<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:dc="http://purl.org/dc/elements/1.1/"><channel><title>Codecs on Opensource internals</title><link>https://articles.9j.nz/tags/codecs/</link><description>Posts filed under Codecs on Opensource internals.</description><generator>Hugo</generator><language>en-US</language><managingEditor>Jay Hubbert</managingEditor><lastBuildDate>Thu, 22 Oct 2026 09:00:00 +0000</lastBuildDate><atom:link href="https://articles.9j.nz/tags/codecs/index.xml" rel="self" type="application/rss+xml"/><item><title>How ClickHouse Compresses Columns: Delta, Gorilla and the CODEC Pipeline</title><link>https://articles.9j.nz/posts/how-clickhouse-compresses-columns-with-codec-pipelines/</link><pubDate>Thu, 22 Oct 2026 09:00:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-clickhouse-compresses-columns-with-codec-pipelines/</guid><category>clickhouse</category><category>internals</category><category>compression</category><category>codecs</category><description>ClickHouse's column codecs are bit-level transforms chained under a generic compressor: Delta stores differences, DoubleDelta stores second differences, Gorilla stores XORs, and CODEC(...) nests them.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; A &lt;code&gt;CODEC(...)&lt;/code&gt; clause is a &lt;em&gt;pipeline&lt;/em&gt;, not a single algorithm.&#10;ClickHouse stores a column as a chain: &lt;code&gt;Delta&lt;/code&gt; turns values into differences,&#10;&lt;code&gt;DoubleDelta&lt;/code&gt; turns differences into second differences, &lt;code&gt;Gorilla&lt;/code&gt; stores&#10;XORs of successive values, and a generic compressor like &lt;code&gt;ZSTD&lt;/code&gt; squeezes the&#10;result. Each link is described by one method byte, so the reader knows how to&#10;undo it.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;p&gt;Compression in a columnar database is not one algorithm but two different&#10;problems, and ClickHouse splits them explicitly.&lt;/p&gt;&#10;&lt;p&gt;The first problem is &lt;em&gt;entropy&lt;/em&gt;: the bytes have patterns a general-purpose&#10;compressor can exploit — repeated strings, correlated fields, common prefixes.&#10;This is what LZ4 and ZSTD are for, and it is a general-purpose job.&lt;/p&gt;&#10;&lt;p&gt;The second problem is &lt;em&gt;structure&lt;/em&gt;: the column has a shape that a general-purpose&#10;compressor cannot see. A timestamp column that increases by exactly 1000 every&#10;row has almost zero entropy, but the bytes of the timestamps look like random&#10;noise to ZSTD, because the &lt;em&gt;relationship&lt;/em&gt; between adjacent values is not&#10;visible in any single byte. A &lt;code&gt;Delta&lt;/code&gt; preprocessor restores that structure, and&#10;&lt;em&gt;then&lt;/em&gt; ZSTD does its job.&lt;/p&gt;&#10;&lt;p&gt;So ClickHouse&amp;rsquo;s codecs come in two flavours — &lt;em&gt;preprocessors&lt;/em&gt; that change the&#10;representation, and &lt;em&gt;compressors&lt;/em&gt; that reduce the entropy — and a column can&#10;use several of them in sequence:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;sql&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-sql" data-lang="sql"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;CREATE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;TABLE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;events&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="k"&gt;timestamp&lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;DateTime&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CODEC&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Delta&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ZSTD&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="n"&gt;user_id&lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;UInt32&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CODEC&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T64&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ZSTD&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Float64&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CODEC&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Gorilla&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ZSTD&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="n"&gt;payload&lt;/span&gt;&lt;span class="o"&gt;`&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;String&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CODEC&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ZSTD&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;ENGINE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;MergeTree&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ORDER&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;BY&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;timestamp&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;&lt;code&gt;Delta, ZSTD(1)&lt;/code&gt; means: first turn the timestamps into differences, then&#10;compress the differences with ZSTD level 1. This article is about how that&#10;pipeline is built, what each stage actually does to the bits, and why the&#10;framing around it is what it is.&lt;/p&gt;&#10;&lt;h2 id="the-block-format"&gt;The block format&lt;/h2&gt;&#10;&lt;p&gt;Before the codecs, the frame. Every compressed block on disk is:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;text&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; +----------------+-----------------+-------------------+---------------+&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | checksum (16B) | method (1 byte) | compressed size | uncompressed |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | CityHash128 | | (4 bytes, LE) | size (4B, LE) |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; +----------------+-----------------+-------------------+---------------+&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | compressed payload |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; +--------------------------------------------------------------+&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The checksum covers the method byte, the sizes, and the payload — everything&#10;after itself. And the header size is a compile-time constant:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionInfo.h:16&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt;/** one byte for method, 4 bytes for compressed size, 4 bytes for uncompressed size */&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="kt"&gt;uint8_t&lt;/span&gt; &lt;span class="n"&gt;COMPRESSED_BLOCK_HEADER_SIZE&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The method byte identifies the codec, and the values are frozen forever:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionInfo.h:43&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;enum&lt;/span&gt; &lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;CompressionMethodByte&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="kt"&gt;uint8_t&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;NONE&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x02&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;LZ4&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x82&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ZSTD&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x90&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Multiple&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x91&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Delta&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x92&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;T64&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x93&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;DoubleDelta&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x94&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Gorilla&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x95&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;AES_128_GCM_SIV&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x96&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;AES_256_GCM_SIV&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x97&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;FPC&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x98&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// DeflateQpl = 0x99, /// Removed, don&amp;#39;t reuse for another codec&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;GCD&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x9a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// ZSTD_QPL = 0x9b, /// Removed, don&amp;#39;t reuse for another codec&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ALP&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x9c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;SZ3&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x9d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Quantized&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x9e&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ZXC&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0x9f&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;PCO&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mh"&gt;0xa0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The removed entries are interesting: &lt;code&gt;0x99&lt;/code&gt; and &lt;code&gt;0x9b&lt;/code&gt; were codecs that no&#10;longer exist, and rather than reuse the numbers, ClickHouse burns them. A&#10;codec byte is a permanent, on-disk identifier; reusing one would mean old&#10;data silently decoding as the wrong thing.&lt;/p&gt;&#10;&lt;p&gt;The header itself is written by one function:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/ICompressionCodec.cpp:63&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;ICompressionCodec&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;writeHeader&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;body_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;uncompressed_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;block_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getHeaderSize&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;body_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getMethodByte&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;unalignedStoreLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt32&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;block_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;unalignedStoreLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt32&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;uncompressed_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;block_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Note that the &lt;em&gt;compressed size&lt;/em&gt; in the header includes the header itself&#10;(&lt;code&gt;getHeaderSize() + body_size&lt;/code&gt;), which is what lets a reader skip a block&#10;without decompressing it.&lt;/p&gt;&#10;&lt;h2 id="the-dont-bother-rule"&gt;The &amp;ldquo;don&amp;rsquo;t bother&amp;rdquo; rule&lt;/h2&gt;&#10;&lt;p&gt;Compression is not always a win. Random data compresses to slightly &lt;em&gt;more&lt;/em&gt;&#10;than its original size, and the block would be both bigger and slower to read.&#10;ClickHouse&amp;rsquo;s writer has an escape hatch for exactly this:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressedWriteBuffer.cpp:53&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;compressed_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;codec&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;compress&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;working_buffer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;decompressed_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;compressed_ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The block is stored as is if compression saves less than 1/8 of its size.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;uncompressed_codec&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt64&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compressed_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt64&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;decompressed_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;compressed_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;uncompressed_codec&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;compress&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;working_buffer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;decompressed_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;compressed_ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;uncompressed_codec&lt;/code&gt; is a &lt;code&gt;NONE&lt;/code&gt; codec, and the rule is a 12.5% threshold:&#10;if compression did not save at least 1/8 of the block, the block is stored&#10;uncompressed. That is not a micro-optimisation — for a column of random UUIDs&#10;it is the difference between a part that grows and one that does not.&lt;/p&gt;&#10;&lt;p&gt;The checksum is computed over the &lt;em&gt;compressed&lt;/em&gt; bytes, and written before them:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressedWriteBuffer.cpp:59&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;CityHash_v1_0_2&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;uint128&lt;/span&gt; &lt;span class="n"&gt;checksum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;CityHash_v1_0_2&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CityHash128&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compressed_ptr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;compressed_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writeBinaryLittleEndian&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;checksum&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;low64&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;out&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writeBinaryLittleEndian&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;checksum&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;high64&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;out&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compress_in_place&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;out&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;position&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;compressed_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;else&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;out&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compressed_buffer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;compressed_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;And on the read side, the checksum failure handler does something rather&#10;charming: it tries every single-bit flip of the block to find the culprit.&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressedReadBufferBase.cpp:87&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1ULL&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// We need to copy data from ReadBuffer to flip bits as ReadBuffer should be immutable&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;PODArray&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;tmp_buffer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;tmp_data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tmp_buffer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Check if the difference caused by single bit flip in data.