Zola 2025-02-03T00:00:00+00:00 https://jhpratt.dev/atom.xml 2025-02-03T00:00:00+00:00 2025-02-03T00:00:00+00:00 Unknown https://jhpratt.dev/blog/optimizing-with-novel-calendrical-algorithms/ <h2 id="background"><a class="anchor" href="#background" aria-label="Anchor link for: background" tabindex="-1">Background</a></h2> <p>I have maintained the <code>time</code> crate for over five years now. In that time, tens of thousands of lines of code have been added, probably just as many removed, and countless more written but never committed. While benchmarks have been present for quite a while, I had never done one thing: truly optimize. Sure, some algorithms have been changed over the years, but I have never <em>created</em> a nontrivial date-time algorithm from scratch. The speed was <em>good enough</em>, even if it was slower than comparable crates.</p> <p>So why now? Well, I have a private board with 40+ tasks for <code>time</code> (in addition to the public issue tracker). Many of these are breaking changes, some have already been implemented, others don't neatly fit into the current API, and a few haven't even been "accepted", meaning it may not be a good idea. There's one item that is quite literally at the bottom of the list: a general performance audit. It's at the bottom because it's not a priority and requires significant effort. It's not a priority because no one has complained. But I wanted to do something different, and this seemed like a good idea. It's my project, after all, so I can work on what I want.</p> <h2 id="starting-point"><a class="anchor" href="#starting-point" aria-label="Anchor link for: starting-point" tabindex="-1">Starting point</a></h2> <p>Looking through the code, there were some clear candidates for where I could start, based largely on my knowledge of where well-known algorithms were used, where I rolled my own without much thought beyond correctness, and methods that were likely used with disproportionate frequency. One method in particular stood out: <code>Date::to_calendar_date</code>.</p> <p>For the purposes of this post, I am writing a method that accepts <code>year</code> and <code>ordinal</code> as parameters and returns a <code>(year, month, day)</code> tuple. The actual implementation is slightly different, but the differences are not relevant to the optimization.</p> <h2 id="status-quo"><a class="anchor" href="#status-quo" aria-label="Anchor link for: status-quo" tabindex="-1">Status quo</a></h2> <p>The pre-existing implementation is about as simple as it gets. Using a lookup table, it finds the number of days in the year preceding the desired month, excluding January as it's the final case. Subtracting that number from the ordinal day gives us the day of the month, with the month itself being determined by reverse iteration.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">const</span> <span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_calendar_date</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-storage z-type z-rust">i32</span>, <span class="z-storage z-type z-rust">u8</span>, <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-comment z-line z-documentation z-rust"><span class="z-punctuation z-definition z-comment z-rust">///</span> The number of days up to and including the given month. Common years </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-comment z-line z-documentation z-rust"><span class="z-punctuation z-definition z-comment z-rust">///</span> are first, followed by leap years. </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">const</span> <span class="z-constant z-other z-rust">CUMULATIVE_DAYS_IN_MONTH_COMMON_LEAP</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-storage z-type z-rust">u16</span><span class="z-punctuation z-separator z-rust">;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">11</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span><span class="z-punctuation z-separator z-rust">;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-group z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">31</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">90</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">120</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">151</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">181</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">212</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">243</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">273</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">304</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">334</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span><span class="z-punctuation z-separator z-rust">,</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-group z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">31</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">60</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">91</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">121</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">152</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">182</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">213</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">244</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">274</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">305</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">335</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span><span class="z-punctuation z-separator z-rust">,</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-group z-rust"> <span class="z-punctuation z-section z-group z-end z-rust">]</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> days <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-other z-rust">CUMULATIVE_DAYS_IN_MONTH_COMMON_LEAP</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">usize</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month<span class="z-punctuation z-separator z-rust">,</span> day</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">10</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">12</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">10</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">9</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">11</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">9</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">8</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">10</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">8</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">9</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">6</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">8</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">6</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">5</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">5</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">4</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">6</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">4</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">3</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">5</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">3</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">4</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">1</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">3</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">1</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&gt;</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-section z-group z-end z-rust">]</span></span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">1</span><span class="z-punctuation z-separator z-rust">,</span> ordinal <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year<span class="z-punctuation z-separator z-rust">,</span> month<span class="z-punctuation z-separator z-rust">,</span> day</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> <h3 id="binary-search"><a class="anchor" href="#binary-search" aria-label="Anchor link for: binary-search" tabindex="-1">Binary search?</a></h3> <p>The first thing that came to mind was a binary search. The lookup table is sorted, so it is certainly possible. However, the table is small — only 11 elements after determining if it's a leap year — and the cost of a binary search is likely higher than the cost of a linear search. I have previously benchmarked this and quickly found that the linear search was faster. Manually unrolling the search improves performance some, but I wanted to keep investigating.