Merge branch 'TheRealDeath:main' into main

Author: TheRealDeath

.breakpoints

@@ -4,7 +4,7 @@
       {
         "id": "008e99a4-cee4-4ff3-8095-6f1c04512119",
         "line": 1,
-        "version": 539,
+        "version": 540,
         "index": 0
       }
     ]

cpp_scripts/mathematical_algorithms/binary_exponentiation.cpp

@@ -0,0 +1,29 @@
+#include <iostream>
+using namespace std;
+
+long long binpow(long long a, long long b)
+{
+  long long res = 1;
+  while (b > 0)
+  {
+    if (b & 1)
+      res = res * a;
+    a = a * a;
+    b >>= 1;
+  }
+  return res;
+}
+
+long long modulo_binpow(long long a, long long b, long long m)
+{
+  a %= m;
+  long long res = 1;
+  while (b > 0)
+  {
+    if (b & 1)
+      res = res * a % m;
+    a = a * a % m;
+    b >>= 1;
+  }
+  return res;
+}

cpp_scripts/mathematical_algorithms/Fibonacci.cpp renamed to cpp_scripts/mathematical_algorithms/fibonacci.cpp

@@ -0,0 +1,52 @@
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+bool millerTest(int n, int d)
+{
+  // 2.1 Pick a random number 'a' in range [2, n-2]
+  int a = 2 + std::rand() % (n - 4);
+
+  // 2.2 Find: x = pow(a, d) % n
+  int x = std::pow(a, d) % n;
+
+  // 2.3 x == 1 or x == n-1, return true.
+  if (x == 1 || x == n - 1) return true;
+
+  // 2.4 While d does not become n-1:
+  while (d != n - 1)
+  {
+    x = (x*x) % n;
+    if (x == 1) return false;
+    if (x == n-1) return true;
+  }
+}
+
+bool isPrime(int n, int k)
+{
+  // 1.1 Handle base cases for n < 3
+  if (n <= 1 || n == 4) return false;
+  if (n <= 3) return true;
+
+  // 1.2 If n is even, return false.
+  if (n % 2 == 0) return false;
+
+  /* 1.3
+  Find an odd number d such that n-1 can be written as d*(2^r).
+  Note that since n is odd, (n-1) must be even and r must be greater than 0.
+  */
+
+  int d = n - 1;
+  while (d % 2 == 0)
+    d /= 2;
+
+  // 1.4 Use the millerTest k times.
+  for (int i = 0; i < k; ++i)
+  {
+    if (millerTest(n, d) == false)
+      return false;
+  }
+
+  // 1.5 If millerTest() does not return false, then the number is prime.
+  return true;
+}

cpp_scripts/mathematical_algorithms/miller_rabin.cpp

@@ -0,0 +1,62 @@
+// Solovay-Strassen Primality Test
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <algorithm>
+#include "binary_exponentiation.cpp"
+
+// No comments for code. Do not use, unless you understand it.
+int calculateJacobian(long long a, long long n)
+{
+  if (!a) return 0;
+  int ans = 1;
+  if a < 0
+  {
+    a = -a;
+    if (n % 4 == 3)
+    ans = -ans;
+  }
+  if (a == 1) return ans;
+  while (a)
+  {
+    if (a < 0)
+    {
+      a = -a;
+      if (n % 4 == 3)
+        ans = -ans;
+    }
+    while (a % 2 == 0)
+    {
+      a = a / 2;
+      if (n % 8 == 3 || n % 8 == 5)
+        ans = -ans;
+    }
+
+    swap(a, n);
+
+    if (a % 4 == 3 && n % 4 == 3)
+      ans = -ans;
+    if (a > n / 2)
+      a = a - n;
+  }
+
+  if (n == 1) return ans;
+  return 0;
+
+}
+
+bool solovayStrassen(long long p, int iterations)
+{
+  if (p < 2) return false;
+  if (p != 2 && p % 2 == 0) return false;
+
+  for (int i = 0; i < iterations; i++)
+  {
+    long long a = 1 + rand() % (p - 1);
+    long long jacobian = (p + calculateJacobian(a, p)) % p;
+    long long mod = modulo_binpow(a, (p - 1) / 2, p);
+
+    if (!jacobian || mod != jacobian) return false;
+  }
+  return true;
+}