[auto-verifier] docs commit 9151361

index.md

@@ -27,8 +27,8 @@ data:
   - name: src/math
     pages:
     - icon: ':heavy_check_mark:'
-      path: src/math/FastGCD.hpp
-      title: src/math/FastGCD.hpp
+      path: src/math/BinaryGCD.hpp
+      title: Binary GCD
   - name: src/modint
     pages:
     - icon: ':heavy_check_mark:'
@@ -84,8 +84,8 @@ data:
   - name: test/math
     pages:
     - icon: ':heavy_check_mark:'
-      path: test/math/FastGCD.test.cpp
-      title: test/math/FastGCD.test.cpp
+      path: test/math/BinaryGCD.test.cpp
+      title: test/math/BinaryGCD.test.cpp
   - name: test/modint
     pages:
     - icon: ':heavy_check_mark:'

notebook.html

@@ -37,6 +37,7 @@ <h1 id="title">ICPC Notebook</h1>
     </ol>
     <li><a class="section" href="#math">math</a></li>
     <ol>
+    <li><a href="#BinaryGCD.hpp">BinaryGCD.hpp</a></li>
     </ol>
     <li><a class="section" href="#modint">modint</a></li>
     <ol>
@@ -223,6 +224,26 @@ <h2 id="FastSet.hpp">FastSet.hpp</h2>
 
     <h2 class="section" id="math">math</h2>
 
+    <div class="filename">
+        <h2 id="BinaryGCD.hpp">BinaryGCD.hpp</h2>
+        md5: f3ab31
+
+    </div>
+    <div class="content content-hpp">
+    <pre><code>u64 <span class="token function">ctz</span><span class="token punctuation">(</span>u64 x<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">return</span> <span class="token function">countr_zero</span><span class="token punctuation">(</span>x<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span>
+u64 <span class="token function">binary_gcd</span><span class="token punctuation">(</span>u64 x<span class="token punctuation">,</span> u64 y<span class="token punctuation">)</span> <span class="token punctuation">{</span>
+   <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>x <span class="token operator">||</span> <span class="token operator">!</span>y<span class="token punctuation">)</span> <span class="token keyword">return</span> x <span class="token operator">|</span> y<span class="token punctuation">;</span>
+   u64 n <span class="token operator">=</span> <span class="token function">ctz</span><span class="token punctuation">(</span>x<span class="token punctuation">)</span><span class="token punctuation">,</span> m <span class="token operator">=</span> <span class="token function">ctz</span><span class="token punctuation">(</span>y<span class="token punctuation">)</span><span class="token punctuation">;</span>
+   x <span class="token operator">>>=</span> n<span class="token punctuation">,</span> y <span class="token operator">>>=</span> m<span class="token punctuation">;</span>
+   <span class="token keyword">while</span><span class="token punctuation">(</span>x <span class="token operator">!=</span> y<span class="token punctuation">)</span> <span class="token punctuation">{</span>
+      <span class="token keyword">if</span><span class="token punctuation">(</span>x <span class="token operator">></span> y<span class="token punctuation">)</span> x <span class="token operator">=</span> <span class="token punctuation">(</span>x <span class="token operator">-</span> y<span class="token punctuation">)</span> <span class="token operator">>></span> <span class="token function">ctz</span><span class="token punctuation">(</span>x <span class="token operator">-</span> y<span class="token punctuation">)</span><span class="token punctuation">;</span>
+      <span class="token keyword">else</span> y <span class="token operator">=</span> <span class="token punctuation">(</span>y <span class="token operator">-</span> x<span class="token punctuation">)</span> <span class="token operator">>></span> <span class="token function">ctz</span><span class="token punctuation">(</span>y <span class="token operator">-</span> x<span class="token punctuation">)</span><span class="token punctuation">;</span>
+   <span class="token punctuation">}</span>
+   <span class="token keyword">return</span> x <span class="token operator">&lt;&lt;</span> <span class="token function">min</span><span class="token punctuation">(</span>n<span class="token punctuation">,</span> m<span class="token punctuation">)</span><span class="token punctuation">;</span>
+<span class="token punctuation">}</span>
+</code></pre>
+</div>
+
     <h2 class="section" id="modint">modint</h2>
 
