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c5b2052e3d
@ -13,19 +13,36 @@ const double PI = std::acos(-1);
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void fast_fourier_transform(std::valarray<std::complex<double>>& a) {
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if (a.size() == 1) return;
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int m = a.size() >> 1;
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// assert(a.size() == 1 << std::__lg(a.size()));
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int k = std::__lg(a.size());
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std::valarray<std::complex<double>>
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even = a[std::slice(0, m, 2)],
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odd = a[std::slice(1, m, 2)];
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for (int i = 0; i < a.size(); i++) {
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int t = 0;
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fast_fourier_transform(even);
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fast_fourier_transform(odd);
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for (int j = 0; j < k; j++) {
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if (i & (1 << j)) {
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t |= 1 << (k - j - 1);
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}
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}
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for (int i = 0; i < m; i++) {
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auto t = std::polar(1.0, -2 * PI * i / a.size()) * odd[i];
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a[i] = even[i] + t;
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a[i + m] = even[i] - t;
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if (i < t) std::swap(a[i], a[t]);
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}
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for (int len = 2; len <= a.size(); len <<= 1) {
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std::complex<double> wlen(std::cos(2 * PI / len), std::sin(2 * PI / len));
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for (int i = 0; i < a.size(); i += len) {
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std::complex<double> w(1);
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for (int j = 0; j < len / 2; j++) {
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std::complex<double> u = a[i + j],
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v = a[i + j + len / 2] * w;
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a[i + j] = u + v;
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a[i + j + len / 2] = u - v;
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w *= wlen;
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}
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}
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}
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}
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