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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/num-bigint-0.3.3/src/biguint/division.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>division.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../../num_bigint/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../num_bigint/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span>
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</pre><pre class="rust"><code><span class="kw">use </span><span class="kw">super</span>::addition::__add2;
<span class="attribute">#[cfg(not(u64_digit))]
</span><span class="kw">use </span><span class="kw">super</span>::u32_to_u128;
<span class="kw">use </span><span class="kw">super</span>::BigUint;
<span class="kw">use </span><span class="kw">crate</span>::big_digit::{<span class="self">self</span>, BigDigit, DoubleBigDigit};
<span class="kw">use </span><span class="kw">crate</span>::UsizePromotion;
<span class="kw">use </span>core::cmp::Ordering::{Equal, Greater, Less};
<span class="kw">use </span>core::mem;
<span class="kw">use </span>core::ops::{Div, DivAssign, Rem, RemAssign};
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::{CheckedDiv, One, ToPrimitive, Zero};
<span class="doccomment">/// Divide a two digit numerator by a one digit divisor, returns quotient and remainder:
///
/// Note: the caller must ensure that both the quotient and remainder will fit into a single digit.
/// This is _not_ true for an arbitrary numerator/denominator.
///
/// (This function also matches what the x86 divide instruction does).
</span><span class="attribute">#[inline]
</span><span class="kw">fn </span>div_wide(hi: BigDigit, lo: BigDigit, divisor: BigDigit) -&gt; (BigDigit, BigDigit) {
<span class="macro">debug_assert!</span>(hi &lt; divisor);
<span class="kw">let </span>lhs = big_digit::to_doublebigdigit(hi, lo);
<span class="kw">let </span>rhs = DoubleBigDigit::from(divisor);
((lhs / rhs) <span class="kw">as </span>BigDigit, (lhs % rhs) <span class="kw">as </span>BigDigit)
}
<span class="doccomment">/// For small divisors, we can divide without promoting to `DoubleBigDigit` by
/// using half-size pieces of digit, like long-division.
</span><span class="attribute">#[inline]
</span><span class="kw">fn </span>div_half(rem: BigDigit, digit: BigDigit, divisor: BigDigit) -&gt; (BigDigit, BigDigit) {
<span class="kw">use </span><span class="kw">crate</span>::big_digit::{HALF, HALF_BITS};
<span class="macro">debug_assert!</span>(rem &lt; divisor &amp;&amp; divisor &lt;= HALF);
<span class="kw">let </span>(hi, rem) = ((rem &lt;&lt; HALF_BITS) | (digit &gt;&gt; HALF_BITS)).div_rem(<span class="kw-2">&amp;</span>divisor);
<span class="kw">let </span>(lo, rem) = ((rem &lt;&lt; HALF_BITS) | (digit &amp; HALF)).div_rem(<span class="kw-2">&amp;</span>divisor);
((hi &lt;&lt; HALF_BITS) | lo, rem)
}
<span class="attribute">#[inline]
</span><span class="kw">pub</span>(<span class="kw">super</span>) <span class="kw">fn </span>div_rem_digit(<span class="kw-2">mut </span>a: BigUint, b: BigDigit) -&gt; (BigUint, BigDigit) {
<span class="kw">let </span><span class="kw-2">mut </span>rem = <span class="number">0</span>;
<span class="kw">if </span>b &lt;= big_digit::HALF {
<span class="kw">for </span>d <span class="kw">in </span>a.data.iter_mut().rev() {
<span class="kw">let </span>(q, r) = div_half(rem, <span class="kw-2">*</span>d, b);
<span class="kw-2">*</span>d = q;
rem = r;
}
} <span class="kw">else </span>{
<span class="kw">for </span>d <span class="kw">in </span>a.data.iter_mut().rev() {
<span class="kw">let </span>(q, r) = div_wide(rem, <span class="kw-2">*</span>d, b);
<span class="kw-2">*</span>d = q;
rem = r;
}
}
(a.normalized(), rem)
}
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_digit(a: <span class="kw-2">&amp;</span>BigUint, b: BigDigit) -&gt; BigDigit {
<span class="kw">let </span><span class="kw-2">mut </span>rem = <span class="number">0</span>;
<span class="kw">if </span>b &lt;= big_digit::HALF {
<span class="kw">for </span><span class="kw-2">&amp;</span>digit <span class="kw">in </span>a.data.iter().rev() {
<span class="kw">let </span>(<span class="kw">_</span>, r) = div_half(rem, digit, b);
rem = r;
}
} <span class="kw">else </span>{
<span class="kw">for </span><span class="kw-2">&amp;</span>digit <span class="kw">in </span>a.data.iter().rev() {
<span class="kw">let </span>(<span class="kw">_</span>, r) = div_wide(rem, digit, b);
rem = r;
}
}
rem
}
<span class="doccomment">/// Subtract a multiple.
