<!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 to the Rust file `libcore/num/bignum.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>bignum.rs.html -- source</title><link rel="stylesheet" type="text/css" href="../../../normalize.css"><link rel="stylesheet" type="text/css" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../../dark.css"><link rel="stylesheet" type="text/css" href="../../../light.css" id="themeStyle"><script src="../../../storage.js"></script><link rel="shortcut icon" href="https://doc.rust-lang.org/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../../core/index.html'><img src='https://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png' alt='logo' width='100'></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><input class="search-input" name="search" autocomplete="off" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><a id="settings-menu" href="../../../settings.html"><img src="../../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><pre class="line-numbers"><span id="1"> 1</span>
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</pre><pre class="rust ">
<span class="comment">// Copyright 2015 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! Custom arbitrary-precision number (bignum) implementation.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! This is designed to avoid the heap allocation at expense of stack memory.</span>
<span class="doccomment">//! The most used bignum type, `Big32x40`, is limited by 32 × 40 = 1,280 bits</span>
<span class="doccomment">//! and will take at most 160 bytes of stack memory. This is more than enough</span>
<span class="doccomment">//! for round-tripping all possible finite `f64` values.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! In principle it is possible to have multiple bignum types for different</span>
<span class="doccomment">//! inputs, but we don't do so to avoid the code bloat. Each bignum is still</span>
<span class="doccomment">//! tracked for the actual usages, so it normally doesn't matter.</span>
<span class="comment">// This module is only for dec2flt and flt2dec, and only public because of coretests.</span>
<span class="comment">// It is not intended to ever be stabilized.</span>
<span class="attribute">#![<span class="ident">doc</span>(<span class="ident">hidden</span>)]</span>
<span class="attribute">#![<span class="ident">unstable</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"core_private_bignum"</span>,
<span class="ident">reason</span> <span class="op">=</span> <span class="string">"internal routines only exposed for testing"</span>,
<span class="ident">issue</span> <span class="op">=</span> <span class="string">"0"</span>)]</span>
<span class="attribute">#![<span class="ident">macro_use</span>]</span>
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">use</span> <span class="ident">intrinsics</span>;
<span class="doccomment">/// Arithmetic operations required by bignums.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">FullOps</span>: <span class="ident">Sized</span> {
<span class="doccomment">/// Returns `(carry', v')` such that `carry' * 2^W + v' = self + other + carry`,</span>
<span class="doccomment">/// where `W` is the number of bits in `Self`.</span>
<span class="kw">fn</span> <span class="ident">full_add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>, <span class="ident">carry</span>: <span class="ident">bool</span>) <span class="op">-></span> (<span class="ident">bool</span> <span class="comment">/* carry */</span>, <span class="self">Self</span>);
<span class="doccomment">/// Returns `(carry', v')` such that `carry' * 2^W + v' = self * other + carry`,</span>
<span class="doccomment">/// where `W` is the number of bits in `Self`.</span>
<span class="kw">fn</span> <span class="ident">full_mul</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>, <span class="ident">carry</span>: <span class="self">Self</span>) <span class="op">-></span> (<span class="self">Self</span> <span class="comment">/* carry */</span>, <span class="self">Self</span>);
<span class="doccomment">/// Returns `(carry', v')` such that `carry' * 2^W + v' = self * other + other2 + carry`,</span>
<span class="doccomment">/// where `W` is the number of bits in `Self`.</span>
<span class="kw">fn</span> <span class="ident">full_mul_add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="self">Self</span>, <span class="ident">other2</span>: <span class="self">Self</span>, <span class="ident">carry</span>: <span class="self">Self</span>) <span class="op">-></span> (<span class="self">Self</span> <span class="comment">/* carry */</span>, <span class="self">Self</span>);
<span class="doccomment">/// Returns `(quo, rem)` such that `borrow * 2^W + self = quo * other + rem`</span>
<span class="doccomment">/// and `0 <= rem < other`, where `W` is the number of bits in `Self`.</span>
<span class="kw">fn</span> <span class="ident">full_div_rem</span>(<span class="self">self</span>,
<span class="ident">other</span>: <span class="self">Self</span>,
<span class="ident">borrow</span>: <span class="self">Self</span>)
<span class="op">-></span> (<span class="self">Self</span> <span class="comment">/* quotient */</span>, <span class="self">Self</span> <span class="comment">/* remainder */</span>);
}
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">impl_full_ops</span> {
($(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>:<span class="ident">ty</span>: <span class="ident">add</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">addfn</span>:<span class="ident">path</span>), <span class="ident">mul</span><span class="op">/</span><span class="ident">div</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>:<span class="ident">ident</span>);)<span class="kw-2">*</span>) <span class="op">=></span> (
$(
<span class="kw">impl</span> <span class="ident">FullOps</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span> {
<span class="kw">fn</span> <span class="ident">full_add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">carry</span>: <span class="ident">bool</span>) <span class="op">-></span> (<span class="ident">bool</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) {
<span class="comment">// this cannot overflow, the output is between 0 and 2*2^nbits - 1</span>
