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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/multiplication.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>multiplication.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, add2};
<span class="kw">use </span><span class="kw">super</span>::subtraction::sub2;
<span class="attribute">#[cfg(not(u64_digit))]
</span><span class="kw">use </span><span class="kw">super</span>::u32_from_u128;
<span class="kw">use super</span>::{biguint_from_vec, cmp_slice, 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>::Sign::{<span class="self">self</span>, Minus, NoSign, Plus};
<span class="kw">use crate</span>::{BigInt, UsizePromotion};
<span class="kw">use </span>core::cmp::Ordering;
<span class="kw">use </span>core::iter::Product;
<span class="kw">use </span>core::ops::{Mul, MulAssign};
<span class="kw">use </span>num_traits::{CheckedMul, One, Zero};
<span class="attribute">#[inline]
</span><span class="kw">pub</span>(<span class="kw">super</span>) <span class="kw">fn </span>mac_with_carry(
a: BigDigit,
b: BigDigit,
c: BigDigit,
acc: <span class="kw-2">&amp;mut </span>DoubleBigDigit,
) -&gt; BigDigit {
<span class="kw-2">*</span>acc += DoubleBigDigit::from(a);
<span class="kw-2">*</span>acc += DoubleBigDigit::from(b) * DoubleBigDigit::from(c);
<span class="kw">let </span>lo = <span class="kw-2">*</span>acc <span class="kw">as </span>BigDigit;
<span class="kw-2">*</span>acc &gt;&gt;= big_digit::BITS;
lo
}
<span class="attribute">#[inline]
</span><span class="kw">fn </span>mul_with_carry(a: BigDigit, b: BigDigit, acc: <span class="kw-2">&amp;mut </span>DoubleBigDigit) -&gt; BigDigit {
<span class="kw-2">*</span>acc += DoubleBigDigit::from(a) * DoubleBigDigit::from(b);
<span class="kw">let </span>lo = <span class="kw-2">*</span>acc <span class="kw">as </span>BigDigit;
<span class="kw-2">*</span>acc &gt;&gt;= big_digit::BITS;
lo
}
<span class="doccomment">/// Three argument multiply accumulate:
/// acc += b * c
</span><span class="kw">fn </span>mac_digit(acc: <span class="kw-2">&amp;mut </span>[BigDigit], b: <span class="kw-2">&amp;</span>[BigDigit], c: BigDigit) {
<span class="kw">if </span>c == <span class="number">0 </span>{
<span class="kw">return</span>;
}
<span class="kw">let </span><span class="kw-2">mut </span>carry = <span class="number">0</span>;
<span class="kw">let </span>(a_lo, a_hi) = acc.split_at_mut(b.len());
<span class="kw">for </span>(a, <span class="kw-2">&amp;</span>b) <span class="kw">in </span>a_lo.iter_mut().zip(b) {
<span class="kw-2">*</span>a = mac_with_carry(<span class="kw-2">*</span>a, b, c, <span class="kw-2">&amp;mut </span>carry);
}
<span class="kw">let </span>(carry_hi, carry_lo) = big_digit::from_doublebigdigit(carry);
<span class="kw">let </span>final_carry = <span class="kw">if </span>carry_hi == <span class="number">0 </span>{
__add2(a_hi, <span class="kw-2">&amp;</span>[carry_lo])
} <span class="kw">else </span>{
__add2(a_hi, <span class="kw-2">&amp;</span>[carry_hi, carry_lo])
};
<span class="macro">assert_eq!</span>(final_carry, <span class="number">0</span>, <span class="string">&quot;carry overflow during multiplication!&quot;</span>);
}
<span class="kw">fn </span>bigint_from_slice(slice: <span class="kw-2">&amp;</span>[BigDigit]) -&gt; BigInt {
BigInt::from(biguint_from_vec(slice.to_vec()))
}
<span class="doccomment">/// Three argument multiply accumulate:
/// acc += b * c
</span><span class="attribute">#[allow(clippy::many_single_char_names)]
</span><span class="kw">fn </span>mac3(acc: <span class="kw-2">&amp;mut </span>[BigDigit], b: <span class="kw-2">&amp;</span>[BigDigit], c: <span class="kw-2">&amp;</span>[BigDigit]) {
<span class="kw">let </span>(x, y) = <span class="kw">if </span>b.len() &lt; c.len() { (b, c) } <span class="kw">else </span>{ (c, b) };
<span class="comment">// We use three algorithms for different input sizes.
