MillerRabin.cpp

Author: lxylxy123456

MillerRabin.cpp

@@ -0,0 +1,78 @@
+//  
+//  algorithm - some algorithms in "Introduction to Algorithms", third edition
+//  Copyright (C) 2018  lxylxy123456
+//  
+//  This program is free software: you can redistribute it and/or modify
+//  it under the terms of the GNU Affero General Public License as
+//  published by the Free Software Foundation, either version 3 of the
+//  License, or (at your option) any later version.
+//  
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU Affero General Public License for more details.
+//  
+//  You should have received a copy of the GNU Affero General Public License
+//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//  
+
+#ifndef MAIN
+#define MAIN
+#define MAIN_MillerRabin
+#endif
+
+#ifndef FUNC_MillerRabin
+#define FUNC_MillerRabin
+
+#include "utils.h"
+
+#include "ModularExponentiation.cpp"
+
+template <typename T>
+bool Witness(T a, T n) {
+	T t = 0, u = n - 1; 
+	while (!(u & 1)) {
+		t++; 
+		u >>= 1; 
+	}
+	T x0 = ModularExponentiation(a, u, n); 
+	for (T i = 0; i < t; i++) {
+		T x1 = x0 * x0 % n; 
+		if (x1 == 1 && x0 != 1 && x0 != n - 1)
+			return true; 
+		x0 = x1; 
+	}
+	if (x0 != 1)
+		return true; 
+	return false; 
+}
+
+template <typename T>
+bool MillerRabin(T n, size_t s) {
+	std::vector<T> a; 
+	random_integers<T>(a, 1, n - 1, s); 
+	for (auto i = a.begin(); i != a.end(); i++) {
+		if (Witness(*i, n))
+			return false; 
+	}
+	return true; 
+}
+#endif
+
+#ifdef MAIN_MillerRabin
+int main(int argc, char *argv[]) {
+	const size_t nn = get_argv(argc, argv, 1, 30); 
+	const size_t s = get_argv(argc, argv, 2, 5); 
+	const size_t tries = get_argv(argc, argv, 3, 1); 
+	using T = long long int; 
+    std::random_device rd; 
+    std::uniform_int_distribution<T> dis(1 << (nn - 1), 1 << nn); 
+    for (size_t i = 0; i < tries; i++) {
+		T n = get_argv(argc, argv, 4 + i, dis(rd) << 1 | 1); 
+		bool ans = MillerRabin(n, s); 
+		std::cout << n << "\t" << std::boolalpha << ans << std::endl;
+	}
+	return 0; 
+}
+#endif
+

Pseudoprime.cpp

@@ -0,0 +1,54 @@
+//  
+//  algorithm - some algorithms in "Introduction to Algorithms", third edition
+//  Copyright (C) 2018  lxylxy123456
+//  
+//  This program is free software: you can redistribute it and/or modify
+//  it under the terms of the GNU Affero General Public License as
+//  published by the Free Software Foundation, either version 3 of the
+//  License, or (at your option) any later version.
+//  
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU Affero General Public License for more details.
+//  
+//  You should have received a copy of the GNU Affero General Public License
+//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//  
+
+#ifndef MAIN
+#define MAIN
+#define MAIN_Pseudoprime
+#endif
+
+#ifndef FUNC_Pseudoprime
+#define FUNC_Pseudoprime
+
+#include "utils.h"
+
+#include "ModularExponentiation.cpp"
+
+template <typename T>
+bool Pseudoprime(T n) {
+	if (ModularExponentiation((T) 2, n - 1, n) != 1)
+		return false; 
+	else
+		return true; 
+}
+#endif
+
+#ifdef MAIN_Pseudoprime
+int main(int argc, char *argv[]) {
+	const size_t nn = get_argv(argc, argv, 1, 30); 
+	const size_t tries = get_argv(argc, argv, 2, 1); 
+	using T = long long int; 
+    std::random_device rd; 
+    std::uniform_int_distribution<T> dis(1 << (nn - 1), 1 << nn); 
+    for (size_t i = 0; i < tries; i++) {
+		T n = get_argv(argc, argv, 3 + i, dis(rd) << 1 | 1); 
+		std::cout << n << "\t" << std::boolalpha << Pseudoprime(n) << std::endl;
+	}
+	return 0; 
+}
+#endif
+

README.md

@@ -201,6 +201,9 @@
 | 31 | Euclid.cpp					| Extended Euclid						|  937 |
 | 31 | ModLinEquationSolver.cpp		| Modular Linear Equation Solver		|  949 |
 | 31 | ModularExponentiation.cpp	| Modular Exponentiation				|  957 |
+| 31 | Pseudoprime.cpp				| Pseudoprime							|  967 |
+| 31 | MillerRabin.cpp				| Witness								|  969 |
+| 31 | MillerRabin.cpp				| Miller Rabin							|  970 |
 
 # Supplementary Files
 * `utils.h`: Utils