/// a -= b * c
/// Returns a borrow (if a &lt; b then borrow &gt; 0).
</span><span class="kw">fn </span>sub_mul_digit_same_len(a: <span class="kw-2">&amp;mut </span>[BigDigit], b: <span class="kw-2">&amp;</span>[BigDigit], c: BigDigit) -&gt; BigDigit {
<span class="macro">debug_assert!</span>(a.len() == b.len());
<span class="comment">// carry is between -big_digit::MAX and 0, so to avoid overflow we store
// offset_carry = carry + big_digit::MAX
</span><span class="kw">let </span><span class="kw-2">mut </span>offset_carry = big_digit::MAX;
<span class="kw">for </span>(x, y) <span class="kw">in </span>a.iter_mut().zip(b) {
<span class="comment">// We want to calculate sum = x - y * c + carry.
// sum &gt;= -(big_digit::MAX * big_digit::MAX) - big_digit::MAX
// sum &lt;= big_digit::MAX
// Offsetting sum by (big_digit::MAX &lt;&lt; big_digit::BITS) puts it in DoubleBigDigit range.
</span><span class="kw">let </span>offset_sum = big_digit::to_doublebigdigit(big_digit::MAX, <span class="kw-2">*</span>x)
- big_digit::MAX <span class="kw">as </span>DoubleBigDigit
+ offset_carry <span class="kw">as </span>DoubleBigDigit
- <span class="kw-2">*</span>y <span class="kw">as </span>DoubleBigDigit * c <span class="kw">as </span>DoubleBigDigit;
<span class="kw">let </span>(new_offset_carry, new_x) = big_digit::from_doublebigdigit(offset_sum);
offset_carry = new_offset_carry;
<span class="kw-2">*</span>x = new_x;
}
<span class="comment">// Return the borrow.
</span>big_digit::MAX - offset_carry
}
<span class="kw">fn </span>div_rem(<span class="kw-2">mut </span>u: BigUint, <span class="kw-2">mut </span>d: BigUint) -&gt; (BigUint, BigUint) {
<span class="kw">if </span>d.is_zero() {
<span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>)
}
<span class="kw">if </span>u.is_zero() {
<span class="kw">return </span>(Zero::zero(), Zero::zero());
}
<span class="kw">if </span>d.data.len() == <span class="number">1 </span>{
<span class="kw">if </span>d.data == [<span class="number">1</span>] {
<span class="kw">return </span>(u, Zero::zero());
}
<span class="kw">let </span>(div, rem) = div_rem_digit(u, d.data[<span class="number">0</span>]);
<span class="comment">// reuse d
</span>d.data.clear();
d += rem;
<span class="kw">return </span>(div, d);
}
<span class="comment">// Required or the q_len calculation below can underflow:
</span><span class="kw">match </span>u.cmp(<span class="kw-2">&amp;</span>d) {
Less =&gt; <span class="kw">return </span>(Zero::zero(), u),
Equal =&gt; {
u.set_one();
<span class="kw">return </span>(u, Zero::zero());
}
Greater =&gt; {} <span class="comment">// Do nothing
</span>}
<span class="comment">// This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D:
//
// First, normalize the arguments so the highest bit in the highest digit of the divisor is
// set: the main loop uses the highest digit of the divisor for generating guesses, so we
// want it to be the largest number we can efficiently divide by.
