bignum class for C++

BigInt.cpp

// In the name of Allah.
// We're nothing and you're everything.
// Ya Ali!
 
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
const int maxn = 1e2 + 14, lg = 15;

/*
  ######################################################################
  #######################   THE   BIG   INT   ##########################
*/
const int base = 1000000000;
const int base_digits = 9; 
struct bigint {
	vector<int> a;
	int sign;
	/*<arpa>*/
	int size(){
		if(a.empty())return 0;
		int ans=(a.size()-1)*base_digits;
		int ca=a.back();
		while(ca)
			ans++,ca/=10;
		return ans;
	}
	bigint operator ^(const bigint &v){
		bigint ans=1,a=*this,b=v;
		while(!b.isZero()){
			if(b%2)
				ans*=a;
			a*=a,b/=2;
		}
		return ans;
	}
	bigint modPow(bigint base, bigint exp, const bigint &mod) {
		bigint result = 1;
		base %= mod;
		while (!exp.isZero()) {
			if (exp % 2)
				result = (result * base) % mod;
			base = (base * base) % mod;
			exp /= 2;
		}
		return result;
	}
	string to_string(){
		stringstream ss;
		ss << *this;
		string s;
		ss >> s;
		return s;
	}
	int sumof(){
		string s = to_string();
		int ans = 0;
		for(auto c : s)  ans += c - '0';
		return ans;
	}
	/*</arpa>*/
	bigint() :
		sign(1) {
	}
 
	bigint(long long v) {
		*this = v;
	}
 
	bigint(const string &s) {
		read(s);
	}
 
	void operator=(const bigint &v) {
		sign = v.sign;
		a = v.a;
	}
 
	void operator=(long long v) {
		sign = 1;
		a.clear();
		if (v < 0)
			sign = -1, v = -v;
		for (; v > 0; v = v / base)
			a.push_back(v % base);
	}
 
	bigint operator+(const bigint &v) const {
		if (sign == v.sign) {
			bigint res = v;
 
			for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
				if (i == (int) res.a.size())
					res.a.push_back(0);
				res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
				carry = res.a[i] >= base;
				if (carry)
					res.a[i] -= base;
			}
			return res;
		}
		return *this - (-v);
	}
 
	bigint operator-(const bigint &v) const {
		if (sign == v.sign) {
			if (abs() >= v.abs()) {
				bigint res = *this;
				for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
					res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
					carry = res.a[i] < 0;
					if (carry)
						res.a[i] += base;
				}
				res.trim();
				return res;
			}
			return -(v - *this);
		}
		return *this + (-v);
	}
 
	void operator*=(int v) {
		if (v < 0)
			sign = -sign, v = -v;
		for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
			if (i == (int) a.size())
				a.push_back(0);
			long long cur = a[i] * (long long) v + carry;
			carry = (int) (cur / base);
			a[i] = (int) (cur % base);
			//asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
		}
		trim();
	}
 
	bigint operator*(int v) const {
		bigint res = *this;
		res *= v;
		return res;
	}
 
	void operator*=(long long v) {
		if (v < 0)
			sign = -sign, v = -v;
		if(v > base){
			*this = *this * (v / base) * base + *this * (v % base);
			return ;
		}
		for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
			if (i == (int) a.size())
				a.push_back(0);
			long long cur = a[i] * (long long) v + carry;
			carry = (int) (cur / base);
			a[i] = (int) (cur % base);
			//asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
		}
		trim();
	}
 
	bigint operator*(long long v) const {
		bigint res = *this;
		res *= v;
		return res;
	}
 
	friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
		int norm = base / (b1.a.back() + 1);
		bigint a = a1.abs() * norm;
		bigint b = b1.abs() * norm;
		bigint q, r;
		q.a.resize(a.a.size());
 
		for (int i = a.a.size() - 1; i >= 0; i--) {
			r *= base;
			r += a.a[i];
			int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
			int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
			int d = ((long long) base * s1 + s2) / b.a.back();
			r -= b * d;
			while (r < 0)
				r += b, --d;
			q.a[i] = d;
		}
 
		q.sign = a1.sign * b1.sign;
		r.sign = a1.sign;
		q.trim();
		r.trim();
		return make_pair(q, r / norm);
	}
 
