From 416962c482e7d6dcf3efd8739dd888bf9bb62288 Mon Sep 17 00:00:00 2001
From: Noobie99 <noob999noob999@gmail.com>
Date: Sat, 20 May 2023 14:38:47 +0200
Subject: increase fft precision

---
 math/transforms/all.cpp          | 17 ++++++++++-------
 math/transforms/andTransform.cpp |  2 +-
 math/transforms/fft.cpp          | 15 +++++++++------
 3 files changed, 20 insertions(+), 14 deletions(-)

(limited to 'math')

diff --git a/math/transforms/all.cpp b/math/transforms/all.cpp
index 66e6a41..ebed881 100644
--- a/math/transforms/all.cpp
+++ b/math/transforms/all.cpp
@@ -5,19 +5,22 @@ using cplx = complex<double>;
 
 //void fft(vector<ll> &a, bool inverse = 0) { @\hl{NTT, xor, or, and}@
 void fft(vector<cplx>& a, bool inverse = 0) {
-	int n = a.size();
+	int n = sz(a);
 	for (int i = 0, j = 1; j < n - 1; ++j) {
 		for (int k = n >> 1; k > (i ^= k); k >>= 1);
 		if (j < i) swap(a[i], a[j]);
 	}
+	static vector<cplx> ws(2, 1);
+	for (static int k = 2; k < n; k *= 2) {
+		ws.resize(n);
+		cplx w = polar(1.0, acos(-1.0) / k);
+		for (int i=k; i<2*k; i++) ws[i] = ws[i/2] * (i % 2 ? w : 1);
+	}
 	for (int s = 1; s < n; s *= 2) {
 		/*ll ws = powMod(root, (mod - 1) / s >> 1, mod); @\hl{NTT only}@
 		if (inverse) ws = powMod(ws, mod - 2, mod);*/
-		double angle = PI / s * (inverse ? -1 : 1);
-		cplx ws(cos(angle), sin(angle));
-		for (int j = 0; j < n; j+= 2 * s) {
+		for (int j = 0; j < n; j += 2 * s) {
 			//ll w = 1; @\hl{NTT only}@
-			cplx w = 1;
 			for (int k = 0; k < s; k++) {
 				/*ll u = a[j + k], t = a[j + s + k] * w; @\hl{NTT only}@
 				t %= mod;
@@ -41,11 +44,11 @@ void fft(vector<cplx>& a, bool inverse = 0) {
 					a[j + k] = t - u;
 					a[j + s + k] = u;
 				}*/
-				cplx u = a[j + k], t = a[j + s + k] * w;
+				cplx u = a[j + k], t = a[j + s + k];
+				t *= (inverse ? conj(ws[s + k]) : ws[s + k]);
 				a[j + k] = u + t;
 				a[j + s + k] = u - t;
 				if (inverse) a[j + k] /= 2, a[j + s + k] /= 2;
-				w *= ws;
 	}}}
 	/*if (inverse) { @\hl{NTT only}@
 		ll div = powMod(n, mod - 2, mod);
diff --git a/math/transforms/andTransform.cpp b/math/transforms/andTransform.cpp
index 32496d8..ab2bd40 100644
--- a/math/transforms/andTransform.cpp
+++ b/math/transforms/andTransform.cpp
@@ -14,4 +14,4 @@ void fft(vector<cplx>& a, bool inverse = 0) {
 				} else {
 					a[j + k] = t - u;
 					a[j + s + k] = u;
-}}}}
+}}}}}
diff --git a/math/transforms/fft.cpp b/math/transforms/fft.cpp
index 6c5f5a8..53a2d8d 100644
--- a/math/transforms/fft.cpp
+++ b/math/transforms/fft.cpp
@@ -6,15 +6,18 @@ void fft(vector<cplx>& a, bool inverse = 0) {
 		for (int k = n >> 1; k > (i ^= k); k >>= 1);
 		if (j < i) swap(a[i], a[j]);
 	}
+	static vector<cplx> ws(2, 1);
+	for (static int k = 2; k < n; k *= 2) {
+		ws.resize(n);
+		cplx w = polar(1.0, acos(-1.0) / k);
+		for (int i=k; i<2*k; i++) ws[i] = ws[i/2] * (i % 2 ? w : 1);
+	}
 	for (int s = 1; s < n; s *= 2) {
-		double angle = PI / s * (inverse ? -1 : 1);
-		cplx ws(cos(angle), sin(angle));
-		for (int j = 0; j < n; j+= 2 * s) {
-			cplx w = 1;
+		for (int j = 0; j < n; j += 2 * s) {
 			for (int k = 0; k < s; k++) {
-				cplx u = a[j + k], t = a[j + s + k] * w;
+				cplx u = a[j + k], t = a[j + s + k];
+				t *= (inverse ? conj(ws[s + k]) : ws[s + k]);
 				a[j + k] = u + t;
 				a[j + s + k] = u - t;
 				if (inverse) a[j + k] /= 2, a[j + s + k] /= 2;
-				w *= ws;
 }}}}
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