</p> <h3 id="loop"><a class="anchor" href="#loop" aria-label="Anchor link for: loop" tabindex="-1">Loop?</a></h3> <p>Why not a loop instead of a series of <code>if</code> statements? I investigated this possibility at the same time as the binary search, as it would be more idiomatic in <em>any</em> language. For whatever reason, Rust had difficulty optimizing this. Performance was worse than writing out the <code>if</code> statements manually.</p> <h2 id="designing-a-new-algorithm"><a class="anchor" href="#designing-a-new-algorithm" aria-label="Anchor link for: designing-a-new-algorithm" tabindex="-1">Designing a new algorithm</a></h2> <p>Despite maintaining <code>time</code> for years, I have never written a date-time algorithm from scratch. Doing so <a rel="nofollow noreferrer" href="https://youtu.be/-5wpm-gesOY">is known to be a fun endeavor</a>. However, I recently ran across <a rel="nofollow noreferrer" href="https://onlinelibrary.wiley.com/doi/full/10.1002/spe.3172">a paper from Cassio Neri and Lorenz Schneider</a> introducing me to Euclidean affine functions and their potential applications in date-time calculations. Using methods similar to theirs, I decided to give it a shot.</p> <p>I had a few guiding principles in mind when designing the new algorithm:</p> <ul> <li><strong>Correctness</strong>: It must be correct. I won't be performing a rigorous mathematical analysis, though, as I'm proving correctness by exhaustion (365 cases for common years and 366 for leap years).</li> <li><strong>Performance</strong>: It must be faster than the existing one. This is the entire point of optimizing it, after all.</li> <li><strong>Integers only</strong>: Floating point operations are significantly slower than integer operations, so I wanted to avoid them. I have previously adapted floating point algorithms to use integers, so I was confident that I could do so again.</li> <li><strong><code>const</code> compatible</strong>: <code>Date::to_calendar_date</code> is currently a <code>const fn</code>. Breaking changes are unacceptable, so the new algorithm must be a <code>const fn</code> as well. Given Rust's limitations on what is permitted in <code>const</code> nowadays, this is largely a non-issue.</li> </ul> <h2 id="calculating-the-month"><a class="anchor" href="#calculating-the-month" aria-label="Anchor link for: calculating-the-month" tabindex="-1">Calculating the month</a></h2> <p>The first step was to determine the month. For this, I actually knew where to start. The Gregorian calendar (which most of the world uses) has two five-month "blocks": March through July and August through December, both of which contain 153 days. Neri and Schneider use a "computational calendar" that starts on March 1, but that is not what I was interested in. I wanted to calculate it from the <em>true</em> ordinal, not a contrived one. Additionally, treating January and February as the start of a 153-day block would work flawlessly, as the first month in the block has 31 days (as January does).</p> <p>Perhaps a visualization helps.</p> <div style='display:flex;gap:1em;flex-wrap:wrap;'> <table><thead><tr><th>Month</th><th>Days in month</th></tr></thead><tbody> <tr><td>January</td><td>31</td></tr> <tr><td>February</td><td>28/29</td></tr> <tr><td> </td><td></td></tr> <tr><td> </td><td></td></tr> <tr><td> </td><td></td></tr> </tbody></table> <table><thead><tr><th>Month</th><th>Days in month</th></tr></thead><tbody> <tr><td>March</td><td>31</td></tr> <tr><td>April</td><td>30</td></tr> <tr><td>May</td><td>31</td></tr> <tr><td>June</td><td>30</td></tr> <tr><td>July</td><td>31</td></tr> </tbody></table> <table><thead><tr><th>Month</th><th>Days in month</th></tr></thead><tbody> <tr><td>August</td><td>31</td></tr> <tr><td>September</td><td>30</td></tr> <tr><td>October</td><td>31</td></tr> <tr><td>November</td><td>30</td></tr> <tr><td>December</td><td>31</td></tr> </tbody></table> </div> <p>Programming the algorithm directly without figuring out the formula ahead of time would have been tricky, so I opted for a simpler solution: a spreadsheet. While not originating from a March-based ordinal, I believed that doing so for calculation purposes was in fact a good idea. The spreadsheet started off with three columns: the adjusted ordinal day (starting from March 1), the <em>actual</em> month (entered manually) and the <em>calculated</em> month (determined by a to-be-created algorithm). If the latter two columns were identical, the algorithm was necessarily correct.</p> <p>Let's start by taking a view at the mapping of ordinal days from the true ordinal day.</p> <div class='table-scroll'> <table><thead><tr><th>Month &amp; day</th><th>Ordinal day</th><th>Mapped ordinal day</th></tr></thead><tbody> <tr><td>January 1</td><td>1</td><td>1</td></tr> <tr><td>January 31</td><td>31</td><td>31</td></tr> <tr><td>February 1</td><td>32</td><td>32</td></tr> <tr><td>February 28</td><td>59</td><td>59</td></tr> <tr><td>February 29</td><td>60</td><td>60</td></tr> <tr><td>March 1</td><td>60/61</td><td>1</td></tr> <tr><td>April 1</td><td>91/92</td><td>32</td></tr> <tr><td>December 31</td><td>365/366</td><td>306</td></tr> </tbody></table> </div> <p>To achieve this, it is necessary to determine the number of days in January and February combined. This is easy to do.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_calendar_date</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-storage z-type z-rust">i32</span>, <span class="z-storage z-type z-rust">u8</span>, <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> jan_feb_len <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u16</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-support z-macro z-rust">todo!</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> <div class="tip" role="note" aria-label="Tip"><p>The <code>todo!()</code> macro is a great way to indicate that you plan to implement something later.</p> </div> <p>Now we can shift the ordinal day if necessary. We will need to disambiguate January and March as well as February and April later, but for the time being let's ignore those two months entirely.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> ordinal_adj <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"> jan_feb_len </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Our ordinal day now runs from 1 to 306, consisting solely of the two complete blocks of months. As the range contains 10 months, the average month length is exactly 30.6. So let's start with an approximation; divide the ordinal day by 30.6 and round down. This will give us our first estimate for what the month is, ranging from 0 to 9. We'll correct for that by adding the appropriate value (3 here).</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-variable z-other z-readwrite z-sheet">ordinal</span> <span class="z-keyword z-operator z-arithmetic z-sheet">/</span> <span class="z-meta z-number z-float z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30<span class="z-punctuation z-separator z-decimal z-sheet">.</span>6</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">3</span></span> </span></code></pre> <div class="note" role="note" aria-label="Note"><p>The extra parameters to <code>FLOOR</code> indicate that we want to round towards zero. For positive values it makes no difference, but they are included in case we somehow end up with a negative value in the spreadsheet. This behavior is important as it is the same as integer division when programming.</p> </div> <p>This gets us most of the way there! In fact, only six days are incorrect.</p> <ul> <li>March 31</li> <li>May 31</li> <li>July 31</li> <li>August 31</li> <li>October 31</li> <li>December 31</li> </ul> <p>Interestingly, all the incorrect calculations are for months with 31 days. Thinking about it, this makes sense. The calculation tells us that it only has <code>FLOOR(30.6)</code> days (i.e. 30). We need to "build up" the 31^st day. Perhaps if we force the first month to start with 31 days, the calculation will be correct. Because we're adding 30 days to the start, we need to adjust the result by two instead of three.</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-meta z-group z-sheet"><span class="z-punctuation z-section z-group z-begin z-sheet">(</span><span class="z-variable z-other z-readwrite z-sheet">ordinal</span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30</span></span><span class="z-punctuation z-section z-group z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">/</span> <span class="z-meta z-number z-float z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30<span class="z-punctuation z-separator z-decimal z-sheet">.