//
// - For small inputs, long multiplication is fastest.
// - Next we use Karatsuba multiplication (Toom-2), which we have optimized
// to avoid unnecessary allocations for intermediate values.
// - For the largest inputs we use Toom-3, which better optimizes the
// number of operations, but uses more temporary allocations.
//
// The thresholds are somewhat arbitrary, chosen by evaluating the results
// of `cargo bench --bench bigint multiply`.
</span><span class="kw">if </span>x.len() &lt;= <span class="number">32 </span>{
<span class="comment">// Long multiplication:
</span><span class="kw">for </span>(i, xi) <span class="kw">in </span>x.iter().enumerate() {
mac_digit(<span class="kw-2">&amp;mut </span>acc[i..], y, <span class="kw-2">*</span>xi);
}
} <span class="kw">else if </span>x.len() &lt;= <span class="number">256 </span>{
<span class="comment">// Karatsuba multiplication:
//
// The idea is that we break x and y up into two smaller numbers that each have about half
// as many digits, like so (note that multiplying by b is just a shift):
//
// x = x0 + x1 * b
// y = y0 + y1 * b
//
// With some algebra, we can compute x * y with three smaller products, where the inputs to
// each of the smaller products have only about half as many digits as x and y:
//
// x * y = (x0 + x1 * b) * (y0 + y1 * b)
//
// x * y = x0 * y0
// + x0 * y1 * b
// + x1 * y0 * b
// + x1 * y1 * b^2
//
// Let p0 = x0 * y0 and p2 = x1 * y1:
//
// x * y = p0
// + (x0 * y1 + x1 * y0) * b
// + p2 * b^2
//
// The real trick is that middle term:
//
// x0 * y1 + x1 * y0
//
// = x0 * y1 + x1 * y0 - p0 + p0 - p2 + p2
//
// = x0 * y1 + x1 * y0 - x0 * y0 - x1 * y1 + p0 + p2
//
// Now we complete the square:
//
// = -(x0 * y0 - x0 * y1 - x1 * y0 + x1 * y1) + p0 + p2
//
// = -((x1 - x0) * (y1 - y0)) + p0 + p2
//
// Let p1 = (x1 - x0) * (y1 - y0), and substitute back into our original formula:
//
// x * y = p0
// + (p0 + p2 - p1) * b
// + p2 * b^2
//
// Where the three intermediate products are:
//
// p0 = x0 * y0
// p1 = (x1 - x0) * (y1 - y0)
// p2 = x1 * y1
//
// In doing the computation, we take great care to avoid unnecessary temporary variables
// (since creating a BigUint requires a heap allocation): thus, we rearrange the formula a
// bit so we can use the same temporary variable for all the intermediate products:
//
// x * y = p2 * b^2 + p2 * b
// + p0 * b + p0
// - p1 * b
//
// The other trick we use is instead of doing explicit shifts, we slice acc at the
// appropriate offset when doing the add.
