From 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Mon, 27 Jun 2022 17:19:28 +0200
Subject: updated tcr

---
 math/piLehmer.cpp | 52 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 52 insertions(+)
 create mode 100644 math/piLehmer.cpp

(limited to 'math/piLehmer.cpp')

diff --git a/math/piLehmer.cpp b/math/piLehmer.cpp
new file mode 100644
index 0000000..37eff6b
--- /dev/null
+++ b/math/piLehmer.cpp
@@ -0,0 +1,52 @@
+constexpr ll cacheA = 2 * 3 * 5 * 7 * 11 * 13 * 17;
+constexpr ll cacheB = 7;
+ll memoA[cacheA + 1][cacheB + 1];
+ll memoB[cacheB + 1];
+ll memoC[N];
+
+void init() {
+	primeSieve(); // code from above
+	for (ll i = 0; i < N; i++) {
+		memoC[i] = memoC[i - 1];
+		if (isPrime(i)) memoC[i]++;
+	}
+	memoB[0] = 1;
+	for(ll i = 0; i <= cacheA; i++) memoA[i][0] = i;
+	for(ll i = 1; i <= cacheB; i++) {
+		memoB[i] = primes[i - 1] * memoB[i - 1];
+		for(ll j = 1; j <= cacheA; j++) {
+			memoA[j][i] = memoA[j][i - 1] - memoA[j /
+										primes[i - 1]][i - 1];
+}}}
+
+ll phi(ll n, ll k) {
+	if(k == 0) return n;
+	if(k <= cacheB) 
+		return memoA[n % memoB[k]][k] + 
+					 (n / memoB[k]) * memoA[memoB[k]][k];
+	if(n <= primes[k - 1]*primes[k - 1]) return memoC[n] - k + 1;
+	if(n <= primes[k - 1]*primes[k - 1]*primes[k - 1] && n < N) {
+		ll b = memoC[(ll)sqrtl(n)];
+		ll res = memoC[n] - (b + k - 2) * (b - k + 1) / 2;
+		for(ll i = k; i < b; i++) res += memoC[n / primes[i]];
+		return res;
+	}
+	return phi(n, k - 1) - phi(n / primes[k - 1], k - 1);
+}
+
+ll pi(ll n) {
+	if (n < N) return memoC[n];
+	ll a = pi(sqrtl(sqrtl(n)));
+	ll b = pi(sqrtl(n));
+	ll c = pi(cbrtl(n));
+	ll res = phi(n, a) + (b + a - 2) * (b - a + 1) / 2;
+	for (ll i = a; i < b; i++) {
+		ll w = n / primes[i];
+		res -= pi(w);
+		if (i > c) continue;
+		ll bi = pi(sqrtl(w));
+		for (ll j = i; j < bi; j++) {
+			res -= pi(w / primes[j]) - j;
+	}}
+	return res;
+}
\ No newline at end of file
-- 
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