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;bit_pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;bit_pos&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;bit_pos&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;flip_bit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tmp_data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bit_pos&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;checksum_of_data_with_flipped_bit&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;CityHash_v1_0_2&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CityHash128&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tmp_data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;expected_checksum&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;checksum_of_data_with_flipped_bit&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;If exactly one bit flip explains the mismatch, the error message says &lt;em&gt;which&#10;byte and which bit&lt;/em&gt;, and blames the hardware (&amp;ldquo;bad RAM on network interface&#10;controller &amp;hellip; or disk bit rot&amp;rdquo;). It is a 1 MB block, so at most 8 million&#10;hash computations — expensive, but this is the path where a user is already&#10;losing data and needs to know whether their disk is dying.&lt;/p&gt;&#10;&lt;h2 id="delta-store-the-differences"&gt;Delta: store the differences&lt;/h2&gt;&#10;&lt;p&gt;The simplest useful preprocessor. &lt;code&gt;Delta(4)&lt;/code&gt; on a &lt;code&gt;UInt32&lt;/code&gt; column stores&#10;&lt;code&gt;a[i] - a[i-1]&lt;/code&gt; instead of &lt;code&gt;a[i]&lt;/code&gt;.&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:81&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;template&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;typename&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;compressDataForType&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;source_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source_size&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;Exception&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ErrorCodes&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CANNOT_COMPRESS&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;&amp;#34;Cannot compress with Delta codec, data size {} is not aligned to {}&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;source_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;prev_src&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;source_end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;source_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;source_end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;curr_src&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;unalignedLoadLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;unalignedStoreLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr_src&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;prev_src&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;prev_src&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;curr_src&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;For a timestamp column increasing by one second, every stored value is &lt;code&gt;1&lt;/code&gt;,&#10;and the four bytes of every value are &lt;code&gt;01 00 00 00&lt;/code&gt;. ZSTD turns that into&#10;almost nothing. This is the classic &amp;ldquo;delta encoding&amp;rdquo; of time series, and it&#10;is why &lt;code&gt;CODEC(Delta, ...)&lt;/code&gt; is the default suggestion for &lt;code&gt;DateTime&lt;/code&gt; columns.&lt;/p&gt;&#10;&lt;h3 id="decompressing-deltas-is-a-prefix-sum-and-prefix-sums-vectorise"&gt;Decompressing deltas is a prefix sum, and prefix sums vectorise&lt;/h3&gt;&#10;&lt;p&gt;Delta decoding is an inclusive prefix sum: &lt;code&gt;a[i] = sum(deltas[0..i])&lt;/code&gt;. And a&#10;prefix sum is exactly the kind of thing that SIMD does well — &lt;em&gt;if&lt;/em&gt; you&#10;restructure it. The naive scalar loop is limited to one element per cycle by&#10;the loop-carried accumulator. ClickHouse&amp;rsquo;s version computes the prefix sum&#10;&lt;em&gt;within&lt;/em&gt; a 16-byte register with log2(lanes) shift-and-add steps, then adds&#10;the running total of previous registers:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:100&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt;/** Delta decoding is an inclusive prefix sum of the deltas, and the scalar loop is limited by the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * loop-carried accumulator to at most one element per cycle. Instead, process the data in 16-byte&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * registers: log2(lanes) shift-and-add steps compute the prefix sum within a register, then the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * running total of all previous registers is added to every lane, and the last lane becomes the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * running total for the next register.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; *&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * The kernel is written with generic clang vectors; the shuffles compile to single instructions&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * on the SSE2 (x86_64) and NEON (AArch64) baselines, so no arch-specific code or runtime dispatch&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * is needed. Lanes are loaded in native byte order, so the fast path also requires a little-endian&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; * build to match the little-endian on-disk format; others fall back to the scalar loop below.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cm"&gt; */&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The kernel:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:131&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;template&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;typename&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;decompressBlocks&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;blocks&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;lanes&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_index_sequence&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;lanes&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;{};&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;DeltaVec&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;{};&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;blocks&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;DeltaVec&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;memcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;constexpr&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lanes&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;shiftLanesIn&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;constexpr&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lanes&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;shiftLanesIn&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;constexpr&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lanes&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;shiftLanesIn&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;constexpr&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lanes&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;shiftLanesIn&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Update the running total from the local prefix sum, so that the broadcast stays off&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// the loop-carried dependency chain (which is then a single addition).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;DeltaVec&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;carry&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;broadcastLastLane&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;carry&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;memcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The trick is the ordering of the last two lines. A naive &amp;ldquo;add the carry to&#10;every lane&amp;rdquo; would put the carry on the critical path: the carry depends on the&#10;current block, and the next block&amp;rsquo;s carry depends on this one. Instead, the&#10;running total is updated &lt;em&gt;from the local prefix sum&lt;/em&gt; (&lt;code&gt;carry = broadcastLastLane(x)&lt;/code&gt;,&#10;the last lane of the block&amp;rsquo;s own prefix sum), so the loop-carried dependency is&#10;a single addition of two vectors, and the broadcast — which is a shuffle — sits&#10;off that chain.