1207 lines
119 KiB
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1207 lines
119 KiB
HTML
<!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 `/home/newkirk/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/num-bigint-0.4.6/src/biguint.rs`."><title>biguint.rs - source</title><script>if(window.location.protocol!=="file:")document.head.insertAdjacentHTML("beforeend","SourceSerif4-Regular-6b053e98.ttf.woff2,FiraSans-Italic-81dc35de.woff2,FiraSans-Regular-0fe48ade.woff2,FiraSans-MediumItalic-ccf7e434.woff2,FiraSans-Medium-e1aa3f0a.woff2,SourceCodePro-Regular-8badfe75.ttf.woff2,SourceCodePro-Semibold-aa29a496.ttf.woff2".split(",").map(f=>`<link rel="preload" as="font" type="font/woff2"href="../../static.files/${f}">`).join(""))</script><link rel="stylesheet" href="../../static.files/normalize-9960930a.css"><link rel="stylesheet" href="../../static.files/rustdoc-ca0dd0c4.css"><meta name="rustdoc-vars" data-root-path="../../" data-static-root-path="../../static.files/" data-current-crate="num_bigint" data-themes="" data-resource-suffix="" data-rustdoc-version="1.93.1 (01f6ddf75 2026-02-11) (Arch Linux rust 1:1.93.1-1)" data-channel="1.93.1" data-search-js="search-9e2438ea.js" data-stringdex-js="stringdex-a3946164.js" data-settings-js="settings-c38705f0.js" ><script src="../../static.files/storage-e2aeef58.js"></script><script defer src="../../static.files/src-script-813739b1.js"></script><script defer src="../../src-files.js"></script><script defer src="../../static.files/main-a410ff4d.js"></script><noscript><link rel="stylesheet" href="../../static.files/noscript-263c88ec.css"></noscript><link rel="alternate icon" type="image/png" href="../../static.files/favicon-32x32-eab170b8.png"><link rel="icon" type="image/svg+xml" href="../../static.files/favicon-044be391.svg"></head><body class="rustdoc src"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="src-sidebar-title"><h2>Files</h2></div></nav><div class="sidebar-resizer" title="Drag to resize sidebar"></div><main><section id="main-content" class="content"><div class="main-heading"><h1><div class="sub-heading">num_bigint/</div>biguint.rs</h1><rustdoc-toolbar></rustdoc-toolbar></div><div class="example-wrap digits-4"><pre class="rust"><code><a href=#1 id=1 data-nosnippet>1</a><span class="kw">use </span><span class="kw">crate</span>::big_digit::{<span class="self">self</span>, BigDigit};
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<a href=#2 id=2 data-nosnippet>2</a>
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<a href=#3 id=3 data-nosnippet>3</a><span class="kw">use </span>alloc::string::String;
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<a href=#4 id=4 data-nosnippet>4</a><span class="kw">use </span>alloc::vec::Vec;
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<a href=#5 id=5 data-nosnippet>5</a><span class="kw">use </span>core::cmp;
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<a href=#6 id=6 data-nosnippet>6</a><span class="kw">use </span>core::cmp::Ordering;
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<a href=#7 id=7 data-nosnippet>7</a><span class="kw">use </span>core::default::Default;
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<a href=#8 id=8 data-nosnippet>8</a><span class="kw">use </span>core::fmt;
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<a href=#9 id=9 data-nosnippet>9</a><span class="kw">use </span>core::hash;
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<a href=#10 id=10 data-nosnippet>10</a><span class="kw">use </span>core::mem;
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<a href=#11 id=11 data-nosnippet>11</a><span class="kw">use </span>core::str;
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<a href=#12 id=12 data-nosnippet>12</a>
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<a href=#13 id=13 data-nosnippet>13</a><span class="kw">use </span>num_integer::{Integer, Roots};
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<a href=#14 id=14 data-nosnippet>14</a><span class="kw">use </span>num_traits::{ConstZero, Num, One, Pow, ToPrimitive, Unsigned, Zero};
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<a href=#15 id=15 data-nosnippet>15</a>
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<a href=#16 id=16 data-nosnippet>16</a><span class="kw">mod </span>addition;
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<a href=#17 id=17 data-nosnippet>17</a><span class="kw">mod </span>division;
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<a href=#18 id=18 data-nosnippet>18</a><span class="kw">mod </span>multiplication;
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<a href=#19 id=19 data-nosnippet>19</a><span class="kw">mod </span>subtraction;
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<a href=#20 id=20 data-nosnippet>20</a>
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<a href=#21 id=21 data-nosnippet>21</a><span class="kw">mod </span>arbitrary;
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<a href=#22 id=22 data-nosnippet>22</a><span class="kw">mod </span>bits;
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<a href=#23 id=23 data-nosnippet>23</a><span class="kw">mod </span>convert;
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<a href=#24 id=24 data-nosnippet>24</a><span class="kw">mod </span>iter;
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<a href=#25 id=25 data-nosnippet>25</a><span class="kw">mod </span>monty;
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<a href=#26 id=26 data-nosnippet>26</a><span class="kw">mod </span>power;
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<a href=#27 id=27 data-nosnippet>27</a><span class="kw">mod </span>serde;
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<a href=#28 id=28 data-nosnippet>28</a><span class="kw">mod </span>shift;
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<a href=#29 id=29 data-nosnippet>29</a>
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<a href=#30 id=30 data-nosnippet>30</a><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">use </span><span class="self">self</span>::convert::to_str_radix_reversed;
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<a href=#31 id=31 data-nosnippet>31</a><span class="kw">pub use </span><span class="self">self</span>::iter::{U32Digits, U64Digits};
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<a href=#32 id=32 data-nosnippet>32</a>
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<a href=#33 id=33 data-nosnippet>33</a><span class="doccomment">/// A big unsigned integer type.
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<a href=#34 id=34 data-nosnippet>34</a></span><span class="kw">pub struct </span>BigUint {
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<a href=#35 id=35 data-nosnippet>35</a> data: Vec<BigDigit>,
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<a href=#36 id=36 data-nosnippet>36</a>}
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<a href=#37 id=37 data-nosnippet>37</a>
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<a href=#38 id=38 data-nosnippet>38</a><span class="comment">// Note: derived `Clone` doesn't specialize `clone_from`,
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<a href=#39 id=39 data-nosnippet>39</a>// but we want to keep the allocation in `data`.
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<a href=#40 id=40 data-nosnippet>40</a></span><span class="kw">impl </span>Clone <span class="kw">for </span>BigUint {
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<a href=#41 id=41 data-nosnippet>41</a> <span class="attr">#[inline]
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<a href=#42 id=42 data-nosnippet>42</a> </span><span class="kw">fn </span>clone(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
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<a href=#43 id=43 data-nosnippet>43</a> BigUint {
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<a href=#44 id=44 data-nosnippet>44</a> data: <span class="self">self</span>.data.clone(),
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<a href=#45 id=45 data-nosnippet>45</a> }
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<a href=#46 id=46 data-nosnippet>46</a> }
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<a href=#47 id=47 data-nosnippet>47</a>
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<a href=#48 id=48 data-nosnippet>48</a> <span class="attr">#[inline]
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<a href=#49 id=49 data-nosnippet>49</a> </span><span class="kw">fn </span>clone_from(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) {
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<a href=#50 id=50 data-nosnippet>50</a> <span class="self">self</span>.data.clone_from(<span class="kw-2">&</span>other.data);
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<a href=#51 id=51 data-nosnippet>51</a> }
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<a href=#52 id=52 data-nosnippet>52</a>}
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<a href=#53 id=53 data-nosnippet>53</a>
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<a href=#54 id=54 data-nosnippet>54</a><span class="kw">impl </span>hash::Hash <span class="kw">for </span>BigUint {
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<a href=#55 id=55 data-nosnippet>55</a> <span class="attr">#[inline]
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<a href=#56 id=56 data-nosnippet>56</a> </span><span class="kw">fn </span>hash<H: hash::Hasher>(<span class="kw-2">&</span><span class="self">self</span>, state: <span class="kw-2">&mut </span>H) {
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<a href=#57 id=57 data-nosnippet>57</a> <span class="macro">debug_assert!</span>(<span class="self">self</span>.data.last() != <span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>));
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<a href=#58 id=58 data-nosnippet>58</a> <span class="self">self</span>.data.hash(state);
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<a href=#59 id=59 data-nosnippet>59</a> }
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<a href=#60 id=60 data-nosnippet>60</a>}
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<a href=#61 id=61 data-nosnippet>61</a>
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<a href=#62 id=62 data-nosnippet>62</a><span class="kw">impl </span>PartialEq <span class="kw">for </span>BigUint {
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<a href=#63 id=63 data-nosnippet>63</a> <span class="attr">#[inline]
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<a href=#64 id=64 data-nosnippet>64</a> </span><span class="kw">fn </span>eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> bool {
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<a href=#65 id=65 data-nosnippet>65</a> <span class="macro">debug_assert!</span>(<span class="self">self</span>.data.last() != <span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>));
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<a href=#66 id=66 data-nosnippet>66</a> <span class="macro">debug_assert!</span>(other.data.last() != <span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>));
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<a href=#67 id=67 data-nosnippet>67</a> <span class="self">self</span>.data == other.data
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<a href=#68 id=68 data-nosnippet>68</a> }
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<a href=#69 id=69 data-nosnippet>69</a>}
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<a href=#70 id=70 data-nosnippet>70</a><span class="kw">impl </span>Eq <span class="kw">for </span>BigUint {}
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<a href=#71 id=71 data-nosnippet>71</a>
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<a href=#72 id=72 data-nosnippet>72</a><span class="kw">impl </span>PartialOrd <span class="kw">for </span>BigUint {
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<a href=#73 id=73 data-nosnippet>73</a> <span class="attr">#[inline]
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<a href=#74 id=74 data-nosnippet>74</a> </span><span class="kw">fn </span>partial_cmp(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> <span class="prelude-ty">Option</span><Ordering> {
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<a href=#75 id=75 data-nosnippet>75</a> <span class="prelude-val">Some</span>(<span class="self">self</span>.cmp(other))
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<a href=#76 id=76 data-nosnippet>76</a> }
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<a href=#77 id=77 data-nosnippet>77</a>}
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<a href=#78 id=78 data-nosnippet>78</a>
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<a href=#79 id=79 data-nosnippet>79</a><span class="kw">impl </span>Ord <span class="kw">for </span>BigUint {
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<a href=#80 id=80 data-nosnippet>80</a> <span class="attr">#[inline]
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<a href=#81 id=81 data-nosnippet>81</a> </span><span class="kw">fn </span>cmp(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> Ordering {
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<a href=#82 id=82 data-nosnippet>82</a> cmp_slice(<span class="kw-2">&</span><span class="self">self</span>.data[..], <span class="kw-2">&</span>other.data[..])
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<a href=#83 id=83 data-nosnippet>83</a> }
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<a href=#84 id=84 data-nosnippet>84</a>}
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<a href=#85 id=85 data-nosnippet>85</a>
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<a href=#86 id=86 data-nosnippet>86</a><span class="attr">#[inline]
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<a href=#87 id=87 data-nosnippet>87</a></span><span class="kw">fn </span>cmp_slice(a: <span class="kw-2">&</span>[BigDigit], b: <span class="kw-2">&</span>[BigDigit]) -> Ordering {
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<a href=#88 id=88 data-nosnippet>88</a> <span class="macro">debug_assert!</span>(a.last() != <span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>));
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<a href=#89 id=89 data-nosnippet>89</a> <span class="macro">debug_assert!</span>(b.last() != <span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>));
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<a href=#90 id=90 data-nosnippet>90</a>
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<a href=#91 id=91 data-nosnippet>91</a> <span class="kw">match </span>Ord::cmp(<span class="kw-2">&</span>a.len(), <span class="kw-2">&</span>b.len()) {
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<a href=#92 id=92 data-nosnippet>92</a> Ordering::Equal => Iterator::cmp(a.iter().rev(), b.iter().rev()),
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<a href=#93 id=93 data-nosnippet>93</a> other => other,
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<a href=#94 id=94 data-nosnippet>94</a> }
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<a href=#95 id=95 data-nosnippet>95</a>}
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<a href=#96 id=96 data-nosnippet>96</a>
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<a href=#97 id=97 data-nosnippet>97</a><span class="kw">impl </span>Default <span class="kw">for </span>BigUint {
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<a href=#98 id=98 data-nosnippet>98</a> <span class="attr">#[inline]
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<a href=#99 id=99 data-nosnippet>99</a> </span><span class="kw">fn </span>default() -> BigUint {
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<a href=#100 id=100 data-nosnippet>100</a> <span class="self">Self</span>::ZERO
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<a href=#101 id=101 data-nosnippet>101</a> }
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<a href=#102 id=102 data-nosnippet>102</a>}
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<a href=#103 id=103 data-nosnippet>103</a>
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<a href=#104 id=104 data-nosnippet>104</a><span class="kw">impl </span>fmt::Debug <span class="kw">for </span>BigUint {
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<a href=#105 id=105 data-nosnippet>105</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#106 id=106 data-nosnippet>106</a> fmt::Display::fmt(<span class="self">self</span>, f)
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<a href=#107 id=107 data-nosnippet>107</a> }
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<a href=#108 id=108 data-nosnippet>108</a>}
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<a href=#109 id=109 data-nosnippet>109</a>
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<a href=#110 id=110 data-nosnippet>110</a><span class="kw">impl </span>fmt::Display <span class="kw">for </span>BigUint {
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<a href=#111 id=111 data-nosnippet>111</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#112 id=112 data-nosnippet>112</a> f.pad_integral(<span class="bool-val">true</span>, <span class="string">""</span>, <span class="kw-2">&</span><span class="self">self</span>.to_str_radix(<span class="number">10</span>))
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<a href=#113 id=113 data-nosnippet>113</a> }
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<a href=#114 id=114 data-nosnippet>114</a>}
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<a href=#115 id=115 data-nosnippet>115</a>
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<a href=#116 id=116 data-nosnippet>116</a><span class="kw">impl </span>fmt::LowerHex <span class="kw">for </span>BigUint {
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<a href=#117 id=117 data-nosnippet>117</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#118 id=118 data-nosnippet>118</a> f.pad_integral(<span class="bool-val">true</span>, <span class="string">"0x"</span>, <span class="kw-2">&</span><span class="self">self</span>.to_str_radix(<span class="number">16</span>))
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<a href=#119 id=119 data-nosnippet>119</a> }
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<a href=#120 id=120 data-nosnippet>120</a>}
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<a href=#121 id=121 data-nosnippet>121</a>
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<a href=#122 id=122 data-nosnippet>122</a><span class="kw">impl </span>fmt::UpperHex <span class="kw">for </span>BigUint {
