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Functionality bash #21

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7 changes: 5 additions & 2 deletions mathx/number_theory.h
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Original file line number Diff line number Diff line change
Expand Up @@ -2,8 +2,11 @@
#define MATHX_NUMBER_THEORY_H_

namespace mathx {
int gcd(int a, int b);
int lcm(int a, int b);
long long gcd(long long a, long long b);
long long lcm(long long a, long long b);
long long pow(long long a, long long e, long long mod);
bool is_miller_rabin_witness(long long a, long long p);
bool is_prime_fast(long long p);
}

#endif
60 changes: 58 additions & 2 deletions src/number_theory.cpp
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
#include <number_theory.h>

namespace mathx {
int gcd(int a, int b) {
long long gcd(long long a, long long b) {
while( a * b ){
if(a > b)
a = a % b;
Expand All @@ -10,7 +10,63 @@ namespace mathx {
}
return a + b;
}
int lcm(int a, int b) {

long long lcm(long long a, long long b) {
return (a * b / gcd(a,b));
}

long long pow(long long a, long long e, long long mod) {
if (e == 0) {
return 1;
}

long long x = mathx::pow(a, e / 2, mod);
if (e % 2 == 0) {
return (x * x) % mod;
}
else {
return (((x * x) % mod) * x) % mod;
}
}

bool is_miller_rabin_witness(long long a, long long p) {
long long g = mathx::gcd(a,p);
if (g == 1) {
return true;
}

long long k = 0;
long long q = p - 1;
while (q % 2 == 0) {
q = q / 2;
++k;
}
long long temp = mathx::pow(a, q, p);
if (temp == 1) {
return false;
}

for (int i = 0; i < k; ++i) {
if (temp == p - 1) {
return false;
}
else {
temp = (temp * temp) % p;
}
}
return true;
}


bool is_prime_fast(long long p) {
if (p == 1) {
return false;
}
for (int i = 0; i < 100; ++i) {
if (mathx::is_miller_rabin_witness(i, p) == true) {
return false;
}
}
return true;
}
}