</span>6</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">2</span></span> </span></code></pre> <p>Perfect! This correctly calculates all cases. Recall that we don't want to use floating point values, so we need to adapt this to integers. Rather than dividing by 30.6, multiply by 10 and divide by 306. Simple enough.</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-meta z-group z-sheet"><span class="z-punctuation z-section z-group z-begin z-sheet">(</span><span class="z-variable z-other z-readwrite z-sheet">ordinal</span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30</span></span><span class="z-punctuation z-section z-group z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">*</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">10</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">/</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">306</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">2</span></span> </span></code></pre> <p>Translating this into code is straightforward.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">30</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Great; we can now calculate the month. But wait a minute, remember how I said we'd have to disambiguate January and March as well as February and April? Now is the time to do that. If the month is January or February, the value is already correct. For other months, we need to add the already-used adjustment. We can code this into the existing calculation.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month_adj<span class="z-punctuation z-separator z-rust">,</span> ordinal_adj</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-separator z-rust">,</span> jan_feb_len</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span><span class="z-source z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">30</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> month_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>At this point, we have calculated the month in an efficient manner.</p> <h2 id="calculating-the-day"><a class="anchor" href="#calculating-the-day" aria-label="Anchor link for: calculating-the-day" tabindex="-1">Calculating the day</a></h2> <p>Calculating the day of the month once we have the month is not terribly difficult. I added more columns to the spreadsheet: the known correct day, the calculated day, and whether the calculation was correct.</p> <p>For this calculation, we will continue using the mapped ordinal day where March 1 is equivalent to January 1. Because of this, it's simplest to defer the month adjustment until later. The code in this section will be between the calculation of the month and the adjustment.</p> <pre data-lang="diff" class="language-diff z-code"><code class="language-diff" data-lang="diff"><span class="z-source z-diff"><span class="z-markup z-deleted z-diff"><span class="z-punctuation z-definition z-deleted z-diff">-</span> let month = (ordinal + 30) * 10 / 306 + month_adj; </span></span><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let month = (ordinal + 30) * 10 / 306; </span></span><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let month = month + month_adj; </span></span></code></pre> <p>As we know the ordinal day, the only other things we need to know is how many days are in all previous months cumulatively. Once we know that, we can subtract that value from the ordinal day to get the day of the month.</p> <p>But how do we calculate the cumulative number of days in previous months? In short, do the opposite calculation of how we calculated the month. Use the average length of the month — 30.6 — and multiply it by the month number less one (to account for the fact that the first month has no preceding days).</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-meta z-group z-sheet"><span class="z-punctuation z-section z-group z-begin z-sheet">(</span><span class="z-variable z-other z-readwrite z-sheet">month</span> <span class="z-keyword z-operator z-arithmetic z-sheet">-</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-section z-group z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">*</span> <span class="z-meta z-number z-float z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30<span class="z-punctuation z-separator z-decimal z-sheet">.</span>6</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> </span></code></pre> <p>It looks like some of the calculations are off by one day, as was the case when calculating the month. That's not too surprising given that we needed a correction before. Experimenting with small values quickly yields something that works.</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-meta z-group z-sheet"><span class="z-punctuation z-section z-group z-begin z-sheet">(</span><span class="z-variable z-other z-readwrite z-sheet">month</span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">3</span></span><span class="z-punctuation z-section z-group z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">*</span> <span class="z-meta z-number z-float z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">30<span class="z-punctuation z-separator z-decimal z-sheet">.</span>6</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">-</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">122</span></span> </span></code></pre> <p>Because we are treating January and February the same as March and April, there is no need to account for a leap day. However, we still need to make a minor alteration to avoid floating point numbers.</p> <pre data-lang="excel" class="language-excel z-code"><code class="language-excel" data-lang="excel"><span class="z-source z-sheet z-basic"><span class="z-keyword z-operator z-assignment z-sheet">=</span><span class="z-meta z-function-call z-sheet"><span class="z-support z-function z-sheet">FLOOR</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-begin z-sheet">(</span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-meta z-group z-sheet"><span class="z-punctuation z-section z-group z-begin z-sheet">(</span><span class="z-variable z-other z-readwrite z-sheet">month</span> <span class="z-keyword z-operator z-arithmetic z-sheet">+</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">3</span></span><span class="z-punctuation z-section z-group z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">*</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">306</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">/</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">10</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span><span class="z-punctuation z-separator z-sequence z-sheet">,</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">1</span></span></span><span class="z-meta z-function-call z-arguments z-sheet"><span class="z-punctuation z-section z-arguments z-end z-sheet">)</span></span> <span class="z-keyword z-operator z-arithmetic z-sheet">-</span> <span class="z-meta z-number z-integer z-decimal z-sheet"><span class="z-constant z-numeric z-value z-sheet">122</span></span> </span></code></pre> <p>Great! This calculation works for all months. We can now translate this into code.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">122</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>We now have all the information we need to perform the final calculation. All that's left to do is subtract the days in the preceding months from the ordinal day. As we've already eliminated the special casing for January and February, this just works™.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> day <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days_in_preceding_months<span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Does it <em>really</em> work? Yes! This algorithm was tested using a straightforward script to compare the results against the original implementation.</p> <details> <summary>Test script</summary> <div class="important" role="note" aria-label="Important"><p>This script requires the nightly compiler as of publishing. It can be run with <code>cargo +nightly script.rs</code>. To use stable, you can add the dependency in a <code>Cargo.toml</code> file in a standard configuration.</p> </div> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-keyword z-operator z-rust">#</span><span class="z-keyword z-operator z-logical z-rust">!