/*******************************************************

lib/math.h

Created at: Feb 25, 2023, 11:24 AM GMT+9

Copyright (C) 2023 e6nlaq

This file is part of aqua.

Licensed under the MIT License.

*******************************************************/

#pragma once

#include "./type.h"

#include <math.h>

inline ll a_gcd(const ll a, const ll b)

{

if (b == 0)

{

return a;

}

else

{

return a_gcd(b, a % b);

}

}

inline ll a_lcm(const ll a, const ll b)

{

return a * b / a_gcd(a, b);

}

inline bool is_prime(const ll num)

{

if (num < 2)

return false;

else if (num == 2)

return true;

else if (num % 2 == 0)

return false; // 偶数はあらかじめ除く

long double sqrtNum = sqrt(num);

for (int i = 3; i <= sqrtNum; i += 2)

{

if (num % i == 0)

{

// 素数ではない

return false;

}

}

// 素数である

return true;

}

inline ll fact(ll x)

{

ll ret = 1;

for (ll i = 1; i <= x; i++)

{

ret *= i;

}

return ret;

}

inline ld log_a(ld x, ld b)

{

return log10l(x) / log10l(b);

}