     <div class="filename">
@@ -663,16 +684,6 @@ <h4>高度合成数</h4>
 <td>768</td>
 <td>1344</td>
 </tr>
-<tr>
-<td>factor</td>
-<td>3111</td>
-<td>3311</td>
-<td>33111</td>
-<td>421111</td>
-<td>631111</td>
-<td>5311111</td>
-<td>6321111</td>
-</tr>
 </tbody></table>
 <table>
 <thead>
@@ -684,6 +695,9 @@ <h4>高度合成数</h4>
 <th>$10^{13}$</th>
 <th>$10^{14}$</th>
 <th>$10^{15}$</th>
+<th>$10^{16}$</th>
+<th>$10^{17}$</th>
+<th>$10^{18}$</th>
 </tr>
 </thead>
 <tbody><tr>
@@ -694,37 +708,65 @@ <h4>高度合成数</h4>
 <td>10752</td>
 <td>17280</td>
 <td>26880</td>
-</tr>
-<tr>
-<td>factor</td>
-<td>53211111</td>
-<td>63221111</td>
-<td>642111111</td>
-<td>6321111111</td>
-<td>5422111111</td>
-<td>64211111111</td>
+<td>41472</td>
+<td>64512</td>
+<td>103680</td>
 </tr>
 </tbody></table>
+<h4>素数階乗</h4>
 <table>
 <thead>
 <tr>
-<th>$≤n$</th>
-<th>$10^{16}$</th>
-<th>$10^{17}$</th>
-<th>$10^{18}$</th>
+<th>$n$</th>
+<th>$2$</th>
+<th>$3$</th>
+<th>$5$</th>
+<th>$7$</th>
+<th>$11$</th>
+<th>$13$</th>
+<th>$17$</th>
+<th>$19$</th>
+<th>$23$</th>
+<th>$29$</th>
 </tr>
 </thead>
 <tbody><tr>
-<td>$d^0(x)$</td>
-<td>41472</td>
-<td>64512</td>
-<td>103680</td>
+<td>$n\#$</td>
+<td>2</td>
+<td>6</td>
+<td>30</td>
+<td>210</td>
+<td>2310</td>
+<td>30030</td>
+<td>510510</td>
+<td>9699690</td>
+<td>$2.2 \times 10^8$</td>
+<td>$6.5 \times 10^9$</td>
 </tr>
+</tbody></table>
+<h4>階乗</h4>
+<table>
+<thead>
 <tr>
-<td>factor</td>
-<td>83221111111</td>
-<td>632211111111</td>
-<td>842211111111</td>
+<th>$5!$</th>
+<th>$6!$</th>
+<th>$7!$</th>
+<th>$8!$</th>
+<th>$9!$</th>
+<th>$10!$</th>
+<th>$11!$</th>
+<th>$12!$</th>
+</tr>
+</thead>
+<tbody><tr>
+<td>120</td>
+<td>720</td>
+<td>5040</td>
+<td>40320</td>
+<td>362880</td>
+<td>3628800</td>
+<td>$4.0 \times 10^7$</td>
+<td>$4.8 \times 10^8$</td>
 </tr>
 </tbody></table>
 </div>