</span><span class="z-keyword z-operator z-arithmetic z-rust">/</span>usr<span class="z-keyword z-operator z-arithmetic z-rust">/</span>bin<span class="z-keyword z-operator z-arithmetic z-rust">/</span>env cargo </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-keyword z-operator z-arithmetic z-rust">-</span><span class="z-keyword z-operator z-arithmetic z-rust">-</span><span class="z-keyword z-operator z-arithmetic z-rust">-</span> </span><span class="z-source z-rust">package<span class="z-punctuation z-accessor z-dot z-rust">.</span>edition <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-string z-quoted z-double z-rust"><span class="z-punctuation z-definition z-string z-begin z-rust">&quot;</span>2021<span class="z-punctuation z-definition z-string z-end z-rust">&quot;</span></span> </span><span class="z-source z-rust"><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">[</span>dependencies<span class="z-punctuation z-section z-group z-end z-rust">]</span></span> </span><span class="z-source z-rust">time <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-string z-quoted z-double z-rust"><span class="z-punctuation z-definition z-string z-begin z-rust">&quot;</span>=0.3.37<span class="z-punctuation z-definition z-string z-end z-rust">&quot;</span></span> <span class="z-keyword z-operator z-rust">#</span> pin to uses the previous algorithm which is known to be correct </span><span class="z-source z-rust"><span class="z-keyword z-operator z-arithmetic z-rust">-</span><span class="z-keyword z-operator z-arithmetic z-rust">-</span><span class="z-keyword z-operator z-arithmetic z-rust">-</span> </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-keyword z-other z-rust">use</span> <span class="z-meta z-path z-rust">time<span class="z-punctuation z-accessor z-rust">::</span></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span><span class="z-meta z-path z-rust">util<span class="z-punctuation z-accessor z-rust">::</span></span>is_leap_year<span class="z-punctuation z-separator z-rust">,</span> Date</span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-storage z-type z-rust">const</span> <span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_calendar_date</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-storage z-type z-rust">i32</span>, <span class="z-storage z-type z-rust">u8</span>, <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> jan_feb_len <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u16</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month_adj<span class="z-punctuation z-separator z-rust">,</span> ordinal_adj</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-separator z-rust">,</span> jan_feb_len</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">30</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">122</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> day <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days_in_preceding_months<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> month <span class="z-keyword z-operator z-arithmetic z-rust">+</span> month_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year<span class="z-punctuation z-separator z-rust">,</span> month <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span><span class="z-punctuation z-separator z-rust">,</span> day <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span><span class="z-source z-rust"> </span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">main</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-keyword z-control z-rust">for</span> ordinal <span class="z-keyword z-operator z-rust">in</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">1</span><span class="z-keyword z-operator z-range z-rust">..</span><span class="z-keyword z-operator z-assignment z-rust">=</span><span class="z-constant z-numeric z-integer z-decimal z-rust">366</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> calculated <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-support z-function z-rust">ordinal_date_to_calendar_date</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2024</span><span class="z-punctuation z-separator z-rust">,</span> ordinal</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> correct <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-path z-rust">Date<span class="z-punctuation z-accessor z-rust">::</span></span>from_ordinal_date<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2024</span><span class="z-punctuation z-separator z-rust">,</span> ordinal</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-support z-function z-rust">unwrap</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-support z-function z-rust">to_calendar_date</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> correct <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">1</span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-separator z-rust">,</span> correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-support z-macro z-rust">assert_eq!</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>calculated<span class="z-punctuation z-separator z-rust">,</span> correct</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-keyword z-control z-rust">for</span> ordinal <span class="z-keyword z-operator z-rust">in</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">1</span><span class="z-keyword z-operator z-range z-rust">..</span><span class="z-keyword z-operator z-assignment z-rust">=</span><span class="z-constant z-numeric z-integer z-decimal z-rust">365</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> calculated <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-support z-function z-rust">ordinal_date_to_calendar_date</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2025</span><span class="z-punctuation z-separator z-rust">,</span> ordinal</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> correct <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-path z-rust">Date<span class="z-punctuation z-accessor z-rust">::</span></span>from_ordinal_date<span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2025</span><span class="z-punctuation z-separator z-rust">,</span> ordinal</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-support z-function z-rust">unwrap</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-support z-function z-rust">to_calendar_date</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> correct <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">1</span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-separator z-rust">,</span> correct<span class="z-punctuation z-accessor z-dot z-rust">.</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-support z-macro z-rust">assert_eq!</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>calculated<span class="z-punctuation z-separator z-rust">,</span> correct</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> </details> <h2 id="preliminary-comparison"><a class="anchor" href="#preliminary-comparison" aria-label="Anchor link for: preliminary-comparison" tabindex="-1">Preliminary comparison</a></h2> <p>Let's look at the generated assembly for both the pre-existing and new algorithm. <a rel="nofollow noreferrer" href="https://crates.io/crates/cargo-show-asm"><code>cargo asm</code></a> is used to generate this.</p> <p><details role="none"><summary>Pre-existing implementation</summary><pre data-lang="asm" class="language-asm z-code"><code class="language-asm" data-lang="asm"><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">c</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">-</span><span class="z-constant z-character z-decimal