From 7e06c5f89158c3a5eb5185c84b01f651ab0f777f Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Fri, 6 Mar 2026 12:02:07 -0700
Subject: [PATCH 1/3] first draft of xor conv

---
 library/convolution/xor_convolution.hpp       | 21 +++++++++++++++++++
 .../convolution/xor_convolution.test.cpp      | 19 +++++++++++++++++
 2 files changed, 40 insertions(+)
 create mode 100644 library/convolution/xor_convolution.hpp
 create mode 100644 tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp

diff --git a/library/convolution/xor_convolution.hpp b/library/convolution/xor_convolution.hpp
new file mode 100644
index 000000000..c81bbb62b
--- /dev/null
+++ b/library/convolution/xor_convolution.hpp
@@ -0,0 +1,21 @@
+#pragma once
+#include "../math/mod_division.hpp"
+void fwht(int n, vi& a) {
+  for (int i = 1; i != n; i <<= 1)
+    for (int j = 0; j != n; j += i << 1)
+      for (int k = 0; k != i; k++) {
+        int x = a[j + k], y = a[i + j + k];
+        a[j + k] = (x + y) % mod;
+        a[i + j + k] = (x - y + mod) % mod;
+      }
+}
+vi xor_conv(vi& a, vi& b) {
+  int n = sz(a), inv = mod_div(1, n);
+  fwht(n, a);
+  fwht(n, b);
+  vi res(n);
+  rep(i, 0, n) res[i] = 1LL * a[i] * b[i] % mod;
+  fwht(n, res);
+  rep(i, 0, n) res[i] = 1LL * res[i] * inv % mod;
+  return res;
+}
diff --git a/tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp b/tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp
new file mode 100644
index 000000000..f3a45752b
--- /dev/null
+++ b/tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp
@@ -0,0 +1,19 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
+#include "../template.hpp"
+#include "../../../library/convolution/xor_convolution.hpp"
+istream& operator>>(istream& is, vector<int>& v) {
+  for (int i = 0; i < sz(v); i++) is >> v[i];
+  return is;
+}
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n;
+  cin >> n;
+  vi a(1 << n), b(1 << n);
+  cin >> a >> b;
+  vi c = xor_conv(a, b);
+  for (int i = 0; i < (1 << n); i++) cout << c[i] << ' ';
+  cout << '\n';
+  return 0;
+}

From 5dd22f5aaa0c43f67df0e8ae186a390c32aa6269 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Fri, 6 Mar 2026 19:03:41 +0000
Subject: [PATCH 2/3] [auto-verifier] verify commit
 7e06c5f89158c3a5eb5185c84b01f651ab0f777f

---
 .verify-helper/timestamps.remote.json | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index 50350ad30..a62a5bf48 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -2,6 +2,7 @@
 "tests/library_checker_aizu_tests/convolution/gcd_convolution.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/convolution/lcm_convolution.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/convolution/min_plus_convolution.test.cpp": "2024-11-17 14:04:03 -0600",
+"tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp": "2026-03-06 12:02:07 -0700",
 "tests/library_checker_aizu_tests/data_structures/binary_search_example.test.cpp": "2024-11-18 10:51:39 -0600",
 "tests/library_checker_aizu_tests/data_structures/binary_trie.test.cpp": "2026-01-18 02:20:40 +0000",
 "tests/library_checker_aizu_tests/data_structures/bit.test.cpp": "2026-01-23 04:31:29 +0000",

From 05e100d83b3db7779f4573cce29167ffe17aa977 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Fri, 6 Mar 2026 12:07:47 -0700
Subject: [PATCH 3/3] add docs now

---
 library/convolution/xor_convolution.hpp | 13 ++++++++++---
 1 file changed, 10 insertions(+), 3 deletions(-)

diff --git a/library/convolution/xor_convolution.hpp b/library/convolution/xor_convolution.hpp
index c81bbb62b..f02bd767a 100644
--- a/library/convolution/xor_convolution.hpp
+++ b/library/convolution/xor_convolution.hpp
@@ -1,9 +1,16 @@
 #pragma once
 #include "../math/mod_division.hpp"
+//! https://codeforces.com/blog/entry/127823
+//! @code
+//!   vi c = xor_conv(a, b);
+//!   // must have sz(a) == sz(b) == a power of 2
+//!   // c[k] = sum of a[i]*b[j] where i^j==k
+//! @endcode
+//! @time O(n log n)
+//! @space O(n)
 void fwht(int n, vi& a) {
-  for (int i = 1; i != n; i <<= 1)
-    for (int j = 0; j != n; j += i << 1)
-      for (int k = 0; k != i; k++) {
+  for (int i = 1; i < n; i *= 2)
+    for (int j = 0; j < n; j += 2 * i) rep(k, 0, i) {
         int x = a[j + k], y = a[i + j + k];
         a[j + k] = (x + y) % mod;
         a[i + j + k] = (x - y + mod) % mod;