// When x is smaller than y, it&#39;s significantly faster to pick b such that x is split in
// half, not y:
</span><span class="kw">let </span>b = x.len() / <span class="number">2</span>;
<span class="kw">let </span>(x0, x1) = x.split_at(b);
<span class="kw">let </span>(y0, y1) = y.split_at(b);
<span class="comment">// We reuse the same BigUint for all the intermediate multiplies and have to size p
// appropriately here: x1.len() &gt;= x0.len and y1.len() &gt;= y0.len():
</span><span class="kw">let </span>len = x1.len() + y1.len() + <span class="number">1</span>;
<span class="kw">let </span><span class="kw-2">mut </span>p = BigUint { data: <span class="macro">vec!</span>[<span class="number">0</span>; len] };
<span class="comment">// p2 = x1 * y1
</span>mac3(<span class="kw-2">&amp;mut </span>p.data[..], x1, y1);
<span class="comment">// Not required, but the adds go faster if we drop any unneeded 0s from the end:
</span>p.normalize();
add2(<span class="kw-2">&amp;mut </span>acc[b..], <span class="kw-2">&amp;</span>p.data[..]);
add2(<span class="kw-2">&amp;mut </span>acc[b * <span class="number">2</span>..], <span class="kw-2">&amp;</span>p.data[..]);
<span class="comment">// Zero out p before the next multiply:
</span>p.data.truncate(<span class="number">0</span>);
p.data.resize(len, <span class="number">0</span>);
<span class="comment">// p0 = x0 * y0
</span>mac3(<span class="kw-2">&amp;mut </span>p.data[..], x0, y0);
p.normalize();
add2(<span class="kw-2">&amp;mut </span>acc[..], <span class="kw-2">&amp;</span>p.data[..]);
add2(<span class="kw-2">&amp;mut </span>acc[b..], <span class="kw-2">&amp;</span>p.data[..]);
<span class="comment">// p1 = (x1 - x0) * (y1 - y0)
// We do this one last, since it may be negative and acc can&#39;t ever be negative:
</span><span class="kw">let </span>(j0_sign, j0) = sub_sign(x1, x0);
<span class="kw">let </span>(j1_sign, j1) = sub_sign(y1, y0);
<span class="kw">match </span>j0_sign * j1_sign {
Plus =&gt; {
p.data.truncate(<span class="number">0</span>);
p.data.resize(len, <span class="number">0</span>);
mac3(<span class="kw-2">&amp;mut </span>p.data[..], <span class="kw-2">&amp;</span>j0.data[..], <span class="kw-2">&amp;</span>j1.data[..]);
p.normalize();
sub2(<span class="kw-2">&amp;mut </span>acc[b..], <span class="kw-2">&amp;</span>p.data[..]);
}
Minus =&gt; {
mac3(<span class="kw-2">&amp;mut </span>acc[b..], <span class="kw-2">&amp;</span>j0.data[..], <span class="kw-2">&amp;</span>j1.data[..]);
}
NoSign =&gt; (),
}
} <span class="kw">else </span>{
<span class="comment">// Toom-3 multiplication:
//
// Toom-3 is like Karatsuba above, but dividing the inputs into three parts.
// Both are instances of Toom-Cook, using `k=3` and `k=2` respectively.
//
// The general idea is to treat the large integers digits as
// polynomials of a certain degree and determine the coefficients/digits
// of the product of the two via interpolation of the polynomial product.
</span><span class="kw">let </span>i = y.len() / <span class="number">3 </span>+ <span class="number">1</span>;
<span class="kw">let </span>x0_len = Ord::min(x.len(), i);
<span class="kw">let </span>x1_len = Ord::min(x.len() - x0_len, i);
<span class="kw">let </span>y0_len = i;
<span class="kw">let </span>y1_len = Ord::min(y.len() - y0_len, i);
<span class="comment">// Break x and y into three parts, representating an order two polynomial.
// t is chosen to be the size of a digit so we can use faster shifts
// in place of multiplications.
//
// x(t) = x2*t^2 + x1*t + x0
</span><span class="kw">let </span>x0 = bigint_from_slice(<span class="kw-2">&amp;</span>x[..x0_len]);
<span class="kw">let </span>x1 = bigint_from_slice(<span class="kw-2">&amp;</span>x[x0_len..x0_len + x1_len]);
<span class="kw">let </span>x2 = bigint_from_slice(<span class="kw-2">&amp;</span>x[x0_len + x1_len..]);
<span class="comment">// y(t) = y2*t^2 + y1*t + y0
</span><span class="kw">let </span>y0 = bigint_from_slice(<span class="kw-2">&amp;</span>y[..y0_len]);
<span class="kw">let </span>y1 = bigint_from_slice(<span class="kw-2">&amp;</span>y[y0_len..y0_len + y1_len]);
<span class="kw">let </span>y2 = bigint_from_slice(<span class="kw-2">&amp;</span>y[y0_len + y1_len..]);
<span class="comment">// Let w(t) = x(t) * y(t)
//
// This gives us the following order-4 polynomial.