z-assembly">1030792151</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">x</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949673</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">15</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">test</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sete</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">al</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">4</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">4</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rip</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">u</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">5</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">20</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">51539607552</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">18</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">4</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">47244640256</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">4</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">16</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">6</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949672960</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">6</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">14</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">8</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">38654705664</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">12</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">34359738368</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">0</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">10</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">30064771072</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">8</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">4</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">25769803776</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">4</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">6</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">6</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">21474836480</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">6</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">4</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">8</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">17179869184</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">word</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-support z-function z-directive z-assembly">ptr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">12884901888</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">jmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">0</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">32</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">setae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">dl</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">31</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">32</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">v</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">b</span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">4294967296</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">.</span><span class="z-entity z-name z-function z-assembly">L</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">B</span><span class="z-entity z-name z-function z-assembly">8</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">2</span><span class="z-entity z-name z-function z-assembly">1</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">l</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">40</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">or</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">or</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rdx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">ret</span> </span><span class="z-source z-assembly"> </span></code></pre> </details> <details role="none"><summary>Preliminary new implementation</summary><pre data-lang="asm" class="language-asm z-code"><code class="language-asm" data-lang="asm"><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">c</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">-</span><span class="z-constant z-character z-decimal z-assembly">1030792151</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">85899344</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">x</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949673</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">15</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">and</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">adc</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">cx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">59</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">cx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">setb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">al</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rsi</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rsi</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">4</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">300</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">cx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">13707</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">22</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">306</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">918</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">dx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">52429</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">19</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">122</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">l</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">40</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">32</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">or</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">ret</span> </span></code></pre> </details> </p> <p>Assembly isn't the easiest to read, but it's clear from a glance that there are significantly fewer instructions. More impressive, in my opinion, is that the new implementation is <em>branchless</em>. This should help with performance, as branches are potentially expensive if mispredicted.</p> <p>Rather than eyeballing it, what does MCA have to say?</p> <div class="table-scroll"><table><thead><tr><th>Measure</th><th>Pre-existing</th><th>Preliminary new</th></tr></thead><tbody> <tr><td>Iterations</td><td>100</td><td>100</td></tr> <tr><td>Instructions</td><td>8000</td><td>3800</td></tr> <tr><td>Total Cycles</td><td>1263</td><td>2219</td></tr> <tr><td>Total uOps</td><td>7300</td><td>4000</td></tr> <tr><td>Dispatch Width</td><td>6</td><td>6</td></tr> <tr><td>uOps per Cycle</td><td>5.78</td><td>1.80</td></tr> <tr><td>IPC</td><td>6.33</td><td>1.71</td></tr> <tr><td>Block RThroughput</td><td>12.2</td><td>7.0</td></tr> </tbody></table> </div> <p>Overall things look good! While there are some negatives, it's worth noting that MCA can be misleading. MCA assumes that all branches fall through, which is certainly not the case. It also is unable to account for cache locality, which are likely to be significant factors in the performance of the new implementation. One item of note is the throughput, which is significantly reduced and is also likely a significant factor.</p> <h2 id="further-improvement"><a class="anchor" href="#further-improvement" aria-label="Anchor link for: further-improvement" tabindex="-1">Further improvement</a></h2> <h3 id="month"><a class="anchor" href="#month" aria-label="Anchor link for: month" tabindex="-1">Month</a></h3> <p>What's left to do? The algorithm is known to be correct and is likely faster than the pre-existing one. There are some further optimizations we can do, including some that are already performed by the compiler.</p> <p>Let's start with the calculation of the month.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">30</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>The first thing that can be done is distributing the multiplication.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">300</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>This is done by the compiler already, but there is one more trick we can do. Compilers <em>love</em> division by powers of two because they are trivially replaced with a bitshift. While 306 is very much not a power of two, we can turn the division into one. The first power of two greater than 306 is 512. By multiplying the integers in the numerator by 512÷306 (≈1.67), we can turn the denominator into a power of two. This is in turn optimized into a bitshift.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">17</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">502</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">512</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>This causes our script to fail. Let's try more powers of two. This is because with greater powers our approximation of the true ratio becomes more accurate.</p> <div class="table-scroll"><table><thead><tr><th>Power of two</th><th>10</th><th>300</th><th>Success?