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<a href=#123 id=123 data-nosnippet>123</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#124 id=124 data-nosnippet>124</a> <span class="kw">let </span><span class="kw-2">mut </span>s = <span class="self">self</span>.to_str_radix(<span class="number">16</span>);
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<a href=#125 id=125 data-nosnippet>125</a> s.make_ascii_uppercase();
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<a href=#126 id=126 data-nosnippet>126</a> f.pad_integral(<span class="bool-val">true</span>, <span class="string">"0x"</span>, <span class="kw-2">&</span>s)
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<a href=#127 id=127 data-nosnippet>127</a> }
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<a href=#128 id=128 data-nosnippet>128</a>}
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<a href=#129 id=129 data-nosnippet>129</a>
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<a href=#130 id=130 data-nosnippet>130</a><span class="kw">impl </span>fmt::Binary <span class="kw">for </span>BigUint {
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<a href=#131 id=131 data-nosnippet>131</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#132 id=132 data-nosnippet>132</a> f.pad_integral(<span class="bool-val">true</span>, <span class="string">"0b"</span>, <span class="kw-2">&</span><span class="self">self</span>.to_str_radix(<span class="number">2</span>))
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<a href=#133 id=133 data-nosnippet>133</a> }
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<a href=#134 id=134 data-nosnippet>134</a>}
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<a href=#135 id=135 data-nosnippet>135</a>
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<a href=#136 id=136 data-nosnippet>136</a><span class="kw">impl </span>fmt::Octal <span class="kw">for </span>BigUint {
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<a href=#137 id=137 data-nosnippet>137</a> <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
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<a href=#138 id=138 data-nosnippet>138</a> f.pad_integral(<span class="bool-val">true</span>, <span class="string">"0o"</span>, <span class="kw-2">&</span><span class="self">self</span>.to_str_radix(<span class="number">8</span>))
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<a href=#139 id=139 data-nosnippet>139</a> }
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<a href=#140 id=140 data-nosnippet>140</a>}
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<a href=#141 id=141 data-nosnippet>141</a>
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<a href=#142 id=142 data-nosnippet>142</a><span class="kw">impl </span>Zero <span class="kw">for </span>BigUint {
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<a href=#143 id=143 data-nosnippet>143</a> <span class="attr">#[inline]
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<a href=#144 id=144 data-nosnippet>144</a> </span><span class="kw">fn </span>zero() -> BigUint {
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<a href=#145 id=145 data-nosnippet>145</a> <span class="self">Self</span>::ZERO
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<a href=#146 id=146 data-nosnippet>146</a> }
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<a href=#147 id=147 data-nosnippet>147</a>
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<a href=#148 id=148 data-nosnippet>148</a> <span class="attr">#[inline]
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<a href=#149 id=149 data-nosnippet>149</a> </span><span class="kw">fn </span>set_zero(<span class="kw-2">&mut </span><span class="self">self</span>) {
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<a href=#150 id=150 data-nosnippet>150</a> <span class="self">self</span>.data.clear();
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<a href=#151 id=151 data-nosnippet>151</a> }
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<a href=#152 id=152 data-nosnippet>152</a>
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<a href=#153 id=153 data-nosnippet>153</a> <span class="attr">#[inline]
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<a href=#154 id=154 data-nosnippet>154</a> </span><span class="kw">fn </span>is_zero(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
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<a href=#155 id=155 data-nosnippet>155</a> <span class="self">self</span>.data.is_empty()
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<a href=#156 id=156 data-nosnippet>156</a> }
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<a href=#157 id=157 data-nosnippet>157</a>}
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<a href=#158 id=158 data-nosnippet>158</a>
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<a href=#159 id=159 data-nosnippet>159</a><span class="kw">impl </span>ConstZero <span class="kw">for </span>BigUint {
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<a href=#160 id=160 data-nosnippet>160</a> <span class="comment">// forward to the inherent const
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<a href=#161 id=161 data-nosnippet>161</a> </span><span class="kw">const </span>ZERO: <span class="self">Self </span>= <span class="self">Self</span>::ZERO; <span class="comment">// BigUint { data: Vec::new() };
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<a href=#162 id=162 data-nosnippet>162</a></span>}
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<a href=#163 id=163 data-nosnippet>163</a>
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<a href=#164 id=164 data-nosnippet>164</a><span class="kw">impl </span>One <span class="kw">for </span>BigUint {
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<a href=#165 id=165 data-nosnippet>165</a> <span class="attr">#[inline]
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<a href=#166 id=166 data-nosnippet>166</a> </span><span class="kw">fn </span>one() -> BigUint {
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<a href=#167 id=167 data-nosnippet>167</a> BigUint { data: <span class="macro">vec!</span>[<span class="number">1</span>] }
|
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<a href=#168 id=168 data-nosnippet>168</a> }
|
|
<a href=#169 id=169 data-nosnippet>169</a>
|
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<a href=#170 id=170 data-nosnippet>170</a> <span class="attr">#[inline]
|
|
<a href=#171 id=171 data-nosnippet>171</a> </span><span class="kw">fn </span>set_one(<span class="kw-2">&mut </span><span class="self">self</span>) {
|
|
<a href=#172 id=172 data-nosnippet>172</a> <span class="self">self</span>.data.clear();
|
|
<a href=#173 id=173 data-nosnippet>173</a> <span class="self">self</span>.data.push(<span class="number">1</span>);
|
|
<a href=#174 id=174 data-nosnippet>174</a> }
|
|
<a href=#175 id=175 data-nosnippet>175</a>
|
|
<a href=#176 id=176 data-nosnippet>176</a> <span class="attr">#[inline]
|
|
<a href=#177 id=177 data-nosnippet>177</a> </span><span class="kw">fn </span>is_one(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
|
|
<a href=#178 id=178 data-nosnippet>178</a> <span class="self">self</span>.data[..] == [<span class="number">1</span>]
|
|
<a href=#179 id=179 data-nosnippet>179</a> }
|
|
<a href=#180 id=180 data-nosnippet>180</a>}
|
|
<a href=#181 id=181 data-nosnippet>181</a>
|
|
<a href=#182 id=182 data-nosnippet>182</a><span class="kw">impl </span>Unsigned <span class="kw">for </span>BigUint {}
|
|
<a href=#183 id=183 data-nosnippet>183</a>
|
|
<a href=#184 id=184 data-nosnippet>184</a><span class="kw">impl </span>Integer <span class="kw">for </span>BigUint {
|
|
<a href=#185 id=185 data-nosnippet>185</a> <span class="attr">#[inline]
|
|
<a href=#186 id=186 data-nosnippet>186</a> </span><span class="kw">fn </span>div_rem(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> (BigUint, BigUint) {
|
|
<a href=#187 id=187 data-nosnippet>187</a> division::div_rem_ref(<span class="self">self</span>, other)
|
|
<a href=#188 id=188 data-nosnippet>188</a> }
|
|
<a href=#189 id=189 data-nosnippet>189</a>
|
|
<a href=#190 id=190 data-nosnippet>190</a> <span class="attr">#[inline]
|
|
<a href=#191 id=191 data-nosnippet>191</a> </span><span class="kw">fn </span>div_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> BigUint {
|
|
<a href=#192 id=192 data-nosnippet>192</a> <span class="kw">let </span>(d, <span class="kw">_</span>) = division::div_rem_ref(<span class="self">self</span>, other);
|
|
<a href=#193 id=193 data-nosnippet>193</a> d
|
|
<a href=#194 id=194 data-nosnippet>194</a> }
|
|
<a href=#195 id=195 data-nosnippet>195</a>
|
|
<a href=#196 id=196 data-nosnippet>196</a> <span class="attr">#[inline]
|
|
<a href=#197 id=197 data-nosnippet>197</a> </span><span class="kw">fn </span>mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> BigUint {
|
|
<a href=#198 id=198 data-nosnippet>198</a> <span class="kw">let </span>(<span class="kw">_</span>, m) = division::div_rem_ref(<span class="self">self</span>, other);
|
|
<a href=#199 id=199 data-nosnippet>199</a> m
|
|
<a href=#200 id=200 data-nosnippet>200</a> }
|
|
<a href=#201 id=201 data-nosnippet>201</a>
|
|
<a href=#202 id=202 data-nosnippet>202</a> <span class="attr">#[inline]
|
|
<a href=#203 id=203 data-nosnippet>203</a> </span><span class="kw">fn </span>div_mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> (BigUint, BigUint) {
|
|
<a href=#204 id=204 data-nosnippet>204</a> division::div_rem_ref(<span class="self">self</span>, other)
|
|
<a href=#205 id=205 data-nosnippet>205</a> }
|
|
<a href=#206 id=206 data-nosnippet>206</a>
|
|
<a href=#207 id=207 data-nosnippet>207</a> <span class="attr">#[inline]
|
|
<a href=#208 id=208 data-nosnippet>208</a> </span><span class="kw">fn </span>div_ceil(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> BigUint {
|
|
<a href=#209 id=209 data-nosnippet>209</a> <span class="kw">let </span>(d, m) = division::div_rem_ref(<span class="self">self</span>, other);
|
|
<a href=#210 id=210 data-nosnippet>210</a> <span class="kw">if </span>m.is_zero() {
|
|
<a href=#211 id=211 data-nosnippet>211</a> d
|
|
<a href=#212 id=212 data-nosnippet>212</a> } <span class="kw">else </span>{
|
|
<a href=#213 id=213 data-nosnippet>213</a> d + <span class="number">1u32
|
|
<a href=#214 id=214 data-nosnippet>214</a> </span>}
|
|
<a href=#215 id=215 data-nosnippet>215</a> }
|
|
<a href=#216 id=216 data-nosnippet>216</a>
|
|
<a href=#217 id=217 data-nosnippet>217</a> <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`.
|
|
<a href=#218 id=218 data-nosnippet>218</a> ///
|
|
<a href=#219 id=219 data-nosnippet>219</a> /// The result is always positive.
|
|
<a href=#220 id=220 data-nosnippet>220</a> </span><span class="attr">#[inline]
|
|
<a href=#221 id=221 data-nosnippet>221</a> </span><span class="kw">fn </span>gcd(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
|
|
<a href=#222 id=222 data-nosnippet>222</a> <span class="attr">#[inline]
|
|
<a href=#223 id=223 data-nosnippet>223</a> </span><span class="kw">fn </span>twos(x: <span class="kw-2">&</span>BigUint) -> u64 {
|
|
<a href=#224 id=224 data-nosnippet>224</a> x.trailing_zeros().unwrap_or(<span class="number">0</span>)
|
|
<a href=#225 id=225 data-nosnippet>225</a> }
|
|
<a href=#226 id=226 data-nosnippet>226</a>
|
|
<a href=#227 id=227 data-nosnippet>227</a> <span class="comment">// Stein's algorithm
|
|
<a href=#228 id=228 data-nosnippet>228</a> </span><span class="kw">if </span><span class="self">self</span>.is_zero() {
|
|
<a href=#229 id=229 data-nosnippet>229</a> <span class="kw">return </span>other.clone();
|
|
<a href=#230 id=230 data-nosnippet>230</a> }
|
|
<a href=#231 id=231 data-nosnippet>231</a> <span class="kw">if </span>other.is_zero() {
|
|
<a href=#232 id=232 data-nosnippet>232</a> <span class="kw">return </span><span class="self">self</span>.clone();
|
|
<a href=#233 id=233 data-nosnippet>233</a> }
|
|
<a href=#234 id=234 data-nosnippet>234</a> <span class="kw">let </span><span class="kw-2">mut </span>m = <span class="self">self</span>.clone();
|
|
<a href=#235 id=235 data-nosnippet>235</a> <span class="kw">let </span><span class="kw-2">mut </span>n = other.clone();
|
|
<a href=#236 id=236 data-nosnippet>236</a>
|
|
<a href=#237 id=237 data-nosnippet>237</a> <span class="comment">// find common factors of 2
|
|
<a href=#238 id=238 data-nosnippet>238</a> </span><span class="kw">let </span>shift = cmp::min(twos(<span class="kw-2">&</span>n), twos(<span class="kw-2">&</span>m));
|
|
<a href=#239 id=239 data-nosnippet>239</a>
|
|
<a href=#240 id=240 data-nosnippet>240</a> <span class="comment">// divide m and n by 2 until odd
|
|
<a href=#241 id=241 data-nosnippet>241</a> // m inside loop
|
|
<a href=#242 id=242 data-nosnippet>242</a> </span>n >>= twos(<span class="kw-2">&</span>n);
|
|
<a href=#243 id=243 data-nosnippet>243</a>
|
|
<a href=#244 id=244 data-nosnippet>244</a> <span class="kw">while </span>!m.is_zero() {
|
|
<a href=#245 id=245 data-nosnippet>245</a> m >>= twos(<span class="kw-2">&</span>m);
|
|
<a href=#246 id=246 data-nosnippet>246</a> <span class="kw">if </span>n > m {
|
|
<a href=#247 id=247 data-nosnippet>247</a> mem::swap(<span class="kw-2">&mut </span>n, <span class="kw-2">&mut </span>m)
|
|
<a href=#248 id=248 data-nosnippet>248</a> }
|
|
<a href=#249 id=249 data-nosnippet>249</a> m -= <span class="kw-2">&</span>n;
|
|
<a href=#250 id=250 data-nosnippet>250</a> }
|
|
<a href=#251 id=251 data-nosnippet>251</a>
|
|
<a href=#252 id=252 data-nosnippet>252</a> n << shift
|
|
<a href=#253 id=253 data-nosnippet>253</a> }
|
|
<a href=#254 id=254 data-nosnippet>254</a>
|
|
<a href=#255 id=255 data-nosnippet>255</a> <span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
|
|
<a href=#256 id=256 data-nosnippet>256</a> </span><span class="attr">#[inline]
|
|
<a href=#257 id=257 data-nosnippet>257</a> </span><span class="kw">fn </span>lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> BigUint {
|
|
<a href=#258 id=258 data-nosnippet>258</a> <span class="kw">if </span><span class="self">self</span>.is_zero() && other.is_zero() {
|
|
<a href=#259 id=259 data-nosnippet>259</a> <span class="self">Self</span>::ZERO
|
|
<a href=#260 id=260 data-nosnippet>260</a> } <span class="kw">else </span>{
|
|
<a href=#261 id=261 data-nosnippet>261</a> <span class="self">self </span>/ <span class="self">self</span>.gcd(other) * other
|
|
<a href=#262 id=262 data-nosnippet>262</a> }
|
|
<a href=#263 id=263 data-nosnippet>263</a> }
|
|
<a href=#264 id=264 data-nosnippet>264</a>
|
|
<a href=#265 id=265 data-nosnippet>265</a> <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
|
|
<a href=#266 id=266 data-nosnippet>266</a> /// Lowest Common Multiple (LCM) together.
|
|
<a href=#267 id=267 data-nosnippet>267</a> </span><span class="attr">#[inline]
|
|
<a href=#268 id=268 data-nosnippet>268</a> </span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
|
|
<a href=#269 id=269 data-nosnippet>269</a> <span class="kw">let </span>gcd = <span class="self">self</span>.gcd(other);
|
|
<a href=#270 id=270 data-nosnippet>270</a> <span class="kw">let </span>lcm = <span class="kw">if </span>gcd.is_zero() {
|
|
<a href=#271 id=271 data-nosnippet>271</a> <span class="self">Self</span>::ZERO
|
|
<a href=#272 id=272 data-nosnippet>272</a> } <span class="kw">else </span>{
|
|
<a href=#273 id=273 data-nosnippet>273</a> <span class="self">self </span>/ <span class="kw-2">&</span>gcd * other
|
|
<a href=#274 id=274 data-nosnippet>274</a> };
|
|
<a href=#275 id=275 data-nosnippet>275</a> (gcd, lcm)
|
|
<a href=#276 id=276 data-nosnippet>276</a> }
|
|
<a href=#277 id=277 data-nosnippet>277</a>
|
|
<a href=#278 id=278 data-nosnippet>278</a> <span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
|
|
<a href=#279 id=279 data-nosnippet>279</a> </span><span class="attr">#[inline]
|
|
<a href=#280 id=280 data-nosnippet>280</a> </span><span class="kw">fn </span>divides(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> bool {
|
|
<a href=#281 id=281 data-nosnippet>281</a> <span class="self">self</span>.is_multiple_of(other)
|
|
<a href=#282 id=282 data-nosnippet>282</a> }
|
|
<a href=#283 id=283 data-nosnippet>283</a>
|
|
<a href=#284 id=284 data-nosnippet>284</a> <span class="doccomment">/// Returns `true` if the number is a multiple of `other`.
|
|
<a href=#285 id=285 data-nosnippet>285</a> </span><span class="attr">#[inline]
|
|
<a href=#286 id=286 data-nosnippet>286</a> </span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>BigUint) -> bool {
|
|
<a href=#287 id=287 data-nosnippet>287</a> <span class="kw">if </span>other.is_zero() {
|
|
<a href=#288 id=288 data-nosnippet>288</a> <span class="kw">return </span><span class="self">self</span>.is_zero();
|
|
<a href=#289 id=289 data-nosnippet>289</a> }
|
|
<a href=#290 id=290 data-nosnippet>290</a> (<span class="self">self </span>% other).is_zero()
|
|
<a href=#291 id=291 data-nosnippet>291</a> }
|
|
<a href=#292 id=292 data-nosnippet>292</a>
|
|
<a href=#293 id=293 data-nosnippet>293</a> <span class="doccomment">/// Returns `true` if the number is divisible by `2`.
|
|
<a href=#294 id=294 data-nosnippet>294</a> </span><span class="attr">#[inline]
|
|
<a href=#295 id=295 data-nosnippet>295</a> </span><span class="kw">fn </span>is_even(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
|
|
<a href=#296 id=296 data-nosnippet>296</a> <span class="comment">// Considering only the last digit.
|
|
<a href=#297 id=297 data-nosnippet>297</a> </span><span class="kw">match </span><span class="self">self</span>.data.first() {
|
|
<a href=#298 id=298 data-nosnippet>298</a> <span class="prelude-val">Some</span>(x) => x.is_even(),
|
|
<a href=#299 id=299 data-nosnippet>299</a> <span class="prelude-val">None </span>=> <span class="bool-val">true</span>,
|
|
<a href=#300 id=300 data-nosnippet>300</a> }
|
|
<a href=#301 id=301 data-nosnippet>301</a> }
|
|
<a href=#302 id=302 data-nosnippet>302</a>
|
|
<a href=#303 id=303 data-nosnippet>303</a> <span class="doccomment">/// Returns `true` if the number is not divisible by `2`.
|
|
<a href=#304 id=304 data-nosnippet>304</a> </span><span class="attr">#[inline]
|
|
<a href=#305 id=305 data-nosnippet>305</a> </span><span class="kw">fn </span>is_odd(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
|
|
<a href=#306 id=306 data-nosnippet>306</a> !<span class="self">self</span>.is_even()
|
|
<a href=#307 id=307 data-nosnippet>307</a> }
|
|
<a href=#308 id=308 data-nosnippet>308</a>
|
|
<a href=#309 id=309 data-nosnippet>309</a> <span class="doccomment">/// Rounds up to nearest multiple of argument.
