| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/git/checkouts/tantivy-65d0bbbddbbd5d02/433372d/fastfield_codecs/src/line.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>line.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../fastfield_codecs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../fastfield_codecs/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="kw">use </span>std::io; |
| <span class="kw">use </span>std::num::NonZeroU32; |
| |
| <span class="kw">use </span>common::{BinarySerializable, VInt}; |
| |
| <span class="kw">use </span><span class="kw">crate</span>::Column; |
| |
| <span class="kw">const </span>MID_POINT: u64 = (<span class="number">1u64 </span><< <span class="number">32</span>) - <span class="number">1u64</span>; |
| |
| <span class="doccomment">/// `Line` describes a line function `y: ax + b` using integer |
| /// arithmetics. |
| /// |
| /// The slope is in fact a decimal split into a 32 bit integer value, |
| /// and a 32-bit decimal value. |
| /// |
| /// The multiplication then becomes. |
| /// `y = m * x >> 32 + b` |
| </span><span class="attribute">#[derive(Debug, Clone, Copy, Default)] |
| </span><span class="kw">pub struct </span>Line { |
| slope: u64, |
| intercept: u64, |
| } |
| |
| <span class="doccomment">/// Compute the line slope. |
| /// |
| /// This function has the nice property of being |
| /// invariant by translation. |
| /// ` |
| /// compute_slope(y0, y1) |
| /// = compute_slope(y0 + X % 2^64, y1 + X % 2^64) |
| /// ` |
| </span><span class="kw">fn </span>compute_slope(y0: u64, y1: u64, num_vals: NonZeroU32) -> u64 { |
| <span class="kw">let </span>dy = y1.wrapping_sub(y0); |
| <span class="kw">let </span>sign = dy <= (<span class="number">1 </span><< <span class="number">63</span>); |
| <span class="kw">let </span>abs_dy = <span class="kw">if </span>sign { |
| y1.wrapping_sub(y0) |
| } <span class="kw">else </span>{ |
| y0.wrapping_sub(y1) |
| }; |
| <span class="kw">if </span>abs_dy >= <span class="number">1 </span><< <span class="number">32 </span>{ |
| <span class="comment">// This is outside of realm we handle. |
| // Let's just bail. |
| </span><span class="kw">return </span><span class="number">0u64</span>; |
| } |
| |
| <span class="kw">let </span>abs_slope = (abs_dy << <span class="number">32</span>) / num_vals.get() <span class="kw">as </span>u64; |
| <span class="kw">if </span>sign { |
| abs_slope |
| } <span class="kw">else </span>{ |
| <span class="comment">// The complement does indeed create the |
| // opposite decreasing slope... |
| // |
| // Intuitively (without the bitshifts and % u64::MAX) |
| // ``` |
| // (x + shift)*(u64::MAX - abs_slope) |
| // - (x * (u64::MAX - abs_slope)) |
| // = - shift * abs_slope |
| // ``` |
| </span>u64::MAX - abs_slope |
| } |
| } |
| |
| <span class="kw">impl </span>Line { |
| <span class="attribute">#[inline(always)] |
| </span><span class="kw">pub fn </span>eval(<span class="kw-2">&</span><span class="self">self</span>, x: u32) -> u64 { |
| <span class="kw">let </span>linear_part = ((x <span class="kw">as </span>u64).wrapping_mul(<span class="self">self</span>.slope) >> <span class="number">32</span>) <span class="kw">as </span>i32 <span class="kw">as </span>u64; |
| <span class="self">self</span>.intercept.wrapping_add(linear_part) |
| } |
| |
| <span class="comment">// Same as train, but the intercept is only estimated from provided sample positions |
| </span><span class="kw">pub fn </span>estimate(sample_positions_and_values: <span class="kw-2">&</span>[(u64, u64)]) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>first_val = sample_positions_and_values[<span class="number">0</span>].<span class="number">1</span>; |
| <span class="kw">let </span>last_val = sample_positions_and_values[sample_positions_and_values.len() - <span class="number">1</span>].<span class="number">1</span>; |
| <span class="kw">let </span>num_vals = sample_positions_and_values[sample_positions_and_values.len() - <span class="number">1</span>].<span class="number">0 </span>+ <span class="number">1</span>; |
| <span class="self">Self</span>::train_from( |
| first_val, |
| last_val, |
| num_vals <span class="kw">as </span>u32, |
| sample_positions_and_values.iter().cloned(), |
| ) |
| } |
| |
| <span class="comment">// Intercept is only computed from provided positions |
| </span><span class="kw">fn </span>train_from( |
| first_val: u64, |
| last_val: u64, |