<span class="comment">// FIXME will LLVM optimize this into ADC or similar???</span>
<span class="kw">let</span> (<span class="ident">v</span>, <span class="ident">carry1</span>) <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">intrinsics</span>::<span class="ident">add_with_overflow</span>(<span class="self">self</span>, <span class="ident">other</span>) };
<span class="kw">let</span> (<span class="ident">v</span>, <span class="ident">carry2</span>) <span class="op">=</span> <span class="kw">unsafe</span> {
<span class="ident">intrinsics</span>::<span class="ident">add_with_overflow</span>(<span class="ident">v</span>, <span class="kw">if</span> <span class="ident">carry</span> {<span class="number">1</span>} <span class="kw">else</span> {<span class="number">0</span>})
};
(<span class="ident">carry1</span> <span class="op">||</span> <span class="ident">carry2</span>, <span class="ident">v</span>)
}
<span class="kw">fn</span> <span class="ident">full_mul</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">carry</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) {
<span class="comment">// this cannot overflow, the output is between 0 and 2^nbits * (2^nbits - 1)</span>
<span class="kw">let</span> <span class="ident">nbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> (<span class="self">self</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op">*</span> (<span class="ident">other</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op">+</span> (<span class="ident">carry</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>);
((<span class="ident">v</span> <span class="op">>></span> <span class="ident">nbits</span>) <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">v</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>)
}
<span class="kw">fn</span> <span class="ident">full_mul_add</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">other2</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">carry</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) {
<span class="comment">// this cannot overflow, the output is between 0 and 2^(2*nbits) - 1</span>
<span class="kw">let</span> <span class="ident">nbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> (<span class="self">self</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op">*</span> (<span class="ident">other</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op">+</span> (<span class="ident">other2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op">+</span>
(<span class="ident">carry</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>);
((<span class="ident">v</span> <span class="op">>></span> <span class="ident">nbits</span>) <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">v</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>)
}
<span class="kw">fn</span> <span class="ident">full_div_rem</span>(<span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="ident">borrow</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) {
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">borrow</span> <span class="op"><</span> <span class="ident">other</span>);
<span class="comment">// this cannot overflow, the dividend is between 0 and other * 2^nbits - 1</span>
<span class="kw">let</span> <span class="ident">nbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="ident">lhs</span> <span class="op">=</span> ((<span class="ident">borrow</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>) <span class="op"><<</span> <span class="ident">nbits</span>) <span class="op">|</span> (<span class="self">self</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>);
<span class="kw">let</span> <span class="ident">rhs</span> <span class="op">=</span> <span class="ident">other</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">bigty</span>;
((<span class="ident">lhs</span> <span class="op">/</span> <span class="ident">rhs</span>) <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>, (<span class="ident">lhs</span> <span class="op">%</span> <span class="ident">rhs</span>) <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>)
}
}
)<span class="op">*</span>
)
}
<span class="macro">impl_full_ops</span><span class="macro">!</span> {
<span class="ident">u8</span>: <span class="ident">add</span>(<span class="ident">intrinsics</span>::<span class="ident">u8_add_with_overflow</span>), <span class="ident">mul</span><span class="op">/</span><span class="ident">div</span>(<span class="ident">u16</span>);
<span class="ident">u16</span>: <span class="ident">add</span>(<span class="ident">intrinsics</span>::<span class="ident">u16_add_with_overflow</span>), <span class="ident">mul</span><span class="op">/</span><span class="ident">div</span>(<span class="ident">u32</span>);
<span class="ident">u32</span>: <span class="ident">add</span>(<span class="ident">intrinsics</span>::<span class="ident">u32_add_with_overflow</span>), <span class="ident">mul</span><span class="op">/</span><span class="ident">div</span>(<span class="ident">u64</span>);
<span class="comment">// u64: add(intrinsics::u64_add_with_overflow), mul/div(u128); // see RFC #521 for enabling this.</span>
}
<span class="doccomment">/// Table of powers of 5 representable in digits. Specifically, the largest {u8, u16, u32} value</span>
<span class="doccomment">/// that's a power of five, plus the corresponding exponent. Used in `mul_pow5`.</span>
<span class="kw">const</span> <span class="ident">SMALL_POW5</span>: [(<span class="ident">u64</span>, <span class="ident">usize</span>); <span class="number">3</span>] <span class="op">=</span> [(<span class="number">125</span>, <span class="number">3</span>), (<span class="number">15625</span>, <span class="number">6</span>), (<span class="number">1_220_703_125</span>, <span class="number">13</span>)];
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">define_bignum</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>:<span class="ident">ident</span>: <span class="kw">type</span><span class="op">=</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>:<span class="ident">ty</span>, <span class="ident">n</span><span class="op">=</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>:<span class="ident">expr</span>) <span class="op">=></span> (