&lt;/p&gt;&#10;&lt;p&gt;The whole thing is guarded by a portability check:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:111&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#if (((defined(__x86_64__) || defined(__i386__)) &amp;amp;&amp;amp; defined(__SSE2__)) || (defined(__aarch64__) &amp;amp;&amp;amp; defined(__ARM_NEON))) \&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt; &amp;amp;&amp;amp; __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#define DELTA_CODEC_SIMD_DECOMPRESS&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Note the &lt;code&gt;__ORDER_LITTLE_ENDIAN__&lt;/code&gt; condition: the vector lanes are loaded in&#10;native byte order, so the fast path only works where native order &lt;em&gt;is&lt;/em&gt; the&#10;on-disk order. On a big-endian build the code falls back to the scalar loop,&#10;which explicitly byte-swaps:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:181&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;source_end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;accumulator&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;unalignedLoadLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;unalignedStoreLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;accumulator&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;&lt;code&gt;Delta&lt;/code&gt; is &lt;em&gt;not&lt;/em&gt; a compressor by itself — it is a preprocessor, and the class&#10;says so:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDelta.cpp:33&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;isCompression&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;override&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;isGenericCompression&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;override&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;isDeltaCompression&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;override&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;so &lt;code&gt;Delta&lt;/code&gt; alone on a column would make it &lt;em&gt;bigger&lt;/em&gt; (it adds a 2-byte header&#10;and stores &lt;code&gt;bytes_to_skip&lt;/code&gt; bytes of alignment padding). It only pays off when&#10;something follows it.&lt;/p&gt;&#10;&lt;h2 id="doubledelta-store-the-differences-of-the-differences"&gt;DoubleDelta: store the differences of the differences&lt;/h2&gt;&#10;&lt;p&gt;If &lt;code&gt;Delta&lt;/code&gt; works because consecutive values are close, &lt;code&gt;DoubleDelta&lt;/code&gt; works&#10;because the &lt;em&gt;deltas&lt;/em&gt; are close — a sequence with a constant stride has a&#10;constant second difference, which is zero.&lt;/p&gt;&#10;&lt;p&gt;The bit-level encoding is the interesting part. Instead of storing the second&#10;differences as fixed-width integers, they are stored with a &lt;em&gt;variable-length&#10;prefix&lt;/em&gt;:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:44&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Given&lt;/span&gt; &lt;span class="n"&gt;input&lt;/span&gt; &lt;span class="n"&gt;sequence&lt;/span&gt; &lt;span class="nl"&gt;a&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;a0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;...&lt;/span&gt; &lt;span class="n"&gt;an&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;First&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;items&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;int32&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Then&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;first&lt;/span&gt; &lt;span class="n"&gt;item&lt;/span&gt; &lt;span class="n"&gt;as&lt;/span&gt; &lt;span class="n"&gt;is&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Second&lt;/span&gt; &lt;span class="n"&gt;item&lt;/span&gt; &lt;span class="n"&gt;is&lt;/span&gt; &lt;span class="n"&gt;written&lt;/span&gt; &lt;span class="n"&gt;as&lt;/span&gt; &lt;span class="n"&gt;delta&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Loop&lt;/span&gt; &lt;span class="n"&gt;over&lt;/span&gt; &lt;span class="n"&gt;remaining&lt;/span&gt; &lt;span class="n"&gt;items&lt;/span&gt; &lt;span class="n"&gt;and&lt;/span&gt; &lt;span class="n"&gt;calculate&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="nl"&gt;delta&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Write&lt;/span&gt; &lt;span class="n"&gt;it&lt;/span&gt; &lt;span class="n"&gt;in&lt;/span&gt; &lt;span class="n"&gt;compact&lt;/span&gt; &lt;span class="n"&gt;binary&lt;/span&gt; &lt;span class="n"&gt;form&lt;/span&gt; &lt;span class="n"&gt;with&lt;/span&gt; &lt;span class="err"&gt;`&lt;/span&gt;&lt;span class="n"&gt;BitWriter&lt;/span&gt;&lt;span class="err"&gt;`&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="nl"&gt;bit&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;63&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="kt"&gt;signed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;xxxxxx&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;255&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;256&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;110&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="kt"&gt;signed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;xxxxxxxx&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2047&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;2048&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1110&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="kt"&gt;signed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;12&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;xxxxxxxxxxx&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="n"&gt;fits&lt;/span&gt; &lt;span class="n"&gt;into&lt;/span&gt; &lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;11110&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="kt"&gt;signed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;xxxxxxxxxxx&lt;/span&gt;&lt;span class="p"&gt;...&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;11111&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="kt"&gt;signed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;xxxxxxxxxxx&lt;/span&gt;&lt;span class="p"&gt;...&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The prefix is a &lt;em&gt;unary-ish&lt;/em&gt; code: &lt;code&gt;0&lt;/code&gt; means zero (one bit!), &lt;code&gt;10&lt;/code&gt; means a&#10;7-bit magnitude, &lt;code&gt;110&lt;/code&gt; a 9-bit one, &lt;code&gt;1110&lt;/code&gt; a 12-bit one, &lt;code&gt;11110&lt;/code&gt; a 32-bit&#10;one, &lt;code&gt;11111&lt;/code&gt; a 64-bit one. The prefix lengths are increasing but the &lt;em&gt;code&lt;/em&gt;&#10;is a prefix code, so a decoder can dispatch on the first 5 bits with a&#10;lookup table:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:185&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// delta size prefix and data lengths based on few high bits peeked from binary stream&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;WriteSpec&lt;/span&gt; &lt;span class="n"&gt;WRITE_SPEC_LUT&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// 0b0 - 1-bit prefix, no data to read&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="cm"&gt;/* 00000 */&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mb"&gt;0b0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The table has 32 entries because the decoder peeks the top 5 bits:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:455&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;static_assert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;WRITE_SPEC_LUT&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;WRITE_SPEC_LUT&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// 5-bit prefix lookup table&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;write_spec&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;WRITE_SPEC_LUT&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;reader&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;peekByte&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)];&lt;/span&gt; &lt;span class="c1"&gt;// only 5 high bits of peeked byte value&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;-1&lt;/code&gt; in &lt;code&gt;abs(double_delta - 1)&lt;/code&gt; is a classic trick: zero is already&#10;encoded by the &lt;code&gt;0&lt;/code&gt; prefix, so the magnitude can be shifted down by one and&#10;still represent &lt;code&gt;1&lt;/code&gt; in one bit less.