<?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>Buffer-Manager on Opensource internals</title><link>https://articles.9j.nz/tags/buffer-manager/</link><description>Posts filed under Buffer-Manager on Opensource internals.</description><generator>Hugo</generator><language>en-US</language><managingEditor>Jay Hubbert</managingEditor><lastBuildDate>Sun, 25 Oct 2026 09:10:00 +0000</lastBuildDate><atom:link href="https://articles.9j.nz/tags/buffer-manager/index.xml" rel="self" type="application/rss+xml"/><item><title>The Block Allocator: One mmap Arena, Per-Thread Free Lists and Lazy Commit</title><link>https://articles.9j.nz/posts/how-the-block-allocator-keeps-per-thread-free-lists/</link><pubDate>Sun, 25 Oct 2026 09:10:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-the-block-allocator-keeps-per-thread-free-lists/</guid><category>duckdb</category><category>memory</category><category>buffer-manager</category><category>performance</category><category>internals</category><description>DuckDB hands out 256 KiB blocks from one mmap arena, finds them by integer division, caches them in per-thread free lists, and commits them lazily.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; DuckDB does not &lt;code&gt;malloc&lt;/code&gt; a 256 KiB block every time the buffer&#10;manager needs one. It reserves one big anonymous &lt;code&gt;mmap&lt;/code&gt; arena up front, hands&#10;out fixed-size slices of it, and finds a slice&amp;rsquo;s identity with a shift —&#10;&lt;code&gt;(pointer - base) &amp;gt;&amp;gt; 18&lt;/code&gt; — because the block size is a power of two. Freed&#10;blocks go onto per-thread free lists, are batched back to shared queues in&#10;groups of 16, and are committed and decommitted lazily with &lt;code&gt;madvise&lt;/code&gt;, so the&#10;arena&amp;rsquo;s &lt;em&gt;address space&lt;/em&gt; is cheap but its &lt;em&gt;resident pages&lt;/em&gt; are not. A rolling&#10;retention estimate packs an epoch and a count into one &lt;code&gt;uint64&lt;/code&gt; so the&#10;allocator can estimate how much it is really holding without walking a list.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;h2 id="the-problem-with-malloc256--1024"&gt;The problem with &lt;code&gt;malloc(256 * 1024)&lt;/code&gt;&lt;/h2&gt;&#10;&lt;p&gt;Every time DuckDB&amp;rsquo;s buffer manager needs a block, it needs 256 KiB — that is&#10;&lt;code&gt;DEFAULT_BLOCK_ALLOC_SIZE&lt;/code&gt;, and it is not negotiable, because the block size&#10;is baked into the on-disk format.&lt;/p&gt;&#10;&lt;p&gt;The obvious implementation is &lt;code&gt;malloc(256 * 1024)&lt;/code&gt;. It works, and it is a&#10;bad idea for a database that allocates and frees blocks in bursts from dozens&#10;of threads:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;glibc will serve it from a per-thread arena, so it is not &lt;em&gt;that&lt;/em&gt; bad, but&#10;each allocation still goes through the allocator&amp;rsquo;s bookkeeping and, for&#10;large chunks, &lt;code&gt;mmap&lt;/code&gt;/&lt;code&gt;munmap&lt;/code&gt; on the kernel.&lt;/li&gt;&#10;&lt;li&gt;&lt;code&gt;munmap&lt;/code&gt; returns the pages to the kernel. The next allocation gets fresh&#10;zero pages, which means page faults and a cold cache on every reuse.&lt;/li&gt;&#10;&lt;li&gt;There is no way to ask &amp;ldquo;how much is this allocator holding right now?&amp;rdquo;&#10;without walking the allocator&amp;rsquo;s own data structures.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;DuckDB&amp;rsquo;s answer is to own the address space itself.&lt;/p&gt;&#10;&lt;h2 id="one-arena-reserved-but-not-committed"&gt;One arena, reserved but not committed&lt;/h2&gt;&#10;&lt;p&gt;The arena is one &lt;code&gt;mmap&lt;/code&gt; of anonymous private memory:&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/storage/block_allocator.cpp:139&#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&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="nf"&gt;AllocateVirtualMemory&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;size&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="cp"&gt;#if INTPTR_MAX == INT32_MAX&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// Disable on 32-bit&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;nullptr&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="cp"&gt;#endif&#10;&lt;/span&gt;&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="cp"&gt;#if defined(_WIN32)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// This returns nullptr on failure&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;VirtualAlloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;nullptr&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="n"&gt;MEM_RESERVE&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;PAGE_NOACCESS&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="cp"&gt;#else&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;flags&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;MAP_PRIVATE&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;MAP_ANONYMOUS&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="cp"&gt;#if defined(__linux__)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// Reserve address space without charging the entire pool against the commit limit.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;flags&lt;/span&gt; &lt;span class="o"&gt;|=&lt;/span&gt; &lt;span class="n"&gt;MAP_NORESERVE&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="cp"&gt;#endif&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;mmap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;nullptr&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="n"&gt;PROT_READ&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;PROT_WRITE&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;flags&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="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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;MAP_FAILED&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="k"&gt;nullptr&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;data_ptr_cast&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;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;&lt;span class="cp"&gt;#endif&#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&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;MAP_NORESERVE&lt;/code&gt; is the interesting flag. Without it, the kernel counts the&#10;&lt;em&gt;whole&lt;/em&gt; mapping against the process&amp;rsquo;s commit limit — and on Linux,&#10;&lt;code&gt;overcommit_memory=2&lt;/code&gt; (the strict setting) will refuse the mapping outright&#10;if the reserved size exceeds the limit. With it, the reservation is free:&#10;the kernel promises you the address range but does not promise the pages.&lt;/p&gt;&#10;&lt;p&gt;That matters because DuckDB&amp;rsquo;s pool can be much larger than the memory limit&#10;the user configured. The memory limit governs how much of the arena is&#10;&lt;em&gt;supposed&lt;/em&gt; to be resident; the arena itself is just address space.&lt;/p&gt;&#10;&lt;p&gt;On Windows the equivalent is &lt;code&gt;VirtualAlloc(..., MEM_RESERVE, PAGE_NOACCESS)&lt;/code&gt;&#10;— reserve the range, forbid access, and let the pages be committed later.&lt;/p&gt;&#10;&lt;p&gt;The pool is initialised lazily and published with a release store, so a&#10;failed reservation permanently disables the pool rather than being retried on&#10;every allocation:&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/storage/block_allocator.cpp:576&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;AllocateVirtualMemory&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool_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;&#9;&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;pointer&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;&#9;&#9;&lt;span class="n"&gt;pool_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;store&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;PoolState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;UNAVAILABLE&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;memory_order_release&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;&#9;&#9;&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;&#9;&lt;span class="n"&gt;untouched&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;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;queue&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;&#9;&lt;span class="n"&gt;pool_base&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&lt;span class="n"&gt;pool_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;store&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;PoolState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;READY&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;memory_order_release&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;&#9;&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;&#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 free list is seeded with &lt;em&gt;every&lt;/em&gt; block id in the pool, enqueued in&#10;batches of &lt;code&gt;STANDARD_VECTOR_SIZE&lt;/code&gt; (2048) so the initial fill is a handful of&#10;bulk operations rather than thousands of pushes.&lt;/p&gt;&#10;&lt;h2 id="finding-a-block-with-a-shift"&gt;Finding a block with a shift&lt;/h2&gt;&#10;&lt;p&gt;The arena is carved into fixed-size blocks. The block size is a power of two,&#10;and the allocator computes the shift once, in its constructor:&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/storage/block_allocator.cpp:493&#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;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Allocator&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;allocator_p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;block_size_p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;pool_size_p&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;uuid&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;UUID&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;GenerateRandomUUID&lt;/span&gt;&lt;span class="p"&gt;()),&lt;/span&gt; &lt;span class="n"&gt;allocator&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;allocator_p&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;allocation_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;make_uniq&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;AllocationCache&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;allocator&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;block_size&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_size_p&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;block_size_div_shift&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CountZeros&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;Trailing&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;pool_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="kt"&gt;void&lt;/span&gt; &lt;span class="o"&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;8&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;pool_size_p&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;pool_size_p&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nl"&gt;block_size&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="n"&gt;pool_state&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool_size&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;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;DivBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;NumericLimits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;Maximum&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;PoolState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="nl"&gt;UNINITIALIZED&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="n"&gt;PoolState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;UNAVAILABLE&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;touched&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;make_unsafe_uniq&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockQueue&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;lifetime_state&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;make_shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockAllocatorLifetimeState&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&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;&#9;&lt;span class="k"&gt;static_assert&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;tuple_size&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;decltype&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;retention_buckets&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;value&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_BUCKETS&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;&#9; &lt;span class="s"&gt;&amp;#34;Retention bucket storage must match the decay configuration&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;IsPowerOfTwo&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;&#9;&lt;span class="n"&gt;InitializeRetention&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RetentionTimeMillis&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;CountZeros&amp;lt;idx_t&amp;gt;::Trailing(block_size)&lt;/code&gt; is the number of trailing zero bits&#10;of the block size — for 256 KiB that is 18. The pool size is rounded &lt;em&gt;down&lt;/em&gt; to&#10;a whole number of blocks, and on 32-bit systems the pool is disabled&#10;entirely (&lt;code&gt;pool_size&lt;/code&gt; becomes 0) because there is not enough address space&#10;to make it worthwhile.&lt;/p&gt;&#10;&lt;p&gt;With the shift in hand, the two conversions are a subtract and a 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/storage/block_allocator.cpp:600&#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;idx_t&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ModuloBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_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="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;idx_t&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;DivBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;block_size_div_shift&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="kt"&gt;uint32_t&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;GetBlockID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;IsInPool&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;offset&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;NumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;pointer&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;pool_base&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ModuloBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;offset&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;block_id&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;NumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_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;DivBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;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;&#9;&lt;span class="n"&gt;VerifyBlockID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_id&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;block_id&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="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;VerifyBlockID&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;block_id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_id&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;DivBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool_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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;GetPointer&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;block_id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="n"&gt;VerifyBlockID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_id&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pool_base&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;NumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;block_id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&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="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;pointer → id&lt;/code&gt; is &lt;code&gt;(pointer - pool_base) &amp;gt;&amp;gt; 18&lt;/code&gt;. &lt;code&gt;id → pointer&lt;/code&gt; is&#10;&lt;code&gt;pool_base + id * block_size&lt;/code&gt;. No lookup table, no hash, no map. The block&#10;id &lt;em&gt;is&lt;/em&gt; its offset divided by the block size, and the division is a shift&#10;because the size is a power of two.&lt;/p&gt;&#10;&lt;p&gt;This is what makes the design work: the free lists store 32-bit integers, not&#10;pointers. A batch of 16 freed blocks is 64 bytes of bookkeeping that the CPU&#10;can push around in registers, and the address is recomputed on demand.&lt;/p&gt;&#10;&lt;p&gt;&lt;code&gt;ModuloBlockSize&lt;/code&gt; is the mask for the opposite direction — it is the&#10;assertion that the pointer really is block-aligned.&lt;/p&gt;&#10;&lt;h2 id="per-thread-free-lists"&gt;Per-thread free lists&lt;/h2&gt;&#10;&lt;p&gt;The allocator has two levels of free lists. At the top, two shared&#10;&lt;code&gt;ConcurrentQueue&lt;/code&gt;s of block ids — &lt;code&gt;touched&lt;/code&gt; (blocks that have been used and&#10;returned) and &lt;code&gt;untouched&lt;/code&gt; (blocks that were never touched). At the bottom,&#10;each thread keeps its own two &lt;code&gt;vector&amp;lt;uint32_t&amp;gt;&lt;/code&gt; caches.&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/storage/block_allocator.cpp:226&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="nf"&gt;Allocate&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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;TryAllocateFromLocal&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// We have run out of local blocks&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TryGetBatch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;touched&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;touched&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;TryGetBatch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;untouched&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;untouched&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;&#9;&#9;&#9;&lt;span class="c1"&gt;// We have refilled local blocks&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;TryAllocateFromLocal&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;&#9;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// We have also run out of global blocks, use fallback allocator&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;allocator&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;AllocateData&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;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;&#9;&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 fast path is &lt;code&gt;TryAllocateFromLocal&lt;/code&gt;, and it is a &lt;code&gt;pop_back&lt;/code&gt; on a vector:&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/storage/block_allocator.cpp:292&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="nf"&gt;TryAllocateFromLocal&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;&#9;&#9;&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;touched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;&#9;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetPointer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;touched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;back&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;&#9;&#9;&#9;&lt;span class="n"&gt;touched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pop_back&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;&#9;&#9;&#9;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;UpdateCachedBlocks&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="n"&gt;cache_slot&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&#9;&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;&#9;&#9;&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;untouched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;&#9;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetPointer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;untouched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;back&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;&#9;&#9;&#9;&lt;span class="n"&gt;OnFirstAllocation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;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;&#9;&#9;&#9;&lt;span class="n"&gt;untouched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pop_back&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&#9;&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;nullptr&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;&#9;&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;No atomics, no locks, no CAS. A thread that frees a block pushes the id onto&#10;its own vector; a thread that allocates pops from its own vector. The shared&#10;queues are only touched when a thread&amp;rsquo;s local cache runs dry, and then it&#10;takes a whole batch at once:&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/storage/block_allocator.cpp:308&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;TryGetBatch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;local&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;BlockQueue&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;global&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;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;local&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;&#9;&#9;&lt;span class="n"&gt;local&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;resize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BATCH_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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;global&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;try_dequeue_bulk&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;local&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;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BATCH_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;&#9;&#9;&lt;span class="n"&gt;local&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;resize&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;&#9;&#9;&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;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;RefersToSameObject&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;global&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;touched&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;&#9;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;now&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;RetentionTimeMillis&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;&#9;&#9;&#9;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;ReuseRetention&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="n"&gt;now&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;&#9;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;now&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;next_decay_check&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;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;next_decay_check&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;now&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ACTIVE_DECAY_INTERVAL_MS&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;&#9;&#9;&#9;&#9;&lt;span class="k"&gt;try&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;&#9;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;FreeInternal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;optional_idx&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;MAX_FLUSH_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;&#9;&#9;&#9;&#9;&#9; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ReclaimMode&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;OPPORTUNISTIC&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;&#9;&#9;&#9;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;catch&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;&#9;&#9;&#9;&#9;&#9;&lt;span class="c1"&gt;// Failed reclamation leaves blocks available for reuse.