<span class="doccomment">/// Stack-allocated arbitrary-precision (up to certain limit) integer.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This is backed by a fixed-size array of given type ("digit").</span>
<span class="doccomment">/// While the array is not very large (normally some hundred bytes),</span>
<span class="doccomment">/// copying it recklessly may result in the performance hit.</span>
<span class="doccomment">/// Thus this is intentionally not `Copy`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// All operations available to bignums panic in the case of overflows.</span>
<span class="doccomment">/// The caller is responsible to use large enough bignum types.</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="doccomment">/// One plus the offset to the maximum "digit" in use.</span>
<span class="doccomment">/// This does not decrease, so be aware of the computation order.</span>
<span class="doccomment">/// `base[size..]` should be zero.</span>
<span class="ident">size</span>: <span class="ident">usize</span>,
<span class="doccomment">/// Digits. `[a, b, c, ...]` represents `a + b*2^W + c*2^(2W) + ...`</span>
<span class="doccomment">/// where `W` is the number of bits in the digit type.</span>
<span class="ident">base</span>: [<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>; <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>]
}
<span class="kw">impl</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="doccomment">/// Makes a bignum from one digit.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_small</span>(<span class="ident">v</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">base</span> <span class="op">=</span> [<span class="number">0</span>; <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>];
<span class="ident">base</span>[<span class="number">0</span>] <span class="op">=</span> <span class="ident">v</span>;
<span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> { <span class="ident">size</span>: <span class="number">1</span>, <span class="ident">base</span>: <span class="ident">base</span> }
}
<span class="doccomment">/// Makes a bignum from `u64` value.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_u64</span>(<span class="kw-2">mut</span> <span class="ident">v</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">base</span> <span class="op">=</span> [<span class="number">0</span>; <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>];
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sz</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">while</span> <span class="ident">v</span> <span class="op">></span> <span class="number">0</span> {
<span class="ident">base</span>[<span class="ident">sz</span>] <span class="op">=</span> <span class="ident">v</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>;
<span class="ident">v</span> <span class="op">>>=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="ident">sz</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> { <span class="ident">size</span>: <span class="ident">sz</span>, <span class="ident">base</span>: <span class="ident">base</span> }
}
<span class="doccomment">/// Returns the internal digits as a slice `[a, b, c, ...]` such that the numeric</span>
<span class="doccomment">/// value is `a + b * 2^W + c * 2^(2W) + ...` where `W` is the number of bits in</span>
<span class="doccomment">/// the digit type.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">digits</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-></span> <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>] {
<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">base</span>[..<span class="self">self</span>.<span class="ident">size</span>]
}
<span class="doccomment">/// Returns the `i`-th bit where bit 0 is the least significant one.</span>
<span class="doccomment">/// In other words, the bit with weight `2^i`.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">get_bit</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">i</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="ident">u8</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">let</span> <span class="ident">digitbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="ident">d</span> <span class="op">=</span> <span class="ident">i</span> <span class="op">/</span> <span class="ident">digitbits</span>;
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="ident">i</span> <span class="op">%</span> <span class="ident">digitbits</span>;
((<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">d</span>] <span class="op">>></span> <span class="ident">b</span>) <span class="op">&</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">u8</span>
}
<span class="doccomment">/// Returns `true` if the bignum is zero.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">is_zero</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">digits</span>().<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="kw-2">&</span><span class="ident">v</span><span class="op">|</span> <span class="ident">v</span> <span class="op">==</span> <span class="number">0</span>)
}
<span class="doccomment">/// Returns the number of bits necessary to represent this value. Note that zero</span>
<span class="doccomment">/// is considered to need 0 bits.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">bit_length</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-></span> <span class="ident">usize</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="comment">// Skip over the most significant digits which are zero.</span>
<span class="kw">let</span> <span class="ident">digits</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">digits</span>();
<span class="kw">let</span> <span class="ident">zeros</span> <span class="op">=</span> <span class="ident">digits</span>.<span class="ident">iter</span>().<span class="ident">rev</span>().<span class="ident">take_while</span>(<span class="op">|</span><span class="op">&&</span><span class="ident">x</span><span class="op">|</span> <span class="ident">x</span> <span class="op">==</span> <span class="number">0</span>).<span class="ident">count</span>();
<span class="kw">let</span> <span class="ident">end</span> <span class="op">=</span> <span class="ident">digits</span>.<span class="ident">len</span>() <span class="op">-</span> <span class="ident">zeros</span>;