</th></tr></thead><tbody> <tr><td>512</td><td>17</td><td>502</td><td>❌</td></tr> <tr><td>1024</td><td>33</td><td>1004</td><td>❌</td></tr> <tr><td>2048</td><td>67</td><td>2008</td><td>❌</td></tr> <tr><td>4096</td><td>134</td><td>4016</td><td>❌</td></tr> <tr><td>8192</td><td>268</td><td>8031</td><td>✅</td></tr> </tbody></table> </div> <p>Turns out that 8192 (i.e. 2¹³) is the magic number! Our final code for calculating the month is</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">268</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">8031</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">13</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Hm. That didn't work. Rust is great, though, so it tells us why.</p> <blockquote> <p>attempt to multiply with overflow</p> </blockquote> <p>Given the range of <code>ordinal</code> (1 to 306), the result of the multiplication is larger than a <code>u16</code> can hold, so we need to cast <code>ordinal</code> and its adjustment to a <code>u32</code>.</p> <pre data-lang="diff" class="language-diff z-code"><code class="language-diff" data-lang="diff"><span class="z-source z-diff"><span class="z-markup z-deleted z-diff"><span class="z-punctuation z-definition z-deleted z-diff">-</span> let ordinal = ordinal - ordinal_adj; </span></span><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let ordinal = ordinal as u32 - ordinal_adj as u32; </span></span></code></pre> <p>With this minor change, the code runs successfully.</p> <h3 id="day"><a class="anchor" href="#day" aria-label="Anchor link for: day" tabindex="-1">Day</a></h3> <p>Let's try the same with the day calculation.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">122</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>First, we distribute the multiplication.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">918</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">122</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Since 122 is being added to the result of a division by 10, we can subtract 1220 from the numerator.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">306</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">302</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">/</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">10</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <p>Now for the same trick utilizing powers of two, starting with 16.</p> <div class="table-scroll"><table><thead><tr><th>Power of two</th><th>306</th><th>302</th><th>Success?</th></tr></thead><tbody> <tr><td>16</td><td>490</td><td>483</td><td>❌</td></tr> <tr><td>32</td><td>979</td><td>966</td><td>❌</td></tr> <tr><td>64</td><td>1958</td><td>1933</td><td>❌</td></tr> <tr><td>128</td><td>3917</td><td>3866</td><td>✅</td></tr> </tbody></table> </div> <p>By utilizing these new constants, we end up with the following code.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3917</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3866</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-terminator z-rust">;</span> </span></code></pre> <h3 id="one-final-change"><a class="anchor" href="#one-final-change" aria-label="Anchor link for: one-final-change" tabindex="-1">One final change</a></h3> <p>Remember how we had to zero-extend the adjusted ordinal? I tried moving around the cast in a few ways to see if it might optimize differently. And it did, just always as a slight regression. <em>While writing this post</em>, I considered one scenario I had not before: moving the cast to be the very first thing the function does. This allows eliminating subsequent casts and ensures that all operations are performed on <code>u32</code> values, no extending or truncating necessary.</p> <pre data-lang="diff" class="language-diff z-code"><code class="language-diff" data-lang="diff"><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let ordinal = ordinal as u32; </span></span><span class="z-source z-diff"> </span><span class="z-source z-diff"><span class="z-markup z-deleted z-diff"><span class="z-punctuation z-definition z-deleted z-diff">-</span> let jan_feb_len = 59 + is_leap_year(year) as u16; </span></span><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let jan_feb_len = 59 + is_leap_year(year); </span></span><span class="z-source z-diff"> </span><span class="z-source z-diff"><span class="z-markup z-deleted z-diff"><span class="z-punctuation z-definition z-deleted z-diff">-</span> let ordinal = ordinal as u32 - ordinal_adj as u32; </span></span><span class="z-source z-diff"><span class="z-markup z-inserted z-diff"><span class="z-punctuation z-definition z-inserted z-diff">+</span> let ordinal = ordinal - ordinal_adj; </span></span></code></pre> <div class="note" role="note" aria-label="Note"><p>The reason <code>ordinal</code> is not a <code>u32</code> from the start is because the field is semantically a <code>u16</code>.</p> </div> <h2 id="final-code"><a class="anchor" href="#final-code" aria-label="Anchor link for: final-code" tabindex="-1">Final code</a></h2> <p>After designing the new algorithm from the ground up, optimizing it along the way, making it work better for computers, and performing one final optimization, we have the following code.</p> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">const</span> <span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_calendar_date</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-storage z-type z-rust">i32</span>, <span class="z-storage z-type z-rust">u8</span>, <span class="z-storage z-type z-rust">u8</span><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> jan_feb_len <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month_adj<span class="z-punctuation z-separator z-rust">,</span> ordinal_adj</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-separator z-rust">,</span> jan_feb_len</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">268</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">8031</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">13</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3917</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3866</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> day <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days_in_preceding_months<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> month <span class="z-keyword z-operator z-arithmetic z-rust">+</span> month_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year<span class="z-punctuation z-separator z-rust">,</span> month <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span><span class="z-punctuation z-separator z-rust">,</span> day <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> <p>Does this code make any sense whatsoever on its own? No, not in the slightest. <em>But</em> the end result is a solid piece of code that is faster than the pre-existing implementation, leverages optimizations that the compiler does not perform, and is branchless. When a new implementation is all upsides with only one downside (being less readable code), it would be foolish not to use it.</p> <h3 id="comparison"><a class="anchor" href="#comparison" aria-label="Anchor link for: comparison" tabindex="-1">Comparison</a></h3> <p>Looking at the assembly for the final code, we see many of the constants we introduced verbatim. This is a good sign that there isn't much more (if anything) that can be done for further optimizations within this style of algorithm. That is not to say that this code is perfect, but it is likely as good as it will get unless I have missed something obvious.</p> <details role="none"><summary>Assembly for the final code</summary><pre data-lang="asm" class="language-asm z-code"><code class="language-asm" data-lang="asm"><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">c</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">-</span><span class="z-constant z-character z-decimal z-assembly">1030792151</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">x</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949673</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">15</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">and</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">adc</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">59</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">setb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">l</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">268</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">8031</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">13</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3917</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">28902</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">7</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rsi</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">al</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">40</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">cl</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shl</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">32</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">or</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">or</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">rcx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">ret</span> </span></code></pre> </details> <p>MCA analysis shows that the new implementation is <em>significantly</em> better than the pre-existing code. The only "negatives" are the slight declines in micro-operations per cycle and instructions per cycle, but that is a non-issue given the significant decrease in total cycles.