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&#9;&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;&#9;&#9;&#9;&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;local&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;local&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;local&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;&#9;&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;try_dequeue_bulk&lt;/code&gt; moves up to &lt;code&gt;BATCH_SIZE&lt;/code&gt; (16) ids in one go, and the ids&#10;are then sorted — sorting matters later, because the reclamation path&#10;coalesces &lt;em&gt;contiguous&lt;/em&gt; block ids into a single &lt;code&gt;madvise&lt;/code&gt; call.&lt;/p&gt;&#10;&lt;p&gt;Freeing is the mirror image, with a batching threshold:&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/storage/block_allocator.cpp:244&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;Free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="n"&gt;pointer&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;&#9;&#9;&lt;span class="n"&gt;touched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetBlockID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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;&#9;&#9;&lt;span class="n"&gt;block_allocator&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;UpdateCachedBlocks&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;cache_slot&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;touched&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;lt;&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;FREE_THRESHOLD&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// Upon reaching the threshold, we return a local batch to global&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;touched&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;touched&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;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;&#9;&#9;&lt;span class="n"&gt;ReturnTouched&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BATCH_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;&#9;&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;FREE_THRESHOLD&lt;/code&gt; is &lt;code&gt;BATCH_SIZE * 2&lt;/code&gt; = 32. A thread frees blocks; when it&#10;has 32 sitting locally, it sorts them and hands 16 back to the shared queue.&#10;The sort is not cosmetic — sorted ids make the contiguous-run coalescing in&#10;the reclamation path possible.&lt;/p&gt;&#10;&lt;p&gt;The two queues are distinguished by whether the block has ever been used.&#10;&lt;code&gt;untouched&lt;/code&gt; blocks are still unmapped from the process&amp;rsquo;s point of view&#10;(never committed); &lt;code&gt;touched&lt;/code&gt; blocks have resident pages. The distinction&#10;lets the allocator decommit a run of touched blocks with one syscall, and&#10;lets it skip the decommit entirely for blocks that were never committed.&lt;/p&gt;&#10;&lt;h2 id="commit-lazily-decommit-with-madvise"&gt;Commit lazily, decommit with &lt;code&gt;madvise&lt;/code&gt;&lt;/h2&gt;&#10;&lt;p&gt;The arena&amp;rsquo;s pages are committed on first use and decommitted on release. On&#10;Linux that is &lt;code&gt;madvise(MADV_DONTNEED)&lt;/code&gt;; on macOS it is&#10;&lt;code&gt;MADV_FREE_REUSABLE&lt;/code&gt;; on Windows it is &lt;code&gt;VirtualFree(MEM_DECOMMIT)&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/storage/block_allocator.cpp:171&#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&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;OnFirstAllocation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;size&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;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;success&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&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="cp"&gt;#if defined(_WIN32)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;success&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;VirtualAlloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="n"&gt;MEM_COMMIT&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;PAGE_READWRITE&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="cp"&gt;#elif defined(__APPLE__)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// Reclaimed pages remain reusable until explicitly claimed again.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;success&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;madvise&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="n"&gt;MADV_FREE_REUSE&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="cp"&gt;#endif&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;success&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;&#9;&#9;&lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;InternalException&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;OnFirstAllocation failed&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;&#9;&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="k"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;OnDeallocation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;data_ptr_t&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;size&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="cp"&gt;#if defined(_WIN32)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;VirtualFree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="n"&gt;MEM_DECOMMIT&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="cp"&gt;#elif defined(__APPLE__)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;madvise&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="n"&gt;MADV_FREE_REUSABLE&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="cp"&gt;#elif defined(__MVS__)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// the madvice functionality is not available on z/OS in any form&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#else&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;madvise&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="n"&gt;MADV_DONTNEED&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="cp"&gt;#endif&#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&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 on Linux &lt;code&gt;OnFirstAllocation&lt;/code&gt; is a no-op: &lt;code&gt;mmap&lt;/code&gt; with&#10;&lt;code&gt;MAP_PRIVATE | MAP_ANONYMOUS&lt;/code&gt; already gives readable, writable pages, and&#10;the kernel commits them on first touch. The interesting half is&#10;&lt;code&gt;OnDeallocation&lt;/code&gt;, which &lt;em&gt;gives the pages back&lt;/em&gt; without giving up the&#10;address space. &lt;code&gt;MADV_DONTNEED&lt;/code&gt; on an anonymous private mapping zeroes the&#10;pages and drops them; the next touch is a page fault and a fresh zero page.&#10;That is precisely the behaviour you want for a block cache: a cold block&#10;should read as zeros, not as the previous tenant&amp;rsquo;s data.&lt;/p&gt;&#10;&lt;p&gt;The decommit is done in runs. Because the ids are sorted, contiguous runs can&#10;be collapsed into one call:&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/storage/block_allocator.cpp:1086&#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="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;FreeContiguousBlocks&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;block_id_start&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;block_id_end_including&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pointer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;GetPointer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_id_start&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;num_blocks&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_id_end_including&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;block_id_start&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;num_blocks&lt;/span&gt; &lt;span class="o"&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;OnDeallocation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pointer&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="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;One &lt;code&gt;madvise&lt;/code&gt; for a run of 64 adjacent blocks instead of 64 syscalls. The&#10;whole point of sorting the ids on the way out of the thread-local cache is&#10;to make this possible.&lt;/p&gt;&#10;&lt;p&gt;There is a subtlety on the way back in. A block that was decommitted with&#10;&lt;code&gt;MADV_DONTNEED&lt;/code&gt; and is then re-allocated gets fresh zero pages — but a block&#10;that was &lt;em&gt;never&lt;/em&gt; touched still has its original (zero) pages. Both cases end&#10;up zeroed, so the allocator does not need to track &amp;ldquo;was this decommitted?&amp;rdquo;&#10;per block. The &lt;code&gt;touched&lt;/code&gt;/&lt;code&gt;untouched&lt;/code&gt; split exists for a different reason: it&#10;tells the reclamation path which blocks actually have resident pages worth&#10;releasing.&lt;/p&gt;&#10;&lt;h2 id="the-packed-retention-estimate"&gt;The packed retention estimate&lt;/h2&gt;&#10;&lt;p&gt;Here is a small trick that I like a lot.&lt;/p&gt;&#10;&lt;p&gt;The allocator wants to know how much memory it is really holding, so it can&#10;decide when to start giving pages back to the kernel. Walking every free&#10;list to count would be O(pool size) and would need a lock.&lt;/p&gt;&#10;&lt;p&gt;Instead, DuckDB keeps a rolling, bucketed count of recently returned blocks.&#10;Time is divided into 500 ms buckets; each bucket holds &lt;em&gt;how many blocks were&#10;returned during it&lt;/em&gt;. A bucket is packed into a single &lt;code&gt;uint64&lt;/code&gt; — 32 bits of&#10;epoch, 32 bits of count:&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/storage/block_allocator.cpp:58&#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&lt;/span&gt; &lt;span class="kt"&gt;uint64_t&lt;/span&gt; &lt;span class="nf"&gt;PackRetentionBucket&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;epoch&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;uint32_t&lt;/span&gt; &lt;span class="n"&gt;count&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;uint64_t&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;epoch&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&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="n"&gt;count&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="k"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;uint32_t&lt;/span&gt; &lt;span class="nf"&gt;RetentionBucketEpoch&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;uint64_t&lt;/span&gt; &lt;span class="n"&gt;bucket&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;&#9;&lt;span class="k"&gt;return&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="kt"&gt;uint32_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;bucket&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;32&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="k"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;uint32_t&lt;/span&gt; &lt;span class="nf"&gt;RetentionBucketCount&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;uint64_t&lt;/span&gt; &lt;span class="n"&gt;bucket&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;&#9;&lt;span class="k"&gt;return&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="kt"&gt;uint32_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;bucket&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;One atomic &lt;code&gt;uint64&lt;/code&gt; per bucket, updated with a compare-exchange. The epoch&#10;makes the bucket self-describing: you can tell &lt;em&gt;when&lt;/em&gt; a count was recorded&#10;and how stale it is, without a separate array of timestamps.&lt;/p&gt;&#10;&lt;p&gt;There are three buckets, because the decay window is one second and the&#10;bucket width is 500 ms:&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/storage/block_allocator.cpp:119&#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;idx_t&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RetentionTarget&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;now_ms&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;epoch&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;now_ms&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_INTERVAL_MS&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;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;weighted&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;offset&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;now_ms&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_INTERVAL_MS&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;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&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="nl"&gt;bucket&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;retention_buckets&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;age&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="kt"&gt;uint32_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;epoch&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;RetentionBucketEpoch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;age&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;retention_buckets&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="k"&gt;continue&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;&#9;&#9;&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;age_ms&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;age&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; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;age&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;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_INTERVAL_MS&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;remaining_ms&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_DECAY_MS&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;age_ms&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;&#9;&#9;&lt;span class="n"&gt;weighted&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;RetentionBucketCount&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;remaining_ms&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;&#9;&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;weighted&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_DECAY_MS&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 estimate is a &lt;em&gt;linear decay&lt;/em&gt;, not a step function. Each bucket&amp;rsquo;s count&#10;is weighted by how much of the decay window it still has left, and the&#10;weighted sum is divided by the window length. A block returned one&#10;millisecond ago counts almost fully; one returned 900 ms ago counts about a&#10;tenth. That is the &amp;ldquo;bundled jemalloc&amp;rdquo; decay behaviour the config comment&#10;mentions.&lt;/p&gt;&#10;&lt;p&gt;Because the epoch is packed in, the bucket&amp;rsquo;s age is known without a&#10;timestamp array, and because the count saturates at the pool size, the&#10;arithmetic cannot overflow:&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/storage/block_allocator.cpp:79&#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;void&lt;/span&gt; &lt;span class="n"&gt;BlockAllocator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;AddRetention&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;now_ms&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;epoch&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;now_ms&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;BlockAllocatorConfig&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;RETENTION_INTERVAL_MS&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;DivBlockSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool_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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bucket&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;retention_buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;epoch&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;retention_buckets&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&lt;span class="k"&gt;do&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;elapsed&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="kt"&gt;uint32_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;epoch&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;RetentionBucketEpoch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;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;&#9;&#9;&lt;span class="c1"&gt;// Modular ordering assumes generations are less than half the epoch range apart.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;elapsed&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;uint32_t&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;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;31&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&#9;&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;retained&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;elapsed&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; &lt;span class="n"&gt;RetentionBucketCount&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;updated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;PackRetentionBucket&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;&#9;&#9; &lt;span class="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_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;epoch&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;&#9;&#9; &lt;span class="n"&gt;NumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_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;retained&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;retained&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;updated&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;compare_exchange_weak&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;updated&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;memory_order_relaxed&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&#9;&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;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;true&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 &lt;code&gt;elapsed &amp;gt;= 1 &amp;lt;&amp;lt; 31&lt;/code&gt; check is a wraparound guard: the epochs are&#10;compared modulo 2^32, so a generation that is more than half the epoch range&#10;old is ambiguous and the update is simply dropped. &lt;code&gt;capacity&lt;/code&gt; is the number&#10;of blocks in the pool, so the count can never exceed it.&lt;/p&gt;&#10;&lt;p&gt;The result is an O(1) estimate — three atomic loads and a bit of arithmetic&#10;— of how many blocks the allocator is holding onto, with sub-second time&#10;resolution. No list walking, no locks.&lt;/p&gt;&#10;&lt;h2 id="the-other-size-classes"&gt;The other size classes&lt;/h2&gt;&#10;&lt;p&gt;Everything above is about the 256 KiB pool blocks. DuckDB also allocates&#10;plenty of other sizes, and those go through a separate, sharded cache of&#10;power-of-two classes:&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/storage/block_allocator.cpp:358&#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;AllocationCache&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;&#9;&lt;span class="k"&gt;using&lt;/span&gt; &lt;span class="n"&gt;Queue&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;duckdb_moodycamel&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ConcurrentQueue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;data_ptr_t&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;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MIN_SHIFT&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;19&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;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MAX_SHIFT&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;26&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;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MAX_SHARDS&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;256&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;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;CPUS_PER_SHARD&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MAX_LOCAL_SPARES&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// An admission ceiling, independent of pressure-driven reclamation.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MAX_CACHED_BYTES_PER_BUCKET&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1024ULL&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;1024&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;1024&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;MIN_SHIFT = 19&lt;/code&gt; is 512 KiB, &lt;code&gt;MAX_SHIFT = 26&lt;/code&gt; is 64 MiB. The bucket index is&#10;again just a shift — &lt;code&gt;CountZeros::Trailing(size) - MIN_SHIFT&lt;/code&gt; — so a size&#10;maps to its class with the same trick the pool uses for block ids. Sizes&#10;outside the range, or sizes that are not powers of two, are not cached at&#10;all and go straight to the fallback allocator.&lt;/p&gt;&#10;&lt;p&gt;The cache is sharded by CPU (&lt;code&gt;CPUS_PER_SHARD = 4&lt;/code&gt;, up to 256 shards), so a&#10;thread almost always finds a free buffer in its own shard&amp;rsquo;s queue. When it&#10;does not, it steals from a neighbouring shard — but only after checking that&#10;the donor is above its spare allowance, so the cache never lets one hot&#10;thread drain a cold shard entirely.