NEW UPD :

This morning, I begin with BigInteger in C++ (because I usually use BigInteger in Java). I want to check the correction about my code, so that I post this blog to hope you can check it.

Thank knst, I have more update :

• I use typedef vector<int> BigInt; to make one BigInteger

• I use only with positive numbers.

• In my code have the functioninitialize one BigInt :

BigInt a = Integer(string);
BigInt a = Integer(char[]);
BigInt a = Integer(int);
BigInt a = Integer(long long);

• I have function print one BigInt :

Print(BigInt);

• I have iostream BigInt : NEW

cin >> BigInt;
cout << BigInt;

• I have operators on BigInt : have NEW

BigInt + BigInt   (the value return is BigInt)
BigInt + int      (the value return is BigInt)
++BigInt          (the value of BigInt set to BigInt+1 and the value return is BigInt)
BigInt += BigInt  (no return value)
BigInt += int     (no return value)

BigInt - BigInt   (the value return is BigInt, that is positive numbers)
BigInt - int      (the value return is BigInt)
--BigInt          (the value of BigInt set to BigInt-1 and the value return is BigInt)
BigInt -= BigInt  (no return value)
BigInt -= int     (no return value)

BigInt * BigInt   (the value return is BigInt)
BigInt * int      (the value return is BigInt)
BigInt *= BigInt  (no return value)
BigInt *= int     (no return value)

BigInt / BigInt   (the value return is BigInt)     (need optimal)
BigInt / int      (the value return is BigInt)     (NEW - quickly)
BigInt /= BigInt  (no return value)
BigInt /= int     (no return value)

BigInt % BigInt   (the value return is BigInt)
BigInt % int      (the value return is int, that is in [0..int-1])
BigInt %= BigInt  (no return value)
BigInt %= int     (no return value)

NEW : Compare 
         BigInt - BigInt
         BigInt - int

> , < , == , >= , <=  (the value return is bool) 

• I have functions on BigInt :

max(BigInt, BigInt) (the value return is BigInt)
min(BigInt, BigInt) (the value return is BigInt)

gcd(BigInt, BigInt) (the value return is BigInt)
lcm(BigInt, BigInt) (the value return is BigInt)

sqrt(BigInt)        (the value return is BigInt)  
NEW : quickly : knst comment (http://codeforces.net/blog/entry/16380#comment-213120)

log(int, BigInt)    (the value return is int, log(int, BigInt) is small)

I hope you can check the correction of this code

Sorry for my bad English.

Hope have more comments to improve BigInt perfectly.

This is my code :

https://github.com/Stupid-Dog/BigInteger/blob/stupid/BigInteger.cpp

http://paste.ubuntu.com/10270983/

#include <bits/stdc++.h>

using namespace std;

typedef int64_t ll;
typedef long long ll;

#define EL printf("\n")
#define pb push_back
#define FOR(i,l,r) for (int i=l;i<=r;i++)
#define FORD(i,r,l) for (int i=r;i>=l;i--)

const int base = 1e9;
typedef vector<int> BigInt;

void Set(BigInt &a) {
    while (a.size() > 1 && a.back() == 0) a.pop_back();
}

void Print(BigInt a) {
    Set(a);
    printf("%d", (a.size() == 0) ? 0 : a.back());
    FORD(i,a.size()-2,0) printf("%09d", a[i]); EL;
}

BigInt Integer(string s) {
    BigInt ans;
    if (s[0] == '-') return ans;
    if (s.size() == 0) {ans.pb(0); return ans;}
    while (s.size()%9 != 0) s = '0'+s;
    for (int i=0;i<s.size();i+=9) {
        int v = 0;
        for (int j=i;j<i+9;j++) v = v*10+(s[j]-'0');
        ans.insert(ans.begin(),v);
    }
    Set(ans);
    return ans;
}

BigInt Integer(char c[]) {
    string s = "";
    FOR(i,0,strlen(c)-1) s = s + c[i];
    return Integer(s);
}

BigInt Integer(ll x) {
    string s = "";
    while (x > 0) s = char(x%10+'0') + s, x /= 10;
    return Integer(s);
}

BigInt Integer(int x) {
    return Integer((ll) x);
}

void operator >> (istream &in, BigInt &a) {
    string s;
    getline(cin, s);
    a = Integer(s);
}

void operator << (ostream &out, BigInt a) {
    Print(a);
}

bool operator < (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    if (a.size() != b.size()) return (a.size() < b.size());
    FORD(i,a.size()-1,0)
        if (a[i] != b[i]) return (a[i] < b[i]);
    return false;
}

bool operator > (BigInt a, BigInt b) {
    return (b < a);
}

bool operator == (BigInt a, BigInt b) {
    return (!(a < b) && !(b < a));
}

bool operator <= (BigInt a, BigInt b) {
    return (a < b || a == b);
}

bool operator >= (BigInt a, BigInt b) {
    return (b < a || b == a);
}

bool operator < (BigInt a, int b) {
    return (a < Integer(b));
}

bool operator > (BigInt a, int b) {
    return (a > Integer(b));
}

bool operator == (BigInt a, int b) {
    return (a == Integer(b));
}

bool operator >= (BigInt a, int b) {
    return (a >= Integer(b));
}

bool operator <= (BigInt a, int b) {
    return (a <= Integer(b));
}

BigInt max(BigInt a, BigInt b) {
    if (a > b) return a;
    return b;
}

BigInt min(BigInt a, BigInt b) {
    if (a < b) return a;
    return b;
}

BigInt operator + (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    BigInt ans;
    int carry = 0;
    FOR(i,0,max(a.size(), b.size())-1) {
        if (i < a.size()) carry += a[i];
        if (i < b.size()) carry += b[i];
        ans.pb(carry%base);
        carry /= base;
    }
    if (carry) ans.pb(carry);
    Set(ans);
    return ans;
}