<span class="kw">let</span> <span class="ident">nonzero</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">digits</span>[..<span class="ident">end</span>];
<span class="kw">if</span> <span class="ident">nonzero</span>.<span class="ident">is_empty</span>() {
<span class="comment">// There are no non-zero digits, i.e. the number is zero.</span>
<span class="kw">return</span> <span class="number">0</span>;
}
<span class="comment">// This could be optimized with leading_zeros() and bit shifts, but that's</span>
<span class="comment">// probably not worth the hassle.</span>
<span class="kw">let</span> <span class="ident">digitbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>()<span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">nonzero</span>.<span class="ident">len</span>() <span class="op">*</span> <span class="ident">digitbits</span> <span class="op">-</span> <span class="number">1</span>;
<span class="kw">while</span> <span class="self">self</span>.<span class="ident">get_bit</span>(<span class="ident">i</span>) <span class="op">==</span> <span class="number">0</span> {
<span class="ident">i</span> <span class="op">-=</span> <span class="number">1</span>;
}
<span class="ident">i</span> <span class="op">+</span> <span class="number">1</span>
}
<span class="doccomment">/// Adds `other` to itself and returns its own mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">add</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span>(<span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">cmp</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sz</span> <span class="op">=</span> <span class="ident">cmp</span>::<span class="ident">max</span>(<span class="self">self</span>.<span class="ident">size</span>, <span class="ident">other</span>.<span class="ident">size</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">carry</span> <span class="op">=</span> <span class="bool-val">false</span>;
<span class="kw">for</span> (<span class="ident">a</span>, <span class="ident">b</span>) <span class="kw">in</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span>].<span class="ident">iter_mut</span>().<span class="ident">zip</span>(<span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">base</span>[..<span class="ident">sz</span>]) {
<span class="kw">let</span> (<span class="ident">c</span>, <span class="ident">v</span>) <span class="op">=</span> (<span class="kw-2">*</span><span class="ident">a</span>).<span class="ident">full_add</span>(<span class="kw-2">*</span><span class="ident">b</span>, <span class="ident">carry</span>);
<span class="kw-2">*</span><span class="ident">a</span> <span class="op">=</span> <span class="ident">v</span>;
<span class="ident">carry</span> <span class="op">=</span> <span class="ident">c</span>;
}
<span class="kw">if</span> <span class="ident">carry</span> {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">sz</span>] <span class="op">=</span> <span class="number">1</span>;
<span class="ident">sz</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">sz</span>;
<span class="self">self</span>
}
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">add_small</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="kw">let</span> (<span class="kw-2">mut</span> <span class="ident">carry</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">base</span>[<span class="number">0</span>].<span class="ident">full_add</span>(<span class="ident">other</span>, <span class="bool-val">false</span>);
<span class="self">self</span>.<span class="ident">base</span>[<span class="number">0</span>] <span class="op">=</span> <span class="ident">v</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="number">1</span>;
<span class="kw">while</span> <span class="ident">carry</span> {
<span class="kw">let</span> (<span class="ident">c</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>].<span class="ident">full_add</span>(<span class="number">0</span>, <span class="ident">carry</span>);
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>] <span class="op">=</span> <span class="ident">v</span>;
<span class="ident">carry</span> <span class="op">=</span> <span class="ident">c</span>;
<span class="ident">i</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="kw">if</span> <span class="ident">i</span> <span class="op">></span> <span class="self">self</span>.<span class="ident">size</span> {
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">i</span>;
}
<span class="self">self</span>
}
<span class="doccomment">/// Subtracts `other` from itself and returns its own mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">sub</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span>(<span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">cmp</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="kw">let</span> <span class="ident">sz</span> <span class="op">=</span> <span class="ident">cmp</span>::<span class="ident">max</span>(<span class="self">self</span>.<span class="ident">size</span>, <span class="ident">other</span>.<span class="ident">size</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">noborrow</span> <span class="op">=</span> <span class="bool-val">true</span>;
<span class="kw">for</span> (<span class="ident">a</span>, <span class="ident">b</span>) <span class="kw">in</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span>].<span class="ident">iter_mut</span>().<span class="ident">zip</span>(<span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">base</span>[..<span class="ident">sz</span>]) {
<span class="kw">let</span> (<span class="ident">c</span>, <span class="ident">v</span>) <span class="op">=</span> (<span class="kw-2">*</span><span class="ident">a</span>).<span class="ident">full_add</span>(<span class="op">!</span><span class="kw-2">*</span><span class="ident">b</span>, <span class="ident">noborrow</span>);
<span class="kw-2">*</span><span class="ident">a</span> <span class="op">=</span> <span class="ident">v</span>;
<span class="ident">noborrow</span> <span class="op">=</span> <span class="ident">c</span>;
}
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">noborrow</span>);
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">sz</span>;
