add inv, log, exp of formal power series

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;
+}
\ No newline at end of file