| <!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/registry/src/github.com-1ecc6299db9ec823/adler-1.0.2/src/algo.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>algo.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="../../adler/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="../../adler/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><span class="kw">crate</span>::Adler32; |
| <span class="kw">use </span>std::ops::{AddAssign, MulAssign, RemAssign}; |
| |
| <span class="kw">impl </span>Adler32 { |
| <span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>compute(<span class="kw-2">&mut </span><span class="self">self</span>, bytes: <span class="kw-2">&</span>[u8]) { |
| <span class="comment">// The basic algorithm is, for every byte: |
| // a = (a + byte) % MOD |
| // b = (b + a) % MOD |
| // where MOD = 65521. |
| // |
| // For efficiency, we can defer the `% MOD` operations as long as neither a nor b overflows: |
| // - Between calls to `write`, we ensure that a and b are always in range 0..MOD. |
| // - We use 32-bit arithmetic in this function. |
| // - Therefore, a and b must not increase by more than 2^32-MOD without performing a `% MOD` |
| // operation. |
| // |
| // According to Wikipedia, b is calculated as follows for non-incremental checksumming: |
| // b = n×D1 + (n−1)×D2 + (n−2)×D3 + ... + Dn + n*1 (mod 65521) |
| // Where n is the number of bytes and Di is the i-th Byte. We need to change this to account |
| // for the previous values of a and b, as well as treat every input Byte as being 255: |
| // b_inc = n×255 + (n-1)×255 + ... + 255 + n*65520 |
| // Or in other words: |
| // b_inc = n*65520 + n(n+1)/2*255 |
| // The max chunk size is thus the largest value of n so that b_inc <= 2^32-65521. |
| // 2^32-65521 = n*65520 + n(n+1)/2*255 |
| // Plugging this into an equation solver since I can't math gives n = 5552.18..., so 5552. |
| // |
| // On top of the optimization outlined above, the algorithm can also be parallelized with a |
| // bit more work: |
| // |
| // Note that b is a linear combination of a vector of input bytes (D1, ..., Dn). |
| // |
| // If we fix some value k<N and rewrite indices 1, ..., N as |
| // |
| // 1_1, 1_2, ..., 1_k, 2_1, ..., 2_k, ..., (N/k)_k, |
| // |
| // then we can express a and b in terms of sums of smaller sequences kb and ka: |
| // |
| // ka(j) := D1_j + D2_j + ... + D(N/k)_j where j <= k |
| // kb(j) := (N/k)*D1_j + (N/k-1)*D2_j + ... + D(N/k)_j where j <= k |
| // |
| // a = ka(1) + ka(2) + ... + ka(k) + 1 |
| // b = k*(kb(1) + kb(2) + ... + kb(k)) - 1*ka(2) - ... - (k-1)*ka(k) + N |
| // |
| // We use this insight to unroll the main loop and process k=4 bytes at a time. |
| // The resulting code is highly amenable to SIMD acceleration, although the immediate speedups |
| // stem from increased pipeline parallelism rather than auto-vectorization. |
| // |
| // This technique is described in-depth (here:)[https://software.intel.com/content/www/us/\ |
| // en/develop/articles/fast-computation-of-fletcher-checksums.html] |
| |
| </span><span class="kw">const </span>MOD: u32 = <span class="number">65521</span>; |
| <span class="kw">const </span>CHUNK_SIZE: usize = <span class="number">5552 </span>* <span class="number">4</span>; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>a = u32::from(<span class="self">self</span>.a); |
| <span class="kw">let </span><span class="kw-2">mut </span>b = u32::from(<span class="self">self</span>.b); |
| <span class="kw">let </span><span class="kw-2">mut </span>a_vec = U32X4([<span class="number">0</span>; <span class="number">4</span>]); |
| <span class="kw">let </span><span class="kw-2">mut </span>b_vec = a_vec; |
| |
| <span class="kw">let </span>(bytes, remainder) = bytes.split_at(bytes.len() - bytes.len() % <span class="number">4</span>); |
| |
| <span class="comment">// iterate over 4 bytes at a time |
| </span><span class="kw">let </span>chunk_iter = bytes.chunks_exact(CHUNK_SIZE); |
| <span class="kw">let </span>remainder_chunk = chunk_iter.remainder(); |
| <span class="kw">for </span>chunk <span class="kw">in </span>chunk_iter { |