|
|
<a href=#310 id=310 data-nosnippet>310</a> </span><span class="attr">#[inline]
|
|
<a href=#311 id=311 data-nosnippet>311</a> </span><span class="kw">fn </span>next_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
|
|
<a href=#312 id=312 data-nosnippet>312</a> <span class="kw">let </span>m = <span class="self">self</span>.mod_floor(other);
|
|
<a href=#313 id=313 data-nosnippet>313</a> <span class="kw">if </span>m.is_zero() {
|
|
<a href=#314 id=314 data-nosnippet>314</a> <span class="self">self</span>.clone()
|
|
<a href=#315 id=315 data-nosnippet>315</a> } <span class="kw">else </span>{
|
|
<a href=#316 id=316 data-nosnippet>316</a> <span class="self">self </span>+ (other - m)
|
|
<a href=#317 id=317 data-nosnippet>317</a> }
|
|
<a href=#318 id=318 data-nosnippet>318</a> }
|
|
<a href=#319 id=319 data-nosnippet>319</a> <span class="doccomment">/// Rounds down to nearest multiple of argument.
|
|
<a href=#320 id=320 data-nosnippet>320</a> </span><span class="attr">#[inline]
|
|
<a href=#321 id=321 data-nosnippet>321</a> </span><span class="kw">fn </span>prev_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
|
|
<a href=#322 id=322 data-nosnippet>322</a> <span class="self">self </span>- <span class="self">self</span>.mod_floor(other)
|
|
<a href=#323 id=323 data-nosnippet>323</a> }
|
|
<a href=#324 id=324 data-nosnippet>324</a>
|
|
<a href=#325 id=325 data-nosnippet>325</a> <span class="kw">fn </span>dec(<span class="kw-2">&mut </span><span class="self">self</span>) {
|
|
<a href=#326 id=326 data-nosnippet>326</a> <span class="kw-2">*</span><span class="self">self </span>-= <span class="number">1u32</span>;
|
|
<a href=#327 id=327 data-nosnippet>327</a> }
|
|
<a href=#328 id=328 data-nosnippet>328</a>
|
|
<a href=#329 id=329 data-nosnippet>329</a> <span class="kw">fn </span>inc(<span class="kw-2">&mut </span><span class="self">self</span>) {
|
|
<a href=#330 id=330 data-nosnippet>330</a> <span class="kw-2">*</span><span class="self">self </span>+= <span class="number">1u32</span>;
|
|
<a href=#331 id=331 data-nosnippet>331</a> }
|
|
<a href=#332 id=332 data-nosnippet>332</a>}
|
|
<a href=#333 id=333 data-nosnippet>333</a>
|
|
<a href=#334 id=334 data-nosnippet>334</a><span class="attr">#[inline]
|
|
<a href=#335 id=335 data-nosnippet>335</a></span><span class="kw">fn </span>fixpoint<F>(<span class="kw-2">mut </span>x: BigUint, max_bits: u64, f: F) -> BigUint
|
|
<a href=#336 id=336 data-nosnippet>336</a><span class="kw">where
|
|
<a href=#337 id=337 data-nosnippet>337</a> </span>F: Fn(<span class="kw-2">&</span>BigUint) -> BigUint,
|
|
<a href=#338 id=338 data-nosnippet>338</a>{
|
|
<a href=#339 id=339 data-nosnippet>339</a> <span class="kw">let </span><span class="kw-2">mut </span>xn = f(<span class="kw-2">&</span>x);
|
|
<a href=#340 id=340 data-nosnippet>340</a>
|
|
<a href=#341 id=341 data-nosnippet>341</a> <span class="comment">// If the value increased, then the initial guess must have been low.
|
|
<a href=#342 id=342 data-nosnippet>342</a> // Repeat until we reverse course.
|
|
<a href=#343 id=343 data-nosnippet>343</a> </span><span class="kw">while </span>x < xn {
|
|
<a href=#344 id=344 data-nosnippet>344</a> <span class="comment">// Sometimes an increase will go way too far, especially with large
|
|
<a href=#345 id=345 data-nosnippet>345</a> // powers, and then take a long time to walk back. We know an upper
|
|
<a href=#346 id=346 data-nosnippet>346</a> // bound based on bit size, so saturate on that.
|
|
<a href=#347 id=347 data-nosnippet>347</a> </span>x = <span class="kw">if </span>xn.bits() > max_bits {
|
|
<a href=#348 id=348 data-nosnippet>348</a> BigUint::one() << max_bits
|
|
<a href=#349 id=349 data-nosnippet>349</a> } <span class="kw">else </span>{
|
|
<a href=#350 id=350 data-nosnippet>350</a> xn
|
|
<a href=#351 id=351 data-nosnippet>351</a> };
|
|
<a href=#352 id=352 data-nosnippet>352</a> xn = f(<span class="kw-2">&</span>x);
|
|
<a href=#353 id=353 data-nosnippet>353</a> }
|
|
<a href=#354 id=354 data-nosnippet>354</a>
|
|
<a href=#355 id=355 data-nosnippet>355</a> <span class="comment">// Now keep repeating while the estimate is decreasing.
|
|
<a href=#356 id=356 data-nosnippet>356</a> </span><span class="kw">while </span>x > xn {
|
|
<a href=#357 id=357 data-nosnippet>357</a> x = xn;
|
|
<a href=#358 id=358 data-nosnippet>358</a> xn = f(<span class="kw-2">&</span>x);
|
|
<a href=#359 id=359 data-nosnippet>359</a> }
|
|
<a href=#360 id=360 data-nosnippet>360</a> x
|
|
<a href=#361 id=361 data-nosnippet>361</a>}
|
|
<a href=#362 id=362 data-nosnippet>362</a>
|
|
<a href=#363 id=363 data-nosnippet>363</a><span class="kw">impl </span>Roots <span class="kw">for </span>BigUint {
|
|
<a href=#364 id=364 data-nosnippet>364</a> <span class="comment">// nth_root, sqrt and cbrt use Newton's method to compute
|
|
<a href=#365 id=365 data-nosnippet>365</a> // principal root of a given degree for a given integer.
|
|
<a href=#366 id=366 data-nosnippet>366</a>
|
|
<a href=#367 id=367 data-nosnippet>367</a> // Reference:
|
|
<a href=#368 id=368 data-nosnippet>368</a> // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.14
|
|
<a href=#369 id=369 data-nosnippet>369</a> </span><span class="kw">fn </span>nth_root(<span class="kw-2">&</span><span class="self">self</span>, n: u32) -> <span class="self">Self </span>{
|
|
<a href=#370 id=370 data-nosnippet>370</a> <span class="macro">assert!</span>(n > <span class="number">0</span>, <span class="string">"root degree n must be at least 1"</span>);
|
|
<a href=#371 id=371 data-nosnippet>371</a>
|
|
<a href=#372 id=372 data-nosnippet>372</a> <span class="kw">if </span><span class="self">self</span>.is_zero() || <span class="self">self</span>.is_one() {
|
|
<a href=#373 id=373 data-nosnippet>373</a> <span class="kw">return </span><span class="self">self</span>.clone();
|
|
<a href=#374 id=374 data-nosnippet>374</a> }
|
|
<a href=#375 id=375 data-nosnippet>375</a>
|
|
<a href=#376 id=376 data-nosnippet>376</a> <span class="kw">match </span>n {
|
|
<a href=#377 id=377 data-nosnippet>377</a> <span class="comment">// Optimize for small n
|
|
<a href=#378 id=378 data-nosnippet>378</a> </span><span class="number">1 </span>=> <span class="kw">return </span><span class="self">self</span>.clone(),
|
|
<a href=#379 id=379 data-nosnippet>379</a> <span class="number">2 </span>=> <span class="kw">return </span><span class="self">self</span>.sqrt(),
|
|
<a href=#380 id=380 data-nosnippet>380</a> <span class="number">3 </span>=> <span class="kw">return </span><span class="self">self</span>.cbrt(),
|
|
<a href=#381 id=381 data-nosnippet>381</a> <span class="kw">_ </span>=> (),
|
|
<a href=#382 id=382 data-nosnippet>382</a> }
|
|
<a href=#383 id=383 data-nosnippet>383</a>
|
|
<a href=#384 id=384 data-nosnippet>384</a> <span class="comment">// The root of non-zero values less than 2ⁿ can only be 1.
|
|
<a href=#385 id=385 data-nosnippet>385</a> </span><span class="kw">let </span>bits = <span class="self">self</span>.bits();
|
|
<a href=#386 id=386 data-nosnippet>386</a> <span class="kw">let </span>n64 = u64::from(n);
|
|
<a href=#387 id=387 data-nosnippet>387</a> <span class="kw">if </span>bits <= n64 {
|
|
<a href=#388 id=388 data-nosnippet>388</a> <span class="kw">return </span>BigUint::one();
|
|
<a href=#389 id=389 data-nosnippet>389</a> }
|
|
<a href=#390 id=390 data-nosnippet>390</a>
|
|
<a href=#391 id=391 data-nosnippet>391</a> <span class="comment">// If we fit in `u64`, compute the root that way.
|
|
<a href=#392 id=392 data-nosnippet>392</a> </span><span class="kw">if let </span><span class="prelude-val">Some</span>(x) = <span class="self">self</span>.to_u64() {
|
|
<a href=#393 id=393 data-nosnippet>393</a> <span class="kw">return </span>x.nth_root(n).into();
|
|
<a href=#394 id=394 data-nosnippet>394</a> }
|
|
<a href=#395 id=395 data-nosnippet>395</a>
|
|
<a href=#396 id=396 data-nosnippet>396</a> <span class="kw">let </span>max_bits = bits / n64 + <span class="number">1</span>;
|
|
<a href=#397 id=397 data-nosnippet>397</a>
|
|
<a href=#398 id=398 data-nosnippet>398</a> <span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
|
|
<a href=#399 id=399 data-nosnippet>399</a> </span><span class="kw">let </span>guess = <span class="kw">match </span><span class="self">self</span>.to_f64() {
|
|
<a href=#400 id=400 data-nosnippet>400</a> <span class="prelude-val">Some</span>(f) <span class="kw">if </span>f.is_finite() => {
|
|
<a href=#401 id=401 data-nosnippet>401</a> <span class="kw">use </span>num_traits::FromPrimitive;
|
|
<a href=#402 id=402 data-nosnippet>402</a>
|
|
<a href=#403 id=403 data-nosnippet>403</a> <span class="comment">// We fit in `f64` (lossy), so get a better initial guess from that.
|
|
<a href=#404 id=404 data-nosnippet>404</a> </span>BigUint::from_f64((f.ln() / f64::from(n)).exp()).unwrap()
|
|
<a href=#405 id=405 data-nosnippet>405</a> }
|
|
<a href=#406 id=406 data-nosnippet>406</a> <span class="kw">_ </span>=> {
|
|
<a href=#407 id=407 data-nosnippet>407</a> <span class="comment">// Try to guess by scaling down such that it does fit in `f64`.
|
|
<a href=#408 id=408 data-nosnippet>408</a> // With some (x * 2ⁿᵏ), its nth root ≈ (ⁿ√x * 2ᵏ)
|
|
<a href=#409 id=409 data-nosnippet>409</a> </span><span class="kw">let </span>extra_bits = bits - (f64::MAX_EXP <span class="kw">as </span>u64 - <span class="number">1</span>);
|
|
<a href=#410 id=410 data-nosnippet>410</a> <span class="kw">let </span>root_scale = Integer::div_ceil(<span class="kw-2">&</span>extra_bits, <span class="kw-2">&</span>n64);
|
|
<a href=#411 id=411 data-nosnippet>411</a> <span class="kw">let </span>scale = root_scale * n64;
|
|
<a href=#412 id=412 data-nosnippet>412</a> <span class="kw">if </span>scale < bits && bits - scale > n64 {
|
|
<a href=#413 id=413 data-nosnippet>413</a> (<span class="self">self </span>>> scale).nth_root(n) << root_scale
|
|
<a href=#414 id=414 data-nosnippet>414</a> } <span class="kw">else </span>{
|
|
<a href=#415 id=415 data-nosnippet>415</a> BigUint::one() << max_bits
|
|
<a href=#416 id=416 data-nosnippet>416</a> }
|
|
<a href=#417 id=417 data-nosnippet>417</a> }
|
|
<a href=#418 id=418 data-nosnippet>418</a> };
|
|
<a href=#419 id=419 data-nosnippet>419</a>
|
|
<a href=#420 id=420 data-nosnippet>420</a> <span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
|
|
<a href=#421 id=421 data-nosnippet>421</a> </span><span class="kw">let </span>guess = BigUint::one() << max_bits;
|
|
<a href=#422 id=422 data-nosnippet>422</a>
|
|
<a href=#423 id=423 data-nosnippet>423</a> <span class="kw">let </span>n_min_1 = n - <span class="number">1</span>;
|
|
<a href=#424 id=424 data-nosnippet>424</a> fixpoint(guess, max_bits, <span class="kw">move </span>|s| {
|
|
<a href=#425 id=425 data-nosnippet>425</a> <span class="kw">let </span>q = <span class="self">self </span>/ s.pow(n_min_1);
|
|
<a href=#426 id=426 data-nosnippet>426</a> <span class="kw">let </span>t = n_min_1 * s + q;
|
|
<a href=#427 id=427 data-nosnippet>427</a> t / n
|
|
<a href=#428 id=428 data-nosnippet>428</a> })
|
|
<a href=#429 id=429 data-nosnippet>429</a> }
|
|
<a href=#430 id=430 data-nosnippet>430</a>
|
|
<a href=#431 id=431 data-nosnippet>431</a> <span class="comment">// Reference:
|
|
<a href=#432 id=432 data-nosnippet>432</a> // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13
|
|
<a href=#433 id=433 data-nosnippet>433</a> </span><span class="kw">fn </span>sqrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
|
|
<a href=#434 id=434 data-nosnippet>434</a> <span class="kw">if </span><span class="self">self</span>.is_zero() || <span class="self">self</span>.is_one() {
|
|
<a href=#435 id=435 data-nosnippet>435</a> <span class="kw">return </span><span class="self">self</span>.clone();
|
|
<a href=#436 id=436 data-nosnippet>436</a> }
|
|
<a href=#437 id=437 data-nosnippet>437</a>
|
|
<a href=#438 id=438 data-nosnippet>438</a> <span class="comment">// If we fit in `u64`, compute the root that way.
|
|
<a href=#439 id=439 data-nosnippet>439</a> </span><span class="kw">if let </span><span class="prelude-val">Some</span>(x) = <span class="self">self</span>.to_u64() {
|
|
<a href=#440 id=440 data-nosnippet>440</a> <span class="kw">return </span>x.sqrt().into();
|
|
<a href=#441 id=441 data-nosnippet>441</a> }
|
|
<a href=#442 id=442 data-nosnippet>442</a>
|
|
<a href=#443 id=443 data-nosnippet>443</a> <span class="kw">let </span>bits = <span class="self">self</span>.bits();
|
|
<a href=#444 id=444 data-nosnippet>444</a> <span class="kw">let </span>max_bits = bits / <span class="number">2 </span>+ <span class="number">1</span>;
|
|
<a href=#445 id=445 data-nosnippet>445</a>
|
|
<a href=#446 id=446 data-nosnippet>446</a> <span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
|
|
<a href=#447 id=447 data-nosnippet>447</a> </span><span class="kw">let </span>guess = <span class="kw">match </span><span class="self">self</span>.to_f64() {
|
|
<a href=#448 id=448 data-nosnippet>448</a> <span class="prelude-val">Some</span>(f) <span class="kw">if </span>f.is_finite() => {
|
|
<a href=#449 id=449 data-nosnippet>449</a> <span class="kw">use </span>num_traits::FromPrimitive;
|
|
<a href=#450 id=450 data-nosnippet>450</a>
|
|
<a href=#451 id=451 data-nosnippet>451</a> <span class="comment">// We fit in `f64` (lossy), so get a better initial guess from that.
|
|
<a href=#452 id=452 data-nosnippet>452</a> </span>BigUint::from_f64(f.sqrt()).unwrap()
|
|
<a href=#453 id=453 data-nosnippet>453</a> }
|
|
<a href=#454 id=454 data-nosnippet>454</a> <span class="kw">_ </span>=> {
|
|
<a href=#455 id=455 data-nosnippet>455</a> <span class="comment">// Try to guess by scaling down such that it does fit in `f64`.