//
// w(t) = w4*t^4 + w3*t^3 + w2*t^2 + w1*t + w0
//
// We need to find the coefficients w4, w3, w2, w1 and w0. Instead
// of simply multiplying the x and y in total, we can evaluate w
// at 5 points. An n-degree polynomial is uniquely identified by (n + 1)
// points.
//
// It is arbitrary as to what points we evaluate w at but we use the
// following.
//
// w(t) at t = 0, 1, -1, -2 and inf
//
// The values for w(t) in terms of x(t)*y(t) at these points are:
//
// let a = w(0) = x0 * y0
// let b = w(1) = (x2 + x1 + x0) * (y2 + y1 + y0)
// let c = w(-1) = (x2 - x1 + x0) * (y2 - y1 + y0)
// let d = w(-2) = (4*x2 - 2*x1 + x0) * (4*y2 - 2*y1 + y0)
// let e = w(inf) = x2 * y2 as t -&gt; inf
// x0 + x2, avoiding temporaries
</span><span class="kw">let </span>p = <span class="kw-2">&amp;</span>x0 + <span class="kw-2">&amp;</span>x2;
<span class="comment">// y0 + y2, avoiding temporaries
</span><span class="kw">let </span>q = <span class="kw-2">&amp;</span>y0 + <span class="kw-2">&amp;</span>y2;
<span class="comment">// x2 - x1 + x0, avoiding temporaries
</span><span class="kw">let </span>p2 = <span class="kw-2">&amp;</span>p - <span class="kw-2">&amp;</span>x1;
<span class="comment">// y2 - y1 + y0, avoiding temporaries
</span><span class="kw">let </span>q2 = <span class="kw-2">&amp;</span>q - <span class="kw-2">&amp;</span>y1;
<span class="comment">// w(0)
</span><span class="kw">let </span>r0 = <span class="kw-2">&amp;</span>x0 * <span class="kw-2">&amp;</span>y0;
<span class="comment">// w(inf)
</span><span class="kw">let </span>r4 = <span class="kw-2">&amp;</span>x2 * <span class="kw-2">&amp;</span>y2;
<span class="comment">// w(1)
</span><span class="kw">let </span>r1 = (p + x1) * (q + y1);
<span class="comment">// w(-1)
</span><span class="kw">let </span>r2 = <span class="kw-2">&amp;</span>p2 * <span class="kw-2">&amp;</span>q2;
<span class="comment">// w(-2)
</span><span class="kw">let </span>r3 = ((p2 + x2) * <span class="number">2 </span>- x0) * ((q2 + y2) * <span class="number">2 </span>- y0);
<span class="comment">// Evaluating these points gives us the following system of linear equations.
//
// 0 0 0 0 1 | a
// 1 1 1 1 1 | b
// 1 -1 1 -1 1 | c
// 16 -8 4 -2 1 | d
// 1 0 0 0 0 | e
//
// The solved equation (after gaussian elimination or similar)
// in terms of its coefficients:
//
// w0 = w(0)
// w1 = w(0)/2 + w(1)/3 - w(-1) + w(2)/6 - 2*w(inf)
// w2 = -w(0) + w(1)/2 + w(-1)/2 - w(inf)
// w3 = -w(0)/2 + w(1)/6 + w(-1)/2 - w(1)/6
// w4 = w(inf)
//
// This particular sequence is given by Bodrato and is an interpolation
// of the above equations.
