This is my first time actually trying to contribute something, so please go easy on me....

Hello Codeforces! After a long time of search for a cure for precision errors in C++ while dealing with just integers, I was motivated to write a blog for a curated collection of one. Sure some common ones do already exist in the previous blogs, some really cool ones can be found while browsing other programmers' templates, but why not have a blog which saves the time of search and makes it easier for CP Enthusiasts to improve?

I have implemented a few as follows (may include the common ones):

1) ceil(a/b) and floor(a/b): Handling negative division as well...

ll divceil(ll a,ll b){ return a/b+(a%b>0);}
ll divfloor(ll a,ll b){ return a/b-(a%b<0);}

2) power(a,b):

ll binpow(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1) res*=a;
        a*=a,b>>=1;
    }
    return res;
}

3) Floor(logb(x)):

ll lg(ll x,ll b=2){
    if(b==1) return -1; //Modify this as per need
    if(b==2) return 63-__builtin_clzll(x); //O(1) for log2
    ll p=1,ans=0;
    while(true){
        if(p>x) return ans-1;
        if(p>LLONG_MAX/b) return ans;
        p*=b,ans++;
    }
}

4) nth-root (general): Thanks to LeoPro for the trick to deal with overflows

const ll INF = LLONG_MAX  // You may change ll to ull and LLONG_MAX to ULLONG_MAX 

ll mult(ll a,ll b){
    if(b==0) return 0;
    return a>INF/b?INF:a*b;
}

ll binpow(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1) res=mult(res,a);
        a=mult(a,a),b>>=1; 
    }
    return res;
}

ll bin_nth_rt(ll x,ll n){
    if(x==1||n==1) return x;
    if(x==INF) x--;    // Doesn't make a difference in answer, and check function fails for INF 
    ll l=0,r=x,m;
    while(r-l>1){
        m=l+(r-l)/2;
        if(binpow(m,n)>x) r=m;
        else l=m;
    }
    return l;
}

Please feel free to highlight any errors, or areas with room for improvement in performance, handling overflows, divide by zero, etc and contributing your own in the comments.

Thanks for reading!

UPD: Changed divfloor and divceil according to bicsi 's idea.

UPD: nth-root has now been updated to handle entire integer range.