|
|
<a href=#456 id=456 data-nosnippet>456</a> // With some (x * 2²ᵏ), its sqrt ≈ (√x * 2ᵏ)
|
|
<a href=#457 id=457 data-nosnippet>457</a> </span><span class="kw">let </span>extra_bits = bits - (f64::MAX_EXP <span class="kw">as </span>u64 - <span class="number">1</span>);
|
|
<a href=#458 id=458 data-nosnippet>458</a> <span class="kw">let </span>root_scale = (extra_bits + <span class="number">1</span>) / <span class="number">2</span>;
|
|
<a href=#459 id=459 data-nosnippet>459</a> <span class="kw">let </span>scale = root_scale * <span class="number">2</span>;
|
|
<a href=#460 id=460 data-nosnippet>460</a> (<span class="self">self </span>>> scale).sqrt() << root_scale
|
|
<a href=#461 id=461 data-nosnippet>461</a> }
|
|
<a href=#462 id=462 data-nosnippet>462</a> };
|
|
<a href=#463 id=463 data-nosnippet>463</a>
|
|
<a href=#464 id=464 data-nosnippet>464</a> <span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
|
|
<a href=#465 id=465 data-nosnippet>465</a> </span><span class="kw">let </span>guess = BigUint::one() << max_bits;
|
|
<a href=#466 id=466 data-nosnippet>466</a>
|
|
<a href=#467 id=467 data-nosnippet>467</a> fixpoint(guess, max_bits, <span class="kw">move </span>|s| {
|
|
<a href=#468 id=468 data-nosnippet>468</a> <span class="kw">let </span>q = <span class="self">self </span>/ s;
|
|
<a href=#469 id=469 data-nosnippet>469</a> <span class="kw">let </span>t = s + q;
|
|
<a href=#470 id=470 data-nosnippet>470</a> t >> <span class="number">1
|
|
<a href=#471 id=471 data-nosnippet>471</a> </span>})
|
|
<a href=#472 id=472 data-nosnippet>472</a> }
|
|
<a href=#473 id=473 data-nosnippet>473</a>
|
|
<a href=#474 id=474 data-nosnippet>474</a> <span class="kw">fn </span>cbrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
|
|
<a href=#475 id=475 data-nosnippet>475</a> <span class="kw">if </span><span class="self">self</span>.is_zero() || <span class="self">self</span>.is_one() {
|
|
<a href=#476 id=476 data-nosnippet>476</a> <span class="kw">return </span><span class="self">self</span>.clone();
|
|
<a href=#477 id=477 data-nosnippet>477</a> }
|
|
<a href=#478 id=478 data-nosnippet>478</a>
|
|
<a href=#479 id=479 data-nosnippet>479</a> <span class="comment">// If we fit in `u64`, compute the root that way.
|
|
<a href=#480 id=480 data-nosnippet>480</a> </span><span class="kw">if let </span><span class="prelude-val">Some</span>(x) = <span class="self">self</span>.to_u64() {
|
|
<a href=#481 id=481 data-nosnippet>481</a> <span class="kw">return </span>x.cbrt().into();
|
|
<a href=#482 id=482 data-nosnippet>482</a> }
|
|
<a href=#483 id=483 data-nosnippet>483</a>
|
|
<a href=#484 id=484 data-nosnippet>484</a> <span class="kw">let </span>bits = <span class="self">self</span>.bits();
|
|
<a href=#485 id=485 data-nosnippet>485</a> <span class="kw">let </span>max_bits = bits / <span class="number">3 </span>+ <span class="number">1</span>;
|
|
<a href=#486 id=486 data-nosnippet>486</a>
|
|
<a href=#487 id=487 data-nosnippet>487</a> <span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
|
|
<a href=#488 id=488 data-nosnippet>488</a> </span><span class="kw">let </span>guess = <span class="kw">match </span><span class="self">self</span>.to_f64() {
|
|
<a href=#489 id=489 data-nosnippet>489</a> <span class="prelude-val">Some</span>(f) <span class="kw">if </span>f.is_finite() => {
|
|
<a href=#490 id=490 data-nosnippet>490</a> <span class="kw">use </span>num_traits::FromPrimitive;
|
|
<a href=#491 id=491 data-nosnippet>491</a>
|
|
<a href=#492 id=492 data-nosnippet>492</a> <span class="comment">// We fit in `f64` (lossy), so get a better initial guess from that.
|
|
<a href=#493 id=493 data-nosnippet>493</a> </span>BigUint::from_f64(f.cbrt()).unwrap()
|
|
<a href=#494 id=494 data-nosnippet>494</a> }
|
|
<a href=#495 id=495 data-nosnippet>495</a> <span class="kw">_ </span>=> {
|
|
<a href=#496 id=496 data-nosnippet>496</a> <span class="comment">// Try to guess by scaling down such that it does fit in `f64`.
|
|
<a href=#497 id=497 data-nosnippet>497</a> // With some (x * 2³ᵏ), its cbrt ≈ (∛x * 2ᵏ)
|
|
<a href=#498 id=498 data-nosnippet>498</a> </span><span class="kw">let </span>extra_bits = bits - (f64::MAX_EXP <span class="kw">as </span>u64 - <span class="number">1</span>);
|
|
<a href=#499 id=499 data-nosnippet>499</a> <span class="kw">let </span>root_scale = (extra_bits + <span class="number">2</span>) / <span class="number">3</span>;
|
|
<a href=#500 id=500 data-nosnippet>500</a> <span class="kw">let </span>scale = root_scale * <span class="number">3</span>;
|
|
<a href=#501 id=501 data-nosnippet>501</a> (<span class="self">self </span>>> scale).cbrt() << root_scale
|
|
<a href=#502 id=502 data-nosnippet>502</a> }
|
|
<a href=#503 id=503 data-nosnippet>503</a> };
|
|
<a href=#504 id=504 data-nosnippet>504</a>
|
|
<a href=#505 id=505 data-nosnippet>505</a> <span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
|
|
<a href=#506 id=506 data-nosnippet>506</a> </span><span class="kw">let </span>guess = BigUint::one() << max_bits;
|
|
<a href=#507 id=507 data-nosnippet>507</a>
|
|
<a href=#508 id=508 data-nosnippet>508</a> fixpoint(guess, max_bits, <span class="kw">move </span>|s| {
|
|
<a href=#509 id=509 data-nosnippet>509</a> <span class="kw">let </span>q = <span class="self">self </span>/ (s * s);
|
|
<a href=#510 id=510 data-nosnippet>510</a> <span class="kw">let </span>t = (s << <span class="number">1</span>) + q;
|
|
<a href=#511 id=511 data-nosnippet>511</a> t / <span class="number">3u32
|
|
<a href=#512 id=512 data-nosnippet>512</a> </span>})
|
|
<a href=#513 id=513 data-nosnippet>513</a> }
|
|
<a href=#514 id=514 data-nosnippet>514</a>}
|
|
<a href=#515 id=515 data-nosnippet>515</a>
|
|
<a href=#516 id=516 data-nosnippet>516</a><span class="doccomment">/// A generic trait for converting a value to a [`BigUint`].
|
|
<a href=#517 id=517 data-nosnippet>517</a></span><span class="kw">pub trait </span>ToBigUint {
|
|
<a href=#518 id=518 data-nosnippet>518</a> <span class="doccomment">/// Converts the value of `self` to a [`BigUint`].
|
|
<a href=#519 id=519 data-nosnippet>519</a> </span><span class="kw">fn </span>to_biguint(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><BigUint>;
|
|
<a href=#520 id=520 data-nosnippet>520</a>}
|
|
<a href=#521 id=521 data-nosnippet>521</a>
|
|
<a href=#522 id=522 data-nosnippet>522</a><span class="doccomment">/// Creates and initializes a [`BigUint`].
|
|
<a href=#523 id=523 data-nosnippet>523</a>///
|
|
<a href=#524 id=524 data-nosnippet>524</a>/// The digits are in little-endian base matching `BigDigit`.
|
|
<a href=#525 id=525 data-nosnippet>525</a></span><span class="attr">#[inline]
|
|
<a href=#526 id=526 data-nosnippet>526</a></span><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>biguint_from_vec(digits: Vec<BigDigit>) -> BigUint {
|
|
<a href=#527 id=527 data-nosnippet>527</a> BigUint { data: digits }.normalized()
|
|
<a href=#528 id=528 data-nosnippet>528</a>}
|
|
<a href=#529 id=529 data-nosnippet>529</a>
|
|
<a href=#530 id=530 data-nosnippet>530</a><span class="kw">impl </span>BigUint {
|
|
<a href=#531 id=531 data-nosnippet>531</a> <span class="doccomment">/// A constant `BigUint` with value 0, useful for static initialization.
|
|
<a href=#532 id=532 data-nosnippet>532</a> </span><span class="kw">pub const </span>ZERO: <span class="self">Self </span>= BigUint { data: Vec::new() };
|
|
<a href=#533 id=533 data-nosnippet>533</a>
|
|
<a href=#534 id=534 data-nosnippet>534</a> <span class="doccomment">/// Creates and initializes a [`BigUint`].
|
|
<a href=#535 id=535 data-nosnippet>535</a> ///
|
|
<a href=#536 id=536 data-nosnippet>536</a> /// The base 2<sup>32</sup> digits are ordered least significant digit first.
|
|
<a href=#537 id=537 data-nosnippet>537</a> </span><span class="attr">#[inline]
|
|
<a href=#538 id=538 data-nosnippet>538</a> </span><span class="kw">pub fn </span>new(digits: Vec<u32>) -> BigUint {
|
|
<a href=#539 id=539 data-nosnippet>539</a> <span class="kw">let </span><span class="kw-2">mut </span>big = <span class="self">Self</span>::ZERO;
|
|
<a href=#540 id=540 data-nosnippet>540</a>
|
|
<a href=#541 id=541 data-nosnippet>541</a> <span class="macro">cfg_digit_expr!</span>(
|
|
<a href=#542 id=542 data-nosnippet>542</a> {
|
|
<a href=#543 id=543 data-nosnippet>543</a> big.data = digits;
|
|
<a href=#544 id=544 data-nosnippet>544</a> big.normalize();
|
|
<a href=#545 id=545 data-nosnippet>545</a> },
|
|
<a href=#546 id=546 data-nosnippet>546</a> big.assign_from_slice(<span class="kw-2">&</span>digits)
|
|
<a href=#547 id=547 data-nosnippet>547</a> );
|
|
<a href=#548 id=548 data-nosnippet>548</a>
|
|
<a href=#549 id=549 data-nosnippet>549</a> big
|
|
<a href=#550 id=550 data-nosnippet>550</a> }
|
|
<a href=#551 id=551 data-nosnippet>551</a>
|
|
<a href=#552 id=552 data-nosnippet>552</a> <span class="doccomment">/// Creates and initializes a [`BigUint`].
|
|
<a href=#553 id=553 data-nosnippet>553</a> ///
|
|
<a href=#554 id=554 data-nosnippet>554</a> /// The base 2<sup>32</sup> digits are ordered least significant digit first.
|
|
<a href=#555 id=555 data-nosnippet>555</a> </span><span class="attr">#[inline]
|
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<a href=#556 id=556 data-nosnippet>556</a> </span><span class="kw">pub fn </span>from_slice(slice: <span class="kw-2">&</span>[u32]) -> BigUint {
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<a href=#557 id=557 data-nosnippet>557</a> <span class="kw">let </span><span class="kw-2">mut </span>big = <span class="self">Self</span>::ZERO;
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<a href=#558 id=558 data-nosnippet>558</a> big.assign_from_slice(slice);
|
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<a href=#559 id=559 data-nosnippet>559</a> big
|
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<a href=#560 id=560 data-nosnippet>560</a> }
|
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<a href=#561 id=561 data-nosnippet>561</a>
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<a href=#562 id=562 data-nosnippet>562</a> <span class="doccomment">/// Assign a value to a [`BigUint`].
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<a href=#563 id=563 data-nosnippet>563</a> ///
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<a href=#564 id=564 data-nosnippet>564</a> /// The base 2<sup>32</sup> digits are ordered least significant digit first.
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<a href=#565 id=565 data-nosnippet>565</a> </span><span class="attr">#[inline]
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<a href=#566 id=566 data-nosnippet>566</a> </span><span class="kw">pub fn </span>assign_from_slice(<span class="kw-2">&mut </span><span class="self">self</span>, slice: <span class="kw-2">&</span>[u32]) {
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<a href=#567 id=567 data-nosnippet>567</a> <span class="self">self</span>.data.clear();
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<a href=#568 id=568 data-nosnippet>568</a>
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<a href=#569 id=569 data-nosnippet>569</a> <span class="macro">cfg_digit_expr!</span>(
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<a href=#570 id=570 data-nosnippet>570</a> <span class="self">self</span>.data.extend_from_slice(slice),
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<a href=#571 id=571 data-nosnippet>571</a> <span class="self">self</span>.data.extend(slice.chunks(<span class="number">2</span>).map(u32_chunk_to_u64))
|
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<a href=#572 id=572 data-nosnippet>572</a> );
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<a href=#573 id=573 data-nosnippet>573</a>
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<a href=#574 id=574 data-nosnippet>574</a> <span class="self">self</span>.normalize();
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<a href=#575 id=575 data-nosnippet>575</a> }
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<a href=#576 id=576 data-nosnippet>576</a>
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<a href=#577 id=577 data-nosnippet>577</a> <span class="doccomment">/// Creates and initializes a [`BigUint`].
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<a href=#578 id=578 data-nosnippet>578</a> ///
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<a href=#579 id=579 data-nosnippet>579</a> /// The bytes are in big-endian byte order.
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<a href=#580 id=580 data-nosnippet>580</a> ///
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<a href=#581 id=581 data-nosnippet>581</a> /// # Examples
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<a href=#582 id=582 data-nosnippet>582</a> ///
|
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<a href=#583 id=583 data-nosnippet>583</a> /// ```
|
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<a href=#584 id=584 data-nosnippet>584</a> /// use num_bigint::BigUint;
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<a href=#585 id=585 data-nosnippet>585</a> ///
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<a href=#586 id=586 data-nosnippet>586</a> /// assert_eq!(BigUint::from_bytes_be(b"A"),
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<a href=#587 id=587 data-nosnippet>587</a> /// BigUint::parse_bytes(b"65", 10).unwrap());
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<a href=#588 id=588 data-nosnippet>588</a> /// assert_eq!(BigUint::from_bytes_be(b"AA"),
|
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<a href=#589 id=589 data-nosnippet>589</a> /// BigUint::parse_bytes(b"16705", 10).unwrap());
|
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<a href=#590 id=590 data-nosnippet>590</a> /// assert_eq!(BigUint::from_bytes_be(b"AB"),
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<a href=#591 id=591 data-nosnippet>591</a> /// BigUint::parse_bytes(b"16706", 10).unwrap());
|
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<a href=#592 id=592 data-nosnippet>592</a> /// assert_eq!(BigUint::from_bytes_be(b"Hello world!"),
|
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<a href=#593 id=593 data-nosnippet>593</a> /// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap());
|
|
<a href=#594 id=594 data-nosnippet>594</a> /// ```
|
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<a href=#595 id=595 data-nosnippet>595</a> </span><span class="attr">#[inline]
|
|
<a href=#596 id=596 data-nosnippet>596</a> </span><span class="kw">pub fn </span>from_bytes_be(bytes: <span class="kw-2">&</span>[u8]) -> BigUint {
|
|
<a href=#597 id=597 data-nosnippet>597</a> <span class="kw">if </span>bytes.is_empty() {
|
|
<a href=#598 id=598 data-nosnippet>598</a> <span class="self">Self</span>::ZERO
|
|
<a href=#599 id=599 data-nosnippet>599</a> } <span class="kw">else </span>{
|
|
<a href=#600 id=600 data-nosnippet>600</a> <span class="kw">let </span><span class="kw-2">mut </span>v = bytes.to_vec();
|
|
<a href=#601 id=601 data-nosnippet>601</a> v.reverse();
|
|
<a href=#602 id=602 data-nosnippet>602</a> BigUint::from_bytes_le(<span class="kw-2">&</span>v)
|
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<a href=#603 id=603 data-nosnippet>603</a> }
|
|
<a href=#604 id=604 data-nosnippet>604</a> }
|
|
<a href=#605 id=605 data-nosnippet>605</a>
|
|
<a href=#606 id=606 data-nosnippet>606</a> <span class="doccomment">/// Creates and initializes a [`BigUint`].
|
|
<a href=#607 id=607 data-nosnippet>607</a> ///
|
|
<a href=#608 id=608 data-nosnippet>608</a> /// The bytes are in little-endian byte order.
|
|
<a href=#609 id=609 data-nosnippet>609</a> </span><span class="attr">#[inline]
|
|
<a href=#610 id=610 data-nosnippet>610</a> </span><span class="kw">pub fn </span>from_bytes_le(bytes: <span class="kw-2">&</span>[u8]) -> BigUint {
|
|
<a href=#611 id=611 data-nosnippet>611</a> <span class="kw">if </span>bytes.is_empty() {
|
|
<a href=#612 id=612 data-nosnippet>612</a> <span class="self">Self</span>::ZERO
|
|
<a href=#613 id=613 data-nosnippet>613</a> } <span class="kw">else </span>{
|
|
<a href=#614 id=614 data-nosnippet>614</a> convert::from_bitwise_digits_le(bytes, <span class="number">8</span>)
|
|
<a href=#615 id=615 data-nosnippet>615</a> }
|
|
<a href=#616 id=616 data-nosnippet>616</a> }
|
|
<a href=#617 id=617 data-nosnippet>617</a>
|
|
<a href=#618 id=618 data-nosnippet>618</a> <span class="doccomment">/// Creates and initializes a [`BigUint`]. The input slice must contain
|
|
<a href=#619 id=619 data-nosnippet>619</a> /// ascii/utf8 characters in [0-9a-zA-Z].
|
|
<a href=#620 id=620 data-nosnippet>620</a> /// `radix` must be in the range `2...36`.
|
|
<a href=#621 id=621 data-nosnippet>621</a> ///
|
|
<a href=#622 id=622 data-nosnippet>622</a> /// The function `from_str_radix` from the `Num` trait provides the same logic
|
|
<a href=#623 id=623 data-nosnippet>623</a> /// for `&str` buffers.
