From 1ebff0b1e41a2d782f344e2c0f542b86e7dbfa24 Mon Sep 17 00:00:00 2001
From: errorgorn <ashleykhoo2@gmail.com>
Date: Fri, 25 Oct 2019 16:41:49 +0800
Subject: [PATCH 1/2] Added deterministic version to miller rabin algorithm

---
 .../miller_rabin_deterministic.cpp            | 81 +++++++++++++++++++
 1 file changed, 81 insertions(+)
 create mode 100644 Math/miller_rabin_primality_test/miller_rabin_deterministic.cpp

diff --git a/Math/miller_rabin_primality_test/miller_rabin_deterministic.cpp b/Math/miller_rabin_primality_test/miller_rabin_deterministic.cpp
new file mode 100644
index 00000000..f43674d6
--- /dev/null
+++ b/Math/miller_rabin_primality_test/miller_rabin_deterministic.cpp
@@ -0,0 +1,81 @@
+#include <cstdio>
+#include <iterator>
+#include <vector>
+using namespace std;
+const int witness[]={2,3,5,7};
+const int witness_size=4; ///remember to edit this value too
+/* Note that different witness arrays will cause the function to have different accuracies.
+But according to wikipedia: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
+
+    if n < 2,047, it is enough to test a = 2;
+    if n < 1,373,653, it is enough to test a = 2 and 3;
+    if n < 9,080,191, it is enough to test a = 31 and 73;
+    if n < 25,326,001, it is enough to test a = 2, 3, and 5;
+    if n < 3,215,031,751, it is enough to test a = 2, 3, 5, and 7; (I am using this)
+    if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
+    if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
+    if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
+    if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
+    if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.
+
+    Note that for the correctness of the algorithm, the witness array should only be filled with prime numbers.
+*/
+
+bool isPrime(int i){
+    ///check for the simple cases
+    if (i==1) return false;
+    if (i==2) return true;
+    if (!(i&1)) return false;
+    for (int x=0;x<witness_size;x++){
+        if (witness[x]==i) return true;
+    }
+
+    vector<int> pow;  ///this holds the bits of i with all the trailing zeros striped off
+    int s=0; ///number of trailing zeros
+
+    int _i=i-1;
+    while (!(_i&1)){
+        s++;
+        _i>>=1;
+    }
+
+    while (_i){
+        pow.push_back(_i&1);
+        _i>>=1;
+    }
+
+    long long curr;
+    for (int x=0;x<witness_size;x++){
+        curr=1;
+        for (vector<int>::reverse_iterator it=pow.rbegin();it!=pow.rend();it++){
+            if (*it){
+                curr=(curr*curr)%i;
+                curr=(curr*witness[x])%i;
+            }
+            else{
+                curr=(curr*curr)%i;
+            }
+        }
+
+        if (curr==1 || curr==i-1) goto _end;
+
+        for (int x=1;x<s;x++){
+            if (curr!=i-1) {
+                curr=(curr*curr)%i;
+                if (curr==1) return false;
+            }
+            else goto _end;
+        }
+        if (curr!=i-1) return false;
+        _end:;
+    }
+
+    return true;
+}
+
+int main(){
+    ///program to test if it works
+    for (int x=1;x<=1000;x++){
+        if (isPrime(x)) printf("%d\n",x);
+    }
+}

From 11127d3faba2033dfbd47f2e64fd8ec67237f4bb Mon Sep 17 00:00:00 2001
From: errorgorn <ashleykhoo2@gmail.com>
Date: Fri, 25 Oct 2019 16:55:55 +0800
Subject: [PATCH 2/2] replaced functions to count number of bits to
 __builtin_popcount

refer to https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html for more details
---
 ..._of_bits_to_be_flipped_to_convert_a_to_b.cpp | 15 ++-------------
 BitManipulation/count_ones/count_ones.cpp       | 17 ++++++-----------
 2 files changed, 8 insertions(+), 24 deletions(-)

diff --git a/BitManipulation/count_number_of_bits_to_be_flipped_to_convert_a_to_b/count_number_of_bits_to_be_flipped_to_convert_a_to_b.cpp b/BitManipulation/count_number_of_bits_to_be_flipped_to_convert_a_to_b/count_number_of_bits_to_be_flipped_to_convert_a_to_b.cpp
index be64de7f..acf95ec8 100644
--- a/BitManipulation/count_number_of_bits_to_be_flipped_to_convert_a_to_b/count_number_of_bits_to_be_flipped_to_convert_a_to_b.cpp
+++ b/BitManipulation/count_number_of_bits_to_be_flipped_to_convert_a_to_b/count_number_of_bits_to_be_flipped_to_convert_a_to_b.cpp
@@ -1,26 +1,15 @@
 #include<iostream>
 using namespace std;
 
-int countSetBits(int n) {
-    int setBits = 0;
-    while(n > 0){
-        if(n&1){
-            setBits++;
-        }
-        n>>=1;
-    }
-    return setBits;
-}
-
 int main(){
     int a,b;
     cin>>a>>b;
 
     // take the XOR of both the numbers and then count the set bits in that XOR
     int _xor = a^b;
-    int answer = countSetBits(_xor);
+    int answer = __builtin_popcount(_xor);
 
     cout<<"number of bits to be flipped "<<answer<<endl;
 
     return 0;
-}
\ No newline at end of file
+}
diff --git a/BitManipulation/count_ones/count_ones.cpp b/BitManipulation/count_ones/count_ones.cpp
index be250c3b..5e99e045 100644
--- a/BitManipulation/count_ones/count_ones.cpp
+++ b/BitManipulation/count_ones/count_ones.cpp
@@ -3,21 +3,16 @@
 
 #include <iostream>
 
-using namespace std; 
+using namespace std;
 
 short count_ones(unsigned int x) {
-	short num_bits = 0; 
-	while (x) {
-		num_bits += x & 1; // mask one
-		x >>= 1; 
-	}
-	return num_bits; 
+	return __builtin_popcount(x);
 }
 
-int main() { 
+int main() {
 
-	int number = 10; // use any number 
-	short result = count_ones(number); 
-	cout << "result: " << result << endl; 	
+	int number = 10; // use any number
+	short result = count_ones(number);
+	cout << "result: " << result << endl;
 	return 0;
 }