polars-row

polars-row is an internal sub-crate of the Polars library, that provides row encodings for the Polars DataFrame Library.

Important Note: This crate is not intended for external usage. Please refer to the main Polars crate for intended usage.

lib.rs:

Row format as defined in arrow-rs. This currently partially implements that format only for needed types. For completeness sake the format as defined by arrow-rs is as followed: Converts ArrayRef columns into a row-oriented format.

Overview

The row format is a variable length byte sequence created by concatenating the encoded form of each column. The encoding for each column depends on its datatype (and sort options).

The encoding is carefully designed in such a way that escaping is unnecessary: it is never ambiguous as to whether a byte is part of a sentinel (e.g. null) or a value.

Unsigned Integer Encoding

A null integer is encoded as a 0_u8, followed by a zero-ed number of bytes corresponding to the integer's length.

A valid integer is encoded as 1_u8, followed by the big-endian representation of the integer.

              ┌──┬──┬──┬──┐      ┌──┬──┬──┬──┬──┐
   3          │03│00│00│00│      │01│00│00│00│03│
              └──┴──┴──┴──┘      └──┴──┴──┴──┴──┘
              ┌──┬──┬──┬──┐      ┌──┬──┬──┬──┬──┐
  258         │02│01│00│00│      │01│00│00│01│02│
              └──┴──┴──┴──┘      └──┴──┴──┴──┴──┘
              ┌──┬──┬──┬──┐      ┌──┬──┬──┬──┬──┐
 23423        │7F│5B│00│00│      │01│00│00│5B│7F│
              └──┴──┴──┴──┘      └──┴──┴──┴──┴──┘
              ┌──┬──┬──┬──┐      ┌──┬──┬──┬──┬──┐
 NULL         │??│??│??│??│      │00│00│00│00│00│
              └──┴──┴──┴──┘      └──┴──┴──┴──┴──┘

             32-bit (4 bytes)        Row Format
 Value        Little Endian

Signed Integer Encoding

Signed integers have their most significant sign bit flipped, and are then encoded in the same manner as an unsigned integer.

       ┌──┬──┬──┬──┐       ┌──┬──┬──┬──┐       ┌──┬──┬──┬──┬──┐
    5  │05│00│00│00│       │05│00│00│80│       │01│80│00│00│05│
       └──┴──┴──┴──┘       └──┴──┴──┴──┘       └──┴──┴──┴──┴──┘
       ┌──┬──┬──┬──┐       ┌──┬──┬──┬──┐       ┌──┬──┬──┬──┬──┐
   -5  │FB│FF│FF│FF│       │FB│FF│FF│7F│       │01│7F│FF│FF│FB│
       └──┴──┴──┴──┘       └──┴──┴──┴──┘       └──┴──┴──┴──┴──┘

 Value  32-bit (4 bytes)    High bit flipped      Row Format
         Little Endian

Float Encoding

Floats are converted from IEEE 754 representation to a signed integer representation by flipping all bar the sign bit if they are negative after normalizing nans and signed zeros to a canonical representation.

They are then encoded in the same manner as a signed integer.

Fixed Length Bytes Encoding

Fixed length bytes are encoded in the same fashion as primitive types above.

For a fixed length array of length n:

A null is encoded as 0_u8 null sentinel followed by n 0_u8 bytes

A valid value is encoded as 1_u8 followed by the value bytes

Variable Length Bytes (including Strings) Encoding

A null is encoded as a 0_u8.

An empty byte array is encoded as 1_u8.

A non-null, non-empty byte array is encoded as 2_u8 followed by the byte array encoded using a block based scheme described below.

The byte array is broken up into 32-byte blocks, each block is written in turn to the output, followed by 0xFF_u8. The final block is padded to 32-bytes with 0_u8 and written to the output, followed by the un-padded length in bytes of this final block as a u8.

Note the following example encodings use a block size of 4 bytes, as opposed to 32 bytes for brevity:

                      ┌───┬───┬───┬───┬───┬───┐
 "MEEP"               │02 │'M'│'E'│'E'│'P'│04 │
                      └───┴───┴───┴───┴───┴───┘

                      ┌───┐
 ""                   │01 |
                      └───┘

 NULL                 ┌───┐
                      │00 │
                      └───┘

"Defenestration"      ┌───┬───┬───┬───┬───┬───┐
                      │02 │'D'│'e'│'f'│'e'│FF │
                      └───┼───┼───┼───┼───┼───┤
                          │'n'│'e'│'s'│'t'│FF │
                          ├───┼───┼───┼───┼───┤
                          │'r'│'a'│'t'│'r'│FF │
                          ├───┼───┼───┼───┼───┤
                          │'a'│'t'│'i'│'o'│FF │
                          ├───┼───┼───┼───┼───┤
                          │'n'│00 │00 │00 │01 │
                          └───┴───┴───┴───┴───┘

This approach is loosely inspired by COBS encoding, and chosen over more traditional byte stuffing as it is more amenable to vectorisation, in particular AVX-256.

