Miller-Rabin & floor sum

content/number-theory/FloorSum.hpp

@@ -0,0 +1,18 @@
+#pragma once
+
+/**
+ * Author: Teetat T.
+ * Date: 2024-09-21
+ * Description: Floor sum function.
+ *  $f(a, b, c, n) = \sum_{x=0}^n \lfloor \frac{ax+b}{c} \rfloor$
+ *  becareful when a,b,c are negetive (use custom floor division and mod instead)
+ * Time: $O(\log a)$
+ */
+
+ll floor_sum(ll a,ll b,ll c,ll n){
+    ll res=n*(n+1)/2*(a/c)+(n+1)*(b/c);
+    a%=c,b%=c;
+    if(a==0)return res;
+    ll m=(a*n+b)/c;
+    return res+n*m-floor_sum(c,c-b-1,a,m-1);
+}

content/number-theory/MillerRabin.hpp

@@ -0,0 +1,38 @@
+/**
+ * Author: chilli, c1729, Simon Lindholm
+ * Date: 2019-03-28
+ * License: CC0
+ * Source: Wikipedia, https://miller-rabin.appspot.com/
+ * Description: Deterministic Miller-Rabin primality test.
+ * Guaranteed to work for numbers up to $7 \cdot 10^{18}$; for larger numbers, use Python and extend A randomly.
+ * Time: 7 times the complexity of $a^b \mod c$.
+ * Status: Stress-tested
+ */
+#pragma once
+
+using ull = uint64_t;
+
+ull modmul(ull a, ull b, ull M) {
+	ll ret = a * b - M * ull(1.L / M * a * b);
+	return ret + M * (ret < 0) - M * (ret >= (ll)M);
+}
+ull modpow(ull b, ull e, ull mod) {
+	ull ans = 1;
+	for (; e; b = modmul(b, b, mod), e /= 2)
+		if (e & 1) ans = modmul(ans, b, mod);
+	return ans;
+}
+
+bool isPrime(ull n) {
+	if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
+	ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
+	    s = __builtin_ctzll(n-1), d = n >> s;
+	for (ull a : A) {   // ^ count trailing zeroes
+		ull p = modpow(a%n, d, n), i = s;
+		while (p != 1 && p != n - 1 && a % n && i--)
+			p = modmul(p, p, n);
+		if (p != n-1 && i != s) return 0;
+	}
+	return 1;
+}
+

content/number-theory/chapter.tex

@@ -4,8 +4,10 @@ \chapter{Number Theory}
 \kactlimport{euclid.h}
 \kactlimport{CRT.hpp}
 \kactlimport{phiFunction.hpp}
+\kactlimport{FloorSum.hpp}
 
 \section{Prime Numbers}
+  \kactlimport{MillerRabin.hpp}
   \kactlimport{LinearSieve.hpp}
   \kactlimport{FastEratosthenes.hpp}
   \kactlimport{GolbatchConjecture.hpp}