&lt;/p&gt;&#10;&lt;p&gt;The writer side:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:341&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;else&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;SignedDeltaType&lt;/span&gt; &lt;span class="n"&gt;signed_dd&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;SignedDeltaType&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;double_delta&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;signed_dd&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// -1 shrinks dd down to fit into number of bits, and there can&amp;#39;t be 0, so it is OK.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;abs_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;signed_dd&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;numeric_limits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;SignedDeltaType&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UnsignedDeltaType&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UnsignedDeltaType&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;signed_dd&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;write_spec&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getDeltaWriteSpec&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;signed_dd&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;write_spec&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;prefix_bits&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;write_spec&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;sign&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;write_spec&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;abs_value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the &lt;code&gt;BitWriter&lt;/code&gt; that packs it — note the &lt;code&gt;unsigned __int128&lt;/code&gt; accumulator,&#10;which holds 128 bits so the inner loop rarely has to flush:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/IO/BitHelpers.h:151&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;BitWriter&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest_begin&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest_end&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest_current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;using&lt;/span&gt; &lt;span class="n"&gt;BufferType&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="n"&gt;__int128&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;BufferType&lt;/span&gt; &lt;span class="n"&gt;bits_buffer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="n"&gt;bits_count&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="n"&gt;BIT_BUFFER_SIZE&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bits_buffer&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The decompressor has a fast path too: it reads a 64-bit word at a time and&#10;decodes as many deltas as fit, only falling back to the bit reader for the&#10;tail:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:415&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Read up to two words per delta; leave the final bytes to `BitReader`.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;items_read&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;items_count&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;source_end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;UInt64&lt;/span&gt; &lt;span class="n"&gt;word&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;unalignedLoadBigEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt64&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;write_spec&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;WRITE_SPEC_LUT&lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="n"&gt;word&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;bit_offset&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)];&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Note &lt;code&gt;unalignedLoadBigEndian&lt;/code&gt; here, even though the data is little-endian:&#10;the bits are read as a &lt;em&gt;bit stream&lt;/em&gt;, and the byte order of the word is&#10;irrelevant as long as it is consistent — but big-endian load makes the &amp;ldquo;top 5&#10;bits&amp;rdquo; arithmetic work out.&lt;/p&gt;&#10;&lt;h2 id="gorilla-xor-of-successive-values"&gt;Gorilla: XOR of successive values&lt;/h2&gt;&#10;&lt;p&gt;For floating-point gauges — CPU usage, queue depth, temperature — the values&#10;change slowly and the &lt;em&gt;bit pattern&lt;/em&gt; of the change is small. Gorilla stores&#10;&lt;code&gt;a[i] ^ a[i-1]&lt;/code&gt; and describes each XOR with its leading and trailing zero&#10;counts:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecGorilla.cpp:31&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Loop&lt;/span&gt; &lt;span class="n"&gt;over&lt;/span&gt; &lt;span class="n"&gt;remaining&lt;/span&gt; &lt;span class="n"&gt;items&lt;/span&gt; &lt;span class="n"&gt;and&lt;/span&gt; &lt;span class="n"&gt;calculate&lt;/span&gt; &lt;span class="nl"&gt;xor_diff&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;xor_diff&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt; &lt;span class="mo"&gt;00000011&amp;#39;10110100&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Write&lt;/span&gt; &lt;span class="n"&gt;it&lt;/span&gt; &lt;span class="n"&gt;in&lt;/span&gt; &lt;span class="n"&gt;compact&lt;/span&gt; &lt;span class="n"&gt;binary&lt;/span&gt; &lt;span class="n"&gt;form&lt;/span&gt; &lt;span class="n"&gt;with&lt;/span&gt; &lt;span class="err"&gt;`&lt;/span&gt;&lt;span class="n"&gt;BitWriter&lt;/span&gt;&lt;span class="err"&gt;`&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;xor_diff&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="nl"&gt;bit&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;calculate&lt;/span&gt; &lt;span class="n"&gt;leading&lt;/span&gt; &lt;span class="n"&gt;zero&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lzb&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;and&lt;/span&gt; &lt;span class="n"&gt;trailing&lt;/span&gt; &lt;span class="n"&gt;zero&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tzb&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;xor_diff&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt; &lt;span class="n"&gt;and&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;previous&lt;/span&gt; &lt;span class="n"&gt;xor_diff&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt; &lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;prev_lzb&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nl"&gt;prev_tzb&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt; &lt;span class="n"&gt;prev_lzb&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;prev_tzb&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mb"&gt;0b10&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="n"&gt;xor_diff&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;prev_tzb&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;prev_lzb&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;prev_tzb&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&lt;span