tustvold commented on code in PR #264:
URL: https://github.com/apache/arrow-site/pull/264#discussion_r1013731876


##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-2.md:
##########
@@ -0,0 +1,243 @@
+---
+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.
+
+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'│FF │04 │
+                      └───┴───┴───┴───┴───┴───┴───┘

Review Comment:
   ```suggestion
                         ┌───┬───┬───┬───┬───┬───┐
    "MEEP"               │02 │'M'│'E'│'E'│'P'│04 │
                         └───┴───┴───┴───┴───┴───┘
   ```



##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-2.md:
##########
@@ -0,0 +1,243 @@
+---
+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.
+
+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'│FF │04 │
+                      └───┴───┴───┴───┴───┴───┴───┘
+
+                      ┌───┬───┬───┬───┬───┬───┬───┐
+ ""                   │02 │00 │00 │00 │00 │FF │00 │
+                      └───┴───┴───┴───┴───┴───┴───┘

Review Comment:
   ```suggestion
                         ┌───┐
    ""                   │01 |
                         └───┘
   ```



##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-2.md:
##########
@@ -0,0 +1,243 @@
+---
+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.
+
+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'│FF │04 │
+                      └───┴───┴───┴───┴───┴───┴───┘
+
+                      ┌───┬───┬───┬───┬───┬───┬───┐
+ ""                   │02 │00 │00 │00 │00 │FF │00 │
+                      └───┴───┴───┴───┴───┴───┴───┘
+
+ NULL                 ┌───┬───┬───┬───┬───┬───┬───┐
+                      │00 │00 │00 │00 │00 │FF │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 │FF │17 │
+                          └───┴───┴───┴───┴───┴───┘

Review Comment:
   ```suggestion
                             ├───┼───┼───┼───┼───┤
                             │'n'│00 │00 │00 │17 │
                             └───┴───┴───┴───┴───┘
   ```



##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-2.md:
##########
@@ -0,0 +1,243 @@
+---
+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.
+
+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'│FF │04 │
+                      └───┴───┴───┴───┴───┴───┴───┘
+
+                      ┌───┬───┬───┬───┬───┬───┬───┐
+ ""                   │02 │00 │00 │00 │00 │FF │00 │
+                      └───┴───┴───┴───┴───┴───┴───┘
+
+ NULL                 ┌───┬───┬───┬───┬───┬───┬───┐
+                      │00 │00 │00 │00 │00 │FF │00 │
+                      └───┴───┴───┴───┴───┴───┴───┘

Review Comment:
   ```suggestion
    NULL                 ┌───┐
                         │00 │
                         └───┘
   ```



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