</p> <div class="table-scroll"><table><thead><tr><th>Measure</th><th>Pre-existing</th><th>Preliminary new</th><th>Final</th></tr></thead><tbody> <tr><td>Iterations</td><td>100</td><td>100</td><td>100</td></tr> <tr><td>Instructions</td><td>8000</td><td>3800</td><td>3300</td></tr> <tr><td>Total Cycles</td><td>1263</td><td>2219</td><td>731</td></tr> <tr><td>Total uOps</td><td>7300</td><td>4000</td><td>3500</td></tr> <tr><td>Dispatch Width</td><td>6</td><td>6</td><td>6</td></tr> <tr><td>uOps per Cycle</td><td>5.78</td><td>1.80</td><td>4.79</td></tr> <tr><td>IPC</td><td>6.33</td><td>1.71</td><td>4.51</td></tr> <tr><td>Block RThroughput</td><td>12.2</td><td>7.0</td><td>5.8</td></tr> </tbody></table> </div> <h3 id="benchmarks"><a class="anchor" href="#benchmarks" aria-label="Anchor link for: benchmarks" tabindex="-1">Benchmarks</a></h3> <p>For benchmarks, I used a representative sample of 24 values. To avoid giving the branch predictor any hints, the order was randomized. Using <a rel="nofollow noreferrer" href="https://crates.io/crates/criterion"><code>criterion</code></a> and a tight loop around values, we get our results. Note that these results are for all 24 values, not any given one. It also includes the overhead of iteration, but that is almost certainly minimal.</p> <div class="table-scroll"> <table><thead><tr><th>Version</th><th>Best estimate</th><th>95% confidence interval</th></tr></thead><tbody> <tr><td>pre-existing</td><td><span class="tnum">81.244</span> ns</td><td><span class="tnum">80.392</span> – <span class="tnum">82.042</span> ns</td></tr> <tr><td>preliminary</td><td><span class="tnum">48.129</span> ns</td><td><span class="tnum">48.050</span> – <span class="tnum">48.214</span> ns</td></tr> <tr><td>final</td><td><span class="tnum">37.538</span> ns</td><td><span class="tnum">37.485</span> – <span class="tnum">37.595</span> ns</td></tr> <tr><td>no-op iteration</td><td><span class="tnum">5.1690</span> ns</td><td><span class="tnum">5.1626</span> – <span class="tnum">5.1763</span> ns</td></tr> </tbody></table> </div> <p>Subtracting out the no-op iteration as overhead and dividing by the number of calculations performed, this is the time for a single calculation.</p> <div class='table-scroll'> <table><thead><tr><th>Version</th><th>Best estimate</th><th>95% confidence interval</th></tr></thead><tbody> <tr><td>pre-existing</td><td><span class="tnum">3.1698</span> ns</td><td><span class="tnum">3.1340</span> – <span class="tnum">3.2033</span> ns</td></tr> <tr><td>preliminary</td><td><span class="tnum">1.7900</span> ns</td><td><span class="tnum">1.7864</span> – <span class="tnum">1.7938</span> ns</td></tr> <tr><td>final</td><td><span class="tnum">1.3487</span> ns</td><td><span class="tnum">1.3462</span> – <span class="tnum">1.3514</span> ns</td></tr> </tbody></table> </div> <p>With these values, we are able to determine the 43.5% performance improvement from the pre-existing algorithm to the preliminary one, with an additional 24.7% improvement from the preliminary to final algorithm. Combined, this is a 57.5% decrease in time taken to perform the calculation.</p> <h2 id="truncated-algorithms"><a class="anchor" href="#truncated-algorithms" aria-label="Anchor link for: truncated-algorithms" tabindex="-1">Truncated algorithms</a></h2> <p>The final algorithm is not only faster when calculating the month and day together, but also when calculating them separately. This is because some calculations can be entirely omitted as unnecessary when calculating only one of the two. I won't go into detail on how this is done; it should be straightforward. The code, generated assembly, and benchmarks are provided.</p> <h3 id="month-only"><a class="anchor" href="#month-only" aria-label="Anchor link for: month-only" tabindex="-1">Month-only</a></h3> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">const</span> <span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_month</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-storage z-type z-rust">u8</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> jan_feb_len <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month_adj<span class="z-punctuation z-separator z-rust">,</span> ordinal_adj</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">0</span><span class="z-punctuation z-separator z-rust">,</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-constant z-numeric z-integer z-decimal z-rust">2</span><span class="z-punctuation z-separator z-rust">,</span> jan_feb_len</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">268</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">8031</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">13</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> month_adj</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> <details role="none"><summary>Generated assembly</summary><pre data-lang="asm" class="language-asm z-code"><code class="language-asm" data-lang="asm"><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">h</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">-</span><span class="z-constant z-character z-decimal z-assembly">1030792151</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">85899344</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">x</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949673</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">15</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">and</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">adc</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">59</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">esi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">setb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">s</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">l</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">268</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">8031</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">13</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">lea</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">[</span><span class="z-variable z-parameter z-register z-assembly">rax</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">+</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span><span class="z-source z-assembly">*</span><span class="z-variable z-parameter z-register z-assembly">rsi</span><span class="z-source z-assembly">]</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">ret</span> </span></code></pre> </details> <div class="table-scroll"> <table><thead><tr><th>Version</th><th>Best estimate</th><th>95% confidence interval</th></tr></thead><tbody> <tr><td>pre-existing</td><td><span class="tnum">1.4824</span> ns</td><td><span class="tnum">1.4801</span> – <span class="tnum">1.4848</span> ns</td></tr> <tr><td>preliminary</td><td><span class="tnum">910.0</span> ps</td><td><span class="tnum">908.7</span> – <span class="tnum">911.4</span> ps</td></tr> <tr><td>final</td><td><span class="tnum">841.8</span> ps</td><td><span class="tnum">840.3</span> – <span class="tnum">843.3</span> ps</td></tr> </tbody></table> </div> <h3 id="day-only"><a class="anchor" href="#day-only" aria-label="Anchor link for: day-only" tabindex="-1">Day-only</a></h3> <pre data-lang="rust" class="language-rust z-code"><code class="language-rust" data-lang="rust"><span class="z-source z-rust"><span class="z-storage z-type z-rust">const</span> <span class="z-meta z-function z-rust"><span class="z-meta z-function z-rust"><span class="z-storage z-type z-function z-rust">fn</span> </span><span class="z-entity z-name z-function z-rust">ordinal_date_to_day_of_month</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-begin z-rust">(</span><span