|
|
<a href=#624 id=624 data-nosnippet>624</a> ///
|
|
<a href=#625 id=625 data-nosnippet>625</a> /// # Examples
|
|
<a href=#626 id=626 data-nosnippet>626</a> ///
|
|
<a href=#627 id=627 data-nosnippet>627</a> /// ```
|
|
<a href=#628 id=628 data-nosnippet>628</a> /// use num_bigint::{BigUint, ToBigUint};
|
|
<a href=#629 id=629 data-nosnippet>629</a> ///
|
|
<a href=#630 id=630 data-nosnippet>630</a> /// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234));
|
|
<a href=#631 id=631 data-nosnippet>631</a> /// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD));
|
|
<a href=#632 id=632 data-nosnippet>632</a> /// assert_eq!(BigUint::parse_bytes(b"G", 16), None);
|
|
<a href=#633 id=633 data-nosnippet>633</a> /// ```
|
|
<a href=#634 id=634 data-nosnippet>634</a> </span><span class="attr">#[inline]
|
|
<a href=#635 id=635 data-nosnippet>635</a> </span><span class="kw">pub fn </span>parse_bytes(buf: <span class="kw-2">&</span>[u8], radix: u32) -> <span class="prelude-ty">Option</span><BigUint> {
|
|
<a href=#636 id=636 data-nosnippet>636</a> <span class="kw">let </span>s = str::from_utf8(buf).ok()<span class="question-mark">?</span>;
|
|
<a href=#637 id=637 data-nosnippet>637</a> BigUint::from_str_radix(s, radix).ok()
|
|
<a href=#638 id=638 data-nosnippet>638</a> }
|
|
<a href=#639 id=639 data-nosnippet>639</a>
|
|
<a href=#640 id=640 data-nosnippet>640</a> <span class="doccomment">/// Creates and initializes a [`BigUint`]. Each `u8` of the input slice is
|
|
<a href=#641 id=641 data-nosnippet>641</a> /// interpreted as one digit of the number
|
|
<a href=#642 id=642 data-nosnippet>642</a> /// and must therefore be less than `radix`.
|
|
<a href=#643 id=643 data-nosnippet>643</a> ///
|
|
<a href=#644 id=644 data-nosnippet>644</a> /// The bytes are in big-endian byte order.
|
|
<a href=#645 id=645 data-nosnippet>645</a> /// `radix` must be in the range `2...256`.
|
|
<a href=#646 id=646 data-nosnippet>646</a> ///
|
|
<a href=#647 id=647 data-nosnippet>647</a> /// # Examples
|
|
<a href=#648 id=648 data-nosnippet>648</a> ///
|
|
<a href=#649 id=649 data-nosnippet>649</a> /// ```
|
|
<a href=#650 id=650 data-nosnippet>650</a> /// use num_bigint::{BigUint};
|
|
<a href=#651 id=651 data-nosnippet>651</a> ///
|
|
<a href=#652 id=652 data-nosnippet>652</a> /// let inbase190 = &[15, 33, 125, 12, 14];
|
|
<a href=#653 id=653 data-nosnippet>653</a> /// let a = BigUint::from_radix_be(inbase190, 190).unwrap();
|
|
<a href=#654 id=654 data-nosnippet>654</a> /// assert_eq!(a.to_radix_be(190), inbase190);
|
|
<a href=#655 id=655 data-nosnippet>655</a> /// ```
|
|
<a href=#656 id=656 data-nosnippet>656</a> </span><span class="kw">pub fn </span>from_radix_be(buf: <span class="kw-2">&</span>[u8], radix: u32) -> <span class="prelude-ty">Option</span><BigUint> {
|
|
<a href=#657 id=657 data-nosnippet>657</a> convert::from_radix_be(buf, radix)
|
|
<a href=#658 id=658 data-nosnippet>658</a> }
|
|
<a href=#659 id=659 data-nosnippet>659</a>
|
|
<a href=#660 id=660 data-nosnippet>660</a> <span class="doccomment">/// Creates and initializes a [`BigUint`]. Each `u8` of the input slice is
|
|
<a href=#661 id=661 data-nosnippet>661</a> /// interpreted as one digit of the number
|
|
<a href=#662 id=662 data-nosnippet>662</a> /// and must therefore be less than `radix`.
|
|
<a href=#663 id=663 data-nosnippet>663</a> ///
|
|
<a href=#664 id=664 data-nosnippet>664</a> /// The bytes are in little-endian byte order.
|
|
<a href=#665 id=665 data-nosnippet>665</a> /// `radix` must be in the range `2...256`.
|
|
<a href=#666 id=666 data-nosnippet>666</a> ///
|
|
<a href=#667 id=667 data-nosnippet>667</a> /// # Examples
|
|
<a href=#668 id=668 data-nosnippet>668</a> ///
|
|
<a href=#669 id=669 data-nosnippet>669</a> /// ```
|
|
<a href=#670 id=670 data-nosnippet>670</a> /// use num_bigint::{BigUint};
|
|
<a href=#671 id=671 data-nosnippet>671</a> ///
|
|
<a href=#672 id=672 data-nosnippet>672</a> /// let inbase190 = &[14, 12, 125, 33, 15];
|
|
<a href=#673 id=673 data-nosnippet>673</a> /// let a = BigUint::from_radix_be(inbase190, 190).unwrap();
|
|
<a href=#674 id=674 data-nosnippet>674</a> /// assert_eq!(a.to_radix_be(190), inbase190);
|
|
<a href=#675 id=675 data-nosnippet>675</a> /// ```
|
|
<a href=#676 id=676 data-nosnippet>676</a> </span><span class="kw">pub fn </span>from_radix_le(buf: <span class="kw-2">&</span>[u8], radix: u32) -> <span class="prelude-ty">Option</span><BigUint> {
|
|
<a href=#677 id=677 data-nosnippet>677</a> convert::from_radix_le(buf, radix)
|
|
<a href=#678 id=678 data-nosnippet>678</a> }
|
|
<a href=#679 id=679 data-nosnippet>679</a>
|
|
<a href=#680 id=680 data-nosnippet>680</a> <span class="doccomment">/// Returns the byte representation of the [`BigUint`] in big-endian byte order.
|
|
<a href=#681 id=681 data-nosnippet>681</a> ///
|
|
<a href=#682 id=682 data-nosnippet>682</a> /// # Examples
|
|
<a href=#683 id=683 data-nosnippet>683</a> ///
|
|
<a href=#684 id=684 data-nosnippet>684</a> /// ```
|
|
<a href=#685 id=685 data-nosnippet>685</a> /// use num_bigint::BigUint;
|
|
<a href=#686 id=686 data-nosnippet>686</a> ///
|
|
<a href=#687 id=687 data-nosnippet>687</a> /// let i = BigUint::parse_bytes(b"1125", 10).unwrap();
|
|
<a href=#688 id=688 data-nosnippet>688</a> /// assert_eq!(i.to_bytes_be(), vec![4, 101]);
|
|
<a href=#689 id=689 data-nosnippet>689</a> /// ```
|
|
<a href=#690 id=690 data-nosnippet>690</a> </span><span class="attr">#[inline]
|
|
<a href=#691 id=691 data-nosnippet>691</a> </span><span class="kw">pub fn </span>to_bytes_be(<span class="kw-2">&</span><span class="self">self</span>) -> Vec<u8> {
|
|
<a href=#692 id=692 data-nosnippet>692</a> <span class="kw">let </span><span class="kw-2">mut </span>v = <span class="self">self</span>.to_bytes_le();
|
|
<a href=#693 id=693 data-nosnippet>693</a> v.reverse();
|
|
<a href=#694 id=694 data-nosnippet>694</a> v
|
|
<a href=#695 id=695 data-nosnippet>695</a> }
|
|
<a href=#696 id=696 data-nosnippet>696</a>
|
|
<a href=#697 id=697 data-nosnippet>697</a> <span class="doccomment">/// Returns the byte representation of the [`BigUint`] in little-endian byte order.
|
|
<a href=#698 id=698 data-nosnippet>698</a> ///
|
|
<a href=#699 id=699 data-nosnippet>699</a> /// # Examples
|
|
<a href=#700 id=700 data-nosnippet>700</a> ///
|
|
<a href=#701 id=701 data-nosnippet>701</a> /// ```
|
|
<a href=#702 id=702 data-nosnippet>702</a> /// use num_bigint::BigUint;
|
|
<a href=#703 id=703 data-nosnippet>703</a> ///
|
|
<a href=#704 id=704 data-nosnippet>704</a> /// let i = BigUint::parse_bytes(b"1125", 10).unwrap();
|
|
<a href=#705 id=705 data-nosnippet>705</a> /// assert_eq!(i.to_bytes_le(), vec![101, 4]);
|
|
<a href=#706 id=706 data-nosnippet>706</a> /// ```
|
|
<a href=#707 id=707 data-nosnippet>707</a> </span><span class="attr">#[inline]
|
|
<a href=#708 id=708 data-nosnippet>708</a> </span><span class="kw">pub fn </span>to_bytes_le(<span class="kw-2">&</span><span class="self">self</span>) -> Vec<u8> {
|
|
<a href=#709 id=709 data-nosnippet>709</a> <span class="kw">if </span><span class="self">self</span>.is_zero() {
|
|
<a href=#710 id=710 data-nosnippet>710</a> <span class="macro">vec!</span>[<span class="number">0</span>]
|
|
<a href=#711 id=711 data-nosnippet>711</a> } <span class="kw">else </span>{
|
|
<a href=#712 id=712 data-nosnippet>712</a> convert::to_bitwise_digits_le(<span class="self">self</span>, <span class="number">8</span>)
|
|
<a href=#713 id=713 data-nosnippet>713</a> }
|
|
<a href=#714 id=714 data-nosnippet>714</a> }
|
|
<a href=#715 id=715 data-nosnippet>715</a>
|
|
<a href=#716 id=716 data-nosnippet>716</a> <span class="doccomment">/// Returns the `u32` digits representation of the [`BigUint`] ordered least significant digit
|
|
<a href=#717 id=717 data-nosnippet>717</a> /// first.
|
|
<a href=#718 id=718 data-nosnippet>718</a> ///
|
|
<a href=#719 id=719 data-nosnippet>719</a> /// # Examples
|
|
<a href=#720 id=720 data-nosnippet>720</a> ///
|
|
<a href=#721 id=721 data-nosnippet>721</a> /// ```
|
|
<a href=#722 id=722 data-nosnippet>722</a> /// use num_bigint::BigUint;
|
|
<a href=#723 id=723 data-nosnippet>723</a> ///
|
|
<a href=#724 id=724 data-nosnippet>724</a> /// assert_eq!(BigUint::from(1125u32).to_u32_digits(), vec![1125]);
|
|
<a href=#725 id=725 data-nosnippet>725</a> /// assert_eq!(BigUint::from(4294967295u32).to_u32_digits(), vec![4294967295]);
|
|
<a href=#726 id=726 data-nosnippet>726</a> /// assert_eq!(BigUint::from(4294967296u64).to_u32_digits(), vec![0, 1]);
|
|
<a href=#727 id=727 data-nosnippet>727</a> /// assert_eq!(BigUint::from(112500000000u64).to_u32_digits(), vec![830850304, 26]);
|
|
<a href=#728 id=728 data-nosnippet>728</a> /// ```
|
|
<a href=#729 id=729 data-nosnippet>729</a> </span><span class="attr">#[inline]
|
|
<a href=#730 id=730 data-nosnippet>730</a> </span><span class="kw">pub fn </span>to_u32_digits(<span class="kw-2">&</span><span class="self">self</span>) -> Vec<u32> {
|
|
<a href=#731 id=731 data-nosnippet>731</a> <span class="self">self</span>.iter_u32_digits().collect()
|
|
<a href=#732 id=732 data-nosnippet>732</a> }
|
|
<a href=#733 id=733 data-nosnippet>733</a>
|
|
<a href=#734 id=734 data-nosnippet>734</a> <span class="doccomment">/// Returns the `u64` digits representation of the [`BigUint`] ordered least significant digit
|
|
<a href=#735 id=735 data-nosnippet>735</a> /// first.
|
|
<a href=#736 id=736 data-nosnippet>736</a> ///
|
|
<a href=#737 id=737 data-nosnippet>737</a> /// # Examples
|
|
<a href=#738 id=738 data-nosnippet>738</a> ///
|
|
<a href=#739 id=739 data-nosnippet>739</a> /// ```
|
|
<a href=#740 id=740 data-nosnippet>740</a> /// use num_bigint::BigUint;
|
|
<a href=#741 id=741 data-nosnippet>741</a> ///
|
|
<a href=#742 id=742 data-nosnippet>742</a> /// assert_eq!(BigUint::from(1125u32).to_u64_digits(), vec![1125]);
|
|
<a href=#743 id=743 data-nosnippet>743</a> /// assert_eq!(BigUint::from(4294967295u32).to_u64_digits(), vec![4294967295]);
|
|
<a href=#744 id=744 data-nosnippet>744</a> /// assert_eq!(BigUint::from(4294967296u64).to_u64_digits(), vec![4294967296]);
|
|
<a href=#745 id=745 data-nosnippet>745</a> /// assert_eq!(BigUint::from(112500000000u64).to_u64_digits(), vec![112500000000]);
|
|
<a href=#746 id=746 data-nosnippet>746</a> /// assert_eq!(BigUint::from(1u128 << 64).to_u64_digits(), vec![0, 1]);
|
|
<a href=#747 id=747 data-nosnippet>747</a> /// ```
|
|
<a href=#748 id=748 data-nosnippet>748</a> </span><span class="attr">#[inline]
|
|
<a href=#749 id=749 data-nosnippet>749</a> </span><span class="kw">pub fn </span>to_u64_digits(<span class="kw-2">&</span><span class="self">self</span>) -> Vec<u64> {
|
|
<a href=#750 id=750 data-nosnippet>750</a> <span class="self">self</span>.iter_u64_digits().collect()
|
|
<a href=#751 id=751 data-nosnippet>751</a> }
|
|
<a href=#752 id=752 data-nosnippet>752</a>
|
|
<a href=#753 id=753 data-nosnippet>753</a> <span class="doccomment">/// Returns an iterator of `u32` digits representation of the [`BigUint`] ordered least
|
|
<a href=#754 id=754 data-nosnippet>754</a> /// significant digit first.
|
|
<a href=#755 id=755 data-nosnippet>755</a> ///
|
|
<a href=#756 id=756 data-nosnippet>756</a> /// # Examples
|
|
<a href=#757 id=757 data-nosnippet>757</a> ///
|
|
<a href=#758 id=758 data-nosnippet>758</a> /// ```
|
|
<a href=#759 id=759 data-nosnippet>759</a> /// use num_bigint::BigUint;
|
|
<a href=#760 id=760 data-nosnippet>760</a> ///
|
|
<a href=#761 id=761 data-nosnippet>761</a> /// assert_eq!(BigUint::from(1125u32).iter_u32_digits().collect::<Vec<u32>>(), vec![1125]);
|
|
<a href=#762 id=762 data-nosnippet>762</a> /// assert_eq!(BigUint::from(4294967295u32).iter_u32_digits().collect::<Vec<u32>>(), vec![4294967295]);
|
|
<a href=#763 id=763 data-nosnippet>763</a> /// assert_eq!(BigUint::from(4294967296u64).iter_u32_digits().collect::<Vec<u32>>(), vec![0, 1]);
|
|
<a href=#764 id=764 data-nosnippet>764</a> /// assert_eq!(BigUint::from(112500000000u64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);
|
|
<a href=#765 id=765 data-nosnippet>765</a> /// ```
|
|
<a href=#766 id=766 data-nosnippet>766</a> </span><span class="attr">#[inline]
|
|
<a href=#767 id=767 data-nosnippet>767</a> </span><span class="kw">pub fn </span>iter_u32_digits(<span class="kw-2">&</span><span class="self">self</span>) -> U32Digits<<span class="lifetime">'_</span>> {
|
|
<a href=#768 id=768 data-nosnippet>768</a> U32Digits::new(<span class="self">self</span>.data.as_slice())
|
|
<a href=#769 id=769 data-nosnippet>769</a> }
|
|
<a href=#770 id=770 data-nosnippet>770</a>
|
|
<a href=#771 id=771 data-nosnippet>771</a> <span class="doccomment">/// Returns an iterator of `u64` digits representation of the [`BigUint`] ordered least
|
|
<a href=#772 id=772 data-nosnippet>772</a> /// significant digit first.