&lt;/p&gt;&#10;&lt;h2 id="what-it-costs"&gt;What it costs&lt;/h2&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;One &lt;code&gt;mmap&lt;/code&gt; of the whole pool.&lt;/strong&gt; The address space is reserved up front.&#10;On a 64-bit machine that is free; on 32-bit the pool is disabled.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;One page fault per newly touched block.&lt;/strong&gt; A block that was decommitted&#10;and comes back faults. That is the price of giving the pages back, and it&#10;is paid only for blocks that were idle long enough to be reclaimed.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;A &lt;code&gt;madvise&lt;/code&gt; syscall per contiguous run on reclamation.&lt;/strong&gt; Not per block.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;An atomic &lt;code&gt;uint64&lt;/code&gt; CAS per batch of frees&lt;/strong&gt; to maintain the retention&#10;estimate, amortised over 16 blocks.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;A per-thread cache that can hold memory the pool is not using.&lt;/strong&gt; This is&#10;the interesting one. The per-thread lists mean a block freed on thread A&#10;may sit on thread A&amp;rsquo;s list while thread B allocates from the global queue.&#10;The retention buckets exist precisely to bound this: they estimate how&#10;much is being held and drive the reclamation path back toward the pool&amp;rsquo;s&#10;target.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;And the win: &lt;strong&gt;no &lt;code&gt;malloc&lt;/code&gt;, no &lt;code&gt;munmap&lt;/code&gt;, no glibc arena, no allocator&#10;lock on the hot path.&lt;/strong&gt; The buffer manager&amp;rsquo;s block allocation is a&#10;&lt;code&gt;pop_back&lt;/code&gt; from a thread-local vector.&lt;/p&gt;&#10;&lt;h2 id="the-bottom-line"&gt;The bottom line&lt;/h2&gt;&#10;&lt;p&gt;The ideas here are old-fashioned in the best way: pick a layout that makes&#10;the arithmetic trivial, and pay the costs in the places nobody looks at&#10;often.&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;Own the address space.&lt;/strong&gt; One &lt;code&gt;mmap(MAP_NORESERVE)&lt;/code&gt; gives you a pool&#10;without paying commit limits for it, and gives you a place to put the&#10;pages when you actually want them.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Make identity arithmetic.&lt;/strong&gt; A power-of-two block size plus a shift turns&#10;&lt;code&gt;pointer → id&lt;/code&gt; into a subtract and a shift, and turns the free lists into&#10;vectors of 32-bit integers.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Batch everything that touches shared state.&lt;/strong&gt; Free lists are per-thread;&#10;the shared queues move 16 ids at a time; reclamation coalesces contiguous&#10;runs into a single &lt;code&gt;madvise&lt;/code&gt;.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Estimate, do not measure, when measuring is expensive.&lt;/strong&gt; The packed&#10;epoch-and-count bucket gives an O(1) answer to &amp;ldquo;how much am I holding?&amp;rdquo;&#10;that is good enough to make a decision, and costs one atomic CAS per&#10;batch.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;None of this makes the buffer manager faster in the way a new compression&#10;codec would. It makes it &lt;em&gt;boring&lt;/em&gt;, which is the point: an allocator that&#10;never calls into the C library&amp;rsquo;s allocator is an allocator whose behaviour&#10;you can reason about.&lt;/p&gt;&#10;</content:encoded></item><item><title>The Temporary Memory Manager Solves a Convex Optimization to Split Memory</title><link>https://articles.9j.nz/posts/how-the-temporary-memory-manager-solves-a-convex-optimization/</link><pubDate>Sat, 24 Oct 2026 13:40:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-the-temporary-memory-manager-solves-a-convex-optimization/</guid><category>duckdb</category><category>memory</category><category>buffer-manager</category><category>performance</category><category>internals</category><description>DuckDB splits a shared memory budget between concurrent operators by differentiating a convex cost function in closed form, then handing out bytes greedily.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; When several operators want memory at the same time, DuckDB does&#10;not divide the budget by the number of operators. Each operator registers a&#10;&lt;code&gt;TemporaryMemoryState&lt;/code&gt; with a &lt;em&gt;remaining size&lt;/em&gt; and a &lt;em&gt;materialization&#10;penalty&lt;/em&gt;, and the manager minimises a convex cost function over the whole&#10;set. The gradient of that function has a closed form, so the manager can&#10;evaluate it in O(n) and then hand out the free memory to whichever operator&#10;has the most negative gradient — five rounds per operator. The result is&#10;deterministic, needs no search, and gives memory to whoever is closest to&#10;finishing.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;h2 id="the-query-that-breaks-an-even-split"&gt;The query that breaks an even split&lt;/h2&gt;&#10;&lt;p&gt;You write a join between two large tables. The hash join&amp;rsquo;s build side does not&#10;fit in memory, so it spills. At the same moment the scan feeding the probe&#10;side is buffering vectors, and the aggregate on top of it is holding a hash&#10;table. Three operators, one memory limit.&lt;/p&gt;&#10;&lt;p&gt;The naive answer is to give each a third. That is wrong in two directions at&#10;once. The aggregate might need 1 MB and be done in a millisecond; the hash&#10;join might need 40 GB and run for an hour. An even split starves the join&#10;into spilling when it did not have to, while handing the aggregate 30 GB it&#10;will never touch.&lt;/p&gt;&#10;&lt;p&gt;What you actually want is a rule that answers: given the operators that are&#10;running right now, and the bytes each of them still needs, how should the&#10;budget be divided so that the &lt;em&gt;system&lt;/em&gt; finishes fastest?&lt;/p&gt;&#10;&lt;p&gt;DuckDB answers that with a small optimisation problem, solved on every&#10;reservation change.&lt;/p&gt;&#10;&lt;h2 id="the-state-what-an-operator-tells-the-manager"&gt;The state: what an operator tells the manager&lt;/h2&gt;&#10;&lt;p&gt;An operator that might need to spill registers a &lt;code&gt;TemporaryMemoryState&lt;/code&gt;.&#10;Three numbers matter:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;remaining size&lt;/strong&gt; (&lt;code&gt;s_i&lt;/code&gt;): how many bytes this operator would need if it&#10;could hold everything in memory.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;reservation&lt;/strong&gt; (&lt;code&gt;r_i&lt;/code&gt;): how many bytes it has actually been granted.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;materialization penalty&lt;/strong&gt; (&lt;code&gt;p_i&lt;/code&gt;): how expensive it is to spill this&#10;operator&amp;rsquo;s data, in arbitrary units.&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/include/duckdb/storage/temporary_memory_manager.hpp:59&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! The remaining size needed if it could fit fully in memory&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;remaining_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;&#9;&lt;span class="c1"&gt;//! The minimum reservation for this state&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;minimum_reservation&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;&#9;&lt;span class="c1"&gt;//! How much memory this operator has reserved&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;reservation&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;&#9;&lt;span class="c1"&gt;//! The weight used for determining the reservation for this state&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;materialization_penalty&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 penalty is not an abstraction. The hash join sets it to the tuple width&#10;of its probe side — a wide row is expensive to spill to disk, a narrow row is&#10;cheap:&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/execution/operator/join/physical_hash_join.cpp:1066&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;SetMinimumReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_partition_ht_size&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;probe_side_requirement&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;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;all_constant&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;&#9;&lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;SetMaterializationPenalty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GetTupleWidth&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;probe_types&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;all_constant&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;&#9;&lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;SetRemainingSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;gstate&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;total_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;The manager keeps every live state in a set, and every state is registered&#10;with a guaranteed floor so that no operator can be starved to zero:&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/storage/temporary_memory_manager.cpp:105&#10;&lt;/span&gt;&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;unique_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Register&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ClientContext&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;annotated_lock_guard&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;annotated_mutex&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;guard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&lt;span class="n"&gt;UpdateConfiguration&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;unique_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;DefaultMinimumReservation&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;&#9;&lt;span class="n"&gt;SetRemainingSize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMinimumReservation&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;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMinimumReservation&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;&#9;&lt;span class="n"&gt;active_states&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;result&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;&#9;&lt;span class="n"&gt;Verify&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&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;h2 id="the-objective-function"&gt;The objective function&lt;/h2&gt;&#10;&lt;p&gt;Write &lt;code&gt;t_i = r_i / s_i&lt;/code&gt; for the &lt;em&gt;throughput&lt;/em&gt; of state &lt;code&gt;i&lt;/code&gt;: the fraction of&#10;the work it can do without materialising anything. &lt;code&gt;t_i&lt;/code&gt; is in &lt;code&gt;(0, 1]&lt;/code&gt; by&#10;construction — the reservation never exceeds the remaining size.&lt;/p&gt;&#10;&lt;p&gt;Two quantities summarise the whole system.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Materialization cost.&lt;/strong&gt; Every operator that only gets &lt;code&gt;t_i&lt;/code&gt; of its memory&#10;must materialise the other &lt;code&gt;1 - t_i&lt;/code&gt;. Weight that by how expensive that&#10;operator&amp;rsquo;s materialisation 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;pre tabindex="0"&gt;&lt;code&gt;M(r) = Σ_i p_i · (1 - t_i) = Σ_i p_i · (1 - r_i / s_i)&lt;/code&gt;&lt;/pre&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;&lt;strong&gt;Throughput.&lt;/strong&gt; One operator crawling at 10 % does not get rescued by another&#10;one running at 100 %. The system is only as fast as its &lt;em&gt;geometric&lt;/em&gt; mean, so&#10;the shortfall is measured against the geometric mean of the throughputs:&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;pre tabindex="0"&gt;&lt;code&gt;T(r) = ( Π_i t_i )^(1/n)&lt;/code&gt;&lt;/pre&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The cost the manager minimises is the product of the two:&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;pre tabindex="0"&gt;&lt;code&gt;C(r) = M(r) · (1 - T(r))&lt;/code&gt;&lt;/pre&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Read it as: &lt;em&gt;the amount of spilling we will have to do, times how far the&#10;system as a whole is from running at full speed&lt;/em&gt;. If everything fits,&#10;&lt;code&gt;T = 1&lt;/code&gt; and the cost is zero. If one operator is starved, &lt;code&gt;T&lt;/code&gt; drops and the&#10;cost rises sharply — and it rises for &lt;em&gt;everyone&lt;/em&gt;, because the geometric mean&#10;is the one place where a single bad operator contaminates the whole.&lt;/p&gt;&#10;&lt;h3 id="why-this-objective-is-convex"&gt;Why this objective is convex&lt;/h3&gt;&#10;&lt;p&gt;This matters, because it is what makes a gradient useful.&lt;/p&gt;&#10;&lt;p&gt;With &lt;code&gt;s_i&lt;/code&gt; and &lt;code&gt;p_i&lt;/code&gt; fixed, &lt;code&gt;M(r)&lt;/code&gt; is an &lt;strong&gt;affine&lt;/strong&gt; function of &lt;code&gt;r&lt;/code&gt;, and it&#10;is non-negative on the feasible box &lt;code&gt;0 &amp;lt; r_i ≤ s_i&lt;/code&gt; because &lt;code&gt;t_i ≤ 1&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;&lt;code&gt;T(r)&lt;/code&gt; is the geometric mean of the positive affine functions &lt;code&gt;r_i / s_i&lt;/code&gt;.&#10;The geometric mean is concave on the non-negative orthant, and it is&#10;non-decreasing in each argument, so the composition is concave. Therefore&#10;&lt;code&gt;1 - T(r)&lt;/code&gt; is &lt;strong&gt;convex&lt;/strong&gt;, and non-negative (since &lt;code&gt;T ≤ 1&lt;/code&gt;).&lt;/p&gt;&#10;&lt;p&gt;The product of two non-negative convex functions is convex. So &lt;code&gt;C(r)&lt;/code&gt; is&#10;convex on the feasible region.&lt;/p&gt;&#10;&lt;p&gt;That is the licence to use first-order information: at any point, the&#10;gradient tells you the direction in which the cost falls fastest, and there&#10;is exactly one local minimum to find.&lt;/p&gt;&#10;&lt;h2 id="the-closed-form-gradient"&gt;The closed-form gradient&lt;/h2&gt;&#10;&lt;p&gt;Here is the part that is genuinely nice. The gradient of &lt;code&gt;C&lt;/code&gt; with respect to&#10;each reservation has a formula you can write on a napkin — no numerical&#10;differentiation, no finite differences, no Newton iterations.&lt;/p&gt;&#10;&lt;p&gt;&lt;code&gt;M&lt;/code&gt; depends on &lt;code&gt;r_i&lt;/code&gt; linearly: &lt;code&gt;∂M/∂r_i = -p_i / s_i&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;&lt;code&gt;T&lt;/code&gt; is an exponential of a mean of logarithms, so&#10;&lt;code&gt;∂T/∂r_i = T / (n · r_i)&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;Chain-ruling on &lt;code&gt;C = M · (1 - T)&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;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;pre tabindex="0"&gt;&lt;code&gt;∂C/∂r_i = (∂M/∂r_i)·(1 - T) - M·(∂T/∂r_i)&#10; = -p_i·(1 - T)/s_i - T·M/(n·r_i)&lt;/code&gt;&lt;/pre&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Both terms are non-positive. That makes sense: giving an operator more&#10;memory never increases the cost. What differs between operators is the&#10;&lt;em&gt;magnitude&lt;/em&gt;, and that magnitude is the marginal benefit of one more byte.&lt;/p&gt;&#10;&lt;p&gt;And here is the code, computing exactly that:&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/storage/temporary_memory_manager.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="k"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;ComputeDerivatives&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;reference&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;states&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;res&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;double&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;n&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;&#9;&lt;span class="c1"&gt;// Cost function takes &amp;#34;throughput&amp;#34; (reservation / size) of each operator as its principal input&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;log_throughput_prod&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;&#9;&lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;mat_cost&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;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;idx_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;n&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="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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;state&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;states&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="n"&gt;get&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;resd&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="kt"&gt;double&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;res&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;sizd&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="kt"&gt;double&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;MaxValue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pend&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="kt"&gt;double&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;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMaterializationPenalty&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;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;resd&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;resd&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;sizd&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;throughput&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;resd&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;sizd&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;&#9;&#9;&lt;span class="n"&gt;log_throughput_prod&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;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;throughput&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;&#9;&#9;&lt;span class="n"&gt;mat_cost&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;pend&lt;/span&gt; &lt;span class="o"&gt;*&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;throughput&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Materialization cost: sum of (1 - throughput)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;nd&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="kt"&gt;double&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;n&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// n as double for convenience&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;throughput_geomean&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;exp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;log_throughput_prod&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;nd&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;tp_mult&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;throughput_geomean&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Throughput multiplier: 1 - geomean throughputs&#10;&lt;/span&gt;&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;&#9;&lt;span class="c1"&gt;// Cost function: materialization cost * (1 - throughput multiplier), but we don&amp;#39;t actually need to compute it&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// here. We need to compute the derivative with respect to every reservation, stored in &amp;#34;der&amp;#34;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// Just use https://www.derivative-calculator.net with this (n = 3) to see what&amp;#39;s going on&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// (3 - (a_1/s_1)-(a_2/s_2)-(a_3/s_3))*(1-((a_1/s_1)*(a_2/s_2)*(a_3/s_3))^(1/3))&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;intermediate&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;throughput_geomean&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;mat_cost&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;nd&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;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;idx_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;n&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="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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;state&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;states&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="n"&gt;get&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;resd&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="kt"&gt;double&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;res&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;sizd&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="kt"&gt;double&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;MaxValue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;pend&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="kt"&gt;double&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;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMaterializationPenalty&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;&#9;&#9;&lt;span class="n"&gt;der&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;intermediate&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;resd&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;pend&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;tp_mult&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;sizd&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;&#9;&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;Read the last line against the formula. &lt;code&gt;intermediate / resd&lt;/code&gt; is&#10;&lt;code&gt;-T·M/(n·r_i)&lt;/code&gt;. &lt;code&gt;pend * tp_mult / sizd&lt;/code&gt; is &lt;code&gt;p_i·(1 - T)/s_i&lt;/code&gt;, subtracted, so&#10;the whole derivative is &lt;code&gt;-T·M/(n·r_i) - p_i·(1 - T)/s_i&lt;/code&gt; — exactly&#10;&lt;code&gt;∂C/∂r_i&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;Two details worth noticing. The product of throughputs is never formed; the&#10;code accumulates &lt;code&gt;log(t_i)&lt;/code&gt; and exponentiates once at the end, so a thousand&#10;operators each running at a thousandth of their requirement cannot underflow&#10;the intermediate product to zero before the &lt;code&gt;1/n&lt;/code&gt;-th root is taken. And the&#10;loop is O(n) with one &lt;code&gt;log&lt;/code&gt; per operator — the derivative of a product of a&#10;hundred terms is not a hundred-term product of derivatives.