class="z-variable z-parameter z-rust">year</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">i32</span>, <span class="z-variable z-parameter z-rust">ordinal</span><span class="z-punctuation z-separator z-rust">:</span> <span class="z-storage z-type z-rust">u16</span></span><span class="z-meta z-function z-rust"><span class="z-meta z-function z-parameters z-rust"><span class="z-punctuation z-section z-parameters z-end z-rust">)</span></span></span></span><span class="z-meta z-function z-rust"> <span class="z-meta z-function z-return-type z-rust"><span class="z-punctuation z-separator z-rust">-&gt;</span> <span class="z-storage z-type z-rust">u8</span></span> </span><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> jan_feb_len <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">59</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-support z-function z-rust">is_leap_year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>year</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-storage z-type z-rust">u32</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal_adj <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-keyword z-control z-rust">if</span> ordinal <span class="z-keyword z-operator z-comparison z-rust">&lt;=</span> jan_feb_len <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> <span class="z-constant z-numeric z-integer z-decimal z-rust">0</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span> <span class="z-keyword z-control z-rust">else</span> <span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-begin z-rust">{</span> </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> jan_feb_len </span></span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"><span class="z-meta z-block z-rust"> </span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> ordinal <span class="z-keyword z-operator z-assignment z-rust">=</span> ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> ordinal_adj<span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> month <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">268</span> <span class="z-keyword z-operator z-arithmetic z-rust">+</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">8031</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">13</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-storage z-type z-rust">let</span> days_in_preceding_months <span class="z-keyword z-operator z-assignment z-rust">=</span> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>month <span class="z-keyword z-operator z-arithmetic z-rust">*</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3917</span> <span class="z-keyword z-operator z-arithmetic z-rust">-</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">3866</span></span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-comparison z-rust">&gt;</span><span class="z-keyword z-operator z-comparison z-rust">&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-rust">7</span><span class="z-punctuation z-terminator z-rust">;</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"> <span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-begin z-rust">(</span>ordinal <span class="z-keyword z-operator z-arithmetic z-rust">-</span> days_in_preceding_months</span><span class="z-meta z-group z-rust"><span class="z-punctuation z-section z-group z-end z-rust">)</span></span> <span class="z-keyword z-operator z-rust">as</span> <span class="z-keyword z-operator z-rust">_</span> </span></span></span><span class="z-source z-rust"><span class="z-meta z-function z-rust"><span class="z-meta z-block z-rust"></span><span class="z-meta z-block z-rust"><span class="z-punctuation z-section z-block z-end z-rust">}</span></span></span> </span></code></pre> <details role="none"><summary>Generated assembly</summary><pre data-lang="asm" class="language-asm z-code"><code class="language-asm" data-lang="asm"><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">i</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">l</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">e</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">d</span><span class="z-entity z-name z-function z-assembly">a</span><span class="z-entity z-name z-function z-assembly">y</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">f</span><span class="z-entity z-name z-function z-assembly">_</span><span class="z-entity z-name z-function z-assembly">m</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">n</span><span class="z-entity z-name z-function z-assembly">t</span><span class="z-entity z-name z-function z-assembly">h</span><span class="z-entity z-name z-function z-assembly">:</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">movzx</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">si</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-source z-assembly">-</span><span class="z-constant z-character z-decimal z-assembly">1030792151</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">85899344</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">o</span><span class="z-entity z-name z-function z-assembly">r</span><span class="z-entity z-name z-function z-assembly">x</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">2</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">42949673</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">15</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovb</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">and</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edi</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">xor</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">1</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">mov</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">0</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">adc</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">59</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmp</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">cmovae</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">edx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">268</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">8031</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">13</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">imul</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">3917</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">add</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">28902</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">shr</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-constant z-character z-decimal z-assembly">7</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">sub</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">eax</span><span class="z-source z-assembly">,</span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-variable z-parameter z-register z-assembly">ecx</span> </span><span class="z-source z-assembly"><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-entity z-name z-function z-assembly"> </span><span class="z-keyword z-control z-assembly">ret</span> </span></code></pre> </details> <div class="table-scroll"> <table><thead><tr><th>Version</th><th>Best estimate</th><th>95% confidence interval</th></tr></thead><tbody> <tr><td>pre-existing</td><td><span class="tnum">1.4759</span> ns</td><td><span class="tnum">1.4697</span> – <span class="tnum">1.4827</span> ns</td></tr> <tr><td>preliminary</td><td><span class="tnum">1.0652</span> ns</td><td><span class="tnum">1.0608</span> – <span class="tnum">1.0715</span> ns</td></tr> <tr><td>final</td><td><span class="tnum">765.7</span> ps</td><td><span class="tnum">764.1</span> – <span class="tnum">767.5</span> ps</td></tr> </tbody></table> </div> <h2 id="summary"><a class="anchor" href="#summary" aria-label="Anchor link for: summary" tabindex="-1">Summary</a></h2> <p>Success! I was able to create performant, branchless, and <code>const</code>-compatible algorithms for converting an ordinal date to a calendar date that is 57.5% faster than the previous implementation, the month-only algorithm 43.2% faster, and the day-only algorithm 48.1% faster. After exercising some creativity and applying some mathematical tricks, I was able to achieve something that I am more than happy with.</p> <p>In the future, I hope to create more algorithms like this. While time-consuming and not straightforward, the end result was well worth it here. Algorithmic improvements may not be glamorous in release notes, but they cumulatively have a significant impact in the real world.</p>