src/math/FastGCD.hpp.md → src/math/BinaryGCD.hpp.md

@@ -4,14 +4,14 @@ data:
   _extendedRequiredBy: []
   _extendedVerifiedWith:
   - icon: ':heavy_check_mark:'
-    path: test/math/FastGCD.test.cpp
-    title: test/math/FastGCD.test.cpp
+    path: test/math/BinaryGCD.test.cpp
+    title: test/math/BinaryGCD.test.cpp
   _isVerificationFailed: false
   _pathExtension: hpp
   _verificationStatusIcon: ':heavy_check_mark:'
   attributes:
     links: []
-  bundledCode: "#line 1 \"src/math/FastGCD.hpp\"\nu64 ctz(u64 x) { return countr_zero(x);\
+  bundledCode: "#line 1 \"src/math/BinaryGCD.hpp\"\nu64 ctz(u64 x) { return countr_zero(x);\
     \ }\nu64 binary_gcd(u64 x, u64 y) {\n   if(!x || !y) return x | y;\n   u64 n =\
     \ ctz(x), m = ctz(y);\n   x >>= n, y >>= m;\n   while(x != y) {\n      if(x >\
     \ y) x = (x - y) >> ctz(x - y);\n      else y = (y - x) >> ctz(y - x);\n   }\n\
@@ -22,16 +22,20 @@ data:
     \   else y = (y - x) >> ctz(y - x);\n   }\n   return x << min(n, m);\n}\n"
   dependsOn: []
   isVerificationFile: false
-  path: src/math/FastGCD.hpp
+  path: src/math/BinaryGCD.hpp
   requiredBy: []
-  timestamp: '2024-05-31 23:58:41+09:00'
+  timestamp: '2024-06-01 01:21:46+09:00'
   verificationStatus: LIBRARY_ALL_AC
   verifiedWith:
-  - test/math/FastGCD.test.cpp
-documentation_of: src/math/FastGCD.hpp
+  - test/math/BinaryGCD.test.cpp
+documentation_of: src/math/BinaryGCD.hpp
 layout: document
-redirect_from:
-- /library/src/math/FastGCD.hpp
-- /library/src/math/FastGCD.hpp.html
-title: src/math/FastGCD.hpp
+title: Binary GCD
 ---
+
+割り算を使わない高速な GCD
+
+## 使い方
+
+- `u64 binary_gcd(u64 x, u64 y)`：$x$ と $y$ の最大公約数を計算する．
+    - $O(\log(x + y))$ 時間

src/modint/BarrettReduction.hpp.md

@@ -34,14 +34,15 @@ documentation_of: src/modint/BarrettReduction.hpp
 layout: document
 title: Barrett Reduction
 ---
+- 参考実装：[AC Library](https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp)
 
 同じ mod でたくさん計算するとき，剰余算を掛け算に変換して高速化する．
 
 ## 使い方
 
 - `Barrett br(mod)`：Barrett Reduction を準備する．
     - 制約：`mod < 2^32`
-- `br.mul(u64 a, u64 b)`：`a * b % mod` を計算する．
+- `u64 br.mul(u64 a, u64 b)`：`a * b % mod` を計算する．
     - 制約：`a * b < 2^64`
 
 ## 仕組み

src/modint/modint.hpp.md

@@ -53,6 +53,7 @@ documentation_of: src/modint/modint.hpp
 layout: document
 title: Modint
 ---
+- 参考実装：[AC Library (初期実装)](https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/atcoder/convolution.hpp)
 
 - タイプ速度重視の簡易 modint
 - 速度が欲しいとき：[32 bit で加減算をちゃんと書いた Modint](../extra/modint_fast.hpp)

