Data type to store value <=10^20 in C/C++

Question

Is there any data type that is capable of storing values within range 0<X<10^20 in c/c++??

Answer 1

Since log2(10^20) = ~66.43 you will need an integer made by 128 bits to store the number with integer precision. Actually, as pointed out by delnan in comment, 67 bits would be sufficient, by rounding to 72 bits with 8 bits alignment or 96 bits with 32 bits alignment.

So, if you don't require an exact integer representation, you could use a float or a double, otherwise you could look for a arbitrary long number library (there are many available either for C or C++).

Answer 2

Both float and double can store numbers of range at least 1E-37 to 1E+37.

If you need exact precision, you can use a big num library like GMP.

Answer 3

float or double can store the range you desire. You can also use a Big Integer library. Here's an example:

// header files

#include <cstdio>
#include <string>
#include <algorithm>
#include <iostream>

using namespace std;

struct Bigint {
    // representations and structures
    string a; // to store the digits
    int sign; // sign = -1 for negative numbers, sign = 1 otherwise

    // constructors
    Bigint() {} // default constructor
    Bigint( string b ) { (*this) = b; } // constructor for string

    // some helpful methods
    int size() { // returns number of digits
        return a.size();
    }
    Bigint inverseSign() { // changes the sign
        sign *= -1;
        return (*this);
    }
    Bigint normalize( int newSign ) { // removes leading 0, fixes sign
        for( int i = a.size() - 1; i > 0 && a[i] == '0'; i-- )
            a.erase(a.begin() + i);
        sign = ( a.size() == 1 && a[0] == '0' ) ? 1 : newSign;
        return (*this);
    }

    // assignment operator
    void operator = ( string b ) { // assigns a string to Bigint
        a = b[0] == '-' ? b.substr(1) : b;
        reverse( a.begin(), a.end() );
        this->normalize( b[0] == '-' ? -1 : 1 );
    }

    // conditional operators
    bool operator < ( const Bigint &b ) const { // less than operator
        if( sign != b.sign ) return sign < b.sign;
        if( a.size() != b.a.size() )
            return sign == 1 ? a.size() < b.a.size() : a.size() > b.a.size();
        for( int i = a.size() - 1; i >= 0; i-- ) if( a[i] != b.a[i] )
            return sign == 1 ? a[i] < b.a[i] : a[i] > b.a[i];
        return false;
    }
    bool operator == ( const Bigint &b ) const { // operator for equality
        return a == b.a && sign == b.sign;
    }



    // mathematical operators
    Bigint operator + ( Bigint b ) { // addition operator overloading
        if( sign != b.sign ) return (*this) - b.inverseSign();
        Bigint c;
        for(int i = 0, carry = 0; i<a.size() || i<b.size() || carry; i++ ) {
            carry+=(i<a.size() ? a[i]-48 : 0)+(i<b.a.size() ? b.a[i]-48 : 0);
            c.a += (carry % 10 + 48);
            carry /= 10;
        }
        return c.normalize(sign);
    }
    Bigint operator - ( Bigint b ) { // subtraction operator overloading
        if( sign != b.sign ) return (*this) + b.inverseSign();
        int s = sign; sign = b.sign = 1;
        if( (*this) < b ) return ((b - (*this)).inverseSign()).normalize(-s);
        Bigint c;
        for( int i = 0, borrow = 0; i < a.size(); i++ ) {
            borrow = a[i] - borrow - (i < b.size() ? b.a[i] : 48);
            c.a += borrow >= 0 ? borrow + 48 : borrow + 58;
            borrow = borrow >= 0 ? 0 : 1;
        }
        return c.normalize(s);
    }
    Bigint operator * ( Bigint b ) { // multiplication operator overloading
        Bigint c("0");
        for( int i = 0, k = a[i] - 48; i < a.size(); i++, k = a[i] - 48 ) {
            while(k--) c = c + b; // ith digit is k, so, we add k times
            b.a.insert(b.a.begin(), '0'); // multiplied by 10
        }
        return c.normalize(sign * b.sign);
    }
    Bigint operator / ( Bigint b ) { // division operator overloading
        if( b.size() == 1 && b.a[0] == '0' ) b.a[0] /= ( b.a[0] - 48 );
        Bigint c("0"), d;
        for( int j = 0; j < a.size(); j++ ) d.a += "0";
        int dSign = sign * b.sign; b.sign = 1;
        for( int i = a.size() - 1; i >= 0; i-- ) {
            c.a.insert( c.a.begin(), '0');
            c = c + a.substr( i, 1 );
            while( !( c < b ) ) c = c - b, d.a[i]++;
        }
        return d.normalize(dSign);
    }
    Bigint operator % ( Bigint b ) { // modulo operator overloading
        if( b.size() == 1 && b.a[0] == '0' ) b.a[0] /= ( b.a[0] - 48 );
        Bigint c("0");
        b.sign = 1;
        for( int i = a.size() - 1; i >= 0; i-- ) {
            c.a.insert( c.a.begin(), '0');
            c = c + a.substr( i, 1 );
            while( !( c < b ) ) c = c - b;
        }
        return c.normalize(sign);
    }



    // output method
    void print() {
        if( sign == -1 ) putchar('-');
        for( int i = a.size() - 1; i >= 0; i-- ) putchar(a[i]);
    }
};

int main() {
    Bigint a, b, c; // declared some Bigint variables

    /////////////////////////
    // taking Bigint input //
    /////////////////////////
    string input; // string to take input

    cin >> input; // take the Big integer as string
    a = input; // assign the string to Bigint a

    cin >> input; // take the Big integer as string
    b = input; // assign the string to Bigint b

    //////////////////////////////////
    // Using mathematical operators //
    //////////////////////////////////

    c = a + b; // adding a and b
    c.print(); // printing the Bigint
    puts(""); // newline

    c = a - b; // subtracting b from a
    c.print(); // printing the Bigint
    puts(""); // newline

    c = a * b; // multiplying a and b
    c.print(); // printing the Bigint
    puts(""); // newline

    c = a / b; // dividing a by b
    c.print(); // printing the Bigint
    puts(""); // newline

    c = a % b; // a modulo b
    c.print(); // printing the Bigint
    puts(""); // newline

    /////////////////////////////////
    // Using conditional operators //
    /////////////////////////////////

    if( a == b ) puts("equal"); // checking equality
    else puts("not equal");

    if( a < b ) puts("a is smaller than b"); // checking less than operator

    return 0;
}

I collect this sample library from here. Maybe it will help you to build your own.

Answer 4

The double type can hold some values up to that range, but it can't represent all integers in that range (because as noted in one of the other answers, you would need 67 bits to represent all such integers while a double has only 52 bits of mantissa).

Answer 5

http://msdn.microsoft.com/en-us/library/s3f49ktz(v=vs.80).aspx

float and double data types would be the answer. But moreover I think DOUBLE data type is ideal.