&lt;/p&gt;&#10;&lt;h2 id="from-gradient-to-split"&gt;From gradient to split&lt;/h2&gt;&#10;&lt;p&gt;&lt;code&gt;ComputeReservation&lt;/code&gt; is the function that actually splits the money. It&#10;collects the live states, computes an initial reservation for each, and then&#10;runs a greedy marginal-allocation 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/storage/temporary_memory_manager.cpp:219&#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;idx_t&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ComputeReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;OPTIMIZATION_ITERATIONS_MULTIPLIER&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;&#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;&#9;&lt;span class="c1"&gt;// Use vectors for ease&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;optional_idx&lt;/span&gt; &lt;span class="n"&gt;state_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;&#9;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;reference&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;states&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;&#9;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;res&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;&#9;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;double&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;der&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;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;sum_of_initial_res&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;&#9;&lt;span class="n"&gt;idx_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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&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="nl"&gt;state&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;active_states&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;initial_reservation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ComputeInitialReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;state&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;&#9;&#9;&lt;span class="n"&gt;sum_of_initial_res&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;initial_reservation&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RefersToSameObject&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;state&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;temporary_memory_state&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;&#9;&#9;&#9;&lt;span class="n"&gt;state_index&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;&#9;&#9;&lt;span class="p"&gt;}&lt;/span&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;initial_reservation&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;state&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;GetRemainingSize&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;&#9;&#9;&#9;&lt;span class="k"&gt;continue&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;states&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;emplace_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;state&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;&#9;&#9;&lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;initial_reservation&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;&#9;&#9;&lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NumericLimits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;double&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;Maximum&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;&#9;&#9;&lt;span class="n"&gt;i&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;&#9;&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;n&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;sum_of_initial_res&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;memory_limit&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;state_index&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetIndex&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;&#9;&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;free_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;memory_limit&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;sum_of_initial_res&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;States that are already fully satisfied (&lt;code&gt;initial_reservation &amp;gt;= remaining size&lt;/code&gt;) are dropped from the optimisation entirely — there is nothing to&#10;decide about them. If the sum of the floors already exceeds the limit, the&#10;answer is simply the floor and the optimiser is skipped.&lt;/p&gt;&#10;&lt;p&gt;Then the loop itself:&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/storage/temporary_memory_manager.cpp:250&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// Distribute memory in OPTIMIZATION_ITERATIONS&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;remaining_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;free_memory&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;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;optimization_iterations&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;OPTIMIZATION_ITERATIONS_MULTIPLIER&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;n&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;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;opt_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;opt_idx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;optimization_iterations&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;remaining_memory&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="n"&gt;opt_idx&lt;/span&gt;&lt;span class="o"&gt;++&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;&#9;&#9;&lt;span class="n"&gt;ComputeDerivatives&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;states&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&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;&#9;&#9;&lt;span class="c1"&gt;// Find the index of the state with the lowest derivative&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;min_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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;min_der&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;NumericLimits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;double&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;Maximum&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;&#9;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;found_candidate&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;false&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;&#9;&#9;&lt;span class="k"&gt;for&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;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;n&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="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;&#9;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;state&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;states&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="n"&gt;get&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;&#9;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;res&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;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#9;&#9;&#9;&#9;&lt;span class="k"&gt;continue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// We can&amp;#39;t increase the reservation of &amp;#34;maxed&amp;#34; states, so we skip these&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&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;&#9;&#9;&#9;&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;found_candidate&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;der&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;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;min_der&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;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;min_idx&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;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;min_der&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;der&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;found_candidate&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&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;&#9;&#9;&#9;&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;&#9;&#9;&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;&#9;&#9;&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;found_candidate&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;&#9;&#9;&#9;&lt;span class="k"&gt;break&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;&#9;&#9;&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 scheme is plain marginal benefit allocation. Each round:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;Evaluate the gradient at the current reservation vector.&lt;/li&gt;&#10;&lt;li&gt;Find the state with the &lt;strong&gt;lowest&lt;/strong&gt; (most negative) derivative — the state&#10;for which one more byte buys the most.&lt;/li&gt;&#10;&lt;li&gt;Give that state a chunk of the remaining memory.&lt;/li&gt;&#10;&lt;li&gt;Repeat, &lt;code&gt;5 × n&lt;/code&gt; times.&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;p&gt;Because the gradient is negative everywhere, &amp;ldquo;lowest&amp;rdquo; is unambiguous: it is&#10;the state with the largest &lt;code&gt;|∂C/∂r_i|&lt;/code&gt;. And because &lt;code&gt;C&lt;/code&gt; is convex, the&#10;marginal benefit of a byte only decreases as you give that operator more —&#10;so the greedy choice cannot be improved by revisiting an earlier decision in&#10;a way the gradient does not already capture.&lt;/p&gt;&#10;&lt;p&gt;The chunk size is chosen so the free memory is exhausted in a fixed number&#10;of rounds rather than all at once:&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/storage/temporary_memory_manager.cpp:274&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;min_state&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;states&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;min_idx&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;&#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;&#9;&#9;&lt;span class="c1"&gt;// This is how much memory we will distribute in this round&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;iter_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ExactNumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&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;&#9;&#9; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ceil&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="kt"&gt;double&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;remaining_memory&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="kt"&gt;double&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;optimization_iterations&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;opt_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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// Compute how much we can add&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;state_room&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;min_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;min_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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;delta&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;iter_memory&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;state_room&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;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;delta&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;remaining_memory&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;&#9;&#9;&lt;span class="c1"&gt;// Update counts&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;res&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;min_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;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;&#9;&#9;&lt;span class="n"&gt;remaining_memory&lt;/span&gt; &lt;span class="o"&gt;-=&lt;/span&gt; &lt;span class="n"&gt;delta&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;state_room&lt;/code&gt;: an operator is never given more than it asked for. A&#10;reservation above the remaining size would make &lt;code&gt;t_i &amp;gt; 1&lt;/code&gt;, which would break&#10;both the model and the &lt;code&gt;D_ASSERT(resd &amp;lt;= sizd)&lt;/code&gt; in &lt;code&gt;ComputeDerivatives&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;There is one more wrinkle, and it is a nice one. &lt;code&gt;ComputeReservation&lt;/code&gt; is&#10;called &lt;em&gt;once per state&lt;/em&gt;, in whatever order the operators happen to ask. So a&#10;naive implementation would be order-dependent: the first state to ask would&#10;soak up the free memory. DuckDB handles this with a second phase: it&#10;re-evaluates the derivative with every state at its &lt;em&gt;maximum&lt;/em&gt; possible&#10;reservation, sorts the states by that derivative, and only then applies the&#10;per-state caps in that order.&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/storage/temporary_memory_manager.cpp:296&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// We computed how the memory should be assigned to the states,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// but we did not yet take into account the upper bound of MAXIMUM_FREE_MEMORY_RATIO * free_memory.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// We don&amp;#39;t simply bound this state&amp;#39;s reservation because order matters,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// and this function is called in arbitrary order for all active states.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// So, we order the states by derivative (as if they got the max reservation),&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// and assign the states with the lowest derivate first.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// This way, order does not matter _as much_, and the &amp;#34;best&amp;#34; states will _likely_ get more memory&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;idxs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&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;&#9;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_res&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&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;&#9;&lt;span class="k"&gt;for&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;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;n&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="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;&#9;&#9;&lt;span class="n"&gt;idxs&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;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;&#9;&#9;&lt;span class="n"&gt;max_res&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;states&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="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#9;&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;&#9;&lt;span class="n"&gt;ComputeDerivatives&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;states&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;max_res&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&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;&#9;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;idxs&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;idxs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&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="p"&gt;](&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;der&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rhs&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;The comment is candid about it: order does not matter &lt;em&gt;as much&lt;/em&gt;. It is a&#10;heuristic that makes the answer approximately order-independent rather than&#10;exactly so.&lt;/p&gt;&#10;&lt;h2 id="the-fairness-floors"&gt;The fairness floors&lt;/h2&gt;&#10;&lt;p&gt;An optimisation that maximises throughput can starve an operator. Two&#10;constants stop that.&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/include/duckdb/storage/temporary_memory_manager.hpp:83&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! 512 blocks per state per thread, which is 0.125GB per thread for DEFAULT_BLOCK_ALLOC_SIZE.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MINIMUM_RESERVATION_PER_STATE_PER_THREAD&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;512ULL&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;DEFAULT_BLOCK_ALLOC_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;&#9;&lt;span class="c1"&gt;//! 1/16th of the available main memory.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;MINIMUM_RESERVATION_MEMORY_LIMIT_DIVISOR&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;16ULL&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;&#9;&lt;span class="c1"&gt;//! The maximum ratio of the memory limit that we reserve using the TemporaryMemoryManager&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;MAXIMUM_MEMORY_LIMIT_RATIO&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;0.9&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;&#9;&lt;span class="c1"&gt;//! The maximum ratio of the remaining memory that we reserve per TemporaryMemoryState&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;MAXIMUM_FREE_MEMORY_RATIO&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;0.9&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;&lt;code&gt;DEFAULT_BLOCK_ALLOC_SIZE&lt;/code&gt; is 262144, so 512 blocks is 128 MiB per thread.&#10;The floor for a state is the smaller of &amp;ldquo;128 MiB × number of threads&amp;rdquo; and&#10;&amp;ldquo;one sixteenth of the whole memory limit&amp;rdquo;:&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/storage/temporary_memory_manager.cpp:74&#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;idx_t&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;DefaultMinimumReservation&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num_threads&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;MINIMUM_RESERVATION_PER_STATE_PER_THREAD&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;&#9; &lt;span class="n"&gt;memory_limit&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;MINIMUM_RESERVATION_MEMORY_LIMIT_DIVISOR&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;On an 8-core machine with a 16 GiB limit both terms are 1 GiB, so every&#10;registered operator is guaranteed 1 GiB. The floor is also capped by the&#10;operator&amp;rsquo;s own remaining size — you cannot reserve more than the operator&#10;needs.&lt;/p&gt;&#10;&lt;p&gt;The manager itself never sees the whole buffer pool budget:&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/storage/temporary_memory_manager.cpp:89&#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;void&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;UpdateConfiguration&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ClientContext&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;buffer_manager&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;BufferManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;GetBufferManager&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;task_scheduler&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;TaskScheduler&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;GetScheduler&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="n"&gt;memory_limit&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;&#9; &lt;span class="n"&gt;LossyNumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;MAXIMUM_MEMORY_LIMIT_RATIO&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="kt"&gt;double&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;buffer_manager&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMaxMemory&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;&#9;&lt;span class="n"&gt;has_temporary_directory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;buffer_manager&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;HasTemporaryDirectory&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;&#9;&lt;span class="n"&gt;num_threads&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;task_scheduler&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;NumberOfThreads&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;&#9;&lt;span class="n"&gt;num_connections&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ConnectionManager&lt;/span&gt;&lt;span class="o"&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;context&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;GetConnectionCount&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;&#9;&lt;span class="n"&gt;query_max_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;buffer_manager&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetOperatorMemoryLimit&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;90 % of the buffer pool&amp;rsquo;s max memory, so there is always headroom for the&#10;buffer manager&amp;rsquo;s own accounting. And &lt;code&gt;MAXIMUM_FREE_MEMORY_RATIO&lt;/code&gt; caps any&#10;single state at 90 % of the free memory — one operator cannot swallow the&#10;budget and starve the rest.&lt;/p&gt;&#10;&lt;p&gt;There is also a special case that short-circuits the whole model: if there&#10;is no temporary directory, nothing can be spilled, so there is no reason to&#10;limit anybody.