tustvold commented on code in PR #264:
URL: https://github.com/apache/arrow-site/pull/264#discussion_r1013746334
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_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-2.md:
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+---
+layout: post
+title: "Fast and Memory Efficient Multi-Column Sorts in Apache Arrow Rust,
Part 2"
+date: "2022-10-30 00:00:00"
+author: "tustvold and alamb"
+categories: [arrow]
+---
+<!--
+{% comment %}
+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.
+{% endcomment %}
+-->
+
+## Introduction
+
+In Part 1 <!-- TODO add link --> of this post, we described the problem of
Multi-Column Sorting and the challenges of implementing it efficiently. This
second post explains how the new [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) in the [Rust
implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/) works and is constructed.
+
+
+## Row Format
+
+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).
+
+```
+ ┌─────┐ ┌─────┐ ┌─────┐
+ │ │ │ │ │ │
+ ├─────┤ ┌ ┼─────┼ ─ ┼─────┼ ┐ ┏━━━━━━━━━━━━━┓
+ │ │ │ │ │ │ ─────────────▶┃ ┃
+ ├─────┤ └ ┼─────┼ ─ ┼─────┼ ┘ ┗━━━━━━━━━━━━━┛
+ │ │ │ │ │ │
+ └─────┘ └─────┘ └─────┘
+ ...
+ ┌─────┐ ┌ ┬─────┬ ─ ┬─────┬ ┐ ┏━━━━━━━━┓
+ │ │ │ │ │ │ ─────────────▶┃ ┃
+ └─────┘ └ ┴─────┴ ─ ┴─────┴ ┘ ┗━━━━━━━━┛
+ Customer State Orders
+ UInt64 Utf8 F64
+
+ Input Arrays Row Format
+ (Columns)
+```
+
+### Unsigned Integers
+
+To encode a non-null unsigned integer, the byte `0x01` is written, followed by
the integer’s bytes starting with the most significant, i.e. big endian. A null
is encoded as a `0x00` byte, followed by the encoded bytes of the integer’s
zero value
+
+```
+ ┌──┬──┬──┬──┐ ┌──┬──┬──┬──┬──┐
+ 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 Integers
+
+In Rust and most modern computer architectures, signed integers are encoded
using [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement),
where a number is negated by flipping all the bits, and adding 1. Therefore,
flipping the top-most bit and treating the result as an unsigned integer
preserves the order. This unsigned integer can then be encoded using the same
encoding for unsigned integers described in the previous section. For example
+
+```
+ ┌──┬──┬──┬──┐ ┌──┬──┬──┬──┐ ┌──┬──┬──┬──┬──┐
+ 5 │05│00│00│00│ │85│00│00│00│ │01│00│00│00│85│
+ └──┴──┴──┴──┘ └──┴──┴──┴──┘ └──┴──┴──┴──┴──┘
+ ┌──┬──┬──┬──┐ ┌──┬──┬──┬──┐ ┌──┬──┬──┬──┬──┐
+ -5 │FB│FF│FF│FF│ │7B│FF│FF│FF│ │01│FF│FF│FF│FF│
+ └──┴──┴──┴──┘ └──┴──┴──┴──┘ └──┴──┴──┴──┴──┘
+
+ Value 32-bit (4 bytes) High bit flipped Row Format
+ Little Endian
+```
+
+### Floating Point
+
+Floating point values can be ordered according to the [IEEE 754 totalOrder
predicate](https://en.wikipedia.org/wiki/IEEE_754#Total-ordering_predicate)
(implemented in Rust by
[f32::total_cmp](https://doc.rust-lang.org/std/primitive.f32.html#method.total_cmp)).
This ordering interprets the bytes of the floating point value as the
correspondingly sized, signed, little-endian integer, flipping all the bits
except the sign bit in the case of negatives.
+
+Floating point values are therefore encoded to row format by converting them
to the appropriate sized signed integer representation, and then using the same
encoding for signed integers described in the previous section.
+
+### Byte Arrays (Including Strings)
+
+Unlike primitive types above, byte arrays are variable length. For short
strings, such as `state` in our example above, it is possible to pad all values
to the length of the longest one with some fixed value such as `0x00` and
produce a fixed length row. This is the approach described in the DuckDB blog
for encoding `c_birth_country`.
+
+However, often values in string columns differ substantially in length or the
maximum length is not known at the start of execution, making it inadvisable
and/or impractical to pad the strings to a fixed length. The Rust Arrow row
format therefore uses a variable length encoding.
+
+We need an encoding that unambiguously terminates the end of the byte array.
This not only permits recovering the original value from the row format, but
ensures that bytes of a longer byte array are not compared against bytes from a
different column when compared against a row containing a shorter byte array.
+
+A null byte array is encoded as a single `0x00` byte. Similarly, an empty byte
array is encoded as a single `0x01` byte.
+
+To encode a non-null, non-empty array, first a single `0x02` byte is written.
Then the array is written in 32-byte blocks, with each block followed by a
`0xFF` byte as a continuation token. The final block is padded to 32-bytes with
`0x00`, and is then followed by the unpadded length of this final block as a
single byte.
Review Comment:
```suggestion
To encode a non-null, non-empty array, first a single `0x02` byte is
written. Then the array is written in 32-byte blocks, with each complete block
followed by a `0xFF` byte as a continuation token. The final block is padded to
32-bytes with `0x00`, and is then followed by the unpadded length of this final
block as a single byte in place of a continuation token
```
I think this makes it clearer that the continuation token is for when the
blocks continue :smile:
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