//
</span><span class="kw">let </span>shift = d.data.last().unwrap().leading_zeros() <span class="kw">as </span>usize;
<span class="kw">let </span>(q, r) = <span class="kw">if </span>shift == <span class="number">0 </span>{
<span class="comment">// no need to clone d
</span>div_rem_core(u, <span class="kw-2">&amp;</span>d)
} <span class="kw">else </span>{
div_rem_core(u &lt;&lt; shift, <span class="kw-2">&amp;</span>(d &lt;&lt; shift))
};
<span class="comment">// renormalize the remainder
</span>(q, r &gt;&gt; shift)
}
<span class="kw">pub</span>(<span class="kw">super</span>) <span class="kw">fn </span>div_rem_ref(u: <span class="kw-2">&amp;</span>BigUint, d: <span class="kw-2">&amp;</span>BigUint) -&gt; (BigUint, BigUint) {
<span class="kw">if </span>d.is_zero() {
<span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>)
}
<span class="kw">if </span>u.is_zero() {
<span class="kw">return </span>(Zero::zero(), Zero::zero());
}
<span class="kw">if </span>d.data.len() == <span class="number">1 </span>{
<span class="kw">if </span>d.data == [<span class="number">1</span>] {
<span class="kw">return </span>(u.clone(), Zero::zero());
}
<span class="kw">let </span>(div, rem) = div_rem_digit(u.clone(), d.data[<span class="number">0</span>]);
<span class="kw">return </span>(div, rem.into());
}
<span class="comment">// Required or the q_len calculation below can underflow:
</span><span class="kw">match </span>u.cmp(d) {
Less =&gt; <span class="kw">return </span>(Zero::zero(), u.clone()),
Equal =&gt; <span class="kw">return </span>(One::one(), Zero::zero()),
Greater =&gt; {} <span class="comment">// Do nothing
</span>}
<span class="comment">// This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D:
//
// First, normalize the arguments so the highest bit in the highest digit of the divisor is
// set: the main loop uses the highest digit of the divisor for generating guesses, so we
// want it to be the largest number we can efficiently divide by.
//
</span><span class="kw">let </span>shift = d.data.last().unwrap().leading_zeros() <span class="kw">as </span>usize;
<span class="kw">let </span>(q, r) = <span class="kw">if </span>shift == <span class="number">0 </span>{
<span class="comment">// no need to clone d
</span>div_rem_core(u.clone(), d)
} <span class="kw">else </span>{
div_rem_core(u &lt;&lt; shift, <span class="kw-2">&amp;</span>(d &lt;&lt; shift))
};
<span class="comment">// renormalize the remainder
</span>(q, r &gt;&gt; shift)
}
<span class="doccomment">/// An implementation of the base division algorithm.
/// Knuth, TAOCP vol 2 section 4.3.1, algorithm D, with an improvement from exercises 19-21.
</span><span class="kw">fn </span>div_rem_core(<span class="kw-2">mut </span>a: BigUint, b: <span class="kw-2">&amp;</span>BigUint) -&gt; (BigUint, BigUint) {
<span class="macro">debug_assert!</span>(
a.data.len() &gt;= b.data.len()
&amp;&amp; b.data.len() &gt; <span class="number">1
</span>&amp;&amp; b.data.last().unwrap().leading_zeros() == <span class="number">0
</span>);
<span class="comment">// The algorithm works by incrementally calculating &quot;guesses&quot;, q0, for the next digit of the
// quotient. Once we have any number q0 such that (q0 &lt;&lt; j) * b &lt;= a, we can set
//
// q += q0 &lt;&lt; j
// a -= (q0 &lt;&lt; j) * b
//
// and then iterate until a &lt; b. Then, (q, a) will be our desired quotient and remainder.
//
// q0, our guess, is calculated by dividing the last three digits of a by the last two digits of
// b - this will give us a guess that is close to the actual quotient, but is possibly greater.
// It can only be greater by 1 and only in rare cases, with probability at most
// 2^-(big_digit::BITS-1) for random a, see TAOCP 4.3.1 exercise 21.
//
// If the quotient turns out to be too large, we adjust it by 1:
// q -= 1 &lt;&lt; j
// a += b &lt;&lt; j
// a0 stores an additional extra most significant digit of the dividend, not stored in a.
</span><span class="kw">let </span><span class="kw-2">mut </span>a0 = <span class="number">0</span>;
<span class="comment">// [b1, b0] are the two most significant digits of the divisor. They never change.