</span><span class="kw">let </span><span class="kw-2">mut </span>comp3: BigInt = (r3 - <span class="kw-2">&amp;</span>r1) / <span class="number">3</span>;
<span class="kw">let </span><span class="kw-2">mut </span>comp1: BigInt = (r1 - <span class="kw-2">&amp;</span>r2) / <span class="number">2</span>;
<span class="kw">let </span><span class="kw-2">mut </span>comp2: BigInt = r2 - <span class="kw-2">&amp;</span>r0;
comp3 = (<span class="kw-2">&amp;</span>comp2 - comp3) / <span class="number">2 </span>+ <span class="kw-2">&amp;</span>r4 * <span class="number">2</span>;
comp2 += <span class="kw-2">&amp;</span>comp1 - <span class="kw-2">&amp;</span>r4;
comp1 -= <span class="kw-2">&amp;</span>comp3;
<span class="comment">// Recomposition. The coefficients of the polynomial are now known.
//
// Evaluate at w(t) where t is our given base to get the result.
</span><span class="kw">let </span>bits = u64::from(big_digit::BITS) * i <span class="kw">as </span>u64;
<span class="kw">let </span>result = r0
+ (comp1 &lt;&lt; bits)
+ (comp2 &lt;&lt; (<span class="number">2 </span>* bits))
+ (comp3 &lt;&lt; (<span class="number">3 </span>* bits))
+ (r4 &lt;&lt; (<span class="number">4 </span>* bits));
<span class="kw">let </span>result_pos = result.to_biguint().unwrap();
add2(<span class="kw-2">&amp;mut </span>acc[..], <span class="kw-2">&amp;</span>result_pos.data);
}
}
<span class="kw">fn </span>mul3(x: <span class="kw-2">&amp;</span>[BigDigit], y: <span class="kw-2">&amp;</span>[BigDigit]) -&gt; BigUint {
<span class="kw">let </span>len = x.len() + y.len() + <span class="number">1</span>;
<span class="kw">let </span><span class="kw-2">mut </span>prod = BigUint { data: <span class="macro">vec!</span>[<span class="number">0</span>; len] };
mac3(<span class="kw-2">&amp;mut </span>prod.data[..], x, y);
prod.normalized()
}
<span class="kw">fn </span>scalar_mul(a: <span class="kw-2">&amp;mut </span>[BigDigit], b: BigDigit) -&gt; BigDigit {
<span class="kw">let </span><span class="kw-2">mut </span>carry = <span class="number">0</span>;
<span class="kw">for </span>a <span class="kw">in </span>a.iter_mut() {
<span class="kw-2">*</span>a = mul_with_carry(<span class="kw-2">*</span>a, b, <span class="kw-2">&amp;mut </span>carry);
}
carry <span class="kw">as </span>BigDigit
}
<span class="kw">fn </span>sub_sign(<span class="kw-2">mut </span>a: <span class="kw-2">&amp;</span>[BigDigit], <span class="kw-2">mut </span>b: <span class="kw-2">&amp;</span>[BigDigit]) -&gt; (Sign, BigUint) {
<span class="comment">// Normalize:
</span>a = <span class="kw-2">&amp;</span>a[..a.iter().rposition(|<span class="kw-2">&amp;</span>x| x != <span class="number">0</span>).map_or(<span class="number">0</span>, |i| i + <span class="number">1</span>)];
b = <span class="kw-2">&amp;</span>b[..b.iter().rposition(|<span class="kw-2">&amp;</span>x| x != <span class="number">0</span>).map_or(<span class="number">0</span>, |i| i + <span class="number">1</span>)];
<span class="kw">match </span>cmp_slice(a, b) {
Ordering::Greater =&gt; {
<span class="kw">let </span><span class="kw-2">mut </span>a = a.to_vec();
sub2(<span class="kw-2">&amp;mut </span>a, b);
(Plus, biguint_from_vec(a))
}
Ordering::Less =&gt; {
<span class="kw">let </span><span class="kw-2">mut </span>b = b.to_vec();
sub2(<span class="kw-2">&amp;mut </span>b, a);
(Minus, biguint_from_vec(b))
}
Ordering::Equal =&gt; (NoSign, Zero::zero()),
}
}
<span class="macro">forward_all_binop_to_ref_ref!</span>(<span class="kw">impl </span>Mul <span class="kw">for </span>BigUint, mul);
<span class="macro">forward_val_assign!</span>(<span class="kw">impl </span>MulAssign <span class="kw">for </span>BigUint, mul_assign);
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>, <span class="lifetime">&#39;b</span>&gt; Mul&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>mul(<span class="self">self</span>, other: <span class="kw-2">&amp;</span>BigUint) -&gt; BigUint {
mul3(<span class="kw-2">&amp;</span><span class="self">self</span>.data[..], <span class="kw-2">&amp;</span>other.data[..])