Dictionary Encoding

RowsEncoded needs to support converting dictionary encoded arrays with unsorted, and potentially distinct dictionaries. One simple mechanism to avoid this would be to reverse the dictionary encoding, and encode the array values directly, however, this would lose the benefits of dictionary encoding to reduce memory and CPU consumption.

As such the RowsEncoded creates an order-preserving mapping for each dictionary encoded column, which allows new dictionary values to be added whilst preserving the sort order.

A null dictionary value is encoded as 0_u8.

A non-null dictionary value is encoded as 1_u8 followed by a null-terminated byte array key determined by the order-preserving dictionary encoding

┌──────────┐                 ┌─────┐
│  "Bar"   │ ───────────────▶│ 01  │
└──────────┘                 └─────┘
┌──────────┐                 ┌─────┬─────┐
│"Fabulous"│ ───────────────▶│ 01  │ 02  │
└──────────┘                 └─────┴─────┘
┌──────────┐                 ┌─────┐
│  "Soup"  │ ───────────────▶│ 05  │
└──────────┘                 └─────┘
┌──────────┐                 ┌─────┐
│   "ZZ"   │ ───────────────▶│ 07  │
└──────────┘                 └─────┘

Example Order Preserving Mapping

Using the map above, the corresponding row format will be

                          ┌─────┬─────┬─────┬─────┐
   "Fabulous"             │ 01  │ 03  │ 05  │ 00  │
                          └─────┴─────┴─────┴─────┘

                          ┌─────┬─────┬─────┐
   "ZZ"                   │ 01  │ 07  │ 00  │
                          └─────┴─────┴─────┘

                          ┌─────┐
    NULL                  │ 00  │
                          └─────┘

     Input                  Row Format

Struct Encoding

A null is encoded as a 0_u8.

A valid value is encoded as 1_u8 followed by the row encoding of each child.

This encoding effectively flattens the schema in a depth-first fashion.

For example

┌───────┬────────────────────────┬───────┐
│ Int32 │ Struct[Int32, Float32] │ Int32 │
└───────┴────────────────────────┴───────┘

Is encoded as

┌───────┬───────────────┬───────┬─────────┬───────┐
│ Int32 │ Null Sentinel │ Int32 │ Float32 │ Int32 │
└───────┴───────────────┴───────┴─────────┴───────┘

List Encoding

Lists are encoded by first encoding all child elements to the row format.

A "canonical byte array" is then constructed by concatenating the row encodings of all their elements into a single binary array, followed by the lengths of each encoded row, and the number of elements, encoded as big endian u32.

This canonical byte array is then encoded using the variable length byte encoding described above.

The lengths are not strictly necessary but greatly simplify decode, they may be removed in a future iteration.

For example given:

[1_u8, 2_u8, 3_u8]
[1_u8, null]
[]
null

The elements would be converted to:

    ┌──┬──┐     ┌──┬──┐     ┌──┬──┐     ┌──┬──┐        ┌──┬──┐
 1  │01│01│  2  │01│02│  3  │01│03│  1  │01│01│  null  │00│00│
    └──┴──┘     └──┴──┘     └──┴──┘     └──┴──┘        └──┴──┘

Which would be grouped into the following canonical byte arrays:

                        ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐
 [1_u8, 2_u8, 3_u8]     │01│01│01│02│01│03│00│00│00│02│00│00│00│02│00│00│00│02│00│00│00│03│
                        └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘
                         └──── rows ────┘   └───────── row lengths ─────────┘  └─ count ─┘

                        ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐
 [1_u8, null]           │01│01│00│00│00│00│00│02│00│00│00│02│00│00│00│02│
                        └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘

With [] represented by an empty byte array, and null a null byte array.

These byte arrays will then be encoded using the variable length byte encoding described above.

Ordering

Float Ordering

Floats are totally ordered just like in the rest of Polars, -inf < neg < -0.0 = 0.0 < pos < inf < nan, with all nans being equal.

Null Ordering

The encoding described above will order nulls first, this can be inverted by representing nulls as 0xFF_u8 instead of 0_u8

Reverse Column Ordering

The order of a given column can be reversed by negating the encoded bytes of non-null values