</span><span class="kw">let </span>b0 = <span class="kw-2">*</span>b.data.last().unwrap();
<span class="kw">let </span>b1 = b.data[b.data.len() - <span class="number">2</span>];
<span class="kw">let </span>q_len = a.data.len() - b.data.len() + <span class="number">1</span>;
<span class="kw">let </span><span class="kw-2">mut </span>q = BigUint {
data: <span class="macro">vec!</span>[<span class="number">0</span>; q_len],
};
<span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0</span>..q_len).rev() {
<span class="macro">debug_assert!</span>(a.data.len() == b.data.len() + j);
<span class="kw">let </span>a1 = <span class="kw-2">*</span>a.data.last().unwrap();
<span class="kw">let </span>a2 = a.data[a.data.len() - <span class="number">2</span>];
<span class="comment">// The first q0 estimate is [a1,a0] / b0. It will never be too small, it may be too large
// by at most 2.
</span><span class="kw">let </span>(<span class="kw-2">mut </span>q0, <span class="kw-2">mut </span>r) = <span class="kw">if </span>a0 &lt; b0 {
<span class="kw">let </span>(q0, r) = div_wide(a0, a1, b0);
(q0, r <span class="kw">as </span>DoubleBigDigit)
} <span class="kw">else </span>{
<span class="macro">debug_assert!</span>(a0 == b0);
<span class="comment">// Avoid overflowing q0, we know the quotient fits in BigDigit.
// [a1,a0] = b0 * (1&lt;&lt;BITS - 1) + (a0 + a1)
</span>(big_digit::MAX, a0 <span class="kw">as </span>DoubleBigDigit + a1 <span class="kw">as </span>DoubleBigDigit)
};
<span class="comment">// r = [a1,a0] - q0 * b0
//
// Now we want to compute a more precise estimate [a2,a1,a0] / [b1,b0] which can only be
// less or equal to the current q0.
//
// q0 is too large if:
// [a2,a1,a0] &lt; q0 * [b1,b0]
// (r &lt;&lt; BITS) + a2 &lt; q0 * b1
</span><span class="kw">while </span>r &lt;= big_digit::MAX <span class="kw">as </span>DoubleBigDigit
&amp;&amp; big_digit::to_doublebigdigit(r <span class="kw">as </span>BigDigit, a2)
&lt; q0 <span class="kw">as </span>DoubleBigDigit * b1 <span class="kw">as </span>DoubleBigDigit
{
q0 -= <span class="number">1</span>;
r += b0 <span class="kw">as </span>DoubleBigDigit;
}
<span class="comment">// q0 is now either the correct quotient digit, or in rare cases 1 too large.
// Subtract (q0 &lt;&lt; j) from a. This may overflow, in which case we will have to correct.
</span><span class="kw">let </span><span class="kw-2">mut </span>borrow = sub_mul_digit_same_len(<span class="kw-2">&amp;mut </span>a.data[j..], <span class="kw-2">&amp;</span>b.data, q0);
<span class="kw">if </span>borrow &gt; a0 {
<span class="comment">// q0 is too large. We need to add back one multiple of b.
</span>q0 -= <span class="number">1</span>;
borrow -= __add2(<span class="kw-2">&amp;mut </span>a.data[j..], <span class="kw-2">&amp;</span>b.data);
}
<span class="comment">// The top digit of a, stored in a0, has now been zeroed.
</span><span class="macro">debug_assert!</span>(borrow == a0);
q.data[j] = q0;
<span class="comment">// Pop off the next top digit of a.