| num_vals: u32, |
| positions_and_values: <span class="kw">impl </span>Iterator<Item = (u64, u64)>, |
| ) -> <span class="self">Self </span>{ |
| <span class="comment">// TODO replace with let else |
| </span><span class="kw">let </span>idx_last_val = <span class="kw">if let </span><span class="prelude-val">Some</span>(idx_last_val) = NonZeroU32::new(num_vals - <span class="number">1</span>) { |
| idx_last_val |
| } <span class="kw">else </span>{ |
| <span class="kw">return </span>Line::default(); |
| }; |
| |
| <span class="kw">let </span>y0 = first_val; |
| <span class="kw">let </span>y1 = last_val; |
| |
| <span class="comment">// We first independently pick our slope. |
| </span><span class="kw">let </span>slope = compute_slope(y0, y1, idx_last_val); |
| |
| <span class="comment">// We picked our slope. Note that it does not have to be perfect. |
| // Now we need to compute the best intercept. |
| // |
| // Intuitively, the best intercept is such that line passes through one of the |
| // `(i, ys[])`. |
| // |
| // The best intercept therefore has the form |
| // `y[i] - line.eval(i)` (using wrapping arithmetics). |
| // In other words, the best intercept is one of the `y - Line::eval(ys[i])` |
| // and our task is just to pick the one that minimizes our error. |
| // |
| // Without sorting our values, this is a difficult problem. |
| // We however rely on the following trick... |
| // |
| // We only focus on the case where the interpolation is half decent. |
| // If the line interpolation is doing its job on a dataset suited for it, |
| // we can hope that the maximum error won't be larger than `u64::MAX / 2`. |
| // |
| // In other words, even without the intercept the values `y - Line::eval(ys[i])` will all be |
| // within an interval that takes less than half of the modulo space of `u64`. |
| // |
| // Our task is therefore to identify this interval. |
| // Here we simply translate all of our values by `y0 - 2^63` and pick the min. |
| </span><span class="kw">let </span><span class="kw-2">mut </span>line = Line { |
| slope, |
| intercept: <span class="number">0</span>, |
| }; |
| <span class="kw">let </span>heuristic_shift = y0.wrapping_sub(MID_POINT); |
| line.intercept = positions_and_values |
| .map(|(pos, y)| y.wrapping_sub(line.eval(pos <span class="kw">as </span>u32))) |
| .min_by_key(|<span class="kw-2">&</span>val| val.wrapping_sub(heuristic_shift)) |
| .unwrap_or(<span class="number">0u64</span>); <span class="comment">//< Never happens. |
| </span>line |
| } |
| |
| <span class="doccomment">/// Returns a line that attemps to approximate a function |
| /// f: i in 0..[ys.num_vals()) -> ys[i]. |
| /// |
| /// - The approximation is always lower than the actual value. |
| /// Or more rigorously, formally `f(i).wrapping_sub(ys[i])` is small |
| /// for any i in [0..ys.len()). |
| /// - It computes without panicking for any value of it. |
| /// |
| /// This function is only invariable by translation if all of the |
| /// `ys` are packaged into half of the space. (See heuristic below) |
| </span><span class="kw">pub fn </span>train(ys: <span class="kw-2">&</span><span class="kw">dyn </span>Column) -> <span class="self">Self </span>{ |
| <span class="kw">let </span>first_val = ys.iter().next().unwrap(); |
| <span class="kw">let </span>last_val = ys.iter().nth(ys.num_vals() <span class="kw">as </span>usize - <span class="number">1</span>).unwrap(); |
| <span class="self">Self</span>::train_from( |
| first_val, |
| last_val, |
| ys.num_vals(), |
| ys.iter().enumerate().map(|(pos, val)| (pos <span class="kw">as </span>u64, val)), |
| ) |
| } |
| } |
| |
| <span class="kw">impl </span>BinarySerializable <span class="kw">for </span>Line { |
| <span class="kw">fn </span>serialize<W: io::Write>(<span class="kw-2">&</span><span class="self">self</span>, writer: <span class="kw-2">&mut </span>W) -> io::Result<()> { |
| VInt(<span class="self">self</span>.slope).serialize(writer)<span class="question-mark">?</span>; |
| VInt(<span class="self">self</span>.intercept).serialize(writer)<span class="question-mark">?</span>; |
| <span class="prelude-val">Ok</span>(()) |
| } |
| |
| <span class="kw">fn </span>deserialize<R: io::Read>(reader: <span class="kw-2">&mut </span>R) -> io::Result<<span class="self">Self</span>> { |
| <span class="kw">let </span>slope = VInt::deserialize(reader)<span class="question-mark">?</span>.<span class="number">0</span>; |