|
|
<a href=#773 id=773 data-nosnippet>773</a> ///
|
|
<a href=#774 id=774 data-nosnippet>774</a> /// # Examples
|
|
<a href=#775 id=775 data-nosnippet>775</a> ///
|
|
<a href=#776 id=776 data-nosnippet>776</a> /// ```
|
|
<a href=#777 id=777 data-nosnippet>777</a> /// use num_bigint::BigUint;
|
|
<a href=#778 id=778 data-nosnippet>778</a> ///
|
|
<a href=#779 id=779 data-nosnippet>779</a> /// assert_eq!(BigUint::from(1125u32).iter_u64_digits().collect::<Vec<u64>>(), vec![1125]);
|
|
<a href=#780 id=780 data-nosnippet>780</a> /// assert_eq!(BigUint::from(4294967295u32).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967295]);
|
|
<a href=#781 id=781 data-nosnippet>781</a> /// assert_eq!(BigUint::from(4294967296u64).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967296]);
|
|
<a href=#782 id=782 data-nosnippet>782</a> /// assert_eq!(BigUint::from(112500000000u64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000]);
|
|
<a href=#783 id=783 data-nosnippet>783</a> /// assert_eq!(BigUint::from(1u128 << 64).iter_u64_digits().collect::<Vec<u64>>(), vec![0, 1]);
|
|
<a href=#784 id=784 data-nosnippet>784</a> /// ```
|
|
<a href=#785 id=785 data-nosnippet>785</a> </span><span class="attr">#[inline]
|
|
<a href=#786 id=786 data-nosnippet>786</a> </span><span class="kw">pub fn </span>iter_u64_digits(<span class="kw-2">&</span><span class="self">self</span>) -> U64Digits<<span class="lifetime">'_</span>> {
|
|
<a href=#787 id=787 data-nosnippet>787</a> U64Digits::new(<span class="self">self</span>.data.as_slice())
|
|
<a href=#788 id=788 data-nosnippet>788</a> }
|
|
<a href=#789 id=789 data-nosnippet>789</a>
|
|
<a href=#790 id=790 data-nosnippet>790</a> <span class="doccomment">/// Returns the integer formatted as a string in the given radix.
|
|
<a href=#791 id=791 data-nosnippet>791</a> /// `radix` must be in the range `2...36`.
|
|
<a href=#792 id=792 data-nosnippet>792</a> ///
|
|
<a href=#793 id=793 data-nosnippet>793</a> /// # Examples
|
|
<a href=#794 id=794 data-nosnippet>794</a> ///
|
|
<a href=#795 id=795 data-nosnippet>795</a> /// ```
|
|
<a href=#796 id=796 data-nosnippet>796</a> /// use num_bigint::BigUint;
|
|
<a href=#797 id=797 data-nosnippet>797</a> ///
|
|
<a href=#798 id=798 data-nosnippet>798</a> /// let i = BigUint::parse_bytes(b"ff", 16).unwrap();
|
|
<a href=#799 id=799 data-nosnippet>799</a> /// assert_eq!(i.to_str_radix(16), "ff");
|
|
<a href=#800 id=800 data-nosnippet>800</a> /// ```
|
|
<a href=#801 id=801 data-nosnippet>801</a> </span><span class="attr">#[inline]
|
|
<a href=#802 id=802 data-nosnippet>802</a> </span><span class="kw">pub fn </span>to_str_radix(<span class="kw-2">&</span><span class="self">self</span>, radix: u32) -> String {
|
|
<a href=#803 id=803 data-nosnippet>803</a> <span class="kw">let </span><span class="kw-2">mut </span>v = to_str_radix_reversed(<span class="self">self</span>, radix);
|
|
<a href=#804 id=804 data-nosnippet>804</a> v.reverse();
|
|
<a href=#805 id=805 data-nosnippet>805</a> <span class="kw">unsafe </span>{ String::from_utf8_unchecked(v) }
|
|
<a href=#806 id=806 data-nosnippet>806</a> }
|
|
<a href=#807 id=807 data-nosnippet>807</a>
|
|
<a href=#808 id=808 data-nosnippet>808</a> <span class="doccomment">/// Returns the integer in the requested base in big-endian digit order.
|
|
<a href=#809 id=809 data-nosnippet>809</a> /// The output is not given in a human readable alphabet but as a zero
|
|
<a href=#810 id=810 data-nosnippet>810</a> /// based `u8` number.
|
|
<a href=#811 id=811 data-nosnippet>811</a> /// `radix` must be in the range `2...256`.
|
|
<a href=#812 id=812 data-nosnippet>812</a> ///
|
|
<a href=#813 id=813 data-nosnippet>813</a> /// # Examples
|
|
<a href=#814 id=814 data-nosnippet>814</a> ///
|
|
<a href=#815 id=815 data-nosnippet>815</a> /// ```
|
|
<a href=#816 id=816 data-nosnippet>816</a> /// use num_bigint::BigUint;
|
|
<a href=#817 id=817 data-nosnippet>817</a> ///
|
|
<a href=#818 id=818 data-nosnippet>818</a> /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_be(159),
|
|
<a href=#819 id=819 data-nosnippet>819</a> /// vec![2, 94, 27]);
|
|
<a href=#820 id=820 data-nosnippet>820</a> /// // 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27
|
|
<a href=#821 id=821 data-nosnippet>821</a> /// ```
|
|
<a href=#822 id=822 data-nosnippet>822</a> </span><span class="attr">#[inline]
|
|
<a href=#823 id=823 data-nosnippet>823</a> </span><span class="kw">pub fn </span>to_radix_be(<span class="kw-2">&</span><span class="self">self</span>, radix: u32) -> Vec<u8> {
|
|
<a href=#824 id=824 data-nosnippet>824</a> <span class="kw">let </span><span class="kw-2">mut </span>v = convert::to_radix_le(<span class="self">self</span>, radix);
|
|
<a href=#825 id=825 data-nosnippet>825</a> v.reverse();
|
|
<a href=#826 id=826 data-nosnippet>826</a> v
|
|
<a href=#827 id=827 data-nosnippet>827</a> }
|
|
<a href=#828 id=828 data-nosnippet>828</a>
|
|
<a href=#829 id=829 data-nosnippet>829</a> <span class="doccomment">/// Returns the integer in the requested base in little-endian digit order.
|
|
<a href=#830 id=830 data-nosnippet>830</a> /// The output is not given in a human readable alphabet but as a zero
|
|
<a href=#831 id=831 data-nosnippet>831</a> /// based u8 number.
|
|
<a href=#832 id=832 data-nosnippet>832</a> /// `radix` must be in the range `2...256`.
|
|
<a href=#833 id=833 data-nosnippet>833</a> ///
|
|
<a href=#834 id=834 data-nosnippet>834</a> /// # Examples
|
|
<a href=#835 id=835 data-nosnippet>835</a> ///
|
|
<a href=#836 id=836 data-nosnippet>836</a> /// ```
|
|
<a href=#837 id=837 data-nosnippet>837</a> /// use num_bigint::BigUint;
|
|
<a href=#838 id=838 data-nosnippet>838</a> ///
|
|
<a href=#839 id=839 data-nosnippet>839</a> /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_le(159),
|
|
<a href=#840 id=840 data-nosnippet>840</a> /// vec![27, 94, 2]);
|
|
<a href=#841 id=841 data-nosnippet>841</a> /// // 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2)
|
|
<a href=#842 id=842 data-nosnippet>842</a> /// ```
|
|
<a href=#843 id=843 data-nosnippet>843</a> </span><span class="attr">#[inline]
|
|
<a href=#844 id=844 data-nosnippet>844</a> </span><span class="kw">pub fn </span>to_radix_le(<span class="kw-2">&</span><span class="self">self</span>, radix: u32) -> Vec<u8> {
|
|
<a href=#845 id=845 data-nosnippet>845</a> convert::to_radix_le(<span class="self">self</span>, radix)
|
|
<a href=#846 id=846 data-nosnippet>846</a> }
|
|
<a href=#847 id=847 data-nosnippet>847</a>
|
|
<a href=#848 id=848 data-nosnippet>848</a> <span class="doccomment">/// Determines the fewest bits necessary to express the [`BigUint`].
|
|
<a href=#849 id=849 data-nosnippet>849</a> </span><span class="attr">#[inline]
|
|
<a href=#850 id=850 data-nosnippet>850</a> </span><span class="kw">pub fn </span>bits(<span class="kw-2">&</span><span class="self">self</span>) -> u64 {
|
|
<a href=#851 id=851 data-nosnippet>851</a> <span class="kw">if </span><span class="self">self</span>.is_zero() {
|
|
<a href=#852 id=852 data-nosnippet>852</a> <span class="kw">return </span><span class="number">0</span>;
|
|
<a href=#853 id=853 data-nosnippet>853</a> }
|
|
<a href=#854 id=854 data-nosnippet>854</a> <span class="kw">let </span>zeros: u64 = <span class="self">self</span>.data.last().unwrap().leading_zeros().into();
|
|
<a href=#855 id=855 data-nosnippet>855</a> <span class="self">self</span>.data.len() <span class="kw">as </span>u64 * u64::from(big_digit::BITS) - zeros
|
|
<a href=#856 id=856 data-nosnippet>856</a> }
|
|
<a href=#857 id=857 data-nosnippet>857</a>
|
|
<a href=#858 id=858 data-nosnippet>858</a> <span class="doccomment">/// Strips off trailing zero bigdigits - comparisons require the last element in the vector to
|
|
<a href=#859 id=859 data-nosnippet>859</a> /// be nonzero.
|
|
<a href=#860 id=860 data-nosnippet>860</a> </span><span class="attr">#[inline]
|
|
<a href=#861 id=861 data-nosnippet>861</a> </span><span class="kw">fn </span>normalize(<span class="kw-2">&mut </span><span class="self">self</span>) {
|
|
<a href=#862 id=862 data-nosnippet>862</a> <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">&</span><span class="number">0</span>) = <span class="self">self</span>.data.last() {
|
|
<a href=#863 id=863 data-nosnippet>863</a> <span class="kw">let </span>len = <span class="self">self</span>.data.iter().rposition(|<span class="kw-2">&</span>d| <span class="macro">d !</span>= <span class="number">0</span>).map_or(<span class="number">0</span>, |i| i + <span class="number">1</span>);
|
|
<a href=#864 id=864 data-nosnippet>864</a> <span class="self">self</span>.data.truncate(len);
|
|
<a href=#865 id=865 data-nosnippet>865</a> }
|
|
<a href=#866 id=866 data-nosnippet>866</a> <span class="kw">if </span><span class="self">self</span>.data.len() < <span class="self">self</span>.data.capacity() / <span class="number">4 </span>{
|
|
<a href=#867 id=867 data-nosnippet>867</a> <span class="self">self</span>.data.shrink_to_fit();
|
|
<a href=#868 id=868 data-nosnippet>868</a> }
|
|
<a href=#869 id=869 data-nosnippet>869</a> }
|
|
<a href=#870 id=870 data-nosnippet>870</a>
|
|
<a href=#871 id=871 data-nosnippet>871</a> <span class="doccomment">/// Returns a normalized [`BigUint`].
|
|
<a href=#872 id=872 data-nosnippet>872</a> </span><span class="attr">#[inline]
|
|
<a href=#873 id=873 data-nosnippet>873</a> </span><span class="kw">fn </span>normalized(<span class="kw-2">mut </span><span class="self">self</span>) -> BigUint {
|
|
<a href=#874 id=874 data-nosnippet>874</a> <span class="self">self</span>.normalize();
|
|
<a href=#875 id=875 data-nosnippet>875</a> <span class="self">self
|
|
<a href=#876 id=876 data-nosnippet>876</a> </span>}
|
|
<a href=#877 id=877 data-nosnippet>877</a>
|
|
<a href=#878 id=878 data-nosnippet>878</a> <span class="doccomment">/// Returns `self ^ exponent`.
|
|
<a href=#879 id=879 data-nosnippet>879</a> </span><span class="kw">pub fn </span>pow(<span class="kw-2">&</span><span class="self">self</span>, exponent: u32) -> <span class="self">Self </span>{
|
|
<a href=#880 id=880 data-nosnippet>880</a> Pow::pow(<span class="self">self</span>, exponent)
|
|
<a href=#881 id=881 data-nosnippet>881</a> }
|
|
<a href=#882 id=882 data-nosnippet>882</a>
|
|
<a href=#883 id=883 data-nosnippet>883</a> <span class="doccomment">/// Returns `(self ^ exponent) % modulus`.
|
|
<a href=#884 id=884 data-nosnippet>884</a> ///
|
|
<a href=#885 id=885 data-nosnippet>885</a> /// Panics if the modulus is zero.
|
|
<a href=#886 id=886 data-nosnippet>886</a> </span><span class="kw">pub fn </span>modpow(<span class="kw-2">&</span><span class="self">self</span>, exponent: <span class="kw-2">&</span><span class="self">Self</span>, modulus: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
|
|
<a href=#887 id=887 data-nosnippet>887</a> power::modpow(<span class="self">self</span>, exponent, modulus)
|
|
<a href=#888 id=888 data-nosnippet>888</a> }
|
|
<a href=#889 id=889 data-nosnippet>889</a>
|
|
<a href=#890 id=890 data-nosnippet>890</a> <span class="doccomment">/// Returns the modular multiplicative inverse if it exists, otherwise `None`.
|
|
<a href=#891 id=891 data-nosnippet>891</a> ///
|
|
<a href=#892 id=892 data-nosnippet>892</a> /// This solves for `x` in the interval `[0, modulus)` such that `self * x ≡ 1 (mod modulus)`.
|
|
<a href=#893 id=893 data-nosnippet>893</a> /// The solution exists if and only if `gcd(self, modulus) == 1`.
|
|
<a href=#894 id=894 data-nosnippet>894</a> ///
|
|
<a href=#895 id=895 data-nosnippet>895</a> /// ```
|
|
<a href=#896 id=896 data-nosnippet>896</a> /// use num_bigint::BigUint;
|
|
<a href=#897 id=897 data-nosnippet>897</a> /// use num_traits::{One, Zero};
|
|
<a href=#898 id=898 data-nosnippet>898</a> ///
|
|
<a href=#899 id=899 data-nosnippet>899</a> /// let m = BigUint::from(383_u32);
|
|
<a href=#900 id=900 data-nosnippet>900</a> ///
|
|
<a href=#901 id=901 data-nosnippet>901</a> /// // Trivial cases
|
|
<a href=#902 id=902 data-nosnippet>902</a> /// assert_eq!(BigUint::zero().modinv(&m), None);
|
|
<a href=#903 id=903 data-nosnippet>903</a> /// assert_eq!(BigUint::one().modinv(&m), Some(BigUint::one()));
|
|
<a href=#904 id=904 data-nosnippet>904</a> /// let neg1 = &m - 1u32;
|
|
<a href=#905 id=905 data-nosnippet>905</a> /// assert_eq!(neg1.modinv(&m), Some(neg1));
|
|
<a href=#906 id=906 data-nosnippet>906</a> ///
|
|
<a href=#907 id=907 data-nosnippet>907</a> /// let a = BigUint::from(271_u32);
|
|
<a href=#908 id=908 data-nosnippet>908</a> /// let x = a.modinv(&m).unwrap();
|
|
<a href=#909 id=909 data-nosnippet>909</a> /// assert_eq!(x, BigUint::from(106_u32));
|
|
<a href=#910 id=910 data-nosnippet>910</a> /// assert_eq!(x.modinv(&m).unwrap(), a);
|
|
<a href=#911 id=911 data-nosnippet>911</a> /// assert!((a * x % m).is_one());
|
|
<a href=#912 id=912 data-nosnippet>912</a> /// ```
|
|
<a href=#913 id=913 data-nosnippet>913</a> </span><span class="kw">pub fn </span>modinv(<span class="kw-2">&</span><span class="self">self</span>, modulus: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
|
|
<a href=#914 id=914 data-nosnippet>914</a> <span class="comment">// Based on the inverse pseudocode listed here:
|
|
<a href=#915 id=915 data-nosnippet>915</a> // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Modular_integers
|
|
<a href=#916 id=916 data-nosnippet>916</a> // TODO: consider Binary or Lehmer's GCD algorithms for optimization.
|
|
<a href=#917 id=917 data-nosnippet>917</a>
|
|
<a href=#918 id=918 data-nosnippet>918</a> </span><span class="macro">assert!</span>(
|
|
<a href=#919 id=919 data-nosnippet>919</a> !modulus.is_zero(),
|
|
<a href=#920 id=920 data-nosnippet>920</a> <span class="string">"attempt to calculate with zero modulus!"
|
|
<a href=#921 id=921 data-nosnippet>921</a> </span>);
|
|
<a href=#922 id=922 data-nosnippet>922</a> <span class="kw">if </span>modulus.is_one() {
|
|
<a href=#923 id=923 data-nosnippet>923</a> <span class="kw">return </span><span class="prelude-val">Some</span>(<span class="self">Self</span>::zero());
|
|
<a href=#924 id=924 data-nosnippet>924</a> }
|
|
<a href=#925 id=925 data-nosnippet>925</a>
|
|
<a href=#926 id=926 data-nosnippet>926</a> <span class="kw">let </span><span class="kw-2">mut </span>r0; <span class="comment">// = modulus.clone();
|
|
<a href=#927 id=927 data-nosnippet>927</a> </span><span class="kw">let </span><span class="kw-2">mut </span>r1 = <span class="self">self </span>% modulus;
|
|
<a href=#928 id=928 data-nosnippet>928</a> <span class="kw">let </span><span class="kw-2">mut </span>t0; <span class="comment">// = Self::zero();
|
|
<a href=#929 id=929 data-nosnippet>929</a> </span><span class="kw">let </span><span class="kw-2">mut </span>t1; <span class="comment">// = Self::one();
|
|
<a href=#930 id=930 data-nosnippet>930</a>
|
|
<a href=#931 id=931 data-nosnippet>931</a> // Lift and simplify the first iteration to avoid some initial allocations.