&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/storage/temporary_memory_manager.cpp:118&#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;void&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;UpdateState&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ClientContext&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;context&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TemporaryMemoryState&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&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;&#9;&lt;span class="n"&gt;UpdateConfiguration&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;context&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;&#9;&lt;span class="c1"&gt;// The lower bound for the reservation of this state is either the minimum reservation or the remaining size&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;lower_bound&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;&#9; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMinimumReservation&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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; &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;&#9;&#9;&lt;span class="c1"&gt;// Sometimes set to 0 to denote end of state (before actually deleting the state)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&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;&#9;&lt;span class="p"&gt;}&lt;/span&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;Settings&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Get&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;DebugForceExternalSetting&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;context&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;&#9;&#9;&lt;span class="c1"&gt;// We&amp;#39;re forcing external processing. Give it the minimum&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;lower_bound&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;&#9;&lt;span class="p"&gt;}&lt;/span&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="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;has_temporary_directory&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;&#9;&#9;&lt;span class="c1"&gt;// We cannot offload, so we cannot limit memory usage. Set reservation equal to the remaining size&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&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;&#9;&lt;span class="p"&gt;}&lt;/span&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;reservation&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetReservation&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;lower_bound&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;memory_limit&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;&#9;&#9;&lt;span class="c1"&gt;// We overshot. Set reservation equal to the minimum&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;lower_bound&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;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&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;&#9;&#9;&lt;span class="c1"&gt;// The upper bound for the reservation of this state is the minimum of:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// 1. Remaining size of the state&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// 2. The max memory per query&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// 3. MAXIMUM_FREE_MEMORY_RATIO * free memory&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;upper_bound&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetRemainingSize&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;query_max_memory&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;&#9;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;free_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;memory_limit&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;reservation&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetReservation&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;&#9;&#9;&lt;span class="n"&gt;upper_bound&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;upper_bound&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;&#9;&#9; &lt;span class="n"&gt;LossyNumericCast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_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;MAXIMUM_FREE_MEMORY_RATIO&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="kt"&gt;double&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;free_memory&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;&#9;&#9;&lt;span class="n"&gt;upper_bound&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;MinValue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;upper_bound&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;free_memory&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;&#9;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;new_reservation&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lower_bound&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;upper_bound&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;&#9;&#9;&#9;&lt;span class="n"&gt;new_reservation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;lower_bound&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;&#9;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&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;&#9;&#9;&#9;&lt;span class="n"&gt;new_reservation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;remaining_size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;memory_limit&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;ComputeReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;upper_bound&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;SetReservation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temporary_memory_state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;new_reservation&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;&#9;&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;&#9;&lt;span class="n"&gt;Verify&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;Notice that the optimiser is only invoked when the system is actually under&#10;pressure (&lt;code&gt;remaining_size &amp;gt; memory_limit&lt;/code&gt;). When everything fits, the upper&#10;bound is simply &amp;ldquo;all of it&amp;rdquo; and there is nothing to optimise.&lt;/p&gt;&#10;&lt;h2 id="what-it-costs"&gt;What it costs&lt;/h2&gt;&#10;&lt;p&gt;The optimisation is not free, so here is the bill.&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;code&gt;ComputeDerivatives&lt;/code&gt; is O(n) with one &lt;code&gt;log&lt;/code&gt; and one &lt;code&gt;exp&lt;/code&gt; per call.&lt;/li&gt;&#10;&lt;li&gt;The allocation loop runs &lt;code&gt;5 × n&lt;/code&gt; rounds, each calling&#10;&lt;code&gt;ComputeDerivatives&lt;/code&gt;, so the whole thing is O(n²) with a small constant.&#10;With three operators that is 15 rounds; with thirty it is 150.&lt;/li&gt;&#10;&lt;li&gt;&lt;code&gt;ComputeReservation&lt;/code&gt; is called under the manager&amp;rsquo;s lock, from&#10;&lt;code&gt;UpdateState&lt;/code&gt;, which is called whenever an operator&amp;rsquo;s remaining size&#10;changes.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;For the operator counts DuckDB actually sees — a handful of concurrent&#10;operators per query, a few dozen at the very worst — this is tens of&#10;microseconds, paid on reservation changes rather than per tuple. The&#10;alternative, a heuristic like &amp;ldquo;half the memory to the biggest operator&amp;rdquo;, is&#10;cheaper and measurably worse at the boundary between &amp;ldquo;just barely fits&amp;rdquo; and&#10;&amp;ldquo;just barely spills&amp;rdquo;. Spilling a hash table to disk is expensive enough that&#10;being right about the threshold pays for the optimiser many times over.&lt;/p&gt;&#10;&lt;p&gt;Two honest caveats:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;The model treats &lt;code&gt;s_i&lt;/code&gt; and &lt;code&gt;p_i&lt;/code&gt; as constants during the optimisation.&#10;If an operator&amp;rsquo;s remaining size changes mid-flight — a hash join that&#10;discovers its build side is larger than it thought — the whole split has&#10;to be recomputed. DuckDB handles this by re-running &lt;code&gt;UpdateState&lt;/code&gt; whenever&#10;the remaining size changes.&lt;/li&gt;&#10;&lt;li&gt;The final phase is a heuristic for order-independence, not a proof of&#10;it. Two states with very similar derivatives can still end up with&#10;different reservations depending on the order in which they ask.&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;h2 id="the-bottom-line"&gt;The bottom line&lt;/h2&gt;&#10;&lt;p&gt;Memory allocation between concurrent operators is an optimisation problem,&#10;and treating it as one pays off.&lt;/p&gt;&#10;&lt;p&gt;The three ideas worth carrying away:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;Model the tradeoff explicitly.&lt;/strong&gt; &amp;ldquo;Bytes needed&amp;rdquo; and &amp;ldquo;bytes granted&amp;rdquo;&#10;give a &lt;em&gt;throughput&lt;/em&gt;; throughputs combine into a geometric mean, and the&#10;shortfall of that mean is what a starved operator does to the whole query.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Get the gradient in closed form.&lt;/strong&gt; The cost is a product of an affine&#10;function and a concave-composed term, so its derivative is a two-line&#10;formula. No numerical differentiation, no black-box solver, and the&#10;gradient costs one pass.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Greedy marginal allocation on a convex objective is enough.&lt;/strong&gt; Pick the&#10;variable with the most negative partial derivative, give it memory, repeat.&#10;Five rounds per operator is a heuristic, but the convexity is what makes it&#10;a good one.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;The floors are the other half of the story. An optimiser that maximises&#10;throughput will happily starve an operator to zero, so DuckDB pairs the&#10;optimisation with a hard per-state minimum and a hard per-state maximum.&#10;The best split of a budget you do not own is the one that does not require&#10;anyone to go hungry.&lt;/p&gt;&#10;</content:encoded></item><item><title>The Lock-Free Eviction Queue: Weak Pointers and Sequence Numbers</title><link>https://articles.9j.nz/posts/how-duckdb-evicts-blocks-with-a-lock-free-weak-pointer-queue/</link><pubDate>Sat, 24 Oct 2026 13:10:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-duckdb-evicts-blocks-with-a-lock-free-weak-pointer-queue/</guid><category>duckdb</category><category>buffer-manager</category><category>memory</category><category>cache</category><category>performance</category><description>DuckDB's eviction queue holds weak pointers to blocks plus a sequence number, so stale entries are detected without taking the block lock.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; The eviction queue is a &lt;code&gt;duckdb_moodycamel::ConcurrentQueue&lt;/code&gt; of&#10;&lt;code&gt;BufferEvictionNode{ weak_ptr&amp;lt;BlockMemory&amp;gt; memory_p; idx_t handle_sequence_number; }&lt;/code&gt;.&#10;Because the queue stores only a &lt;em&gt;weak&lt;/em&gt; pointer, enqueuing a block costs nothing and never&#10;keeps a dead block alive — the queue is allowed to accumulate garbage. An entry is stale&#10;if the weak pointer has expired (the block was destroyed) &lt;strong&gt;or&lt;/strong&gt; if its sequence number no&#10;longer matches the block&amp;rsquo;s current &lt;code&gt;eviction_seq_num&lt;/code&gt; (a newer entry superseded it).&#10;Staleness is therefore detectable &lt;em&gt;without&lt;/em&gt; taking the block lock. Garbage collection is&#10;amortised: a purge runs every 4096 insertions and uses &lt;code&gt;try_dequeue_bulk&lt;/code&gt; +&#10;&lt;code&gt;enqueue_bulk&lt;/code&gt; with a &lt;em&gt;separate producer token&lt;/em&gt;, so the survivors land in a sub-queue the&#10;consumer token has already walked past and FIFO order is preserved.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;h2 id="the-scenario"&gt;The scenario&lt;/h2&gt;&#10;&lt;p&gt;Eight threads are scanning eight different tables. The memory limit is 4 GB. Every time a&#10;scan finishes a block it hands the block back to the pool; every time a scan wants a new&#10;block it takes one. Meanwhile, the pool is over its limit and needs to make room.&lt;/p&gt;&#10;&lt;p&gt;The pool&amp;rsquo;s job is to keep a list of blocks it &lt;em&gt;could&lt;/em&gt; throw away, in roughly the order it&#10;should throw them away. That list has to survive:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;concurrency&lt;/strong&gt; — many threads adding and removing entries at once;&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;blocks that die&lt;/strong&gt; — a &lt;code&gt;BlockHandle&lt;/code&gt; can be destroyed while its entry is still in the&#10;queue, leaving a dangling reference;&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;duplicate entries&lt;/strong&gt; — the same block can be enqueued, evicted-and-reloaded, and&#10;enqueued again, so the queue can hold several entries for the same block, only one of&#10;which is current.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;A naive &lt;code&gt;std::queue&amp;lt;shared_ptr&amp;lt;BlockHandle&amp;gt;&amp;gt;&lt;/code&gt; fails on all three counts: it needs a lock,&#10;and it cannot represent &amp;ldquo;the block this entry refers to is gone&amp;rdquo;.&lt;/p&gt;&#10;&lt;h2 id="the-node-a-weak-pointer-and-a-version-number"&gt;The node: a weak pointer and a version number&lt;/h2&gt;&#10;&lt;p&gt;Here is the whole 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/include/duckdb/storage/buffer/buffer_pool.hpp:27&#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;struct&lt;/span&gt; &lt;span class="nc"&gt;BufferEvictionNode&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;&#9;&lt;span class="n"&gt;BufferEvictionNode&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;&#9;&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;&#9;&lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;weak_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;block_memory_p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;eviction_seq_num&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;&#9;&lt;span class="n"&gt;weak_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;memory_p&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;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;handle_sequence_number&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;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;IsDeadNode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;optional_idx&lt;/span&gt; &lt;span class="n"&gt;debug_sleep_micros&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;optional_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;&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;Two fields. &lt;code&gt;memory_p&lt;/code&gt; is a &lt;strong&gt;weak&lt;/strong&gt; pointer to the block&amp;rsquo;s &lt;code&gt;BlockMemory&lt;/code&gt;; &lt;code&gt;handle_sequence_number&lt;/code&gt;&#10;is a version number.&lt;/p&gt;&#10;&lt;p&gt;Why weak? Because the queue must not keep a block alive. If the queue held a &lt;code&gt;shared_ptr&lt;/code&gt;,&#10;then a block could never be freed while its entry sat in the queue, and the queue would&#10;grow without bound as blocks are loaded and unloaded. With a &lt;code&gt;weak_ptr&lt;/code&gt;, the entry is&#10;&lt;em&gt;allowed&lt;/em&gt; to dangle — the entry survives the block, and the purger notices.&lt;/p&gt;&#10;&lt;p&gt;Why a sequence number? Because a block can be enqueued more than once. Suppose a block&#10;is unpinned (enqueued, sequence 1), then pinned and unpinned again (enqueued, sequence 2).&#10;Now the queue holds two entries for the same block. Only the second is current. Without a&#10;version, the sweeper would happily unload the block twice, or unload it while somebody had&#10;re-pinned it.&lt;/p&gt;&#10;&lt;p&gt;The version lives on the block itself:&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/include/duckdb/storage/buffer/block_handle.hpp:120&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! Returns the eviction sequence number.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="nf"&gt;GetEvictionSequenceNumber&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;eviction_seq_num&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_acquire&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;&#9;&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;&#9;&lt;span class="c1"&gt;//! Increments the eviction sequence number prior to returning it.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="nf"&gt;NextEvictionSequenceNumber&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockLock&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="n"&gt;VerifyMutex&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;new_sequence_number&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;eviction_seq_num&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="c1"&gt;// Publish preceding dead-node accounting to lock-free queue readers.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;eviction_seq_num&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;store&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_sequence_number&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;memory_order_release&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_sequence_number&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;&#9;&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 declaration carries the invariant in a comment:&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/include/duckdb/storage/buffer/block_handle.hpp:242&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! The internal eviction sequence number. Monotonic: it is never reset, so an eviction queue&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! entry is stale if and only if its sequence number differs from this one. Writers hold the block lock.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;idx_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;eviction_seq_num&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;strong&gt;Monotonic. Never reset.&lt;/strong&gt; That is the key property. Because the counter only ever goes&#10;up, &amp;ldquo;the entry&amp;rsquo;s number differs from the block&amp;rsquo;s current number&amp;rdquo; is an unambiguous test&#10;for &amp;ldquo;this entry is from an older generation&amp;rdquo;. No ABA problem, no epoch, no generation&#10;list.&lt;/p&gt;&#10;&lt;h2 id="two-ways-a-node-dies"&gt;Two ways a node dies&lt;/h2&gt;&#10;&lt;p&gt;The liveness test is short:&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/storage/buffer/buffer_pool.cpp:42&#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;BufferEvictionNode&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;weak_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;block_memory_p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;eviction_seq_num&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;memory_p&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;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_memory_p&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt; &lt;span class="n"&gt;handle_sequence_number&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;eviction_seq_num&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;memory_p&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;expired&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="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;IsDeadNode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;optional_idx&lt;/span&gt; &lt;span class="n"&gt;debug_sleep_micros&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;shared_memory_p&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;memory_p&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;debug_sleep_micros&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;IsValid&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;&#9;&#9;&lt;span class="n"&gt;ThreadUtil&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;SleepMicroSeconds&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;debug_sleep_micros&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetIndex&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;&#9;&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;&#9;&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;shared_memory_p&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;&#9;&#9;&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;handle_sequence_number&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;shared_memory_p&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetEvictionSequenceNumber&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;&#9;&#9;&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;&#9;&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;&#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;Two death certificates:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;&lt;code&gt;!shared_memory_p&lt;/code&gt;&lt;/strong&gt; — the weak pointer could not be upgraded. The &lt;code&gt;BlockMemory&lt;/code&gt; was&#10;destroyed, so the block is gone entirely. The entry is garbage.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;&lt;code&gt;handle_sequence_number != shared_memory_p-&amp;gt;GetEvictionSequenceNumber()&lt;/code&gt;&lt;/strong&gt; — the&#10;block is alive, but this entry is from an older generation. A newer entry for the same&#10;block exists, and &lt;em&gt;that&lt;/em&gt; one is the live one.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;p&gt;Note that the second test reads &lt;code&gt;GetEvictionSequenceNumber()&lt;/code&gt; with &lt;code&gt;memory_order_acquire&lt;/code&gt;&#10;while the writer used &lt;code&gt;memory_order_release&lt;/code&gt;. That pairing is what makes the test&#10;well-defined: if the reader sees the new number, it also sees everything the writer did&#10;before storing it.&lt;/p&gt;&#10;&lt;p&gt;And note what is &lt;em&gt;not&lt;/em&gt; here: &lt;strong&gt;no lock&lt;/strong&gt;. &lt;code&gt;IsDeadNode&lt;/code&gt; touches only the weak pointer&amp;rsquo;s&#10;control block and one atomic load. It can be called on a queue full of blocks that other&#10;threads are concurrently locking, loading and unloading. The staleness test is entirely&#10;lock-free.&lt;/p&gt;&#10;&lt;p&gt;The &lt;code&gt;debug_sleep_micros&lt;/code&gt; parameter is a debug-only hook: it makes the thread sleep between&#10;upgrading the weak pointer and checking the sequence number, so that a race between a&#10;block&amp;rsquo;s destruction and the purger can be provoked on purpose. There is a whole DuckDB&#10;setting for it.&lt;/p&gt;&#10;&lt;h2 id="the-queue"&gt;The queue&lt;/h2&gt;&#10;&lt;p&gt;The container is a third-party lock-free MPMC queue:&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/storage/buffer/buffer_pool.cpp:61&#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;typedef&lt;/span&gt; &lt;span class="n"&gt;duckdb_moodycamel&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ConcurrentQueue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;eviction_queue_t&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;duckdb_moodycamel::ConcurrentQueue&lt;/code&gt; is Cameron Desrochers&amp;rsquo; implementation, vendored in&#10;&lt;code&gt;third_party/concurrentqueue&lt;/code&gt;. Its own header describes it as &amp;ldquo;a C++11 implementation of a&#10;multi-producer, multi-consumer lock-free queue&amp;rdquo;, and points at a write-up of the design.&lt;/p&gt;&#10;&lt;p&gt;And DuckDB keeps a no-threads fallback so that single-threaded builds still compile:&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/include/duckdb/parallel/concurrentqueue.hpp:58&#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="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;ConcurrentQueue&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;private&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;&#9;&lt;span class="c1"&gt;//! The standard library queue.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;queue&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="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;deque&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;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;q&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;public&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;&#9;&lt;span class="c1"&gt;//! Default constructor.