	bigint operator/(const bigint &v) const {
		return divmod(*this, v).first;
	}
 
	bigint operator%(const bigint &v) const {
		return divmod(*this, v).second;
	}
 
	void operator/=(int v) {
		if (v < 0)
			sign = -sign, v = -v;
		for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
			long long cur = a[i] + rem * (long long) base;
			a[i] = (int) (cur / v);
			rem = (int) (cur % v);
		}
		trim();
	}
 
	bigint operator/(int v) const {
		bigint res = *this;
		res /= v;
		return res;
	}
 
	int operator%(int v) const {
		if (v < 0)
			v = -v;
		int m = 0;
		for (int i = a.size() - 1; i >= 0; --i)
			m = (a[i] + m * (long long) base) % v;
		return m * sign;
	}
 
	void operator+=(const bigint &v) {
		*this = *this + v;
	}
	void operator-=(const bigint &v) {
		*this = *this - v;
	}
	void operator*=(const bigint &v) {
		*this = *this * v;
	}
	void operator/=(const bigint &v) {
		*this = *this / v;
	}
	void operator%=(const bigint &v){
		*this = *this % v;
	} 
	bool operator<(const bigint &v) const {
		if (sign != v.sign)
			return sign < v.sign;
		if (a.size() != v.a.size())
			return a.size() * sign < v.a.size() * v.sign;
		for (int i = a.size() - 1; i >= 0; i--)
			if (a[i] != v.a[i])
				return a[i] * sign < v.a[i] * sign;
		return false;
	}
 
	bool operator>(const bigint &v) const {
		return v < *this;
	}
	bool operator<=(const bigint &v) const {
		return !(v < *this);
	}
	bool operator>=(const bigint &v) const {
		return !(*this < v);
	}
	bool operator==(const bigint &v) const {
		return !(*this < v) && !(v < *this);
	}
	bool operator!=(const bigint &v) const {
		return *this < v || v < *this;
	}
 
	void trim() {
		while (!a.empty() && !a.back())
			a.pop_back();
		if (a.empty())
			sign = 1;
	}
 
	bool isZero() const {
		return a.empty() || (a.size() == 1 && !a[0]);
	}
 
	bigint operator-() const {
		bigint res = *this;
		res.sign = -sign;
		return res;
	}
 
	bigint abs() const {
		bigint res = *this;
		res.sign *= res.sign;
		return res;
	}
 
	long long longValue() const {
		long long res = 0;
		for (int i = a.size() - 1; i >= 0; i--)
			res = res * base + a[i];
		return res * sign;
	}
 
	friend bigint gcd(const bigint &a, const bigint &b) {
		return b.isZero() ? a : gcd(b, a % b);
	}
	friend bigint lcm(const bigint &a, const bigint &b) {
		return a / gcd(a, b) * b;
	}
 
	void read(const string &s) {
		sign = 1;
		a.clear();
		int pos = 0;
		while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
			if (s[pos] == '-')
				sign = -sign;
			++pos;
		}
		for (int i = s.size() - 1; i >= pos; i -= base_digits) {
			int x = 0;
			for (int j = max(pos, i - base_digits + 1); j <= i; j++)
				x = x * 10 + s[j] - '0';
			a.push_back(x);
		}
		trim();
	}
 
	friend istream& operator>>(istream &stream, bigint &v) {
		string s;
		stream >> s;
		v.read(s);
		return stream;
	}
 
	friend ostream& operator<<(ostream &stream, const bigint &v) {
		if (v.sign == -1)
			stream << '-';
		stream << (v.a.empty() ? 0 : v.a.back());
		for (int i = (int) v.a.size() - 2; i >= 0; --i)
			stream << setw(base_digits) << setfill('0') << v.a[i];
		return stream;
	}
 
	static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
		vector<long long> p(max(old_digits, new_digits) + 1);
		p[0] = 1;
		for (int i = 1; i < (int) p.size(); i++)
			p[i] = p[i - 1] * 10;
		vector<int> res;
		long long cur = 0;
		int cur_digits = 0;
		for (int i = 0; i < (int) a.size(); i++) {
			cur += a[i] * p[cur_digits];
			cur_digits += old_digits;
			while (cur_digits >= new_digits) {
				res.push_back(int(cur % p[new_digits]));
				cur /= p[new_digits];
				cur_digits -= new_digits;
			}
		}
		res.push_back((int) cur);
		while (!res.empty() && !res.back())
			res.pop_back();
		return res;
	}
 