<span class="self">self</span>
}
<span class="doccomment">/// Multiplies itself by a digit-sized `other` and returns its own</span>
<span class="doccomment">/// mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mul_small</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sz</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">size</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">carry</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">for</span> <span class="ident">a</span> <span class="kw">in</span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span>] {
<span class="kw">let</span> (<span class="ident">c</span>, <span class="ident">v</span>) <span class="op">=</span> (<span class="kw-2">*</span><span class="ident">a</span>).<span class="ident">full_mul</span>(<span class="ident">other</span>, <span class="ident">carry</span>);
<span class="kw-2">*</span><span class="ident">a</span> <span class="op">=</span> <span class="ident">v</span>;
<span class="ident">carry</span> <span class="op">=</span> <span class="ident">c</span>;
}
<span class="kw">if</span> <span class="ident">carry</span> <span class="op">></span> <span class="number">0</span> {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">sz</span>] <span class="op">=</span> <span class="ident">carry</span>;
<span class="ident">sz</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">sz</span>;
<span class="self">self</span>
}
<span class="doccomment">/// Multiplies itself by `2^bits` and returns its own mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mul_pow2</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">bits</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">let</span> <span class="ident">digitbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">let</span> <span class="ident">digits</span> <span class="op">=</span> <span class="ident">bits</span> <span class="op">/</span> <span class="ident">digitbits</span>;
<span class="kw">let</span> <span class="ident">bits</span> <span class="op">=</span> <span class="ident">bits</span> <span class="op">%</span> <span class="ident">digitbits</span>;
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">digits</span> <span class="op"><</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>);
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="self">self</span>.<span class="ident">base</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span><span class="op">-</span><span class="ident">digits</span>..].<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="kw-2">&</span><span class="ident">v</span><span class="op">|</span> <span class="ident">v</span> <span class="op">==</span> <span class="number">0</span>));
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">bits</span> <span class="op">==</span> <span class="number">0</span> <span class="op">||</span> (<span class="self">self</span>.<span class="ident">base</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span><span class="op">-</span><span class="ident">digits</span><span class="op">-</span><span class="number">1</span>] <span class="op">>></span> (<span class="ident">digitbits</span> <span class="op">-</span> <span class="ident">bits</span>)) <span class="op">==</span> <span class="number">0</span>);
<span class="comment">// shift by `digits * digitbits` bits</span>
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="self">self</span>.<span class="ident">size</span>).<span class="ident">rev</span>() {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span><span class="op">+</span><span class="ident">digits</span>] <span class="op">=</span> <span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>];
}
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">digits</span> {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>] <span class="op">=</span> <span class="number">0</span>;
}
<span class="comment">// shift by `bits` bits</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sz</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">size</span> <span class="op">+</span> <span class="ident">digits</span>;
<span class="kw">if</span> <span class="ident">bits</span> <span class="op">></span> <span class="number">0</span> {
<span class="kw">let</span> <span class="ident">last</span> <span class="op">=</span> <span class="ident">sz</span>;
<span class="kw">let</span> <span class="ident">overflow</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">base</span>[<span class="ident">last</span><span class="op">-</span><span class="number">1</span>] <span class="op">>></span> (<span class="ident">digitbits</span> <span class="op">-</span> <span class="ident">bits</span>);
<span class="kw">if</span> <span class="ident">overflow</span> <span class="op">></span> <span class="number">0</span> {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">last</span>] <span class="op">=</span> <span class="ident">overflow</span>;
<span class="ident">sz</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">digits</span><span class="op">+</span><span class="number">1</span>..<span class="ident">last</span>).<span class="ident">rev</span>() {
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>] <span class="op">=</span> (<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span>] <span class="op"><<</span> <span class="ident">bits</span>) <span class="op">|</span>
(<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">i</span><span class="op">-</span><span class="number">1</span>] <span class="op">>></span> (<span class="ident">digitbits</span> <span class="op">-</span> <span class="ident">bits</span>));
}
<span class="self">self</span>.<span class="ident">base</span>[<span class="ident">digits</span>] <span class="op"><<=</span> <span class="ident">bits</span>;
<span class="comment">// self.base[..digits] is zero, no need to shift</span>
}
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">sz</span>;
<span class="self">self</span>
}
<span class="doccomment">/// Multiplies itself by `5^e` and returns its own mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mul_pow5</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="kw-2">mut</span> <span class="ident">e</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">SMALL_POW5</span>;