BigInt operator + (BigInt a, int b) {
    return a + Integer(b);
}

BigInt operator ++ (BigInt &a) { // ++a
    a = a + 1;
    return a;
}

void operator += (BigInt &a, BigInt b) {
    a = a + b;
}

void operator += (BigInt &a, int b) {
    a = a + b;
}

BigInt operator &mdash; (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    BigInt ans;
    int carry = 0;
    FOR(i,0,a.size()-1) {
        carry += a[i] &mdash; (i < b.size() ? b[i] : 0);
        if (carry < 0) ans.pb(carry+base), carry = -1;
        else ans.pb(carry), carry = 0;
    }
    Set(ans);
    return ans;
}

BigInt operator &mdash; (BigInt a, int b) {
    return a &mdash; Integer(b);
}

void operator -- (BigInt &a) { // --a
    a = a &mdash; 1;
}

void operator -= (BigInt &a, BigInt b) {
    a = a + b;
}

void operator -= (BigInt &a, int b) {
    a = a &mdash; b;
}

BigInt operator * (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    BigInt ans;
    ans.assign(a.size()+b.size(), 0);
    FOR(i,0,a.size()-1) {
        ll carry = 0ll;
        for (int j=0;j<b.size() || carry > 0;j++) {
            ll s = ans[i+j] + carry + (ll)a[i]*(j<b.size()?(ll)b[j]:0ll);
            ans[i+j] = s%base;
            carry = s/base;
        }
    }
    Set(ans);
    return ans;
}

BigInt operator * (BigInt a, int b) {
    return a * Integer(b);
}

void operator *= (BigInt &a, BigInt b) {
    a = a * b;
}

void operator *= (BigInt &a, int b) {
    a = a * b;
}



BigInt operator / (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    if (b == Integer(0)) return Integer("-1");
    BigInt ans, cur;
    FORD(i,a.size()-1,0) {
        cur.insert(cur.begin(), a[i]);
        int x = 0, L = 0, R = base;
        while (L <= R) {
            int mid = (L+R)>>1;
            if (b*Integer(mid) > cur) {
                x = mid;
                R = mid-1;
            }
            else
                L = mid+1;
        }
        cur = cur &mdash; Integer(x-1)*b;
        ans.insert(ans.begin(),x-1);
    }
    Set(ans);
    return ans;
}

BigInt operator / (BigInt a, int b) {
    Set(a);
    BigInt ans;
    ll cur = 0ll;
    FORD(i,a.size()-1,0) {
        cur = (cur*(ll)base + (ll)a[i]);
        ans.insert(ans.begin(),cur/b);
        cur %= b;
    }
    Set(ans);
    return ans;
}

void operator /= (BigInt &a, BigInt b) {
    a = a / b;
}

void operator /= (BigInt &a, int b) {
    a = a / b;
}

BigInt operator % (BigInt a, BigInt b) {
    Set(a);
    Set(b);
    if (b == Integer(0)) return Integer("-1");
    BigInt ans;
    FORD(i,a.size()-1,0) {
        ans.insert(ans.begin(), a[i]);
        int x = 0, L = 0, R = base;
        while (L <= R) {
            int mid = (L+R)>>1;
            if (b*Integer(mid) > ans) {
                x = mid;
                R = mid-1;
            }
            else
                L = mid+1;
        }
        ans = ans &mdash; Integer(x-1)*b;
    }
    Set(ans);
    return ans;
}

int operator % (BigInt a, int b) {
    Set(a);
    if (b == 0) return -1;
    int ans = 0;
    FORD(i,a.size()-1,0)
        ans = (ans*(base%b) + a[i]%b)%b;
    return ans;
}

void operator %= (BigInt &a, BigInt b) {
    a = a % b;
}

void operator %= (BigInt &a, int b) {
    a = a % Integer(b);
}

BigInt gcd(BigInt a, BigInt b) {
    Set(a);
    Set(b);
    while (b > Integer(0)) {
        BigInt r = a%b;
        a = b;
        b = r;
    }
    Set(a);
    return a;
}

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


BigInt sqrt(BigInt a) {
    BigInt x0 = a, x1 = (a+1)/2;
    while (x1 < x0) {
        x0 = x1;
        x1 = (x1+a/x1)/2;
    }
    return x0;
}

BigInt pow(BigInt a, BigInt b) {
    if (b == Integer(0)) return Integer(1);
    BigInt tmp = pow(a, b/2);
    if (b%2 == 0) return tmp * tmp;
    return tmp * tmp * a;
}

BigInt pow(BigInt a, int b) {
    return pow(a,(Integer(b)));
}

int log(int n, BigInt a) { // log_n(a)
    Set(a);
    int ans = 0;
    while (a > Integer(1)) {
        ans++;
        a /= n;
    }
    return ans;
}

int main()
{
    BigInt B;  cin >> B;
    BigInt A = Integer("123456789");
    BigInt C = Integer(123456789ll);
    int x; x = 123456789;

    if (B <= A) cout << A - B;
    else {
        cout << "-";
        cout << B - A;
    }

    cout << A + B; Print(A + x);
    cout << A * B; Print(A * x);
    cout << A / B; Print(A / x);
    cout << A % B; printf("%d\n", A % x);

    C = ++A; ++B; C += B + x;
    Print(A); Print(B); Print(C);

    cout << max(A,B);
    cout << min(A,B);

    cout << gcd(A,B);
    cout << lcm(A,B);

    cout << sqrt(A);
    printf("%d %d %d\n", log(2,A), log(10,B), log(5,C));

    A = Integer(16); x = 12;
    cout << pow(A,B);
    cout << pow(A,x);

    return 0;
}