	typedef vector<long long> vll;
 
	static vll karatsubaMultiply(const vll &a, const vll &b) {
		int n = a.size();
		vll res(n + n);
		if (n <= 32) {
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					res[i + j] += a[i] * b[j];
			return res;
		}
 
		int k = n >> 1;
		vll a1(a.begin(), a.begin() + k);
		vll a2(a.begin() + k, a.end());
		vll b1(b.begin(), b.begin() + k);
		vll b2(b.begin() + k, b.end());
 
		vll a1b1 = karatsubaMultiply(a1, b1);
		vll a2b2 = karatsubaMultiply(a2, b2);
 
		for (int i = 0; i < k; i++)
			a2[i] += a1[i];
		for (int i = 0; i < k; i++)
			b2[i] += b1[i];
 
		vll r = karatsubaMultiply(a2, b2);
		for (int i = 0; i < (int) a1b1.size(); i++)
			r[i] -= a1b1[i];
		for (int i = 0; i < (int) a2b2.size(); i++)
			r[i] -= a2b2[i];
 
		for (int i = 0; i < (int) r.size(); i++)
			res[i + k] += r[i];
		for (int i = 0; i < (int) a1b1.size(); i++)
			res[i] += a1b1[i];
		for (int i = 0; i < (int) a2b2.size(); i++)
			res[i + n] += a2b2[i];
		return res;
	}
 
	bigint operator*(const bigint &v) const {
		vector<int> a6 = convert_base(this->a, base_digits, 6);
		vector<int> b6 = convert_base(v.a, base_digits, 6);
		vll a(a6.begin(), a6.end());
		vll b(b6.begin(), b6.end());
		while (a.size() < b.size())
			a.push_back(0);
		while (b.size() < a.size())
			b.push_back(0);
		while (a.size() & (a.size() - 1))
			a.push_back(0), b.push_back(0);
		vll c = karatsubaMultiply(a, b);
		bigint res;
		res.sign = sign * v.sign;
		for (int i = 0, carry = 0; i < (int) c.size(); i++) {
			long long cur = c[i] + carry;
			res.a.push_back((int) (cur % 1000000));
			carry = (int) (cur / 1000000);
		}
		res.a = convert_base(res.a, 6, base_digits);
		res.trim();
		return res;
	}
};
/*
  #######################   THE   BIG   INT   ##########################
  ######################################################################
*/

int main(){
	ios::sync_with_stdio(0), cin.tie(0);
	bigint a=99999999;
	a*=1000200000003000LL;
	cout<<a<<'\n';
}

it`s awsome, but what about logical operations, like &, >>, <<?

Hi, I want to use it on my library project, can I change some part and use it?

Hi, I want to use it on my library project, can I change some part and use it?

Yes. No problem.

Hi, I want to use it on my library project, can I change some part and use it?

Yes. No problem.

Thank you so much.

Program is not so good.
I had APPCRASH on sum with digits 2000 signs long. This calss not suitable for work applications.

Sexy!

Thank you so much!!!!

just a suggestion: if you could please add modular exponentiation function into the snippet needed in https://codeforces.com/contest/17/problem/D as (((b - 1) * (b ^ (n - 1))) % c) . Here, ^ is failing since we need modpow to do %c in each pow(^) step for optimizing time complexity. Adding needed snippet :

bigint modPow(bigint base, bigint exp, const bigint &mod) {
bigint result = 1;
base %= mod;
while (!exp.isZero()) {
if (exp % 2)
result = (result * base) % mod;
base = (base * base) % mod;
exp /= 2;
}
return result;
}

just a suggestion: if you could please add modular exponentiation function into the snippet needed in https://codeforces.com/contest/17/problem/D as (((b - 1) * (b ^ (n - 1))) % c) . Here, ^ is failing since we need modpow to do %c in each pow(^) step for optimizing time complexity. Adding needed snippet :

bigint modPow(bigint base, bigint exp, const bigint &mod) { bigint result = 1; base %= mod; while (!exp.isZero()) { if (exp % 2) result = (result * base) % mod; base = (base * base) % mod; exp /= 2; } return result; }

Added.

Thanks. Also, since you did use %= in modpow function, but its not defined here, please do also add in :

void operator%=(const bigint &v){
*this = *this % v;
}