<span class="comment">// There are exactly n trailing zeros on 2^n, and the only relevant digit sizes</span>
<span class="comment">// are consecutive powers of two, so this is well suited index for the table.</span>
<span class="kw">let</span> <span class="ident">table_index</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>().<span class="ident">trailing_zeros</span>() <span class="kw">as</span> <span class="ident">usize</span>;
<span class="kw">let</span> (<span class="ident">small_power</span>, <span class="ident">small_e</span>) <span class="op">=</span> <span class="ident">SMALL_POW5</span>[<span class="ident">table_index</span>];
<span class="kw">let</span> <span class="ident">small_power</span> <span class="op">=</span> <span class="ident">small_power</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>;
<span class="comment">// Multiply with the largest single-digit power as long as possible ...</span>
<span class="kw">while</span> <span class="ident">e</span> <span class="op">>=</span> <span class="ident">small_e</span> {
<span class="self">self</span>.<span class="ident">mul_small</span>(<span class="ident">small_power</span>);
<span class="ident">e</span> <span class="op">-=</span> <span class="ident">small_e</span>;
}
<span class="comment">// ... then finish off the remainder.</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rest_power</span> <span class="op">=</span> <span class="number">1</span>;
<span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">e</span> {
<span class="ident">rest_power</span> <span class="op">*=</span> <span class="number">5</span>;
}
<span class="self">self</span>.<span class="ident">mul_small</span>(<span class="ident">rest_power</span>);
<span class="self">self</span>
}
<span class="doccomment">/// Multiplies itself by a number described by `other[0] + other[1] * 2^W +</span>
<span class="doccomment">/// other[2] * 2^(2W) + ...` (where `W` is the number of bits in the digit type)</span>
<span class="doccomment">/// and returns its own mutable reference.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mul_digits</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span>(<span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>]) <span class="op">-></span> <span class="kw-2">&</span><span class="lifetime">'a</span> <span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="comment">// the internal routine. works best when aa.len() <= bb.len().</span>
<span class="kw">fn</span> <span class="ident">mul_inner</span>(<span class="ident">ret</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> [<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>; <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>], <span class="ident">aa</span>: <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>], <span class="ident">bb</span>: <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>]) <span class="op">-></span> <span class="ident">usize</span> {
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">retsz</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">for</span> (<span class="ident">i</span>, <span class="kw-2">&</span><span class="ident">a</span>) <span class="kw">in</span> <span class="ident">aa</span>.<span class="ident">iter</span>().<span class="ident">enumerate</span>() {
<span class="kw">if</span> <span class="ident">a</span> <span class="op">==</span> <span class="number">0</span> { <span class="kw">continue</span>; }
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sz</span> <span class="op">=</span> <span class="ident">bb</span>.<span class="ident">len</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">carry</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">for</span> (<span class="ident">j</span>, <span class="kw-2">&</span><span class="ident">b</span>) <span class="kw">in</span> <span class="ident">bb</span>.<span class="ident">iter</span>().<span class="ident">enumerate</span>() {
<span class="kw">let</span> (<span class="ident">c</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="ident">a</span>.<span class="ident">full_mul_add</span>(<span class="ident">b</span>, <span class="ident">ret</span>[<span class="ident">i</span> <span class="op">+</span> <span class="ident">j</span>], <span class="ident">carry</span>);
<span class="ident">ret</span>[<span class="ident">i</span> <span class="op">+</span> <span class="ident">j</span>] <span class="op">=</span> <span class="ident">v</span>;
<span class="ident">carry</span> <span class="op">=</span> <span class="ident">c</span>;
}
<span class="kw">if</span> <span class="ident">carry</span> <span class="op">></span> <span class="number">0</span> {
<span class="ident">ret</span>[<span class="ident">i</span> <span class="op">+</span> <span class="ident">sz</span>] <span class="op">=</span> <span class="ident">carry</span>;
<span class="ident">sz</span> <span class="op">+=</span> <span class="number">1</span>;
}
<span class="kw">if</span> <span class="ident">retsz</span> <span class="op"><</span> <span class="ident">i</span> <span class="op">+</span> <span class="ident">sz</span> {
<span class="ident">retsz</span> <span class="op">=</span> <span class="ident">i</span> <span class="op">+</span> <span class="ident">sz</span>;
}
}
<span class="ident">retsz</span>
}
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ret</span> <span class="op">=</span> [<span class="number">0</span>; <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>];
<span class="kw">let</span> <span class="ident">retsz</span> <span class="op">=</span> <span class="kw">if</span> <span class="self">self</span>.<span class="ident">size</span> <span class="op"><</span> <span class="ident">other</span>.<span class="ident">len</span>() {
<span class="ident">mul_inner</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">ret</span>, <span class="kw-2">&</span><span class="self">self</span>.<span class="ident">digits</span>(), <span class="ident">other</span>)
} <span class="kw">else</span> {
<span class="ident">mul_inner</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">ret</span>, <span class="ident">other</span>, <span class="kw-2">&</span><span class="self">self</span>.<span class="ident">digits</span>())
};
<span class="self">self</span>.<span class="ident">base</span> <span class="op">=</span> <span class="ident">ret</span>;