|
|
<a href=#932 id=932 data-nosnippet>932</a> </span><span class="kw">if </span>r1.is_zero() {
|
|
<a href=#933 id=933 data-nosnippet>933</a> <span class="kw">return </span><span class="prelude-val">None</span>;
|
|
<a href=#934 id=934 data-nosnippet>934</a> } <span class="kw">else if </span>r1.is_one() {
|
|
<a href=#935 id=935 data-nosnippet>935</a> <span class="kw">return </span><span class="prelude-val">Some</span>(r1);
|
|
<a href=#936 id=936 data-nosnippet>936</a> } <span class="kw">else </span>{
|
|
<a href=#937 id=937 data-nosnippet>937</a> <span class="kw">let </span>(q, r2) = modulus.div_rem(<span class="kw-2">&</span>r1);
|
|
<a href=#938 id=938 data-nosnippet>938</a> <span class="kw">if </span>r2.is_zero() {
|
|
<a href=#939 id=939 data-nosnippet>939</a> <span class="kw">return </span><span class="prelude-val">None</span>;
|
|
<a href=#940 id=940 data-nosnippet>940</a> }
|
|
<a href=#941 id=941 data-nosnippet>941</a> r0 = r1;
|
|
<a href=#942 id=942 data-nosnippet>942</a> r1 = r2;
|
|
<a href=#943 id=943 data-nosnippet>943</a> t0 = <span class="self">Self</span>::one();
|
|
<a href=#944 id=944 data-nosnippet>944</a> t1 = modulus - q;
|
|
<a href=#945 id=945 data-nosnippet>945</a> }
|
|
<a href=#946 id=946 data-nosnippet>946</a>
|
|
<a href=#947 id=947 data-nosnippet>947</a> <span class="kw">while </span>!r1.is_zero() {
|
|
<a href=#948 id=948 data-nosnippet>948</a> <span class="kw">let </span>(q, r2) = r0.div_rem(<span class="kw-2">&</span>r1);
|
|
<a href=#949 id=949 data-nosnippet>949</a> r0 = r1;
|
|
<a href=#950 id=950 data-nosnippet>950</a> r1 = r2;
|
|
<a href=#951 id=951 data-nosnippet>951</a>
|
|
<a href=#952 id=952 data-nosnippet>952</a> <span class="comment">// let t2 = (t0 - q * t1) % modulus;
|
|
<a href=#953 id=953 data-nosnippet>953</a> </span><span class="kw">let </span>qt1 = q * <span class="kw-2">&</span>t1 % modulus;
|
|
<a href=#954 id=954 data-nosnippet>954</a> <span class="kw">let </span>t2 = <span class="kw">if </span>t0 < qt1 {
|
|
<a href=#955 id=955 data-nosnippet>955</a> t0 + (modulus - qt1)
|
|
<a href=#956 id=956 data-nosnippet>956</a> } <span class="kw">else </span>{
|
|
<a href=#957 id=957 data-nosnippet>957</a> t0 - qt1
|
|
<a href=#958 id=958 data-nosnippet>958</a> };
|
|
<a href=#959 id=959 data-nosnippet>959</a> t0 = t1;
|
|
<a href=#960 id=960 data-nosnippet>960</a> t1 = t2;
|
|
<a href=#961 id=961 data-nosnippet>961</a> }
|
|
<a href=#962 id=962 data-nosnippet>962</a>
|
|
<a href=#963 id=963 data-nosnippet>963</a> <span class="kw">if </span>r0.is_one() {
|
|
<a href=#964 id=964 data-nosnippet>964</a> <span class="prelude-val">Some</span>(t0)
|
|
<a href=#965 id=965 data-nosnippet>965</a> } <span class="kw">else </span>{
|
|
<a href=#966 id=966 data-nosnippet>966</a> <span class="prelude-val">None
|
|
<a href=#967 id=967 data-nosnippet>967</a> </span>}
|
|
<a href=#968 id=968 data-nosnippet>968</a> }
|
|
<a href=#969 id=969 data-nosnippet>969</a>
|
|
<a href=#970 id=970 data-nosnippet>970</a> <span class="doccomment">/// Returns the truncated principal square root of `self` --
|
|
<a href=#971 id=971 data-nosnippet>971</a> /// see [Roots::sqrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.sqrt)
|
|
<a href=#972 id=972 data-nosnippet>972</a> </span><span class="kw">pub fn </span>sqrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
|
|
<a href=#973 id=973 data-nosnippet>973</a> Roots::sqrt(<span class="self">self</span>)
|
|
<a href=#974 id=974 data-nosnippet>974</a> }
|
|
<a href=#975 id=975 data-nosnippet>975</a>
|
|
<a href=#976 id=976 data-nosnippet>976</a> <span class="doccomment">/// Returns the truncated principal cube root of `self` --
|
|
<a href=#977 id=977 data-nosnippet>977</a> /// see [Roots::cbrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.cbrt).
|
|
<a href=#978 id=978 data-nosnippet>978</a> </span><span class="kw">pub fn </span>cbrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
|
|
<a href=#979 id=979 data-nosnippet>979</a> Roots::cbrt(<span class="self">self</span>)
|
|
<a href=#980 id=980 data-nosnippet>980</a> }
|
|
<a href=#981 id=981 data-nosnippet>981</a>
|
|
<a href=#982 id=982 data-nosnippet>982</a> <span class="doccomment">/// Returns the truncated principal `n`th root of `self` --
|
|
<a href=#983 id=983 data-nosnippet>983</a> /// see [Roots::nth_root](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#tymethod.nth_root).
|
|
<a href=#984 id=984 data-nosnippet>984</a> </span><span class="kw">pub fn </span>nth_root(<span class="kw-2">&</span><span class="self">self</span>, n: u32) -> <span class="self">Self </span>{
|
|
<a href=#985 id=985 data-nosnippet>985</a> Roots::nth_root(<span class="self">self</span>, n)
|
|
<a href=#986 id=986 data-nosnippet>986</a> }
|
|
<a href=#987 id=987 data-nosnippet>987</a>
|
|
<a href=#988 id=988 data-nosnippet>988</a> <span class="doccomment">/// Returns the number of least-significant bits that are zero,
|
|
<a href=#989 id=989 data-nosnippet>989</a> /// or `None` if the entire number is zero.
|
|
<a href=#990 id=990 data-nosnippet>990</a> </span><span class="kw">pub fn </span>trailing_zeros(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u64> {
|
|
<a href=#991 id=991 data-nosnippet>991</a> <span class="kw">let </span>i = <span class="self">self</span>.data.iter().position(|<span class="kw-2">&</span>digit| <span class="macro">digit !</span>= <span class="number">0</span>)<span class="question-mark">?</span>;
|
|
<a href=#992 id=992 data-nosnippet>992</a> <span class="kw">let </span>zeros: u64 = <span class="self">self</span>.data[i].trailing_zeros().into();
|
|
<a href=#993 id=993 data-nosnippet>993</a> <span class="prelude-val">Some</span>(i <span class="kw">as </span>u64 * u64::from(big_digit::BITS) + zeros)
|
|
<a href=#994 id=994 data-nosnippet>994</a> }
|
|
<a href=#995 id=995 data-nosnippet>995</a>
|
|
<a href=#996 id=996 data-nosnippet>996</a> <span class="doccomment">/// Returns the number of least-significant bits that are ones.
|
|
<a href=#997 id=997 data-nosnippet>997</a> </span><span class="kw">pub fn </span>trailing_ones(<span class="kw-2">&</span><span class="self">self</span>) -> u64 {
|
|
<a href=#998 id=998 data-nosnippet>998</a> <span class="kw">if let </span><span class="prelude-val">Some</span>(i) = <span class="self">self</span>.data.iter().position(|<span class="kw-2">&</span>digit| !<span class="macro">digit !</span>= <span class="number">0</span>) {
|
|
<a href=#999 id=999 data-nosnippet>999</a> <span class="kw">let </span>ones: u64 = <span class="self">self</span>.data[i].trailing_ones().into();
|
|
<a href=#1000 id=1000 data-nosnippet>1000</a> i <span class="kw">as </span>u64 * u64::from(big_digit::BITS) + ones
|
|
<a href=#1001 id=1001 data-nosnippet>1001</a> } <span class="kw">else </span>{
|
|
<a href=#1002 id=1002 data-nosnippet>1002</a> <span class="self">self</span>.data.len() <span class="kw">as </span>u64 * u64::from(big_digit::BITS)
|
|
<a href=#1003 id=1003 data-nosnippet>1003</a> }
|
|
<a href=#1004 id=1004 data-nosnippet>1004</a> }
|
|
<a href=#1005 id=1005 data-nosnippet>1005</a>
|
|
<a href=#1006 id=1006 data-nosnippet>1006</a> <span class="doccomment">/// Returns the number of one bits.
|
|
<a href=#1007 id=1007 data-nosnippet>1007</a> </span><span class="kw">pub fn </span>count_ones(<span class="kw-2">&</span><span class="self">self</span>) -> u64 {
|
|
<a href=#1008 id=1008 data-nosnippet>1008</a> <span class="self">self</span>.data.iter().map(|<span class="kw-2">&</span>d| u64::from(d.count_ones())).sum()
|
|
<a href=#1009 id=1009 data-nosnippet>1009</a> }
|
|
<a href=#1010 id=1010 data-nosnippet>1010</a>
|
|
<a href=#1011 id=1011 data-nosnippet>1011</a> <span class="doccomment">/// Returns whether the bit in the given position is set
|
|
<a href=#1012 id=1012 data-nosnippet>1012</a> </span><span class="kw">pub fn </span>bit(<span class="kw-2">&</span><span class="self">self</span>, bit: u64) -> bool {
|
|
<a href=#1013 id=1013 data-nosnippet>1013</a> <span class="kw">let </span>bits_per_digit = u64::from(big_digit::BITS);
|
|
<a href=#1014 id=1014 data-nosnippet>1014</a> <span class="kw">if let </span><span class="prelude-val">Some</span>(digit_index) = (bit / bits_per_digit).to_usize() {
|
|
<a href=#1015 id=1015 data-nosnippet>1015</a> <span class="kw">if let </span><span class="prelude-val">Some</span>(digit) = <span class="self">self</span>.data.get(digit_index) {
|
|
<a href=#1016 id=1016 data-nosnippet>1016</a> <span class="kw">let </span>bit_mask = (<span class="number">1 </span><span class="kw">as </span>BigDigit) << (bit % bits_per_digit);
|
|
<a href=#1017 id=1017 data-nosnippet>1017</a> <span class="kw">return </span>(digit & bit_mask) != <span class="number">0</span>;
|
|
<a href=#1018 id=1018 data-nosnippet>1018</a> }
|
|
<a href=#1019 id=1019 data-nosnippet>1019</a> }
|
|
<a href=#1020 id=1020 data-nosnippet>1020</a> <span class="bool-val">false
|
|
<a href=#1021 id=1021 data-nosnippet>1021</a> </span>}
|
|
<a href=#1022 id=1022 data-nosnippet>1022</a>
|
|
<a href=#1023 id=1023 data-nosnippet>1023</a> <span class="doccomment">/// Sets or clears the bit in the given position
|
|
<a href=#1024 id=1024 data-nosnippet>1024</a> ///
|
|
<a href=#1025 id=1025 data-nosnippet>1025</a> /// Note that setting a bit greater than the current bit length, a reallocation may be needed
|
|
<a href=#1026 id=1026 data-nosnippet>1026</a> /// to store the new digits
|
|
<a href=#1027 id=1027 data-nosnippet>1027</a> </span><span class="kw">pub fn </span>set_bit(<span class="kw-2">&mut </span><span class="self">self</span>, bit: u64, value: bool) {
|
|
<a href=#1028 id=1028 data-nosnippet>1028</a> <span class="comment">// Note: we're saturating `digit_index` and `new_len` -- any such case is guaranteed to
|
|
<a href=#1029 id=1029 data-nosnippet>1029</a> // fail allocation, and that's more consistent than adding our own overflow panics.
|
|
<a href=#1030 id=1030 data-nosnippet>1030</a> </span><span class="kw">let </span>bits_per_digit = u64::from(big_digit::BITS);
|
|
<a href=#1031 id=1031 data-nosnippet>1031</a> <span class="kw">let </span>digit_index = (bit / bits_per_digit).to_usize().unwrap_or(usize::MAX);
|
|
<a href=#1032 id=1032 data-nosnippet>1032</a> <span class="kw">let </span>bit_mask = (<span class="number">1 </span><span class="kw">as </span>BigDigit) << (bit % bits_per_digit);
|
|
<a href=#1033 id=1033 data-nosnippet>1033</a> <span class="kw">if </span>value {
|
|
<a href=#1034 id=1034 data-nosnippet>1034</a> <span class="kw">if </span>digit_index >= <span class="self">self</span>.data.len() {
|
|
<a href=#1035 id=1035 data-nosnippet>1035</a> <span class="kw">let </span>new_len = digit_index.saturating_add(<span class="number">1</span>);
|
|
<a href=#1036 id=1036 data-nosnippet>1036</a> <span class="self">self</span>.data.resize(new_len, <span class="number">0</span>);
|
|
<a href=#1037 id=1037 data-nosnippet>1037</a> }
|
|
<a href=#1038 id=1038 data-nosnippet>1038</a> <span class="self">self</span>.data[digit_index] |= bit_mask;
|
|
<a href=#1039 id=1039 data-nosnippet>1039</a> } <span class="kw">else if </span>digit_index < <span class="self">self</span>.data.len() {
|
|
<a href=#1040 id=1040 data-nosnippet>1040</a> <span class="self">self</span>.data[digit_index] &= !bit_mask;
|
|
<a href=#1041 id=1041 data-nosnippet>1041</a> <span class="comment">// the top bit may have been cleared, so normalize
|
|
<a href=#1042 id=1042 data-nosnippet>1042</a> </span><span class="self">self</span>.normalize();
|
|
<a href=#1043 id=1043 data-nosnippet>1043</a> }
|
|
<a href=#1044 id=1044 data-nosnippet>1044</a> }
|
|
<a href=#1045 id=1045 data-nosnippet>1045</a>}
|
|
<a href=#1046 id=1046 data-nosnippet>1046</a>
|
|
<a href=#1047 id=1047 data-nosnippet>1047</a><span class="kw">impl </span>num_traits::FromBytes <span class="kw">for </span>BigUint {
|
|
<a href=#1048 id=1048 data-nosnippet>1048</a> <span class="kw">type </span>Bytes = [u8];
|
|
<a href=#1049 id=1049 data-nosnippet>1049</a>
|
|
<a href=#1050 id=1050 data-nosnippet>1050</a> <span class="kw">fn </span>from_be_bytes(bytes: <span class="kw-2">&</span><span class="self">Self</span>::Bytes) -> <span class="self">Self </span>{
|
|
<a href=#1051 id=1051 data-nosnippet>1051</a> <span class="self">Self</span>::from_bytes_be(bytes)
|
|
<a href=#1052 id=1052 data-nosnippet>1052</a> }
|
|
<a href=#1053 id=1053 data-nosnippet>1053</a>
|
|
<a href=#1054 id=1054 data-nosnippet>1054</a> <span class="kw">fn </span>from_le_bytes(bytes: <span class="kw-2">&</span><span class="self">Self</span>::Bytes) -> <span class="self">Self </span>{
|
|
<a href=#1055 id=1055 data-nosnippet>1055</a> <span class="self">Self</span>::from_bytes_le(bytes)
|
|
<a href=#1056 id=1056 data-nosnippet>1056</a> }
|
|
<a href=#1057 id=1057 data-nosnippet>1057</a>}
|
|
<a href=#1058 id=1058 data-nosnippet>1058</a>
|
|
<a href=#1059 id=1059 data-nosnippet>1059</a><span class="kw">impl </span>num_traits::ToBytes <span class="kw">for </span>BigUint {
|
|
<a href=#1060 id=1060 data-nosnippet>1060</a> <span class="kw">type </span>Bytes = Vec<u8>;
|
|
<a href=#1061 id=1061 data-nosnippet>1061</a>
|
|
<a href=#1062 id=1062 data-nosnippet>1062</a> <span class="kw">fn </span>to_be_bytes(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self</span>::Bytes {
|
|
<a href=#1063 id=1063 data-nosnippet>1063</a> <span class="self">self</span>.to_bytes_be()
|
|
<a href=#1064 id=1064 data-nosnippet>1064</a> }
|
|
<a href=#1065 id=1065 data-nosnippet>1065</a>
|
|
<a href=#1066 id=1066 data-nosnippet>1066</a> <span class="kw">fn </span>to_le_bytes(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self</span>::Bytes {
|
|
<a href=#1067 id=1067 data-nosnippet>1067</a> <span class="self">self</span>.to_bytes_le()
|
|
<a href=#1068 id=1068 data-nosnippet>1068</a> }
|
|
<a href=#1069 id=1069 data-nosnippet>1069</a>}
|
|
<a href=#1070 id=1070 data-nosnippet>1070</a>
|
|
<a href=#1071 id=1071 data-nosnippet>1071</a><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">trait </span>IntDigits {
|
|
<a href=#1072 id=1072 data-nosnippet>1072</a> <span class="kw">fn </span>digits(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>[BigDigit];
|
|
<a href=#1073 id=1073 data-nosnippet>1073</a> <span class="kw">fn </span>digits_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="kw-2">&mut </span>Vec<BigDigit>;
|
|