class="mb"&gt;0b00111011010&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;where&lt;/span&gt; &lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt; &lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="n"&gt;bit&lt;/span&gt; &lt;span class="nl"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mb"&gt;0b11&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="nl"&gt;lzb&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mb"&gt;0b00110&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="mb"&gt;0b001000&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;write&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;X&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;non&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;zero&lt;/span&gt; &lt;span class="n"&gt;bits&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="nl"&gt;xor_diff&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mb"&gt;0b11101101&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;prev_lzb&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;lzb&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;prev_tzb&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tzb&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The clever part is the &lt;code&gt;0b10&lt;/code&gt; case: if the new XOR has &lt;em&gt;at least&lt;/em&gt; as many&#10;leading zeros and &lt;em&gt;at least&lt;/em&gt; as many trailing zeros as the previous one, the&#10;previous window still contains the new value, so only the payload has to be&#10;written — 2 bits of prefix plus the significant bits. A slowly drifting&#10;float usually stays in this case, and each sample then costs a handful of&#10;bits.&lt;/p&gt;&#10;&lt;p&gt;The writer:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecGorilla.cpp:236&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;source_end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;curr_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;unalignedLoadLittleEndian&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;source&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;curr_value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;xored_data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;curr_value&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="n"&gt;prev_value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;BinaryValueInfo&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getBinaryValueInfo&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;xored_data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;xored_data&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="nf"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;prev_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;prev_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;leading_zero_bits&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;leading_zero_bits&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;prev_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;trailing_zero_bits&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;trailing_zero_bits&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mb"&gt;0b10&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;prev_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;xored_data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;prev_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;trailing_zero_bits&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;else&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mb"&gt;0b11&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LEADING_ZEROES_BIT_LENGTH&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;leading_zero_bits&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DATA_BIT_LENGTH&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;writer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;writeBits&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;xored_data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;trailing_zero_bits&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;prev_xored_info&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;prev_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;curr_value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The widths of the &amp;ldquo;leading zero count&amp;rdquo; and &amp;ldquo;data length&amp;rdquo; fields depend on the&#10;type width, which is why they are computed from a table:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecGorilla.cpp:148&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="nf"&gt;getBitLengthOfLength&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="n"&gt;data_bytes_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// 1-byte value is 8 bits, and we need 4 bits to represent 8 : 1000,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// 2-byte 16 bits =&amp;gt; 5&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// 4-byte 32 bits =&amp;gt; 6&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;// 8-byte 64 bits =&amp;gt; 7&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="n"&gt;bit_lengths&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;And the decoder is careful about corrupted input — the widths it reads are&#10;checked against the type&amp;rsquo;s bit size before they are used to shift:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecGorilla.cpp:323&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The encoder derives both widths from a non-zero XOR, so there is at least one data&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// bit and the leading zero bits and the data bits together fit into the value.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;leading_zero_bits&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;curr_xored_info&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;data_bits&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="na"&gt;[[unlikely]]&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;Exception&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ErrorCodes&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CANNOT_DECOMPRESS&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;Cannot decompress Gorilla-encoded data: corrupted input data. &amp;#34;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;It has {} leading zero bits and {} data bits, which is not a valid split of {} bits&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;That is a real hardening measure: without it, a corrupted &lt;code&gt;data_bits&lt;/code&gt; field of&#10;255 would shift by 255 bits and produce garbage — or undefined behaviour.&lt;/p&gt;&#10;&lt;h2 id="the-pipeline-codecdelta-zstd1"&gt;The pipeline: &lt;code&gt;CODEC(Delta, ZSTD(1))&lt;/code&gt;&lt;/h2&gt;&#10;&lt;p&gt;A chain of codecs is stored as a &lt;code&gt;Multiple&lt;/code&gt; codec, whose payload is a list of&#10;method bytes followed by the nested payload:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;text&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; +--------+---------------+------------------------+&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | count | method bytes | stage 0 payload |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | (1B) | (count bytes) | ... |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; +--------+---------------+------------------------+&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The compression side runs the chain in order, alternating between two scratch&#10;buffers:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecMultiple.cpp:132&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;UInt32&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;CompressionCodecMultiple&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;compressBody&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;completed_stages&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;input_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getCodecs&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;chassert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;completed_stages&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt8&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getMethodByte&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;payload_offset&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;payload&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;payload_offset&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Stage outputs alternate between two buffers. The last stage writes into `dest` when its reserve fits there.