<span class="self">self</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">retsz</span>;
<span class="self">self</span>
}
<span class="doccomment">/// Divides itself by a digit-sized `other` and returns its own</span>
<span class="doccomment">/// mutable reference *and* the remainder.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_rem_small</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>, <span class="ident">other</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) <span class="op">-></span> (<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>) {
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">bignum</span>::<span class="ident">FullOps</span>;
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">other</span> <span class="op">></span> <span class="number">0</span>);
<span class="kw">let</span> <span class="ident">sz</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">size</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">borrow</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">for</span> <span class="ident">a</span> <span class="kw">in</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span>].<span class="ident">iter_mut</span>().<span class="ident">rev</span>() {
<span class="kw">let</span> (<span class="ident">q</span>, <span class="ident">r</span>) <span class="op">=</span> (<span class="kw-2">*</span><span class="ident">a</span>).<span class="ident">full_div_rem</span>(<span class="ident">other</span>, <span class="ident">borrow</span>);
<span class="kw-2">*</span><span class="ident">a</span> <span class="op">=</span> <span class="ident">q</span>;
<span class="ident">borrow</span> <span class="op">=</span> <span class="ident">r</span>;
}
(<span class="self">self</span>, <span class="ident">borrow</span>)
}
<span class="doccomment">/// Divide self by another bignum, overwriting `q` with the quotient and `r` with the</span>
<span class="doccomment">/// remainder.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">d</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>, <span class="ident">q</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>, <span class="ident">r</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="comment">// Stupid slow base-2 long division taken from</span>
<span class="comment">// https://en.wikipedia.org/wiki/Division_algorithm</span>
<span class="comment">// FIXME use a greater base ($ty) for the long division.</span>
<span class="macro">assert</span><span class="macro">!</span>(<span class="op">!</span><span class="ident">d</span>.<span class="ident">is_zero</span>());
<span class="kw">let</span> <span class="ident">digitbits</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">8</span>;
<span class="kw">for</span> <span class="ident">digit</span> <span class="kw">in</span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">q</span>.<span class="ident">base</span>[..] {
<span class="kw-2">*</span><span class="ident">digit</span> <span class="op">=</span> <span class="number">0</span>;
}
<span class="kw">for</span> <span class="ident">digit</span> <span class="kw">in</span> <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">r</span>.<span class="ident">base</span>[..] {
<span class="kw-2">*</span><span class="ident">digit</span> <span class="op">=</span> <span class="number">0</span>;
}
<span class="ident">r</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">d</span>.<span class="ident">size</span>;
<span class="ident">q</span>.<span class="ident">size</span> <span class="op">=</span> <span class="number">1</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">q_is_zero</span> <span class="op">=</span> <span class="bool-val">true</span>;
<span class="kw">let</span> <span class="ident">end</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">bit_length</span>();
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="ident">end</span>).<span class="ident">rev</span>() {
<span class="ident">r</span>.<span class="ident">mul_pow2</span>(<span class="number">1</span>);
<span class="ident">r</span>.<span class="ident">base</span>[<span class="number">0</span>] <span class="op">|=</span> <span class="self">self</span>.<span class="ident">get_bit</span>(<span class="ident">i</span>) <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span>;
<span class="kw">if</span> <span class="kw-2">&</span><span class="kw-2">*</span><span class="ident">r</span> <span class="op">>=</span> <span class="ident">d</span> {
<span class="ident">r</span>.<span class="ident">sub</span>(<span class="ident">d</span>);
<span class="comment">// Set bit `i` of q to 1.</span>
<span class="kw">let</span> <span class="ident">digit_idx</span> <span class="op">=</span> <span class="ident">i</span> <span class="op">/</span> <span class="ident">digitbits</span>;
<span class="kw">let</span> <span class="ident">bit_idx</span> <span class="op">=</span> <span class="ident">i</span> <span class="op">%</span> <span class="ident">digitbits</span>;
<span class="kw">if</span> <span class="ident">q_is_zero</span> {
<span class="ident">q</span>.<span class="ident">size</span> <span class="op">=</span> <span class="ident">digit_idx</span> <span class="op">+</span> <span class="number">1</span>;
<span class="ident">q_is_zero</span> <span class="op">=</span> <span class="bool-val">false</span>;
}
<span class="ident">q</span>.<span class="ident">base</span>[<span class="ident">digit_idx</span>] <span class="op">|=</span> <span class="number">1</span> <span class="op"><<</span> <span class="ident">bit_idx</span>;
}
}
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">q</span>.<span class="ident">base</span>[<span class="ident">q</span>.<span class="ident">size</span>..].<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="kw-2">&</span><span class="ident">d</span><span class="op">|</span> <span class="ident">d</span> <span class="op">==</span> <span class="number">0</span>));
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">r</span>.<span class="ident">base</span>[<span class="ident">r</span>.<span class="ident">size</span>..].<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="kw-2">&</span><span class="ident">d</span><span class="op">|</span> <span class="ident">d</span> <span class="op">==</span> <span class="number">0</span>));