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;ConcurrentQueue&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;default&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;&#9;&lt;span class="c1"&gt;//! Constructor reserving capacity.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;explicit&lt;/span&gt; &lt;span class="nf"&gt;ConcurrentQueue&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;capacity&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;&#9;&#9;&lt;span class="n"&gt;q&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;&lt;span class="n"&gt;capacity&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;&#9;&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 real queue is not a ring buffer. It is a &lt;strong&gt;linked list of per-producer sub-queues&lt;/strong&gt;,&#10;which is what makes the producer/consumer &lt;em&gt;token&lt;/em&gt; trick possible.&lt;/p&gt;&#10;&lt;h2 id="adding-to-the-queue"&gt;Adding to the queue&lt;/h2&gt;&#10;&lt;p&gt;Here is the enqueue path, from the &lt;code&gt;BufferPool&lt;/code&gt; down to the queue:&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/storage/buffer/buffer_pool.cpp:274&#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="n"&gt;BufferPool&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;AddToEvictionQueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockLock&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;handle&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&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;&#9;&lt;span class="c1"&gt;// Verify the caller passed this block&amp;#39;s lock before we mutate any of its state.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// The block lock is held throughout: Unpin holds it; ConvertToPersistent acquires the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// (uncontended) lock of the freshly created block before calling.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;VerifyMutex&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;queue&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;GetEvictionQueueForBlockMemory&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;memory&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;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetReaders&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;HasLiveQueueEntry&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&#9;&lt;span class="c1"&gt;// Count the previous live entry before bumping the sequence number. PurgeIteration&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// reads sequence numbers without the block lock; bumping first could let it see the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// previous entry as stale and decrement dead_nodes before this matching increment.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;IncrementDeadNodes&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;&#9;&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;ts&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;NextEvictionSequenceNumber&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;Three things in this excerpt, and all three are about the race between the &lt;em&gt;lock-free&lt;/em&gt;&#10;purger and this &lt;em&gt;locked&lt;/em&gt; writer.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;&lt;code&gt;HasLiveQueueEntry&lt;/code&gt;&lt;/strong&gt; tracks whether the block already has an entry in the queue that has&#10;not been counted as dead. If it does, the &lt;em&gt;previous&lt;/em&gt; entry is about to become stale (we&#10;are about to bump the sequence number), so the dead-node counter is incremented now.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;The ordering comment is the interesting part:&lt;/strong&gt;&lt;/p&gt;&#10;&lt;blockquote&gt;&#10;&lt;p&gt;Count the previous live entry before bumping the sequence number. PurgeIteration reads&#10;sequence numbers without the block lock; bumping first could let it see the previous&#10;entry as stale and decrement dead_nodes before this matching increment.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;p&gt;This is a genuine race, and the code closes it by ordering the two operations. If we&#10;bumped the sequence number first, a concurrent purger could observe the &lt;em&gt;old&lt;/em&gt; entry as&#10;stale, decide it is dead, and decrement &lt;code&gt;total_dead_nodes&lt;/code&gt; — and then our increment would&#10;arrive and push the counter &lt;em&gt;up&lt;/em&gt; by one, leaving the counter permanently one too high.&#10;By counting the dead node first, the counter is momentarily one too low rather than one&#10;too high, and the purger&amp;rsquo;s decrement corrects it.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;&lt;code&gt;NextEvictionSequenceNumber&lt;/code&gt;&lt;/strong&gt; is called last, and it bumps the counter that makes the&#10;previous entry stale. After this point, the new entry is the only live one.&lt;/p&gt;&#10;&lt;p&gt;Then the actual enqueue:&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/storage/buffer/buffer_pool.cpp:144&#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="n"&gt;EvictionQueue&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;AddToEvictionQueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;node&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;&#9;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;enqueue&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;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;evict_queue_insertions&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;INSERT_INTERVAL&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;&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;One line of real work, and then the amortisation trigger: the queue counts its own&#10;insertions and reports &amp;ldquo;time to purge&amp;rdquo; every 4096 of them.&lt;/p&gt;&#10;&lt;h2 id="the-purge"&gt;The purge&lt;/h2&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/storage/buffer/buffer_pool.cpp:154&#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;void&lt;/span&gt; &lt;span class="n"&gt;EvictionQueue&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Purge&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;&#9;&lt;span class="c1"&gt;// only one thread purges the queue, all other threads early-out&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;unique_lock&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;guard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge_lock&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;try_to_lock&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;&#9;&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;guard&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;owns_lock&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;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&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;&#9;&lt;span class="c1"&gt;// we purge INSERT_INTERVAL * PURGE_SIZE_MULTIPLIER nodes&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;purge_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;INSERT_INTERVAL&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;PURGE_SIZE_MULTIPLIER&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;&#9;&lt;span class="c1"&gt;// get an estimate of the queue size as-of now&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;approx_q_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size_approx&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;&#9;&lt;span class="c1"&gt;// early-out, if the queue is not big enough to justify purging&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// - we want to keep the LRU characteristic alive&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;approx_q_size&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;purge_size&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;EARLY_OUT_MULTIPLIER&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;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&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 purge is &lt;em&gt;not&lt;/em&gt; a lock-free operation, and it does not need to be: it is a rare,&#10;batch-oriented garbage collection, and it is explicitly serialised. &lt;code&gt;std::try_to_lock&lt;/code&gt;&#10;means that if another thread is already purging, this thread just gives up — the purge&#10;will happen anyway.&lt;/p&gt;&#10;&lt;p&gt;The early-out is a heuristic with a stated motive: &amp;ldquo;we want to keep the LRU characteristic&#10;alive&amp;rdquo;. Purging a queue that is mostly alive means re-inserting most of its nodes, which&#10;costs time and disturbs the order. So the purge only runs when the queue is big.&lt;/p&gt;&#10;&lt;p&gt;The constants:&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/storage/buffer/buffer_pool.cpp:114&#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;private&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;&#9;&lt;span class="c1"&gt;//! We trigger a purge of the eviction queue every INSERT_INTERVAL insertions&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;INSERT_INTERVAL&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;4096&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;&#9;&lt;span class="c1"&gt;//! We multiply the base purge size by this value.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;PURGE_SIZE_MULTIPLIER&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;&#9;&lt;span class="c1"&gt;//! We multiply the purge size by this value to determine early-outs. This is the minimum queue size.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! We never purge below this point.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;EARLY_OUT_MULTIPLIER&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! We multiply the approximate alive nodes by this value to test whether our total dead nodes&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! exceed their allowed ratio. Must be greater than 1.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;ALIVE_NODE_MULTIPLIER&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&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: purge every 4096 insertions, purge 8192 nodes at a time, and only bother if the queue&#10;has at least 32768 nodes in it.&lt;/p&gt;&#10;&lt;h2 id="the-bulk-purge-and-the-fifo-trick"&gt;The bulk purge, and the FIFO trick&lt;/h2&gt;&#10;&lt;p&gt;Here is the actual garbage collection:&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/storage/buffer/buffer_pool.cpp:215&#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;void&lt;/span&gt; &lt;span class="n"&gt;EvictionQueue&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;PurgeIteration&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;purge_size&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;&#9;&lt;span class="c1"&gt;// if this purge is significantly smaller or bigger than the previous purge, then&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// we need to resize the purge_nodes vector. Note that this barely happens, as we&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// purge queue_insertions * PURGE_SIZE_MULTIPLIER nodes&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;previous_purge_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;purge_nodes&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge_size&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;previous_purge_size&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;purge_size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;previous_purge_size&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;&#9;&#9;&lt;span class="n"&gt;purge_nodes&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;resize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge_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;&#9;&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;&#9;&lt;span class="c1"&gt;// Dequeue using consumer token — progresses through sub-queues sequentially&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;actually_dequeued&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;try_dequeue_bulk&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge_consumer_token&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;purge_nodes&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;purge_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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;actually_dequeued&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&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;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;dead_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;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;alive_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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;raw_sleep_micros&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;debug_eviction_queue_sleep&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&lt;span class="n"&gt;optional_idx&lt;/span&gt; &lt;span class="n"&gt;debug_sleep_micros&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;raw_sleep_micros&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="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;optional_idx&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;raw_sleep_micros&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;optional_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;&#9;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;idx_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;actually_dequeued&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="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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;purge_nodes&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;IsDeadNode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;debug_sleep_micros&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;&#9;&#9;&#9;&lt;span class="n"&gt;dead_count&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;&#9;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&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;&#9;&#9;&#9;&lt;span class="c1"&gt;// Move alive nodes to the front for bulk re-enqueue&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;purge_nodes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;alive_count&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&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;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&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;&#9;&#9;&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;&#9;&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;&#9;&lt;span class="n"&gt;total_dead_nodes&lt;/span&gt; &lt;span class="o"&gt;-=&lt;/span&gt; &lt;span class="n"&gt;dead_count&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;&#9;&lt;span class="c1"&gt;// Re-enqueue alive nodes via producer token — goes into a dedicated sub-queue&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// that the consumer token has already passed&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;alive_count&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&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;purge_producer_token&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;valid&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;&#9;&#9;&#9;&lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="nf"&gt;OutOfMemoryException&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Failed to allocate eviction queue producer&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;enqueue_bulk&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge_producer_token&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;purge_nodes&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;alive_count&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;&#9;&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 algorithm is: dequeue a batch, partition it into dead and alive, and re-enqueue the&#10;alive ones.&lt;/p&gt;&#10;&lt;p&gt;The partition is the compaction trick: alive nodes are moved &lt;em&gt;to the front&lt;/em&gt; of the&#10;&lt;code&gt;purge_nodes&lt;/code&gt; vector (&lt;code&gt;purge_nodes[alive_count++] = std::move(node)&lt;/code&gt;), so the survivors&#10;end up packed in &lt;code&gt;[0, alive_count)&lt;/code&gt; and can be re-enqueued in one bulk call.&lt;/p&gt;&#10;&lt;p&gt;Now the part that deserves a slow look: &lt;strong&gt;why a separate producer token?&lt;/strong&gt;&lt;/p&gt;&#10;&lt;p&gt;The &lt;code&gt;ConcurrentQueue&lt;/code&gt; in moodycamel&amp;rsquo;s design is a list of per-producer sub-queues, and a&#10;&lt;em&gt;consumer token&lt;/em&gt; walks them in a fixed order, remembering which one it was on. If the&#10;purger re-enqueued the survivors into the &lt;em&gt;same&lt;/em&gt; sub-queue the consumer was about to&#10;visit, the survivors would be dequeued again immediately, in a loop, forever. The purger&#10;would make no progress.&lt;/p&gt;&#10;&lt;p&gt;The fix is to give the purge its own producer token. That token is bound to a &lt;em&gt;different&lt;/em&gt;&#10;sub-queue — one the consumer token has already walked past. So the survivors are pushed&#10;&lt;em&gt;behind&lt;/em&gt; the consumer&amp;rsquo;s current position in the traversal, and the consumer will come back&#10;around to them only after it has finished with the sub-queues it has not yet visited.&lt;/p&gt;&#10;&lt;p&gt;The result: the purge preserves the queue&amp;rsquo;s FIFO order. The oldest blocks stay oldest, and&#10;the LRU characteristic the comment mentioned is preserved across a GC cycle.&lt;/p&gt;&#10;&lt;p&gt;The &lt;code&gt;total_dead_nodes&lt;/code&gt; bookkeeping also matters: the purger decrements the counter by&#10;exactly the number of dead nodes it removed. That counter is what drives the &amp;ldquo;purge more&#10;aggressively&amp;rdquo; loop in &lt;code&gt;Purge()&lt;/code&gt; — when the dead-to-alive ratio gets bad, the purger keeps&#10;going until it either reaches a healthy ratio or runs out of queue.&lt;/p&gt;&#10;&lt;h2 id="the-eviction-sweep-itself"&gt;The eviction sweep itself&lt;/h2&gt;&#10;&lt;p&gt;For completeness, here is the consumer side — the part that actually unloads blocks:&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/storage/buffer/buffer_pool.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;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;FN&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;EvictionQueue&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;IterateUnloadableBlocks&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;FN&lt;/span&gt; &lt;span class="n"&gt;fn&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;debug_sleep_micros&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;debug_eviction_queue_sleep&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&lt;span class="k"&gt;for&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;&#9;&#9;&lt;span class="c1"&gt;// get a block to unpin from the queue&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;BufferEvictionNode&lt;/span&gt; &lt;span class="n"&gt;node&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;&#9;&#9;&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;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;try_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&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;&#9;&#9;&#9;&lt;span class="c1"&gt;// we could not dequeue any eviction node, so we try one more time,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="c1"&gt;// but more aggressively&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&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;TryDequeueWithLock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&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;&#9;&#9;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&#9;&#9;&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;&#9;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// get a reference to the underlying block pointer&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;memory_p&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;debug_sleep_micros&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="c1"&gt;// Debug race conditions regarding the ownership of the BlockMemory.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="c1"&gt;// Note that for this to trigger we need at least one purge iteration with the setting active.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;ThreadUtil&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;SleepMicroSeconds&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;debug_sleep_micros&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;&#9;&#9;&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;&#9;&#9;&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;handle&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;&#9;&#9;&#9;&lt;span class="n"&gt;DecrementDeadNodes&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;&#9;&#9;&#9;&lt;span class="k"&gt;continue&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;&#9;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// we might be able to free this block: grab the mutex and check if we can free it&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;lock&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetLock&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;handle_sequence_number&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetEvictionSequenceNumber&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;&#9;&#9;&#9;&lt;span class="c1"&gt;// A newer entry superseded this node: it was counted as dead when that entry was added.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;DecrementDeadNodes&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;&#9;&#9;&#9;&lt;span class="k"&gt;continue&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;&#9;&#9;&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 same sequence-number test appears here, but now it is &lt;em&gt;inside&lt;/em&gt; the block lock. The&#10;difference matters:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;In the purger (lock-free), a mismatch means &amp;ldquo;this entry is stale, drop it&amp;rdquo;.&lt;/li&gt;&#10;&lt;li&gt;Here (holding the lock), a mismatch means &amp;ldquo;this entry is stale, drop it — and it was&#10;already counted as dead when the newer entry was added&amp;rdquo;, so the counter is decremented.