CP/NTT.cpp at master · abhinashgiri/CP · GitHub

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template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {

    vector< Mint > dw, idw;
    int max_base;
    Mint root;

    NumberTheoreticTransformFriendlyModInt(){
        auto tmp = mod - 1;
        max_base = 0;
        while(tmp % 2 == 0) tmp >>= 1, max_base++;
        root = 2;
        while(root.pow(root,(mod - 1) >> 1) == 1) root += 1;
        assert(root.pow(root,mod - 1) == 1);
        dw.resize(max_base);
        idw.resize(max_base);
        for(int i = 0; i < max_base; i++) {
            dw[i] = -root.pow(root,(mod - 1) >> (i + 2));
            idw[i] = Mint(1) / dw[i];
        }
    }

    void ntt(vector< Mint > &a){
        const int n = (int) a.size();
        assert((n & (n - 1)) == 0);
        assert(__builtin_ctz(n) <= max_base);
        for(int m = n; m >>= 1;) {
            Mint w = 1;
            for(int s = 0, k = 0; s < n; s += 2 * m) {
                for(int i = s, j = s + m; i < s + m; ++i, ++j) {
                    auto x = a[i], y = a[j] * w;
                    a[i] = x + y, a[j] = x - y;
                }
                w *= dw[__builtin_ctz(++k)];
            }
        }
    }

    void intt(vector< Mint > &a, bool f = true){
        const int n = (int) a.size();
        assert((n & (n - 1)) == 0);
        assert(__builtin_ctz(n) <= max_base);
        for(int m = 1; m < n; m *= 2) {
            Mint w = 1;
            for(int s = 0, k = 0; s < n; s += 2 * m) {
                for(int i = s, j = s + m; i < s + m; ++i, ++j) {
                    auto x = a[i], y = a[j];
                    a[i] = x + y, a[j] = (x - y) * w;
                }
                w *= idw[__builtin_ctz(++k)];
            }
        }
        if(f) {
            Mint inv_sz = Mint(1) / n;
            for(int i = 0; i < n; i++) a[i] *= inv_sz;
        }
    }

    vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
        int need = a.size() + b.size() - 1;
        int nbase = 1;
        while((1 << nbase) < need) nbase++;
        int sz = 1 << nbase;
        a.resize(sz, 0);
        b.resize(sz, 0);
        ntt(a);
        ntt(b);
        Mint inv_sz = Mint(1) / sz;
        for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        intt(a, false);
        a.resize(need);
        return a;
    }
};