| <span class="kw">let </span>intercept = VInt::deserialize(reader)<span class="question-mark">?</span>.<span class="number">0</span>; |
| <span class="prelude-val">Ok</span>(Line { slope, intercept }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| <span class="kw">use </span><span class="kw">crate</span>::VecColumn; |
| |
| <span class="doccomment">/// Test training a line and ensuring that the maximum difference between |
| /// the data points and the line is `expected`. |
| /// |
| /// This function operates translation over the data for better coverage. |
| </span><span class="attribute">#[track_caller] |
| </span><span class="kw">fn </span>test_line_interpol_with_translation(ys: <span class="kw-2">&</span>[u64], expected: <span class="prelude-ty">Option</span><u64>) { |
| <span class="kw">let </span><span class="kw-2">mut </span>translations = <span class="macro">vec!</span>[<span class="number">0</span>, <span class="number">100</span>, u64::MAX / <span class="number">2</span>, u64::MAX, u64::MAX - <span class="number">1</span>]; |
| translations.extend_from_slice(ys); |
| <span class="kw">for </span>translation <span class="kw">in </span>translations { |
| <span class="kw">let </span>translated_ys: Vec<u64> = ys |
| .iter() |
| .copied() |
| .map(|y| y.wrapping_add(translation)) |
| .collect(); |
| <span class="kw">let </span>largest_err = test_eval_max_err(<span class="kw-2">&</span>translated_ys); |
| <span class="macro">assert_eq!</span>(largest_err, expected); |
| } |
| } |
| |
| <span class="kw">fn </span>test_eval_max_err(ys: <span class="kw-2">&</span>[u64]) -> <span class="prelude-ty">Option</span><u64> { |
| <span class="kw">let </span>line = Line::train(<span class="kw-2">&</span>VecColumn::from(<span class="kw-2">&</span>ys)); |
| ys.iter() |
| .enumerate() |
| .map(|(x, y)| y.wrapping_sub(line.eval(x <span class="kw">as </span>u32))) |
| .max() |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_train() { |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">11</span>, <span class="number">11</span>, <span class="number">12</span>, <span class="number">12</span>, <span class="number">13</span>], <span class="prelude-val">Some</span>(<span class="number">1</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">13</span>, <span class="number">12</span>, <span class="number">12</span>, <span class="number">11</span>, <span class="number">11</span>, <span class="number">11</span>], <span class="prelude-val">Some</span>(<span class="number">1</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">13</span>, <span class="number">13</span>, <span class="number">12</span>, <span class="number">11</span>, <span class="number">11</span>, <span class="number">11</span>], <span class="prelude-val">Some</span>(<span class="number">1</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">13</span>, <span class="number">13</span>, <span class="number">12</span>, <span class="number">11</span>, <span class="number">11</span>, <span class="number">11</span>], <span class="prelude-val">Some</span>(<span class="number">1</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[u64::MAX - <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>], <span class="prelude-val">Some</span>(<span class="number">1</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[u64::MAX - <span class="number">1</span>, u64::MAX, <span class="number">0</span>, <span class="number">1</span>], <span class="prelude-val">Some</span>(<span class="number">0</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">5</span>], <span class="prelude-val">Some</span>(<span class="number">0</span>)); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span>], <span class="prelude-val">Some</span>(<span class="number">0</span>)); |
| |
| <span class="kw">let </span>data: Vec<u64> = (<span class="number">0</span>..<span class="number">255</span>).collect(); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>data, <span class="prelude-val">Some</span>(<span class="number">0</span>)); |
| <span class="kw">let </span>data: Vec<u64> = (<span class="number">0</span>..<span class="number">255</span>).map(|el| el * <span class="number">2</span>).collect(); |
| test_line_interpol_with_translation(<span class="kw-2">&</span>data, <span class="prelude-val">Some</span>(<span class="number">0</span>)); |
| } |
| } |
| </code></pre></div> |
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