<a href=#1074 id=1074 data-nosnippet>1074</a> <span class="kw">fn </span>normalize(<span class="kw-2">&mut </span><span class="self">self</span>);
|
|
<a href=#1075 id=1075 data-nosnippet>1075</a> <span class="kw">fn </span>capacity(<span class="kw-2">&</span><span class="self">self</span>) -> usize;
|
|
<a href=#1076 id=1076 data-nosnippet>1076</a> <span class="kw">fn </span>len(<span class="kw-2">&</span><span class="self">self</span>) -> usize;
|
|
<a href=#1077 id=1077 data-nosnippet>1077</a>}
|
|
<a href=#1078 id=1078 data-nosnippet>1078</a>
|
|
<a href=#1079 id=1079 data-nosnippet>1079</a><span class="kw">impl </span>IntDigits <span class="kw">for </span>BigUint {
|
|
<a href=#1080 id=1080 data-nosnippet>1080</a> <span class="attr">#[inline]
|
|
<a href=#1081 id=1081 data-nosnippet>1081</a> </span><span class="kw">fn </span>digits(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>[BigDigit] {
|
|
<a href=#1082 id=1082 data-nosnippet>1082</a> <span class="kw-2">&</span><span class="self">self</span>.data
|
|
<a href=#1083 id=1083 data-nosnippet>1083</a> }
|
|
<a href=#1084 id=1084 data-nosnippet>1084</a> <span class="attr">#[inline]
|
|
<a href=#1085 id=1085 data-nosnippet>1085</a> </span><span class="kw">fn </span>digits_mut(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="kw-2">&mut </span>Vec<BigDigit> {
|
|
<a href=#1086 id=1086 data-nosnippet>1086</a> <span class="kw-2">&mut </span><span class="self">self</span>.data
|
|
<a href=#1087 id=1087 data-nosnippet>1087</a> }
|
|
<a href=#1088 id=1088 data-nosnippet>1088</a> <span class="attr">#[inline]
|
|
<a href=#1089 id=1089 data-nosnippet>1089</a> </span><span class="kw">fn </span>normalize(<span class="kw-2">&mut </span><span class="self">self</span>) {
|
|
<a href=#1090 id=1090 data-nosnippet>1090</a> <span class="self">self</span>.normalize();
|
|
<a href=#1091 id=1091 data-nosnippet>1091</a> }
|
|
<a href=#1092 id=1092 data-nosnippet>1092</a> <span class="attr">#[inline]
|
|
<a href=#1093 id=1093 data-nosnippet>1093</a> </span><span class="kw">fn </span>capacity(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
|
|
<a href=#1094 id=1094 data-nosnippet>1094</a> <span class="self">self</span>.data.capacity()
|
|
<a href=#1095 id=1095 data-nosnippet>1095</a> }
|
|
<a href=#1096 id=1096 data-nosnippet>1096</a> <span class="attr">#[inline]
|
|
<a href=#1097 id=1097 data-nosnippet>1097</a> </span><span class="kw">fn </span>len(<span class="kw-2">&</span><span class="self">self</span>) -> usize {
|
|
<a href=#1098 id=1098 data-nosnippet>1098</a> <span class="self">self</span>.data.len()
|
|
<a href=#1099 id=1099 data-nosnippet>1099</a> }
|
|
<a href=#1100 id=1100 data-nosnippet>1100</a>}
|
|
<a href=#1101 id=1101 data-nosnippet>1101</a>
|
|
<a href=#1102 id=1102 data-nosnippet>1102</a><span class="doccomment">/// Convert a `u32` chunk (len is either 1 or 2) to a single `u64` digit
|
|
<a href=#1103 id=1103 data-nosnippet>1103</a></span><span class="attr">#[inline]
|
|
<a href=#1104 id=1104 data-nosnippet>1104</a></span><span class="kw">fn </span>u32_chunk_to_u64(chunk: <span class="kw-2">&</span>[u32]) -> u64 {
|
|
<a href=#1105 id=1105 data-nosnippet>1105</a> <span class="comment">// raw could have odd length
|
|
<a href=#1106 id=1106 data-nosnippet>1106</a> </span><span class="kw">let </span><span class="kw-2">mut </span>digit = chunk[<span class="number">0</span>] <span class="kw">as </span>u64;
|
|
<a href=#1107 id=1107 data-nosnippet>1107</a> <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">&</span>hi) = chunk.get(<span class="number">1</span>) {
|
|
<a href=#1108 id=1108 data-nosnippet>1108</a> digit |= (hi <span class="kw">as </span>u64) << <span class="number">32</span>;
|
|
<a href=#1109 id=1109 data-nosnippet>1109</a> }
|
|
<a href=#1110 id=1110 data-nosnippet>1110</a> digit
|
|
<a href=#1111 id=1111 data-nosnippet>1111</a>}
|
|
<a href=#1112 id=1112 data-nosnippet>1112</a>
|
|
<a href=#1113 id=1113 data-nosnippet>1113</a><span class="macro">cfg_32_or_test!</span>(
|
|
<a href=#1114 id=1114 data-nosnippet>1114</a> <span class="doccomment">/// Combine four `u32`s into a single `u128`.
|
|
<a href=#1115 id=1115 data-nosnippet>1115</a> </span><span class="attr">#[inline]
|
|
<a href=#1116 id=1116 data-nosnippet>1116</a> </span><span class="kw">fn </span>u32_to_u128(a: u32, b: u32, c: u32, d: u32) -> u128 {
|
|
<a href=#1117 id=1117 data-nosnippet>1117</a> u128::from(d) | (u128::from(c) << <span class="number">32</span>) | (u128::from(b) << <span class="number">64</span>) | (u128::from(a) << <span class="number">96</span>)
|
|
<a href=#1118 id=1118 data-nosnippet>1118</a> }
|
|
<a href=#1119 id=1119 data-nosnippet>1119</a>);
|
|
<a href=#1120 id=1120 data-nosnippet>1120</a>
|
|
<a href=#1121 id=1121 data-nosnippet>1121</a><span class="macro">cfg_32_or_test!</span>(
|
|
<a href=#1122 id=1122 data-nosnippet>1122</a> <span class="doccomment">/// Split a single `u128` into four `u32`.
|
|
<a href=#1123 id=1123 data-nosnippet>1123</a> </span><span class="attr">#[inline]
|
|
<a href=#1124 id=1124 data-nosnippet>1124</a> </span><span class="kw">fn </span>u32_from_u128(n: u128) -> (u32, u32, u32, u32) {
|
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<a href=#1125 id=1125 data-nosnippet>1125</a> (
|
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<a href=#1126 id=1126 data-nosnippet>1126</a> (n >> <span class="number">96</span>) <span class="kw">as </span>u32,
|
|
<a href=#1127 id=1127 data-nosnippet>1127</a> (n >> <span class="number">64</span>) <span class="kw">as </span>u32,
|
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<a href=#1128 id=1128 data-nosnippet>1128</a> (n >> <span class="number">32</span>) <span class="kw">as </span>u32,
|
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<a href=#1129 id=1129 data-nosnippet>1129</a> n <span class="kw">as </span>u32,
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<a href=#1130 id=1130 data-nosnippet>1130</a> )
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<a href=#1131 id=1131 data-nosnippet>1131</a> }
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<a href=#1132 id=1132 data-nosnippet>1132</a>);
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|
<a href=#1133 id=1133 data-nosnippet>1133</a>
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<a href=#1134 id=1134 data-nosnippet>1134</a><span class="macro">cfg_digit!</span>(
|
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<a href=#1135 id=1135 data-nosnippet>1135</a> <span class="attr">#[test]
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|
<a href=#1136 id=1136 data-nosnippet>1136</a> </span><span class="kw">fn </span>test_from_slice() {
|
|
<a href=#1137 id=1137 data-nosnippet>1137</a> <span class="kw">fn </span>check(slice: <span class="kw-2">&</span>[u32], data: <span class="kw-2">&</span>[BigDigit]) {
|
|
<a href=#1138 id=1138 data-nosnippet>1138</a> <span class="macro">assert_eq!</span>(BigUint::from_slice(slice).data, data);
|
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<a href=#1139 id=1139 data-nosnippet>1139</a> }
|
|
<a href=#1140 id=1140 data-nosnippet>1140</a> check(<span class="kw-2">&</span>[<span class="number">1</span>], <span class="kw-2">&</span>[<span class="number">1</span>]);
|
|
<a href=#1141 id=1141 data-nosnippet>1141</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[]);
|
|
<a href=#1142 id=1142 data-nosnippet>1142</a> check(<span class="kw-2">&</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[<span class="number">1</span>, <span class="number">2</span>]);
|
|
<a href=#1143 id=1143 data-nosnippet>1143</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>]);
|
|
<a href=#1144 id=1144 data-nosnippet>1144</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>]);
|
|
<a href=#1145 id=1145 data-nosnippet>1145</a> check(<span class="kw-2">&</span>[-<span class="number">1i32 </span><span class="kw">as </span>u32], <span class="kw-2">&</span>[-<span class="number">1i32 </span><span class="kw">as </span>BigDigit]);
|
|
<a href=#1146 id=1146 data-nosnippet>1146</a> }
|
|
<a href=#1147 id=1147 data-nosnippet>1147</a>
|
|
<a href=#1148 id=1148 data-nosnippet>1148</a> <span class="attr">#[test]
|
|
<a href=#1149 id=1149 data-nosnippet>1149</a> </span><span class="kw">fn </span>test_from_slice() {
|
|
<a href=#1150 id=1150 data-nosnippet>1150</a> <span class="kw">fn </span>check(slice: <span class="kw-2">&</span>[u32], data: <span class="kw-2">&</span>[BigDigit]) {
|
|
<a href=#1151 id=1151 data-nosnippet>1151</a> <span class="macro">assert_eq!</span>(
|
|
<a href=#1152 id=1152 data-nosnippet>1152</a> BigUint::from_slice(slice).data,
|
|
<a href=#1153 id=1153 data-nosnippet>1153</a> data,
|
|
<a href=#1154 id=1154 data-nosnippet>1154</a> <span class="string">"from {:?}, to {:?}"</span>,
|
|
<a href=#1155 id=1155 data-nosnippet>1155</a> slice,
|
|
<a href=#1156 id=1156 data-nosnippet>1156</a> data
|
|
<a href=#1157 id=1157 data-nosnippet>1157</a> );
|
|
<a href=#1158 id=1158 data-nosnippet>1158</a> }
|
|
<a href=#1159 id=1159 data-nosnippet>1159</a> check(<span class="kw-2">&</span>[<span class="number">1</span>], <span class="kw-2">&</span>[<span class="number">1</span>]);
|
|
<a href=#1160 id=1160 data-nosnippet>1160</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[]);
|
|
<a href=#1161 id=1161 data-nosnippet>1161</a> check(<span class="kw-2">&</span>[<span class="number">1</span>, <span class="number">2</span>], <span class="kw-2">&</span>[<span class="number">8_589_934_593</span>]);
|
|
<a href=#1162 id=1162 data-nosnippet>1162</a> check(<span class="kw-2">&</span>[<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[<span class="number">8_589_934_593</span>]);
|
|
<a href=#1163 id=1163 data-nosnippet>1163</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">8_589_934_593</span>]);
|
|
<a href=#1164 id=1164 data-nosnippet>1164</a> check(<span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>, <span class="number">0</span>], <span class="kw-2">&</span>[<span class="number">0</span>, <span class="number">8_589_934_593</span>]);
|
|
<a href=#1165 id=1165 data-nosnippet>1165</a> check(<span class="kw-2">&</span>[-<span class="number">1i32 </span><span class="kw">as </span>u32], <span class="kw-2">&</span>[(-<span class="number">1i32 </span><span class="kw">as </span>u32) <span class="kw">as </span>BigDigit]);
|
|
<a href=#1166 id=1166 data-nosnippet>1166</a> }
|
|
<a href=#1167 id=1167 data-nosnippet>1167</a>);
|
|
<a href=#1168 id=1168 data-nosnippet>1168</a>
|
|
<a href=#1169 id=1169 data-nosnippet>1169</a><span class="attr">#[test]
|
|
<a href=#1170 id=1170 data-nosnippet>1170</a></span><span class="kw">fn </span>test_u32_u128() {
|
|
<a href=#1171 id=1171 data-nosnippet>1171</a> <span class="macro">assert_eq!</span>(u32_from_u128(<span class="number">0u128</span>), (<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>));
|
|
<a href=#1172 id=1172 data-nosnippet>1172</a> <span class="macro">assert_eq!</span>(
|
|
<a href=#1173 id=1173 data-nosnippet>1173</a> u32_from_u128(u128::MAX),
|
|
<a href=#1174 id=1174 data-nosnippet>1174</a> (u32::MAX, u32::MAX, u32::MAX, u32::MAX)
|
|
<a href=#1175 id=1175 data-nosnippet>1175</a> );
|
|
<a href=#1176 id=1176 data-nosnippet>1176</a>
|
|
<a href=#1177 id=1177 data-nosnippet>1177</a> <span class="macro">assert_eq!</span>(u32_from_u128(u32::MAX <span class="kw">as </span>u128), (<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, u32::MAX));
|
|
<a href=#1178 id=1178 data-nosnippet>1178</a>
|
|
<a href=#1179 id=1179 data-nosnippet>1179</a> <span class="macro">assert_eq!</span>(u32_from_u128(u64::MAX <span class="kw">as </span>u128), (<span class="number">0</span>, <span class="number">0</span>, u32::MAX, u32::MAX));
|
|
<a href=#1180 id=1180 data-nosnippet>1180</a>
|
|
<a href=#1181 id=1181 data-nosnippet>1181</a> <span class="macro">assert_eq!</span>(
|
|
<a href=#1182 id=1182 data-nosnippet>1182</a> u32_from_u128((u64::MAX <span class="kw">as </span>u128) + u32::MAX <span class="kw">as </span>u128),
|
|
<a href=#1183 id=1183 data-nosnippet>1183</a> (<span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, u32::MAX - <span class="number">1</span>)
|
|
<a href=#1184 id=1184 data-nosnippet>1184</a> );
|
|
<a href=#1185 id=1185 data-nosnippet>1185</a>
|
|
<a href=#1186 id=1186 data-nosnippet>1186</a> <span class="macro">assert_eq!</span>(u32_from_u128(<span class="number">36_893_488_151_714_070_528</span>), (<span class="number">0</span>, <span class="number">2</span>, <span class="number">1</span>, <span class="number">0</span>));
|
|
<a href=#1187 id=1187 data-nosnippet>1187</a>}
|
|
<a href=#1188 id=1188 data-nosnippet>1188</a>
|
|
<a href=#1189 id=1189 data-nosnippet>1189</a><span class="attr">#[test]
|
|
<a href=#1190 id=1190 data-nosnippet>1190</a></span><span class="kw">fn </span>test_u128_u32_roundtrip() {
|
|
<a href=#1191 id=1191 data-nosnippet>1191</a> <span class="comment">// roundtrips
|
|
<a href=#1192 id=1192 data-nosnippet>1192</a> </span><span class="kw">let </span>values = <span class="macro">vec!</span>[
|
|
<a href=#1193 id=1193 data-nosnippet>1193</a> <span class="number">0u128</span>,
|
|
<a href=#1194 id=1194 data-nosnippet>1194</a> <span class="number">1u128</span>,
|
|
<a href=#1195 id=1195 data-nosnippet>1195</a> u64::MAX <span class="kw">as </span>u128 * <span class="number">3</span>,
|
|
<a href=#1196 id=1196 data-nosnippet>1196</a> u32::MAX <span class="kw">as </span>u128,
|
|
<a href=#1197 id=1197 data-nosnippet>1197</a> u64::MAX <span class="kw">as </span>u128,
|
|
<a href=#1198 id=1198 data-nosnippet>1198</a> (u64::MAX <span class="kw">as </span>u128) + u32::MAX <span class="kw">as </span>u128,
|
|
<a href=#1199 id=1199 data-nosnippet>1199</a> u128::MAX,
|
|
<a href=#1200 id=1200 data-nosnippet>1200</a> ];
|
|
<a href=#1201 id=1201 data-nosnippet>1201</a>
|
|
<a href=#1202 id=1202 data-nosnippet>1202</a> <span class="kw">for </span>val <span class="kw">in </span><span class="kw-2">&</span>values {
|
|
<a href=#1203 id=1203 data-nosnippet>1203</a> <span class="kw">let </span>(a, b, c, d) = u32_from_u128(<span class="kw-2">*</span>val);
|
|
<a href=#1204 id=1204 data-nosnippet>1204</a> <span class="macro">assert_eq!</span>(u32_to_u128(a, b, c, d), <span class="kw-2">*</span>val);
|
|
<a href=#1205 id=1205 data-nosnippet>1205</a> }
|
|
<a href=#1206 id=1206 data-nosnippet>1206</a>}
|
|
</code></pre></div></section></main></body></html> |