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;PODArray&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;buffers&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;completed_stages&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;codec&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;UInt32&lt;/span&gt; &lt;span class="n"&gt;reserve&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getCheckedReserveSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;codec&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;input_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_last_stage&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;in_place&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;is_last_stage&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;payload_offset&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;reserve&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;output&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;payload&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;in_place&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;buffers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;resize_exact&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;reserve&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;output&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;buffers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;input_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;codec&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;compress&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;input_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;output&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;input&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;output&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The two-buffer alternation is the minimum needed for a pipeline: stage &lt;em&gt;n&lt;/em&gt;&#10;reads from one buffer and writes to the other, and they swap. The last stage&#10;writes directly into the destination if there is room, avoiding a final&#10;&lt;code&gt;memcpy&lt;/code&gt; — and if there is not, the result is copied back:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecMultiple.cpp:165&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;written_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;payload_offset&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;input_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The result is in a buffer after no stage was left to run or a last stage whose reserve did not fit. If so, memcpy it to `dest`.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;payload&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;written_size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;Exception&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ErrorCodes&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CANNOT_COMPRESS&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;Compressed data of size {} does not fit the reserved buffer of size {}&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;written_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;memcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;payload&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;input_size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Decompression runs the chain &lt;em&gt;backwards&lt;/em&gt; — the last stage written is the first&#10;stage undone — and the comment in the source lays out the buffer choreography:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecMultiple.cpp:197&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// source --memcpy--&amp;gt; compressed_buf --decode--&amp;gt; uncompressed_buf --swap--&amp;gt; compressed_buf --decode--&amp;gt; ... --decode--&amp;gt; uncompressed_buf --memcpy--&amp;gt; dest&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Buffers get the codec&amp;#39;s padding, the caller&amp;#39;s `source` and `dest` have none.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// A first stage that needs no padding decodes `source` directly, skipping the first memcpy.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// A last stage that needs no padding decodes into `dest` directly, skipping the last one.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;PODArray&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;compressed_buf&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;PODArray&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;uncompressed_buf&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the loop:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecMultiple.cpp:204&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;compression_methods_size&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;UInt8&lt;/span&gt; &lt;span class="n"&gt;compression_method&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;source&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;codec&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;CompressionCodecFactory&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;instance&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compression_method&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;additional_size_at_the_end_of_buffer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;codec&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getAdditionalSizeAtTheEndOfBuffer&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_first_stage&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;compression_methods_size&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_last_stage&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;additional_size_at_the_end_of_buffer&lt;/code&gt; is a per-codec quirk: LZ4, for&#10;example, needs a few extra bytes at the end of its output buffer to read&#10;past. The chain handles it by padding the intermediate buffers and skipping&#10;the copy at the ends when padding is not needed.&lt;/p&gt;&#10;&lt;p&gt;And the chain length is limited by the format:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecMultiple.cpp:91&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// doCompressData stores the number of codecs in one byte, and doDecompressData reads it back&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// from there, so a longer chain would write a part that cannot be read.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;numeric_limits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt8&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;Exception&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ErrorCodes&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CANNOT_COMPRESS&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;Too many codecs in the codec chain: {}. The number of codecs is stored in one byte, &amp;#34;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;so at most {} are supported.&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;numeric_limits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;UInt8&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;()));&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;255 codecs, because the count is a byte.