _format_metadata_extension_types:

Extension Types
---------------

User-defined "extension" types can be defined setting certain
``KeyValue`` pairs in ``custom_metadata`` in the ``Field`` metadata
structure. These extension keys are:

* ``'ARROW:extension:name'`` for the string name identifying the
  custom data type. We recommend that you use a "namespace"-style
  prefix for extension type names to minimize the possibility of
  conflicts with multiple Arrow readers and writers in the same
  application. For example, use ``myorg.name_of_type`` instead of
  simply ``name_of_type``
* ``'ARROW:extension:metadata'`` for a serialized representation
  of the ``ExtensionType`` necessary to reconstruct the custom type

.. note::
   Extension names beginning with ``arrow.`` are reserved for
   :ref:`canonical extension types <format_canonical_extensions>`,
   they should not be used for third-party extension types.

This extension metadata can annotate any of the built-in Arrow logical
types. The intent is that an implementation that does not support an
extension type can still handle the underlying data. For example a
16-byte UUID value could be embedded in ``FixedSizeBinary(16)``, and
implementations that do not have this extension type can still work
with the underlying binary values and pass along the
``custom_metadata`` in subsequent Arrow protocol messages.

Extension types may or may not use the
``'ARROW:extension:metadata'`` field. Let's consider some example
extension types:

* ``uuid`` represented as ``FixedSizeBinary(16)`` with empty metadata
* ``latitude-longitude`` represented as ``struct<latitude: double,
  longitude: double>``, and empty metadata
* ``tensor`` (multidimensional array) stored as ``Binary`` values and
  having serialized metadata indicating the data type and shape of
  each value. This could be JSON like ``{'type': 'int8', 'shape': [4,
  5]}`` for a 4x5 cell tensor.
* ``trading-time`` represented as ``Timestamp`` with serialized
  metadata indicating the market trading calendar the data corresponds
  to

.. seealso::
   :ref:`format_canonical_extensions`


Implementation guidelines
=========================

An execution engine (or framework, or UDF executor, or storage engine,
etc) can implement only a subset of the Arrow spec and/or extend it
given the following constraints:

Implementing a subset of the spec
---------------------------------

* **If only producing (and not consuming) arrow vectors**: Any subset
  of the vector spec and the corresponding metadata can be implemented.
* **If consuming and producing vectors**: There is a minimal subset of
  vectors to be supported.  Production of a subset of vectors and
  their corresponding metadata is always fine.  Consumption of vectors
  should at least convert the unsupported input vectors to the
  supported subset (for example Timestamp.millis to timestamp.micros
  or int32 to int64).

Extensibility
-------------

An execution engine implementor can also extend their memory
representation with their own vectors internally as long as they are
never exposed. Before sending data to another system expecting Arrow
data, these custom vectors should be converted to a type that exist in
the Arrow spec.

.. _Flatbuffers: http://github.com/google/flatbuffers
.. _Flatbuffers protocol definition files: https://github.com/apache/arrow/tree/main/format
.. _Schema.fbs: https://github.com/apache/arrow/blob/main/format/Schema.fbs
.. _Message.fbs: https://github.com/apache/arrow/blob/main/format/Message.fbs
.. _File.fbs: https://github.com/apache/arrow/blob/main/format/File.fbs
.. _least-significant bit (LSB) numbering: https://en.wikipedia.org/wiki/Bit_numbering
.. _Intel performance guide: https://software.intel.com/en-us/articles/practical-intel-avx-optimization-on-2nd-generation-intel-core-processors
.. _Endianness: https://en.wikipedia.org/wiki/Endianness
.. _SIMD: https://software.intel.com/en-us/cpp-compiler-developer-guide-and-reference-introduction-to-the-simd-data-layout-templates
.. _Parquet: https://parquet.apache.org/documentation/latest/