}
}
<span class="kw">impl</span> ::<span class="ident">cmp</span>::<span class="ident">PartialEq</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">fn</span> <span class="ident">eq</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) <span class="op">-></span> <span class="ident">bool</span> { <span class="self">self</span>.<span class="ident">base</span>[..] <span class="op">==</span> <span class="ident">other</span>.<span class="ident">base</span>[..] }
}
<span class="kw">impl</span> ::<span class="ident">cmp</span>::<span class="ident">Eq</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
}
<span class="kw">impl</span> ::<span class="ident">cmp</span>::<span class="ident">PartialOrd</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">fn</span> <span class="ident">partial_cmp</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) <span class="op">-></span> ::<span class="ident">option</span>::<span class="prelude-ty">Option</span><span class="op"><</span>::<span class="ident">cmp</span>::<span class="ident">Ordering</span><span class="op">></span> {
::<span class="ident">option</span>::<span class="prelude-ty">Option</span>::<span class="prelude-val">Some</span>(<span class="self">self</span>.<span class="ident">cmp</span>(<span class="ident">other</span>))
}
}
<span class="kw">impl</span> ::<span class="ident">cmp</span>::<span class="ident">Ord</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">fn</span> <span class="ident">cmp</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span>) <span class="op">-></span> ::<span class="ident">cmp</span>::<span class="ident">Ordering</span> {
<span class="kw">use</span> <span class="ident">cmp</span>::<span class="ident">max</span>;
<span class="kw">let</span> <span class="ident">sz</span> <span class="op">=</span> <span class="ident">max</span>(<span class="self">self</span>.<span class="ident">size</span>, <span class="ident">other</span>.<span class="ident">size</span>);
<span class="kw">let</span> <span class="ident">lhs</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span>].<span class="ident">iter</span>().<span class="ident">cloned</span>().<span class="ident">rev</span>();
<span class="kw">let</span> <span class="ident">rhs</span> <span class="op">=</span> <span class="ident">other</span>.<span class="ident">base</span>[..<span class="ident">sz</span>].<span class="ident">iter</span>().<span class="ident">cloned</span>().<span class="ident">rev</span>();
<span class="ident">lhs</span>.<span class="ident">cmp</span>(<span class="ident">rhs</span>)
}
}
<span class="kw">impl</span> ::<span class="ident">clone</span>::<span class="ident">Clone</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">fn</span> <span class="ident">clone</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> { <span class="ident">size</span>: <span class="self">self</span>.<span class="ident">size</span>, <span class="ident">base</span>: <span class="self">self</span>.<span class="ident">base</span> }
}
}
<span class="kw">impl</span> ::<span class="ident">fmt</span>::<span class="ident">Debug</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">name</span> {
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> ::<span class="ident">fmt</span>::<span class="ident">Formatter</span>) <span class="op">-></span> ::<span class="ident">fmt</span>::<span class="prelude-ty">Result</span> {
<span class="kw">use</span> <span class="ident">mem</span>;
<span class="kw">let</span> <span class="ident">sz</span> <span class="op">=</span> <span class="kw">if</span> <span class="self">self</span>.<span class="ident">size</span> <span class="op"><</span> <span class="number">1</span> {<span class="number">1</span>} <span class="kw">else</span> {<span class="self">self</span>.<span class="ident">size</span>};
<span class="kw">let</span> <span class="ident">digitlen</span> <span class="op">=</span> <span class="ident">mem</span>::<span class="ident">size_of</span>::<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">ty</span><span class="op">></span>() <span class="op">*</span> <span class="number">2</span>;
<span class="macro">write</span><span class="macro">!</span>(<span class="ident">f</span>, <span class="string">"{:#x}"</span>, <span class="self">self</span>.<span class="ident">base</span>[<span class="ident">sz</span><span class="op">-</span><span class="number">1</span>])<span class="question-mark">?</span>;
<span class="kw">for</span> <span class="kw-2">&</span><span class="ident">v</span> <span class="kw">in</span> <span class="self">self</span>.<span class="ident">base</span>[..<span class="ident">sz</span><span class="op">-</span><span class="number">1</span>].<span class="ident">iter</span>().<span class="ident">rev</span>() {
<span class="macro">write</span><span class="macro">!</span>(<span class="ident">f</span>, <span class="string">"_{:01$x}"</span>, <span class="ident">v</span>, <span class="ident">digitlen</span>)<span class="question-mark">?</span>;
}
::<span class="ident">result</span>::<span class="prelude-ty">Result</span>::<span class="prelude-val">Ok</span>(())
}
}
)
}
<span class="doccomment">/// The digit type for `Big32x40`.</span>
<span class="kw">pub</span> <span class="kw">type</span> <span class="ident">Digit32</span> <span class="op">=</span> <span class="ident">u32</span>;
<span class="macro">define_bignum</span><span class="macro">!</span>(<span class="ident">Big32x40</span>: <span class="kw">type</span><span class="op">=</span><span class="ident">Digit32</span>, <span class="ident">n</span><span class="op">=</span><span class="number">40</span>);
<span class="comment">// this one is used for testing only.</span>
<span class="attribute">#[<span class="ident">doc</span>(<span class="ident">hidden</span>)]</span>
<span class="kw">pub</span> <span class="kw">mod</span> <span class="ident">tests</span> {
<span class="macro">define_bignum</span><span class="macro">!</span>(<span class="ident">Big8x3</span>: <span class="kw">type</span><span class="op">=</span><span class="ident">u8</span>, <span class="ident">n</span><span class="op">=</span><span class="number">3</span>);
}
</pre>
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