From c42d033dcc8bd7e24a94a5815d8df73bc0e885fc Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Mon, 2 Sep 2024 19:00:05 +0800
Subject: [PATCH] Add number/fft.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 number/fft.cc | 48 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 number/fft.cc

diff --git a/number/fft.cc b/number/fft.cc
new file mode 100644
index 0000000..49e17b5
--- /dev/null
+++ b/number/fft.cc
@@ -0,0 +1,48 @@
+void fft(vector<complex<ld>>& y, bool idft) {
+    int n = y.size();
+    vector<int> rev(n);
+    for (int i = 0; i < n; ++i) {
+        rev[i] = rev[i >> 1] >> 1;
+        if (i & 1) {
+            rev[i] |= n >> 1;
+        }
+    }
+    for (int i = 0; i < n; ++i) {
+        if (i < rev[i]) {
+            swap(y[i], y[rev[i]]);
+        }
+    }
+    for (int h = 2; h <= n; h <<= 1) {
+        complex<ld> wn(cos(2 * M_PI / h), sin(2 * M_PI / h));
+        for (int j = 0; j < n; j += h) {
+            complex<ld> w(1);
+            for (int k = j; k < j + h / 2; ++k) {
+                complex<ld> u = y[k], t = w * y[k + h / 2];
+                y[k] = u + t;
+                y[k + h / 2] = u - t;
+                w *= wn;
+            }
+        }
+    }
+    if (idft) {
+        reverse(y.begin() + 1, y.end());
+        for (int i = 0; i < n; ++i) {
+            y[i] /= n;
+        }
+    }
+}
+
+vector<int> multiply(const vector<int>& a, const vector<int>& b) {
+    vector<complex<ld>> A(a.begin(), a.end()), B(b.begin(), b.end());
+    int n = 1;
+    while (n < a.size() + b.size()) n <<= 1;
+    A.resize(n), B.resize(n);
+    fft(A, false), fft(B, false);
+    for (int i = 0; i < n; ++i) {
+        A[i] *= B[i];
+    }
+    fft(A, true);
+    vector<int> res(n);
+    transform(A.begin(), A.end(), res.begin(), expr(int(round(x.real())), auto&& x));
+    return res;
+}