&lt;/p&gt;&#10;&lt;h2 id="adaptive-picking-the-codec-per-block"&gt;Adaptive: picking the codec per block&lt;/h2&gt;&#10;&lt;p&gt;One more mechanism is worth mentioning, because it shows how the framing&#10;enables a trick. The &lt;code&gt;CODEC(Default)&lt;/code&gt; setting does not pick one codec for the&#10;whole column; it picks one &lt;em&gt;per block&lt;/em&gt;, from a pool that depends on the&#10;column&amp;rsquo;s type:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecAdaptive.h:32&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Adaptive codec picks the smallest-output codec per block from a default codec + type-appropriate pool and delegates to it.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// On disk, each block carries the winner&amp;#39;s method byte and reader decodes it with no knowledge of &amp;#34;adaptive&amp;#34;.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// The wrapper itself never appears on disk.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;CompressionCodecAdaptive&lt;/span&gt; &lt;span class="k"&gt;final&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="n"&gt;ICompressionCodec&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The pool is &lt;code&gt;NONE&lt;/code&gt;, the deployment default, plus type-appropriate&#10;candidates:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecAdaptive.cpp:49&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Candidate codecs for the adaptive pool. Each one is also tried followed by the deployment default if it&amp;#39;s a general-purpose compressor.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;CANDIDATES&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;to_array&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;CandidateGroup&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// T64 defaults to the byte flavour (over bit). Good: same size + faster [de]compression.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;T64&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;T64_TYPES&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;ALP(AUTO)&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ALP_TYPES&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;});&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;So for an integer column the pool is &lt;code&gt;NONE&lt;/code&gt;, &lt;code&gt;LZ4&lt;/code&gt;, &lt;code&gt;T64&lt;/code&gt;, &lt;code&gt;T64+LZ4&lt;/code&gt;; for a&#10;float column it is &lt;code&gt;NONE&lt;/code&gt;, &lt;code&gt;LZ4&lt;/code&gt;, &lt;code&gt;ALP&lt;/code&gt;, &lt;code&gt;ALP+LZ4&lt;/code&gt;. Each block is compressed&#10;with every candidate and the smallest output wins — and because the winner&amp;rsquo;s&#10;&lt;em&gt;method byte&lt;/em&gt; is written into the block header, the reader needs no knowledge&#10;of &amp;ldquo;adaptive&amp;rdquo; at all. The wrapper never appears on disk.&lt;/p&gt;&#10;&lt;p&gt;That is a nice payoff of the framing design: because the method byte is&#10;per-block rather than per-column, the choice of codec can be made &lt;em&gt;per&#10;block&lt;/em&gt;, at the cost of compressing the block more than once.&lt;/p&gt;&#10;&lt;h2 id="trade-offs"&gt;Trade-offs&lt;/h2&gt;&#10;&lt;p&gt;What the pipeline buys:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;Structure-aware compression.&lt;/strong&gt; &lt;code&gt;Delta&lt;/code&gt; + &lt;code&gt;ZSTD&lt;/code&gt; on a timestamp column&#10;routinely beats &lt;code&gt;ZSTD&lt;/code&gt; alone by a wide margin, because the differences are&#10;nearly constant and the generic compressor gets to see that.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;A per-block fallback.&lt;/strong&gt; The 1/8 rule means a column of incompressible data&#10;costs 0 bytes of overhead rather than a few percent.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Self-describing blocks.&lt;/strong&gt; Every block carries its own method byte and&#10;sizes, so a file can mix codecs, and a reader can skip a block it does not&#10;understand.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Corruption is detected, and diagnosed.&lt;/strong&gt; A 128-bit CityHash over the&#10;block catches silent bit rot, and the error path can name the exact bit.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;What it costs:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;Preprocessors are not compressors.&lt;/strong&gt; &lt;code&gt;Delta&lt;/code&gt; alone makes a column bigger.&#10;Using it without a compressor is a mistake the API allows.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;The chain is not free.&lt;/strong&gt; Each stage is a full pass over the data, with a&#10;buffer ping-pong between stages. &lt;code&gt;CODEC(Delta, ZSTD(1))&lt;/code&gt; reads the column&#10;twice.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;The chain is positional.&lt;/strong&gt; The method bytes appear &lt;em&gt;before&lt;/em&gt; the payload,&#10;in the chain&amp;rsquo;s order, but the payload is nested — stage 0&amp;rsquo;s output is stage&#10;1&amp;rsquo;s input. A reader must decode from the inside out, and the code has to&#10;juggle two scratch buffers to do it.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Type-specific codecs need the type.&lt;/strong&gt; &lt;code&gt;Gorilla&lt;/code&gt; needs to know the width&#10;(1, 2, 4 or 8 bytes), and &lt;code&gt;T64&lt;/code&gt; and &lt;code&gt;ALP&lt;/code&gt; need the column type. That is&#10;fine inside a MergeTree part, where the type is known, but it makes the&#10;codec non-portable — you cannot apply &lt;code&gt;Gorilla&lt;/code&gt; to a column whose type you&#10;do not know.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Adaptive costs one compression pass per candidate.&lt;/strong&gt; Picking the smallest&#10;output requires trying them all.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;The format is frozen.&lt;/strong&gt; Method bytes are permanent, removed codecs burn&#10;their numbers, and the on-disk layout of every codec is covered by&#10;compatibility tests:&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Compression/CompressionCodecDoubleDelta.cpp:117&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Please&lt;/span&gt; &lt;span class="n"&gt;also&lt;/span&gt; &lt;span class="n"&gt;see&lt;/span&gt; &lt;span class="n"&gt;unit&lt;/span&gt; &lt;span class="n"&gt;tests&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Examples&lt;/span&gt; &lt;span class="n"&gt;on&lt;/span&gt; &lt;span class="n"&gt;what&lt;/span&gt; &lt;span class="n"&gt;output&lt;/span&gt; &lt;span class="err"&gt;`&lt;/span&gt;&lt;span class="n"&gt;BitWriter&lt;/span&gt;&lt;span class="err"&gt;`&lt;/span&gt; &lt;span class="n"&gt;produces&lt;/span&gt; &lt;span class="n"&gt;on&lt;/span&gt; &lt;span class="n"&gt;predefined&lt;/span&gt; &lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;Compatibility&lt;/span&gt; &lt;span class="n"&gt;tests&lt;/span&gt; &lt;span class="n"&gt;solidifying&lt;/span&gt; &lt;span class="n"&gt;encoded&lt;/span&gt; &lt;span class="n"&gt;binary&lt;/span&gt; &lt;span class="n"&gt;output&lt;/span&gt; &lt;span class="n"&gt;on&lt;/span&gt; &lt;span class="n"&gt;set&lt;/span&gt; &lt;span class="n"&gt;of&lt;/span&gt; &lt;span class="n"&gt;predefined&lt;/span&gt; &lt;span class="n"&gt;sequences&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;That last point is the real constraint. Once a codec&amp;rsquo;s bytes are on disk in&#10;somebody&amp;rsquo;s cluster, the exact bit layout — the prefix widths, the order of&#10;the fields, the endianness — is forever. The &lt;code&gt;WRITE_SPEC_LUT&lt;/code&gt; table, the&#10;&lt;code&gt;getBitLengthOfLength&lt;/code&gt; table, the &lt;code&gt;abs(value - 1)&lt;/code&gt; trick: none of it can&#10;change, ever, without a format version bump.&lt;/p&gt;&#10;</content:encoded></item></channel></rss>