</span>a0 = a.data.pop().unwrap();
}
a.data.push(a0);
a.normalize();
<span class="macro">debug_assert!</span>(a &lt; <span class="kw-2">*</span>b);
(q.normalized(), a)
}
<span class="macro">forward_val_ref_binop!</span>(<span class="kw">impl </span>Div <span class="kw">for </span>BigUint, div);
<span class="macro">forward_ref_val_binop!</span>(<span class="kw">impl </span>Div <span class="kw">for </span>BigUint, div);
<span class="macro">forward_val_assign!</span>(<span class="kw">impl </span>DivAssign <span class="kw">for </span>BigUint, div_assign);
<span class="kw">impl </span>Div&lt;BigUint&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">let </span>(q, <span class="kw">_</span>) = div_rem(<span class="self">self</span>, other);
q
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>&gt; Div&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;b </span>BigUint&gt; <span class="kw">for </span><span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: <span class="kw-2">&amp;</span>BigUint) -&gt; BigUint {
<span class="kw">let </span>(q, <span class="kw">_</span>) = <span class="self">self</span>.div_rem(other);
q
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; DivAssign&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>/ other;
}
}
<span class="macro">promote_unsigned_scalars!</span>(<span class="kw">impl </span>Div <span class="kw">for </span>BigUint, div);
<span class="macro">promote_unsigned_scalars_assign!</span>(<span class="kw">impl </span>DivAssign <span class="kw">for </span>BigUint, div_assign);
<span class="macro">forward_all_scalar_binop_to_val_val!</span>(<span class="kw">impl </span>Div&lt;u32&gt; <span class="kw">for </span>BigUint, div);
<span class="macro">forward_all_scalar_binop_to_val_val!</span>(<span class="kw">impl </span>Div&lt;u64&gt; <span class="kw">for </span>BigUint, div);
<span class="macro">forward_all_scalar_binop_to_val_val!</span>(<span class="kw">impl </span>Div&lt;u128&gt; <span class="kw">for </span>BigUint, div);
<span class="kw">impl </span>Div&lt;u32&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: u32) -&gt; BigUint {
<span class="kw">let </span>(q, <span class="kw">_</span>) = div_rem_digit(<span class="self">self</span>, other <span class="kw">as </span>BigDigit);
q
}
}
<span class="kw">impl </span>DivAssign&lt;u32&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u32) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>/ other;
}
}
<span class="kw">impl </span>Div&lt;BigUint&gt; <span class="kw">for </span>u32 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">match </span>other.data.len() {
<span class="number">0 </span>=&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="number">1 </span>=&gt; From::from(<span class="self">self </span><span class="kw">as </span>BigDigit / other.data[<span class="number">0</span>]),
<span class="kw">_ </span>=&gt; Zero::zero(),
}
}
}
<span class="kw">impl </span>Div&lt;u64&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: u64) -&gt; BigUint {
<span class="kw">let </span>(q, <span class="kw">_</span>) = div_rem(<span class="self">self</span>, From::from(other));
q
}
}
<span class="kw">impl </span>DivAssign&lt;u64&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u64) {
<span class="comment">// a vec of size 0 does not allocate, so this is fairly cheap
</span><span class="kw">let </span>temp = mem::replace(<span class="self">self</span>, Zero::zero());
<span class="kw-2">*</span><span class="self">self </span>= temp / other;
}
}
<span class="kw">impl </span>Div&lt;BigUint&gt; <span class="kw">for </span>u64 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[cfg(not(u64_digit))]
#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">match </span>other.data.len() {
<span class="number">0 </span>=&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="number">1 </span>=&gt; From::from(<span class="self">self </span>/ u64::from(other.data[<span class="number">0</span>])),
<span class="number">2 </span>=&gt; From::from(<span class="self">self </span>/ big_digit::to_doublebigdigit(other.data[<span class="number">1</span>], other.data[<span class="number">0</span>])),
<span class="kw">_ </span>=&gt; Zero::zero(),
}
}
<span class="attribute">#[cfg(u64_digit)]
#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">match </span>other.data.len() {
<span class="number">0 </span>=&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="number">1 </span>=&gt; From::from(<span class="self">self </span>/ other.data[<span class="number">0</span>]),
<span class="kw">_ </span>=&gt; Zero::zero(),
}
}
}
<span class="kw">impl </span>Div&lt;u128&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: u128) -&gt; BigUint {
<span class="kw">let </span>(q, <span class="kw">_</span>) = div_rem(<span class="self">self</span>, From::from(other));