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;And when the entry &lt;em&gt;is&lt;/em&gt; current, the block is unloaded, under the lock, and the block&#10;loses its queue entry (&lt;code&gt;SetHasLiveQueueEntry(lock, false)&lt;/code&gt;) so that a later unpin will&#10;re-enqueue it with a fresh sequence number.&lt;/p&gt;&#10;&lt;p&gt;Two failure paths are handled with care. If the block cannot be offloaded because there&#10;is no temporary directory, the node is re-enqueued and the sweep &lt;em&gt;stops&lt;/em&gt; — the block is&#10;not lost. And if the unload itself throws, the node is re-enqueued and the exception is&#10;rethrown, so a failed unload never leaves a block permanently un-evictable.&lt;/p&gt;&#10;&lt;h2 id="costs-and-trade-offs"&gt;Costs and trade-offs&lt;/h2&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The queue can grow without bound between purges.&lt;/strong&gt; That is the deliberate trade: a&#10;&lt;code&gt;weak_ptr&lt;/code&gt; entry costs 16 bytes and never keeps anything alive, so a queue with a&#10;million stale entries costs 16 MB and nothing else. The purger is the garbage&#10;collector, and it runs on a schedule rather than on every operation.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;Purging is &lt;code&gt;O(dead nodes)&lt;/code&gt;, amortised.&lt;/strong&gt; Every 4096 insertions, up to 8192 nodes are&#10;examined. Each examination is one weak-pointer upgrade (an atomic CAS on the control&#10;block) plus one atomic load. There is no per-operation cost beyond the enqueue itself.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The weak-pointer upgrade is not free.&lt;/strong&gt; &lt;code&gt;memory_p.lock()&lt;/code&gt; is an atomic&#10;compare-and-swap on the control block, and it will &lt;em&gt;fail&lt;/em&gt; for dead nodes. But it is&#10;lock-free and wait-free, and it is the only way to know whether the block is still&#10;alive.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The sequence number is a &lt;code&gt;uint64_t&lt;/code&gt; on the block.&lt;/strong&gt; It costs 8 bytes per block and&#10;one atomic increment per enqueue. In exchange, the purger needs no lock and no&#10;epoch-based scheme.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The dead-node counter is approximate by design.&lt;/strong&gt; It is maintained under a mixture of&#10;locked and lock-free operations, and the source comments are explicit about the race&#10;and about which way the error is allowed to go. It is used to decide &lt;em&gt;how hard to&#10;purge&lt;/em&gt;, not for correctness.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The pool is not one queue but several.&lt;/strong&gt; &lt;code&gt;FileBufferTypeToEvictionQueueTypeIdx&lt;/code&gt; maps&#10;buffer types onto three queue &lt;em&gt;types&lt;/em&gt; — &lt;code&gt;BLOCK&lt;/code&gt;/&lt;code&gt;EXTERNAL_FILE&lt;/code&gt; (cheap to discard),&#10;&lt;code&gt;MANAGED_BUFFER&lt;/code&gt; (must be spilled to a temp file), and &lt;code&gt;TINY_BUFFER&lt;/code&gt; (last resort) —&#10;and the sweeper drains them in that order. &lt;code&gt;MANAGED_BUFFER&lt;/code&gt; alone is split into six&#10;queues so that the radix-partitioned row-group allocator can keep a partition&amp;rsquo;s&#10;blocks together. All of that priority lives in &lt;em&gt;which queue a block goes into&lt;/em&gt;, not in&#10;the queue algorithm itself.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The debug sleep hook exists because these races are real.&lt;/strong&gt; &lt;code&gt;IsDeadNode&lt;/code&gt; takes an&#10;optional sleep between upgrading the weak pointer and reading the sequence number,&#10;precisely so a test can widen that window and check that the accounting still balances.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;h2 id="the-bottom-line"&gt;The bottom line&lt;/h2&gt;&#10;&lt;p&gt;The eviction queue is a good example of a design where the &lt;em&gt;data structure&lt;/em&gt; is dumb and&#10;the &lt;em&gt;protocol&lt;/em&gt; is clever. The queue itself is a general-purpose lock-free MPMC container&#10;that knows nothing about blocks. All the block-specific intelligence lives in two fields&#10;of the node: a weak pointer, so the queue never keeps anything alive, and a monotonic&#10;version number, so a stale entry can be recognised without a lock.&lt;/p&gt;&#10;&lt;p&gt;The version number is the trick worth stealing. A weak pointer alone tells you &amp;ldquo;the block&#10;is gone&amp;rdquo;. A weak pointer plus a monotonically increasing per-block counter tells you&#10;&amp;ldquo;this entry is either from a dead block or from a previous generation of a live one&amp;rdquo; —&#10;and both of those questions can be answered with two atomic operations and no lock. No&#10;epochs, no hazard pointers, no generation lists.&lt;/p&gt;&#10;&lt;p&gt;The second trick worth stealing is the &lt;em&gt;separate producer token&lt;/em&gt;. Garbage collection that&#10;re-inserts survivors into the same queue it is draining is a livelock waiting to happen;&#10;giving the collector its own producer token so the survivors land &lt;em&gt;behind&lt;/em&gt; the consumer&amp;rsquo;s&#10;current position is a two-line fix that preserves the queue&amp;rsquo;s ordering guarantees.&lt;/p&gt;&#10;&lt;p&gt;And the general lesson about counters: DuckDB maintains a &lt;code&gt;total_dead_nodes&lt;/code&gt; counter&#10;across a boundary between locked and lock-free code, and the source comments spend more&#10;words explaining which way the error is allowed to go than the arithmetic itself. When a&#10;counter is only a heuristic, say so — loudly — and decide deliberately whether it may&#10;over- or under-count. The decision is written down: &lt;em&gt;under-count first, let the purger&amp;rsquo;s&#10;decrement fix it up&lt;/em&gt;. That is a much better failure mode than the opposite.&lt;/p&gt;&#10;</content:encoded></item><item><title>Pinning Is Ownership: DuckDB's Buffer Handle Is a shared_ptr</title><link>https://articles.9j.nz/posts/how-pinning-is-ownership-in-duckdbs-buffer-manager/</link><pubDate>Sat, 24 Oct 2026 12:40:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-pinning-is-ownership-in-duckdbs-buffer-manager/</guid><category>duckdb</category><category>buffer-manager</category><category>memory</category><category>cache</category><category>internals</category><description>A DuckDB BufferHandle holds a shared_ptr that owns the bytes, so eviction can never happen under a live reader.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; In DuckDB, &amp;ldquo;pinning&amp;rdquo; a block means holding a &lt;code&gt;shared_ptr&lt;/code&gt; to it. A&#10;&lt;code&gt;BufferHandle&lt;/code&gt; owns a &lt;code&gt;shared_ptr&amp;lt;BlockHandle&amp;gt;&lt;/code&gt;; the &lt;code&gt;BlockHandle&lt;/code&gt; owns a&#10;&lt;code&gt;shared_ptr&amp;lt;BlockMemory&amp;gt;&lt;/code&gt;; and the &lt;code&gt;BlockMemory&lt;/code&gt; is the only place the actual &lt;code&gt;FileBuffer&lt;/code&gt;&#10;bytes live. While a reader holds the handle, the bytes cannot be destroyed, so the block&#10;&lt;em&gt;cannot&lt;/em&gt; be evicted underneath it. The &lt;code&gt;readers&lt;/code&gt; atomic counter is &lt;strong&gt;not&lt;/strong&gt; the safety&#10;mechanism — it is an advisory signal that lets the eviction sweeper skip pinned blocks&#10;without taking a lock. The safety comes free from the ownership graph.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;h2 id="the-scenario"&gt;The scenario&lt;/h2&gt;&#10;&lt;p&gt;You run a query over a table that is much bigger than your memory limit:&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;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;o_totalprice&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;orders&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 buffer pool is under pressure. The eviction sweeper is running, deciding which blocks&#10;to throw out to make room for the next one. Meanwhile, the scan is holding several blocks&#10;open and is about to read a &lt;code&gt;DECIMAL&lt;/code&gt; out of one of them.&lt;/p&gt;&#10;&lt;p&gt;The question this article is about is narrow and important: &lt;strong&gt;how does DuckDB guarantee&#10;that the eviction sweeper cannot pull the rug out from under that read?&lt;/strong&gt;&lt;/p&gt;&#10;&lt;p&gt;The naive answer — &amp;ldquo;it keeps a counter of active readers and refuses to evict a block&#10;with a non-zero count&amp;rdquo; — is how a lot of buffer managers work, and it is subtly wrong.&#10;A counter is a &lt;em&gt;hint&lt;/em&gt;. Between the moment the sweeper reads the counter and the moment it&#10;acts on it, the count can change. Any design that relies on the counter for &lt;em&gt;correctness&lt;/em&gt;&#10;has a race in it.&lt;/p&gt;&#10;&lt;p&gt;DuckDB does not rely on the counter for correctness. It relies on ownership.&lt;/p&gt;&#10;&lt;h2 id="the-ownership-chain"&gt;The ownership chain&lt;/h2&gt;&#10;&lt;p&gt;Start at the top. This is the entire &lt;code&gt;BufferHandle&lt;/code&gt; class:&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/include/duckdb/storage/buffer/buffer_handle.hpp:53&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;GetBlockHandle&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;handle&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;&#9;&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;private&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;&#9;&lt;span class="c1"&gt;//! The block handle&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;handle&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;&#9;&lt;span class="c1"&gt;//! The managed buffer node&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;optional_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;FileBuffer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;node&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;Two members. &lt;code&gt;handle&lt;/code&gt; is a &lt;code&gt;shared_ptr&amp;lt;BlockHandle&amp;gt;&lt;/code&gt; — a &lt;em&gt;shared&lt;/em&gt; ownership handle to the&#10;block&amp;rsquo;s metadata. &lt;code&gt;node&lt;/code&gt; is a raw &lt;code&gt;optional_ptr&amp;lt;FileBuffer&amp;gt;&lt;/code&gt; — a &lt;em&gt;non-owning&lt;/em&gt; pointer to the&#10;bytes.&lt;/p&gt;&#10;&lt;p&gt;That split is the whole design. The handle owns the block; the block owns the bytes; the&#10;handle merely &lt;em&gt;points at&lt;/em&gt; the bytes. The pointer is a convenience (it is what&#10;&lt;code&gt;Ptr()&lt;/code&gt; returns), not a lifetime guarantee.&lt;/p&gt;&#10;&lt;p&gt;Here is the &lt;code&gt;BlockHandle&lt;/code&gt; 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/include/duckdb/storage/buffer/block_handle.hpp:292&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! Returns a const reference to the memory of a block.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;BlockMemory&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;memory&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;&#9;&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;&#9;&lt;span class="c1"&gt;//! Returns a reference to the memory of a block.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;BlockMemory&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;memory&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;&#9;&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;&#9;&lt;span class="c1"&gt;//! Returns a weak pointer to the memory of a block.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;weak_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;GetMemoryWeak&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;weak_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&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;memory_p&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;&#9;&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 members at the bottom of the class:&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/include/duckdb/storage/buffer/block_handle.hpp:324&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! Pointer to the underlying memory of the block.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;memory_p&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;&#9;&lt;span class="c1"&gt;//! Memory for fast access to the block memory.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;BlockMemory&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;memory&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;There are two views of the same &lt;code&gt;BlockMemory&lt;/code&gt;:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;code&gt;memory_p&lt;/code&gt; is a &lt;code&gt;shared_ptr&amp;lt;BlockMemory&amp;gt;&lt;/code&gt; — the &lt;strong&gt;owner&lt;/strong&gt;.&lt;/li&gt;&#10;&lt;li&gt;&lt;code&gt;memory&lt;/code&gt; is a &lt;code&gt;BlockMemory &amp;amp;&lt;/code&gt; — a raw reference, for fast access without an atomic&#10;refcount bump.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;p&gt;And &lt;code&gt;BlockMemory&lt;/code&gt; is where the bytes actually live:&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/include/duckdb/storage/buffer/block_handle.hpp:234&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! The number of concurrent readers. Writers hold the block lock; reads may be unlocked.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;atomic&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int32_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;readers&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;&#9;&lt;span class="c1"&gt;//! The memory tag.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;MemoryTag&lt;/span&gt; &lt;span class="n"&gt;tag&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;&#9;&lt;span class="c1"&gt;//! The file buffer type.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;FileBufferType&lt;/span&gt; &lt;span class="n"&gt;buffer_type&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;&#9;&lt;span class="c1"&gt;//! A pointer to the loaded data, if any.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;unique_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;FileBuffer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;buffer&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;buffer&lt;/code&gt; is a &lt;code&gt;unique_ptr&amp;lt;FileBuffer&amp;gt;&lt;/code&gt;. &lt;em&gt;That&lt;/em&gt; is the object that owns the memory the&#10;query is reading.&lt;/p&gt;&#10;&lt;p&gt;So the chain 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;pre tabindex="0"&gt;&lt;code&gt;BufferHandle&#10; └─ shared_ptr&amp;lt;BlockHandle&amp;gt;&#10; └─ shared_ptr&amp;lt;BlockMemory&amp;gt; (memory_p)&#10; └─ unique_ptr&amp;lt;FileBuffer&amp;gt; (buffer)&#10; └─ the actual bytes&lt;/code&gt;&lt;/pre&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Three levels of ownership, and every level is a &lt;code&gt;shared_ptr&lt;/code&gt; or a &lt;code&gt;unique_ptr&lt;/code&gt;. When the&#10;last &lt;code&gt;shared_ptr&lt;/code&gt; to the &lt;code&gt;BlockMemory&lt;/code&gt; goes away, the &lt;code&gt;BlockMemory&lt;/code&gt; is destroyed, its&#10;&lt;code&gt;unique_ptr&amp;lt;FileBuffer&amp;gt;&lt;/code&gt; is destroyed, and the bytes are released. There is no other path&#10;to freeing the bytes, because &lt;code&gt;buffer&lt;/code&gt; is private to &lt;code&gt;BlockMemory&lt;/code&gt; and there is exactly&#10;one &lt;code&gt;BlockMemory&lt;/code&gt; per block.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;This is the invariant&lt;/strong&gt;: the bytes cannot be freed while any &lt;code&gt;BufferHandle&lt;/code&gt; exists,&#10;because a &lt;code&gt;BufferHandle&lt;/code&gt; transitively holds the only &lt;code&gt;shared_ptr&lt;/code&gt; chain to them.&lt;/p&gt;&#10;&lt;h2 id="why-the-readers-counter-is-only-a-hint"&gt;Why the readers counter is only a hint&lt;/h2&gt;&#10;&lt;p&gt;Here is the counter&amp;rsquo;s implementation:&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/include/duckdb/storage/buffer/block_handle.hpp:79&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;//! Increments the number of readers prior to returning it.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="kt"&gt;int32_t&lt;/span&gt; &lt;span class="nf"&gt;IncrementReaders&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockLock&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="n"&gt;VerifyMutex&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="c1"&gt;// Tiny buffers do not decrement on unpin, so their reader count can wrap.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;new_readers&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="kt"&gt;int32_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="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_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;readers&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="n"&gt;readers&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;store&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_readers&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_readers&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;&#9;&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;&#9;&lt;span class="c1"&gt;//! Decrements the number of readers prior to returning it.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="kt"&gt;int32_t&lt;/span&gt; &lt;span class="nf"&gt;DecrementReaders&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockLock&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="n"&gt;VerifyMutex&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;new_readers&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="kt"&gt;int32_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="k"&gt;static_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;uint32_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;readers&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;load&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="n"&gt;readers&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;store&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_readers&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;memory_order_relaxed&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_readers&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;&#9;&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;Two things to notice.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;The comment about tiny buffers.&lt;/strong&gt; &amp;ldquo;Tiny buffers do not decrement on unpin, so their&#10;reader count can wrap.&amp;rdquo; A &lt;code&gt;TINY_BUFFER&lt;/code&gt; is a small allocation that is not managed by the&#10;pool; it is never unloaded, so the counter would only ever grow. Rather than special-case&#10;it, the code explicitly allows the &lt;code&gt;int32_t&lt;/code&gt; to wrap around by doing the arithmetic in&#10;&lt;code&gt;uint32_t&lt;/code&gt; and casting back. This is a deliberate decision to make a &lt;em&gt;hint&lt;/em&gt; wrong rather&#10;than to add a branch to a hot path. And it is safe precisely &lt;em&gt;because&lt;/em&gt; the hint is not&#10;load-bearing for correctness.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;The memory ordering is &lt;code&gt;relaxed&lt;/code&gt;.&lt;/strong&gt; The counter is not a synchronisation primitive. It&#10;is a number that is approximately right. If two threads increment it concurrently, the&#10;result is some number that is not exactly the number of readers — and that is fine,&#10;because the counter is only used to answer &amp;ldquo;should I bother looking at this block?&amp;rdquo;.&lt;/p&gt;&#10;&lt;p&gt;And here is where it is consumed:&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/storage/buffer/block_handle.cpp:105&#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;CanUnloadResult&lt;/span&gt; &lt;span class="n"&gt;BlockMemory&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CanUnload&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GetState&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;BlockState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BLOCK_UNLOADED&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;&#9;&#9;&lt;span class="c1"&gt;// The block has already been unloaded.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;CanUnloadResult&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;ALREADY_UNLOADED&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;&#9;&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GetReaders&lt;/span&gt;&lt;span class="p"&gt;()&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// There are active readers.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;CanUnloadResult&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;PINNED&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;&#9;&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockId&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;MAXIMUM_BLOCK&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;MustWriteToTemporaryFile&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;GetBufferManager&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;HasTemporaryDirectory&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;&#9;&#9;&lt;span class="c1"&gt;// The block memory cannot be destroyed upon eviction/unpinning.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// In order to unload this block we need to write it to a temporary buffer.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// However, no temporary directory is specified, hence, we cannot unload.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;CanUnloadResult&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;NO_TEMP_DIRECTORY&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;&#9;&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;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;CanUnloadResult&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;CAN_UNLOAD&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;GetReaders() &amp;gt; 0&lt;/code&gt; → &lt;code&gt;PINNED&lt;/code&gt;. The sweeper skips it.&lt;/p&gt;&#10;&lt;p&gt;But &lt;em&gt;how&lt;/em&gt; is this safe? The answer is that the sweeper does not free the bytes by&#10;destroying the &lt;code&gt;FileBuffer&lt;/code&gt; out from under a reader. It frees them by &lt;em&gt;unloading the&#10;block&lt;/em&gt; — and unloading requires taking the block&amp;rsquo;s lock, and the block&amp;rsquo;s state transition&#10;to &lt;code&gt;BLOCK_UNLOADED&lt;/code&gt; is guarded by that lock.&lt;/p&gt;&#10;&lt;p&gt;The real safety net is the combination:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;A reader holds a &lt;code&gt;shared_ptr&lt;/code&gt; chain to the &lt;code&gt;BlockMemory&lt;/code&gt;, so the &lt;code&gt;BlockMemory&lt;/code&gt; — and&#10;therefore the &lt;code&gt;FileBuffer&lt;/code&gt; — cannot be destroyed.&lt;/li&gt;&#10;&lt;li&gt;The sweeper&amp;rsquo;s decision to unload is made under the block lock.