test/math/BinaryGCD.test.cpp.md

@@ -0,0 +1,54 @@
+---
+data:
+  _extendedDependsOn:
+  - icon: ':heavy_check_mark:'
+    path: src/math/BinaryGCD.hpp
+    title: Binary GCD
+  - icon: ':heavy_check_mark:'
+    path: test/template.hpp
+    title: test/template.hpp
+  _extendedRequiredBy: []
+  _extendedVerifiedWith: []
+  _isVerificationFailed: false
+  _pathExtension: cpp
+  _verificationStatusIcon: ':heavy_check_mark:'
+  attributes:
+    '*NOT_SPECIAL_COMMENTS*': ''
+    PROBLEM: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A
+    links:
+    - https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A
+  bundledCode: "#line 1 \"test/math/BinaryGCD.test.cpp\"\n#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\
+    \n#line 1 \"test/template.hpp\"\n#include <bits/stdc++.h>\nusing namespace std;\n\
+    using ll = long long;\nconst ll INF = LLONG_MAX / 4;\n#define rep(i, a, b) for(ll\
+    \ i = a; i < (b); i++)\n#define all(a) begin(a), end(a)\n#define sz(a) ssize(a)\n\
+    bool chmin(auto& a, auto b) { return a > b ? a = b, 1 : 0; }\nbool chmax(auto&\
+    \ a, auto b) { return a < b ? a = b, 1 : 0; }\n#line 3 \"test/math/BinaryGCD.test.cpp\"\
+    \nusing u64 = uint64_t;\n#line 1 \"src/math/BinaryGCD.hpp\"\nu64 ctz(u64 x) {\
+    \ return countr_zero(x); }\nu64 binary_gcd(u64 x, u64 y) {\n   if(!x || !y) return\
+    \ x | y;\n   u64 n = ctz(x), m = ctz(y);\n   x >>= n, y >>= m;\n   while(x !=\
+    \ y) {\n      if(x > y) x = (x - y) >> ctz(x - y);\n      else y = (y - x) >>\
+    \ ctz(y - x);\n   }\n   return x << min(n, m);\n}\n#line 5 \"test/math/BinaryGCD.test.cpp\"\
+    \n\nint main() {\n   mt19937_64 rnd;\n   rep(shift, 0, 64) {\n      rep(i, 0,\
+    \ (ll)1e5) {\n         u64 a = rnd() >> shift, b = rnd() >> shift;\n         assert(gcd(a,\
+    \ b) == binary_gcd(a, b));\n      }\n   }\n   puts(\"Hello World\");\n}\n"
+  code: "#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\
+    \n#include \"test/template.hpp\"\nusing u64 = uint64_t;\n#include \"src/math/BinaryGCD.hpp\"\
+    \n\nint main() {\n   mt19937_64 rnd;\n   rep(shift, 0, 64) {\n      rep(i, 0,\
+    \ (ll)1e5) {\n         u64 a = rnd() >> shift, b = rnd() >> shift;\n         assert(gcd(a,\
+    \ b) == binary_gcd(a, b));\n      }\n   }\n   puts(\"Hello World\");\n}\n"
+  dependsOn:
+  - test/template.hpp
+  - src/math/BinaryGCD.hpp
+  isVerificationFile: true
+  path: test/math/BinaryGCD.test.cpp
+  requiredBy: []
+  timestamp: '2024-06-01 01:21:46+09:00'
+  verificationStatus: TEST_ACCEPTED
+  verifiedWith: []
+documentation_of: test/math/BinaryGCD.test.cpp
+layout: document
+redirect_from:
+- /verify/test/math/BinaryGCD.test.cpp
+- /verify/test/math/BinaryGCD.test.cpp.html
+title: test/math/BinaryGCD.test.cpp
+---

test/template.hpp.md

@@ -16,8 +16,8 @@ data:
     path: test/data-structure/FastSet.test.cpp
     title: test/data-structure/FastSet.test.cpp
   - icon: ':heavy_check_mark:'
-    path: test/math/FastGCD.test.cpp
-    title: test/math/FastGCD.test.cpp
+    path: test/math/BinaryGCD.test.cpp
+    title: test/math/BinaryGCD.test.cpp
   - icon: ':heavy_check_mark:'
     path: test/modint/BarrettReduction.test.cpp
     title: test/modint/BarrettReduction.test.cpp
@@ -108,7 +108,7 @@ data:
   - test/string/SuffixArray.test.cpp
   - test/string/RollingHash.test.cpp
   - test/string/Manacher.test.cpp
-  - test/math/FastGCD.test.cpp
+  - test/math/BinaryGCD.test.cpp
   - test/modint/BarrettReduction.test.cpp
   - test/modint/modint.test.cpp
 documentation_of: test/template.hpp