diff options
| -rw-r--r-- | math/transforms/seriesOperations.cpp | 55 |
1 files changed, 55 insertions, 0 deletions
diff --git a/math/transforms/seriesOperations.cpp b/math/transforms/seriesOperations.cpp new file mode 100644 index 0000000..3851a1e --- /dev/null +++ b/math/transforms/seriesOperations.cpp @@ -0,0 +1,55 @@ +vector<ll> poly_inv(vector<ll> a, int n){ + vector<ll> q = {powMod(a[0], mod-2, mod)}; + for(int len = 1; len < n; len *= 2){ + vector<ll> a2 = a, q2 = q; + a2.resize(2*len), q2.resize(2*len); + ntt(q2); + for(int j = 0; j < 2; j++){ + ntt(a2); + for(int i = 0; i < 2*len; i++) a2[i] = a2[i] * q2[i] % mod; + ntt(a2, true); + for(int i = 0; i < len; i++) a2[i] = 0; + } + for(int i = len; i < min(n, 2*len); i++) q.push_back((mod - a2[i]) % mod); + } + return q; +} + +vector<ll> poly_deriv(vector<ll> a){ + for(int i = 0; i < sz(a)-1; i++) + a[i] = a[i+1] * (i+1) % mod; + a.pop_back(); + return a; +} + +vector<ll> poly_integr(vector<ll> a){ + if(a.empty()) return {0}; + a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod); + for(int i = sz(a)-2; i > 0; i--) + a[i] = a[i-1] * powMod(i, mod-2, mod) % mod; + a[0] = 0; + return a; +} + +vector<ll> poly_log(vector<ll> a, int n){ + a = mul(poly_deriv(a), poly_inv(a, n)); + a.resize(n-1); + a = poly_integr(a); + return a; +} + +vector<ll> poly_exp(vector<ll> a, int n){ + vector<ll> q = {1}; + for(int len = 1; len < n; len *= 2){ + vector<ll> p = poly_log(q, 2*len); + for(int i = 0; i < 2*len; i++) + p[i] = (mod - p[i] + (i < sz(a) ? a[i] : 0)) % mod; + vector<ll> q2 = q; + q2.resize(2*len); + ntt(p), ntt(q2); + for(int i = 0; i < 2*len; i++) p[i] = p[i] * q2[i] % mod; + ntt(p, true); + for(int i = len; i < min(n, 2*len); i++) q.push_back(p[i]); + } + return q; +}
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