q
}
}
<span class="kw">impl </span>DivAssign&lt;u128&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>div_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u128) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>/ other;
}
}
<span class="kw">impl </span>Div&lt;BigUint&gt; <span class="kw">for </span>u128 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[cfg(not(u64_digit))]
#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">match </span>other.data.len() {
<span class="number">0 </span>=&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="number">1 </span>=&gt; From::from(<span class="self">self </span>/ u128::from(other.data[<span class="number">0</span>])),
<span class="number">2 </span>=&gt; From::from(
<span class="self">self </span>/ u128::from(big_digit::to_doublebigdigit(other.data[<span class="number">1</span>], other.data[<span class="number">0</span>])),
),
<span class="number">3 </span>=&gt; From::from(<span class="self">self </span>/ u32_to_u128(<span class="number">0</span>, other.data[<span class="number">2</span>], other.data[<span class="number">1</span>], other.data[<span class="number">0</span>])),
<span class="number">4 </span>=&gt; From::from(
<span class="self">self </span>/ u32_to_u128(other.data[<span class="number">3</span>], other.data[<span class="number">2</span>], other.data[<span class="number">1</span>], other.data[<span class="number">0</span>]),
),
<span class="kw">_ </span>=&gt; Zero::zero(),
}
}
<span class="attribute">#[cfg(u64_digit)]
#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">match </span>other.data.len() {
<span class="number">0 </span>=&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="number">1 </span>=&gt; From::from(<span class="self">self </span>/ other.data[<span class="number">0</span>] <span class="kw">as </span>u128),
<span class="number">2 </span>=&gt; From::from(<span class="self">self </span>/ big_digit::to_doublebigdigit(other.data[<span class="number">1</span>], other.data[<span class="number">0</span>])),
<span class="kw">_ </span>=&gt; Zero::zero(),
}
}
}
<span class="macro">forward_val_ref_binop!</span>(<span class="kw">impl </span>Rem <span class="kw">for </span>BigUint, rem);
<span class="macro">forward_ref_val_binop!</span>(<span class="kw">impl </span>Rem <span class="kw">for </span>BigUint, rem);
<span class="macro">forward_val_assign!</span>(<span class="kw">impl </span>RemAssign <span class="kw">for </span>BigUint, rem_assign);
<span class="kw">impl </span>Rem&lt;BigUint&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="kw">if let </span><span class="prelude-val">Some</span>(other) = other.to_u32() {
<span class="kw-2">&amp;</span><span class="self">self </span>% other
} <span class="kw">else </span>{
<span class="kw">let </span>(<span class="kw">_</span>, r) = div_rem(<span class="self">self</span>, other);
r
}
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>&gt; Rem&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;b </span>BigUint&gt; <span class="kw">for </span><span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="self">self</span>, other: <span class="kw-2">&amp;</span>BigUint) -&gt; BigUint {
<span class="kw">if let </span><span class="prelude-val">Some</span>(other) = other.to_u32() {
<span class="self">self </span>% other
} <span class="kw">else </span>{
<span class="kw">let </span>(<span class="kw">_</span>, r) = <span class="self">self</span>.div_rem(other);
r
}
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; RemAssign&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: <span class="kw-2">&amp;</span>BigUint) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>% other;
}
}
<span class="macro">promote_unsigned_scalars!</span>(<span class="kw">impl </span>Rem <span class="kw">for </span>BigUint, rem);
<span class="macro">promote_unsigned_scalars_assign!</span>(<span class="kw">impl </span>RemAssign <span class="kw">for </span>BigUint, rem_assign);
<span class="macro">forward_all_scalar_binop_to_ref_val!</span>(<span class="kw">impl </span>Rem&lt;u32&gt; <span class="kw">for </span>BigUint, rem);
<span class="macro">forward_all_scalar_binop_to_val_val!</span>(<span class="kw">impl </span>Rem&lt;u64&gt; <span class="kw">for </span>BigUint, rem);
<span class="macro">forward_all_scalar_binop_to_val_val!</span>(<span class="kw">impl </span>Rem&lt;u128&gt; <span class="kw">for </span>BigUint, rem);
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; Rem&lt;u32&gt; <span class="kw">for </span><span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="self">self</span>, other: u32) -&gt; BigUint {
rem_digit(<span class="self">self</span>, other <span class="kw">as </span>BigDigit).into()
}
}