| <span class="kw">for </span>byte_vec <span class="kw">in </span>chunk.chunks_exact(<span class="number">4</span>) { |
| <span class="kw">let </span>val = U32X4::from(byte_vec); |
| a_vec += val; |
| b_vec += a_vec; |
| } |
| b += CHUNK_SIZE <span class="kw">as </span>u32 * a; |
| a_vec %= MOD; |
| b_vec %= MOD; |
| b %= MOD; |
| } |
| <span class="comment">// special-case the final chunk because it may be shorter than the rest |
| </span><span class="kw">for </span>byte_vec <span class="kw">in </span>remainder_chunk.chunks_exact(<span class="number">4</span>) { |
| <span class="kw">let </span>val = U32X4::from(byte_vec); |
| a_vec += val; |
| b_vec += a_vec; |
| } |
| b += remainder_chunk.len() <span class="kw">as </span>u32 * a; |
| a_vec %= MOD; |
| b_vec %= MOD; |
| b %= MOD; |
| |
| <span class="comment">// combine the sub-sum results into the main sum |
| </span>b_vec <span class="kw-2">*</span>= <span class="number">4</span>; |
| b_vec.<span class="number">0</span>[<span class="number">1</span>] += MOD - a_vec.<span class="number">0</span>[<span class="number">1</span>]; |
| b_vec.<span class="number">0</span>[<span class="number">2</span>] += (MOD - a_vec.<span class="number">0</span>[<span class="number">2</span>]) * <span class="number">2</span>; |
| b_vec.<span class="number">0</span>[<span class="number">3</span>] += (MOD - a_vec.<span class="number">0</span>[<span class="number">3</span>]) * <span class="number">3</span>; |
| <span class="kw">for </span><span class="kw-2">&</span>av <span class="kw">in </span>a_vec.<span class="number">0</span>.iter() { |
| a += av; |
| } |
| <span class="kw">for </span><span class="kw-2">&</span>bv <span class="kw">in </span>b_vec.<span class="number">0</span>.iter() { |
| b += bv; |
| } |
| |
| <span class="comment">// iterate over the remaining few bytes in serial |
| </span><span class="kw">for </span><span class="kw-2">&</span>byte <span class="kw">in </span>remainder.iter() { |
| a += u32::from(byte); |
| b += a; |
| } |
| |
| <span class="self">self</span>.a = (a % MOD) <span class="kw">as </span>u16; |
| <span class="self">self</span>.b = (b % MOD) <span class="kw">as </span>u16; |
| } |
| } |
| |
| <span class="attribute">#[derive(Copy, Clone)] |
| </span><span class="kw">struct </span>U32X4([u32; <span class="number">4</span>]); |
| |
| <span class="kw">impl </span>U32X4 { |
| <span class="kw">fn </span>from(bytes: <span class="kw-2">&</span>[u8]) -> <span class="self">Self </span>{ |
| U32X4([ |
| u32::from(bytes[<span class="number">0</span>]), |
| u32::from(bytes[<span class="number">1</span>]), |
| u32::from(bytes[<span class="number">2</span>]), |
| u32::from(bytes[<span class="number">3</span>]), |
| ]) |
| } |
| } |
| |
| <span class="kw">impl </span>AddAssign<<span class="self">Self</span>> <span class="kw">for </span>U32X4 { |
| <span class="kw">fn </span>add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="self">Self</span>) { |
| <span class="kw">for </span>(s, o) <span class="kw">in </span><span class="self">self</span>.<span class="number">0</span>.iter_mut().zip(other.<span class="number">0</span>.iter()) { |
| <span class="kw-2">*</span>s += o; |
| } |
| } |
| } |
| |
| <span class="kw">impl </span>RemAssign<u32> <span class="kw">for </span>U32X4 { |
| <span class="kw">fn </span>rem_assign(<span class="kw-2">&mut </span><span class="self">self</span>, quotient: u32) { |
| <span class="kw">for </span>s <span class="kw">in </span><span class="self">self</span>.<span class="number">0</span>.iter_mut() { |
| <span class="kw-2">*</span>s %= quotient; |
| } |
| } |
| } |
| |
| <span class="kw">impl </span>MulAssign<u32> <span class="kw">for </span>U32X4 { |
| <span class="kw">fn </span>mul_assign(<span class="kw-2">&mut </span><span class="self">self</span>, rhs: u32) { |
| <span class="kw">for </span>s <span class="kw">in </span><span class="self">self</span>.<span class="number">0</span>.iter_mut() { |
| <span class="kw-2">*</span>s <span class="kw-2">*</span>= rhs; |
| } |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="adler" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