&lt;/li&gt;&#10;&lt;li&gt;A reader that is &lt;em&gt;about&lt;/em&gt; to read takes the block lock when it loads or increments the&#10;reader count, so it cannot race with an unload.&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;p&gt;The counter, meanwhile, tells the sweeper &amp;ldquo;don&amp;rsquo;t even bother taking the lock for this&#10;one&amp;rdquo;. It is an optimisation. If the counter were wrong, the sweeper would take the lock,&#10;see the true state, and do the right thing anyway.&lt;/p&gt;&#10;&lt;h2 id="pinning-the-double-checked-load"&gt;Pinning: the double-checked load&lt;/h2&gt;&#10;&lt;p&gt;Here is &lt;code&gt;Pin&lt;/code&gt;, the function that turns a &lt;code&gt;BlockHandle&lt;/code&gt; into a &lt;code&gt;BufferHandle&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/storage/standard_buffer_manager.cpp:369&#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;BufferHandle&lt;/span&gt; &lt;span class="n"&gt;StandardBufferManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Pin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;QueryContext&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;context&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;handle&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;&#9;&lt;span class="c1"&gt;// we need to be careful not to return the BufferHandle to this block while holding the BlockHandle&amp;#39;s lock&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// as exiting this function&amp;#39;s scope may cause the destructor of the BufferHandle to be called while holding the lock&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// the destructor calls Unpin, which grabs the BlockHandle&amp;#39;s lock again, causing a deadlock&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;BufferHandle&lt;/span&gt; &lt;span class="n"&gt;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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;idx_t&lt;/span&gt; &lt;span class="n"&gt;required_memory&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&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;&#9;&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;&#9;&#9;&lt;span class="c1"&gt;// lock the block&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;lock&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetLock&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;&#9;&#9;&lt;span class="c1"&gt;// check if the block is already loaded&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetState&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;BlockState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BLOCK_LOADED&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;&#9;&#9;&#9;&lt;span class="c1"&gt;// the block is loaded, increment the reader count and set the BufferHandle&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;buf&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;Load&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;context&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;required_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMemoryUsage&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;&#9;&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;buf&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;IsValid&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;buf&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// the block was already loaded, return it without holding the BlockHandle&amp;#39;s lock&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&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;Read the comment at the top. It is a &lt;em&gt;self-deadlock&lt;/em&gt; warning, and it is the most&#10;instructive line in the whole file:&lt;/p&gt;&#10;&lt;blockquote&gt;&#10;&lt;p&gt;we need to be careful not to return the BufferHandle to this block while holding the&#10;BlockHandle&amp;rsquo;s lock&#10;as exiting this function&amp;rsquo;s scope may cause the destructor of the BufferHandle to be&#10;called while holding the lock&#10;the destructor calls Unpin, which grabs the BlockHandle&amp;rsquo;s lock again, causing a deadlock&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;p&gt;This is the price of the ownership design. &lt;code&gt;BufferHandle&lt;/code&gt;&amp;rsquo;s destructor calls &lt;code&gt;Unpin&lt;/code&gt;,&#10;which takes the block lock. If the handle were returned while the lock was held, the&#10;temporary&amp;rsquo;s destructor would run at the end of the scope — with the lock still held — and&#10;&lt;code&gt;Unpin&lt;/code&gt; would try to take the same non-recursive &lt;code&gt;std::mutex&lt;/code&gt; again. Boom.&lt;/p&gt;&#10;&lt;p&gt;So &lt;code&gt;Pin&lt;/code&gt; deliberately returns the handle &lt;em&gt;outside&lt;/em&gt; the lock&amp;rsquo;s scope. The lock is&#10;acquired in an inner block &lt;code&gt;{ ... }&lt;/code&gt; precisely so that it is released before the return.&lt;/p&gt;&#10;&lt;p&gt;Continue reading the function and you see the classic double-checked pattern:&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/storage/standard_buffer_manager.cpp:392&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="c1"&gt;// evict blocks until we have space for the current block&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="n"&gt;unique_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;FileBuffer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;reusable_buffer&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;reservation&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;&#9; &lt;span class="n"&gt;EvictBlocksOrThrow&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;context&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetMemoryTag&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;required_memory&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;reusable_buffer&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;&#9; &lt;span class="s"&gt;&amp;#34;failed to pin block of size %s%s&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;StringUtil&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BytesToHumanReadableString&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_memory&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;&#9;&lt;span class="c1"&gt;// lock the handle again and repeat the check (in case anybody loaded in the meantime)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;lock&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetLock&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;&#9;&lt;span class="c1"&gt;// check if the block is already loaded&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetState&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;BlockState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BLOCK_LOADED&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;&#9;&#9;&lt;span class="c1"&gt;// the block is loaded, increment the reader count and return a pointer to the handle&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;reservation&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Resize&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;&#9;&#9;&lt;span class="n"&gt;buf&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;Load&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;context&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;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&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;Between releasing the lock and re-acquiring it, we went and evicted blocks to make room —&#10;which takes an unbounded amount of time and releases the lock entirely. Another thread may&#10;have loaded the same block in the meantime. So the state is checked &lt;em&gt;again&lt;/em&gt; under the lock.&#10;If somebody beat us to it, the memory reservation we took is refunded (&lt;code&gt;reservation.Resize(0)&lt;/code&gt;)&#10;and we just take a reader count on the already-loaded block.&lt;/p&gt;&#10;&lt;p&gt;The reservation refund is a nice touch: the memory is charged to the pool the moment we&#10;decide we might need it, and un-charged the moment we discover we don&amp;rsquo;t. The charging is&#10;an RAII token, so the refund is a single call.&lt;/p&gt;&#10;&lt;p&gt;And here is the actual load:&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/storage/buffer/block_handle.cpp:214&#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;BufferHandle&lt;/span&gt; &lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Load&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BlockLock&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;l&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;QueryContext&lt;/span&gt; &lt;span class="n"&gt;context&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;unique_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;FileBuffer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;reusable_buffer&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;&#9;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;VerifyMutex&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetState&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;BlockState&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;BLOCK_LOADED&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;&#9;&#9;&lt;span class="c1"&gt;// The block has already been loaded.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetBuffer&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;&#9;&#9;&lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;IncrementReaders&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l&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;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;BufferHandle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;shared_from_this&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetBuffer&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;&#9;&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;&#9;&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;memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;CanReload&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;&#9;&#9;&lt;span class="c1"&gt;// the buffer was destroyed upon unpin/evict, or the handle was replaced and its disk block&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="c1"&gt;// may be rewritten in place - the caller must re-resolve the block id&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;BufferHandle&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;&#9;&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;BufferHandle(shared_from_this(), memory.GetBuffer())&lt;/code&gt;. The &lt;code&gt;shared_from_this()&lt;/code&gt; is the&#10;crux: the &lt;code&gt;BlockHandle&lt;/code&gt; hands out a &lt;code&gt;shared_ptr&lt;/code&gt; to &lt;em&gt;itself&lt;/em&gt;, and the &lt;code&gt;BufferHandle&lt;/code&gt;&#10;stores it. That is what makes the whole chain hold.&lt;/p&gt;&#10;&lt;p&gt;Note also &lt;code&gt;memory.IncrementReaders(l)&lt;/code&gt; — the counter is bumped &lt;em&gt;here&lt;/em&gt;, under the block&#10;lock, at the same moment the handle is created. So the counter and the ownership are&#10;established atomically with respect to the lock. A sweeper that takes the lock and sees&#10;&lt;code&gt;readers == 0&lt;/code&gt; genuinely knows that at that instant no reader exists.&lt;/p&gt;&#10;&lt;h2 id="unpinning"&gt;Unpinning&lt;/h2&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/storage/standard_buffer_manager.cpp:459&#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;void&lt;/span&gt; &lt;span class="n"&gt;StandardBufferManager&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Unpin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;shared_ptr&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;BlockHandle&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;handle&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;&#9;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;purge&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;false&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;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&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;&#9;&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;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;lock&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetLock&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;&#9;&#9;&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;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetBuffer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetBufferType&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;FileBufferType&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;TINY_BUFFER&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;&#9;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&#9;&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;&#9;&#9;&lt;span class="n"&gt;D_ASSERT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;GetReaders&lt;/span&gt;&lt;span class="p"&gt;()&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;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;new_readers&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;DecrementReaders&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_readers&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="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&#9;&#9;&lt;span class="n"&gt;VerifyZeroReaders&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;handle&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;&#9;&#9;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;MustAddToEvictionQueue&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;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;purge&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;buffer_pool&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;AddToEvictionQueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;handle&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;&#9;&#9;&#9;&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&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;&#9;&#9;&#9;&#9;&lt;span class="n"&gt;block_memory&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Unload&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lock&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;&#9;&#9;&#9;&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;&#9;&#9;&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;&#9;&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;&#9;&lt;span class="c1"&gt;// We do not have to keep the handle locked while purging.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#9;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;purge&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;&#9;&#9;&lt;span class="n"&gt;PurgeQueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;handle&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;&#9;&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;Three things:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;Tiny buffers return early.&lt;/strong&gt; They were never added to the pool, so there is nothing&#10;to unpin. (And, as we saw, that is why their reader counter is allowed to wrap.)&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;When the count hits zero, the block goes on the eviction queue.&lt;/strong&gt; Note the order:&#10;the count is decremented &lt;em&gt;first&lt;/em&gt;, and only then is the block offered to the sweeper.&#10;That ordering is what makes the counter a valid hint.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The purge happens outside the lock.&lt;/strong&gt; The comment says it: &amp;ldquo;We do not have to keep the&#10;handle locked while purging.&amp;rdquo; A purge is a full sweep of the eviction queue — it can&#10;take a while, and holding the block&amp;rsquo;s lock through it would block every other thread&#10;that wants to pin the same block. The &lt;code&gt;purge&lt;/code&gt; flag is set under the lock; the call&#10;happens after the lock is released.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;p&gt;And here is where the handle gives up its ownership:&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/storage/buffer/buffer_handle.cpp:35&#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;void&lt;/span&gt; &lt;span class="n"&gt;BufferHandle&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Destroy&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;&#9;&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;handle&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;IsValid&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;&#9;&#9;&lt;span class="k"&gt;return&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;&#9;&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;&#9;&lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;GetMemory&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;GetBufferManager&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;Unpin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;handle&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;&#9;&lt;span class="n"&gt;handle&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;reset&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;&#9;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;nullptr&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;Unpin&lt;/code&gt; first, then &lt;code&gt;handle.reset()&lt;/code&gt;. The reset is what drops the &lt;code&gt;shared_ptr&lt;/code&gt; — and if&#10;that was the last reference to the &lt;code&gt;BlockMemory&lt;/code&gt;, the bytes are freed right there. If the&#10;block was still in use elsewhere, the &lt;code&gt;shared_ptr&lt;/code&gt; count simply stays above zero and the&#10;bytes survive.&lt;/p&gt;&#10;&lt;p&gt;Note the order: &lt;code&gt;Unpin&lt;/code&gt; &lt;em&gt;before&lt;/em&gt; &lt;code&gt;reset&lt;/code&gt;. If it were the other way round, the&#10;&lt;code&gt;BlockMemory&lt;/code&gt; could be destroyed before &lt;code&gt;Unpin&lt;/code&gt; had decremented the counter, and&#10;&lt;code&gt;Unpin&lt;/code&gt; would be touching freed memory.&lt;/p&gt;&#10;&lt;h2 id="costs-and-trade-offs"&gt;Costs and trade-offs&lt;/h2&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The reference counting is an atomic increment on the hot path.&lt;/strong&gt; Every &lt;code&gt;Pin&lt;/code&gt; that&#10;finds the block already loaded does one &lt;code&gt;shared_from_this()&lt;/code&gt; (an atomic increment on the&#10;&lt;code&gt;BlockHandle&lt;/code&gt;&amp;rsquo;s control block) and one &lt;code&gt;shared_ptr&lt;/code&gt; copy into the &lt;code&gt;BufferHandle&lt;/code&gt;. Every&#10;&lt;code&gt;Unpin&lt;/code&gt; does the matching decrement. On a hot scan, that is a couple of atomic&#10;read-modify-writes per block — cheap, but not free. It is worth it because it replaces&#10;a &lt;em&gt;correctness&lt;/em&gt; mechanism (locking, reference counting by hand, hazard pointers) with a&#10;&lt;em&gt;safety&lt;/em&gt; mechanism (the type system).&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;&lt;code&gt;shared_ptr&lt;/code&gt; is not free in code size either.&lt;/strong&gt; The &lt;code&gt;enable_shared_from_this&lt;/code&gt; base&#10;class on &lt;code&gt;BlockHandle&lt;/code&gt;, the &lt;code&gt;weak_ptr&lt;/code&gt; accessor for the eviction queue, the&#10;&lt;code&gt;ColumnBindingReplacer&lt;/code&gt;-style plumbing — all of it exists because the block is a&#10;&lt;code&gt;shared_ptr&lt;/code&gt; citizen.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The &lt;code&gt;readers&lt;/code&gt; counter is still worth keeping.&lt;/strong&gt; It is an &lt;code&gt;atomic&amp;lt;int32_t&amp;gt;&lt;/code&gt; with&#10;&lt;code&gt;relaxed&lt;/code&gt; ordering, and it lets the eviction sweeper skip pinned blocks without taking&#10;a lock and without constructing a &lt;code&gt;shared_ptr&lt;/code&gt; from the weak one. On a pool with&#10;thousands of blocks, most of which may be pinned, that saves a lot of lock traffic.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The counter is allowed to lie.&lt;/strong&gt; Tiny buffers wrap it. The &lt;code&gt;relaxed&lt;/code&gt; ordering means&#10;concurrent increments can lose a count. Both are fine &lt;em&gt;because&lt;/em&gt; nothing depends on its&#10;exactness. This is the design paying off: an approximate counter is cheap and safe, and&#10;a precise counter would need a lock.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The &lt;code&gt;Pin&lt;/code&gt; path takes the block lock at least once and often twice.&lt;/strong&gt; The&#10;double-checked pattern exists because the eviction step in between is slow. If the&#10;block was already loaded, only the first lock is taken.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;&lt;strong&gt;The deadlock hazard is real and is handled by a comment and by scope.&lt;/strong&gt; Returning a&#10;handle whose destructor takes the same lock is the kind of bug you find in production&#10;once. The fix here — an inner scope — is subtle enough to deserve the three-line&#10;comment that explains it.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;h2 id="the-bottom-line"&gt;The bottom line&lt;/h2&gt;&#10;&lt;p&gt;There are two ways to keep a block alive while someone reads it.&lt;/p&gt;&#10;&lt;p&gt;The first is a counter: &amp;ldquo;readers: 3, do not evict&amp;rdquo;. The second is ownership: &amp;ldquo;here is a&#10;&lt;code&gt;shared_ptr&lt;/code&gt;; the memory is yours until you let go of it&amp;rdquo;. The first requires every&#10;participant to agree on the protocol and to update the counter at exactly the right&#10;moment; the second requires nothing but the discipline to use &lt;code&gt;shared_ptr&lt;/code&gt; correctly.&lt;/p&gt;&#10;&lt;p&gt;DuckDB uses the second for safety and the first for speed, and it is explicit about which&#10;is which. The &lt;code&gt;readers&lt;/code&gt; counter is &lt;code&gt;relaxed&lt;/code&gt;, is allowed to wrap, and is consulted only to&#10;decide whether to bother taking a lock. The &lt;code&gt;shared_ptr&lt;/code&gt; chain is the actual guarantee:&#10;&lt;code&gt;BufferHandle&lt;/code&gt; → &lt;code&gt;BlockHandle&lt;/code&gt; → &lt;code&gt;BlockMemory&lt;/code&gt; → &lt;code&gt;FileBuffer&lt;/code&gt; → the bytes, with a&#10;&lt;code&gt;shared_ptr&lt;/code&gt; at every level that has a lifetime to protect.&lt;/p&gt;&#10;&lt;p&gt;The general lesson: &lt;strong&gt;if you need a lock to make your data structure safe, you probably&#10;have the wrong data structure.&lt;/strong&gt; A lock-free &lt;code&gt;shared_ptr&lt;/code&gt; is not as free as a raw pointer,&#10;but it is free &lt;em&gt;enough&lt;/em&gt;, and it buys you the freedom to let the sweeper guess wrong&#10;occasionally without corrupting anything.&lt;/p&gt;&#10;</content:encoded></item></channel></rss>