<span class="kw">impl </span>RemAssign&lt;u32&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u32) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>% other;
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; Rem&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint&gt; <span class="kw">for </span>u32 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="kw-2">mut </span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint) -&gt; BigUint {
<span class="self">self </span>%= other;
From::from(<span class="self">self</span>)
}
}
<span class="macro">macro_rules! </span>impl_rem_assign_scalar {
(<span class="macro-nonterminal">$scalar</span>:ty, <span class="macro-nonterminal">$to_scalar</span>:ident) =&gt; {
<span class="macro">forward_val_assign_scalar!</span>(<span class="kw">impl </span>RemAssign <span class="kw">for </span>BigUint, <span class="macro-nonterminal">$scalar</span>, rem_assign);
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; RemAssign&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>BigUint&gt; <span class="kw">for </span><span class="macro-nonterminal">$scalar </span>{
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: <span class="kw-2">&amp;</span>BigUint) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw">match </span>other.<span class="macro-nonterminal">$to_scalar</span>() {
<span class="prelude-val">None </span>=&gt; <span class="kw-2">*</span><span class="self">self</span>,
<span class="prelude-val">Some</span>(<span class="number">0</span>) =&gt; <span class="macro">panic!</span>(<span class="string">&quot;attempt to divide by zero&quot;</span>),
<span class="prelude-val">Some</span>(v) =&gt; <span class="kw-2">*</span><span class="self">self </span>% v
};
}
}
}
}
<span class="comment">// we can scalar %= BigUint for any scalar, including signed types
</span><span class="macro">impl_rem_assign_scalar!</span>(u128, to_u128);
<span class="macro">impl_rem_assign_scalar!</span>(usize, to_usize);
<span class="macro">impl_rem_assign_scalar!</span>(u64, to_u64);
<span class="macro">impl_rem_assign_scalar!</span>(u32, to_u32);
<span class="macro">impl_rem_assign_scalar!</span>(u16, to_u16);
<span class="macro">impl_rem_assign_scalar!</span>(u8, to_u8);
<span class="macro">impl_rem_assign_scalar!</span>(i128, to_i128);
<span class="macro">impl_rem_assign_scalar!</span>(isize, to_isize);
<span class="macro">impl_rem_assign_scalar!</span>(i64, to_i64);
<span class="macro">impl_rem_assign_scalar!</span>(i32, to_i32);
<span class="macro">impl_rem_assign_scalar!</span>(i16, to_i16);
<span class="macro">impl_rem_assign_scalar!</span>(i8, to_i8);
<span class="kw">impl </span>Rem&lt;u64&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="self">self</span>, other: u64) -&gt; BigUint {
<span class="kw">let </span>(<span class="kw">_</span>, r) = div_rem(<span class="self">self</span>, From::from(other));
r
}
}
<span class="kw">impl </span>RemAssign&lt;u64&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u64) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>% other;
}
}
<span class="kw">impl </span>Rem&lt;BigUint&gt; <span class="kw">for </span>u64 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="kw-2">mut </span><span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="self">self </span>%= other;
From::from(<span class="self">self</span>)
}
}
<span class="kw">impl </span>Rem&lt;u128&gt; <span class="kw">for </span>BigUint {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="self">self</span>, other: u128) -&gt; BigUint {
<span class="kw">let </span>(<span class="kw">_</span>, r) = div_rem(<span class="self">self</span>, From::from(other));
r
}
}
<span class="kw">impl </span>RemAssign&lt;u128&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u128) {
<span class="kw-2">*</span><span class="self">self </span>= <span class="kw-2">&amp;*</span><span class="self">self </span>% other;
}
}
<span class="kw">impl </span>Rem&lt;BigUint&gt; <span class="kw">for </span>u128 {
<span class="kw">type </span>Output = BigUint;
<span class="attribute">#[inline]
</span><span class="kw">fn </span>rem(<span class="kw-2">mut </span><span class="self">self</span>, other: BigUint) -&gt; BigUint {
<span class="self">self </span>%= other;
From::from(<span class="self">self</span>)
}
}
<span class="kw">impl </span>CheckedDiv <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>checked_div(<span class="kw-2">&amp;</span><span class="self">self</span>, v: <span class="kw-2">&amp;</span>BigUint) -&gt; <span class="prelude-ty">Option</span>&lt;BigUint&gt; {
<span class="kw">if </span>v.is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="prelude-val">Some</span>(<span class="self">self</span>.div(v))
}
}
</code></pre></div>
</section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="num_bigint" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html>