}
}
<span class="kw">impl</span>&lt;<span class="lifetime">&#39;a</span>&gt; MulAssign&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>mul_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>Mul <span class="kw">for </span>BigUint, mul);
<span class="macro">promote_unsigned_scalars_assign!</span>(<span class="kw">impl </span>MulAssign <span class="kw">for </span>BigUint, mul_assign);
<span class="macro">forward_all_scalar_binop_to_val_val_commutative!</span>(<span class="kw">impl </span>Mul&lt;u32&gt; <span class="kw">for </span>BigUint, mul);
<span class="macro">forward_all_scalar_binop_to_val_val_commutative!</span>(<span class="kw">impl </span>Mul&lt;u64&gt; <span class="kw">for </span>BigUint, mul);
<span class="macro">forward_all_scalar_binop_to_val_val_commutative!</span>(<span class="kw">impl </span>Mul&lt;u128&gt; <span class="kw">for </span>BigUint, mul);
<span class="kw">impl </span>Mul&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>mul(<span class="kw-2">mut </span><span class="self">self</span>, other: u32) -&gt; BigUint {
<span class="self">self </span><span class="kw-2">*</span>= other;
<span class="self">self
</span>}
}
<span class="kw">impl </span>MulAssign&lt;u32&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>mul_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u32) {
<span class="kw">if </span>other == <span class="number">0 </span>{
<span class="self">self</span>.data.clear();
} <span class="kw">else </span>{
<span class="kw">let </span>carry = scalar_mul(<span class="kw-2">&amp;mut </span><span class="self">self</span>.data[..], other <span class="kw">as </span>BigDigit);
<span class="kw">if </span>carry != <span class="number">0 </span>{
<span class="self">self</span>.data.push(carry);
}
}
}
}
<span class="kw">impl </span>Mul&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>mul(<span class="kw-2">mut </span><span class="self">self</span>, other: u64) -&gt; BigUint {
<span class="self">self </span><span class="kw-2">*</span>= other;
<span class="self">self
</span>}
}
<span class="kw">impl </span>MulAssign&lt;u64&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[cfg(not(u64_digit))]
#[inline]
</span><span class="kw">fn </span>mul_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u64) {
<span class="kw">if </span>other == <span class="number">0 </span>{
<span class="self">self</span>.data.clear();
} <span class="kw">else if </span>other &lt;= u64::from(BigDigit::max_value()) {
<span class="kw-2">*</span><span class="self">self </span><span class="kw-2">*</span>= other <span class="kw">as </span>BigDigit
} <span class="kw">else </span>{
<span class="kw">let </span>(hi, lo) = big_digit::from_doublebigdigit(other);
<span class="kw-2">*</span><span class="self">self </span>= mul3(<span class="kw-2">&amp;</span><span class="self">self</span>.data[..], <span class="kw-2">&amp;</span>[lo, hi])
}
}
<span class="attribute">#[cfg(u64_digit)]
#[inline]
</span><span class="kw">fn </span>mul_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u64) {
<span class="kw">if </span>other == <span class="number">0 </span>{
<span class="self">self</span>.data.clear();
} <span class="kw">else </span>{
<span class="kw">let </span>carry = scalar_mul(<span class="kw-2">&amp;mut </span><span class="self">self</span>.data[..], other <span class="kw">as </span>BigDigit);
<span class="kw">if </span>carry != <span class="number">0 </span>{
<span class="self">self</span>.data.push(carry);
}
}
}
}
<span class="kw">impl </span>Mul&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>mul(<span class="kw-2">mut </span><span class="self">self</span>, other: u128) -&gt; BigUint {
