Fast power, turtle speed multiplication, light speed multiplication template

fast power

求$a^{b}modp(1\le a,b,p\le 10^{18})$

ll quick_power(ll a, ll b, ll p) {
    
     // ll 是long long类型
    ll ans = 1 % p;
    for(; b; b >>= 1) {
    
    
        if(b & 1) ans = ans * a % p;
        a = a * a % p;
    }
    return ans;
}

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Turtle Speed ​​Multiplication (Solution 1)

Let $a\ast bmodp(1\le a,b,p\le 10^{18})$

ll quick_mul(ll a, ll b, ll p) {
    
     // ll 是long long类型
    ll ans = 0;
    for(; b; b >>= 1) {
    
    
        if(b & 1) ans = (ans + a) % p;
        a = a * 2 % p;
    }
    return ans;
}

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Multiplication of the speed of light (solution 2)

Let $a\ast bmodp(1\le a,b,p\le 10^{18})$

ull mul(ull a, ull b, ull p) {
    
     // ull 是 unsigned long long 类型，ll 是long long类型
    a %= p, b %= p;
    ull c = (long double)a * b / p;
    ull x = a * b, y = c * p;
    ll ans = (long long)(x % p) - (long long)(y % p);
    if(ans < 0) ans += p;
    return ans;
}