<span class="self">self </span><span class="kw-2">*</span>= other;
<span class="self">self
</span>}
}
<span class="kw">impl </span>MulAssign&lt;u128&gt; <span class="kw">for </span>BigUint {
<span class="attribute">#[cfg(not(u64_digit))]
#[inline]
</span><span class="kw">fn </span>mul_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u128) {
<span class="kw">if </span>other == <span class="number">0 </span>{
<span class="self">self</span>.data.clear();
} <span class="kw">else if </span>other &lt;= u128::from(BigDigit::max_value()) {
<span class="kw-2">*</span><span class="self">self </span><span class="kw-2">*</span>= other <span class="kw">as </span>BigDigit
} <span class="kw">else </span>{
<span class="kw">let </span>(a, b, c, d) = u32_from_u128(other);
<span class="kw-2">*</span><span class="self">self </span>= mul3(<span class="kw-2">&amp;</span><span class="self">self</span>.data[..], <span class="kw-2">&amp;</span>[d, c, b, a])
}
}
<span class="attribute">#[cfg(u64_digit)]
#[inline]
</span><span class="kw">fn </span>mul_assign(<span class="kw-2">&amp;mut </span><span class="self">self</span>, other: u128) {
<span class="kw">if </span>other == <span class="number">0 </span>{
<span class="self">self</span>.data.clear();
} <span class="kw">else if </span>other &lt;= BigDigit::max_value() <span class="kw">as </span>u128 {
<span class="kw-2">*</span><span class="self">self </span><span class="kw-2">*</span>= other <span class="kw">as </span>BigDigit
} <span class="kw">else </span>{
<span class="kw">let </span>(hi, lo) = big_digit::from_doublebigdigit(other);
<span class="kw-2">*</span><span class="self">self </span>= mul3(<span class="kw-2">&amp;</span><span class="self">self</span>.data[..], <span class="kw-2">&amp;</span>[lo, hi])
}
}
}
<span class="kw">impl </span>CheckedMul <span class="kw">for </span>BigUint {
<span class="attribute">#[inline]
</span><span class="kw">fn </span>checked_mul(<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="prelude-val">Some</span>(<span class="self">self</span>.mul(v))
}
}
<span class="macro">impl_product_iter_type!</span>(BigUint);
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_sub_sign() {
<span class="kw">use </span><span class="kw">crate</span>::BigInt;
<span class="kw">use </span>num_traits::Num;
<span class="kw">fn </span>sub_sign_i(a: <span class="kw-2">&amp;</span>[BigDigit], b: <span class="kw-2">&amp;</span>[BigDigit]) -&gt; BigInt {
<span class="kw">let </span>(sign, val) = sub_sign(a, b);
BigInt::from_biguint(sign, val)
}
<span class="kw">let </span>a = BigUint::from_str_radix(<span class="string">&quot;265252859812191058636308480000000&quot;</span>, <span class="number">10</span>).unwrap();
<span class="kw">let </span>b = BigUint::from_str_radix(<span class="string">&quot;26525285981219105863630848000000&quot;</span>, <span class="number">10</span>).unwrap();
<span class="kw">let </span>a_i = BigInt::from(a.clone());
<span class="kw">let </span>b_i = BigInt::from(b.clone());
<span class="macro">assert_eq!</span>(sub_sign_i(<span class="kw-2">&amp;</span>a.data[..], <span class="kw-2">&amp;</span>b.data[..]), <span class="kw-2">&amp;</span>a_i - <span class="kw-2">&amp;</span>b_i);
<span class="macro">assert_eq!</span>(sub_sign_i(<span class="kw-2">&amp;</span>b.data[..], <span class="kw-2">&amp;</span>a.data[..]), <span class="kw-2">&amp;</span>b_i - <span class="kw-2">&amp;</span>a_i);
}
</code></pre></div>
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