Tutorial :Handling large numbers in C++?



Question:

What is the best way to handle large numeric inputs in C++ (for example 10^100)?

For algorithms I usually switch over to ruby and I sometimes use strings.

Any other good methods?


Solution:1

It sounds like you're looking for a way to enter Arbitrary Precision numbers. here are two libraries you could use: GMP and MAPM


Solution:2

Check out The Large Integer Case Study in C++.pdf by Owen Astrachan. I found this file extremely useful with detail introduction and code implementation. It doesn't use any 3rd-party library. I have used this to handle huge numbers (as long as you have enough memory to store vector<char>) with no problems.


Idea: It implements an arbitrary precision integer class by storing big int in a vector<char>.

vector<char> myDigits; // stores all digits of number  

Then all operations related to the big int, including <<, >>, +, -, *, ==, <, !=, >, etc., can be done based on operations on this char array.


Taste of the code: Here is the header file, you can find its cpp with codes in the pdf file.

#include <iostream>  #include <string> // for strings  #include <vector> // for sequence of digits  using namespace std;    class BigInt  {  public:      BigInt(); // default constructor, value = 0      BigInt(int); // assign an integer value      BigInt(const string &); // assign a string      // may need these in alternative implementation      // BigInt(const BigInt &); // copy constructor      // ~BigInt(); // destructor      // const BigInt & operator = (const BigInt &);      // assignment operator      // operators: arithmetic, relational      const BigInt & operator += (const BigInt &);      const BigInt & operator -= (const BigInt &);      const BigInt & operator *= (const BigInt &);      const BigInt & operator *= (int num);      string ToString() const; // convert to string      int ToInt() const; // convert to int      double ToDouble() const; // convert to double      // facilitate operators ==, <, << without friends      bool Equal(const BigInt & rhs) const;      bool LessThan(const BigInt & rhs) const;      void Print(ostream & os) const;  private:      // other helper functions      bool IsNegative() const; // return true iff number is negative      bool IsPositive() const; // return true iff number is positive      int NumDigits() const; // return # digits in number      int GetDigit(int k) const;      void AddSigDigit(int value);      void ChangeDigit(int k, int value);      void Normalize();      // private state/instance variables      enum Sign{positive,negative};      Sign mySign; // is number positive or negative      vector<char> myDigits; // stores all digits of number      int myNumDigits; // stores # of digits of number  };    // free functions  ostream & operator <<(ostream &, const BigInt &);  istream & operator >>(istream &, BigInt &);  BigInt operator +(const BigInt & lhs, const BigInt & rhs);  BigInt operator -(const BigInt & lhs, const BigInt & rhs);  BigInt operator *(const BigInt & lhs, const BigInt & rhs);  BigInt operator *(const BigInt & lhs, int num);  BigInt operator *(int num, const BigInt & rhs);  bool operator == (const BigInt & lhs, const BigInt & rhs);  bool operator < (const BigInt & lhs, const BigInt & rhs);  bool operator != (const BigInt & lhs, const BigInt & rhs);  bool operator > (const BigInt & lhs, const BigInt & rhs);  bool operator >= (const BigInt & lhs, const BigInt & rhs);  bool operator <= (const BigInt & lhs, const BigInt & rhs);  


Solution:3

Are you looking for how to perform operations on the large inputs you receive? There is a big integer C++ library (similar to Java) that allows you to perform arithmetic operations...


Solution:4

If you wish to make your own code for the purpose try using strings to store big numbers... you can then create basic ops like + - / * on them... for example -

#include <iostream>    using namespace std;    string add (string &s1, string &s2){      int carry=0,sum,i;        string  min=s1,      max=s2,      result = "";        if (s1.length()>s2.length()){          max = s1;          min = s2;      } else {          max = s2;          min = s1;      }        for (i = min.length()-1; i>=0; i--){          sum = min[i] + max[i + max.length() - min.length()] + carry - 2*'0';            carry = sum/10;          sum %=10;            result = (char)(sum + '0') + result;      }        i = max.length() - min.length()-1;        while (i>=0){          sum = max[i] + carry - '0';          carry = sum/10;          sum%=10;            result = (char)(sum + '0') + result;          i--;      }        if (carry!=0){          result = (char)(carry + '0') + result;      }               return result;  }    int main (){      string a,b;        cin >> a >> b;        cout << add (a,b)<<endl;        return 0;  }  


Solution:5

assuming you are talking about inputting numbers, double precision would get you up to 1.7976931348623157 x 10^308


Solution:6

You might want to have a look to gmplib, an arbitrary precision number handling library for C and C++


Solution:7

If you want it to be accurate, you need a library made to deal with big numbers. Java has BigInt that will always be accurate no matter how many digits you want to take it to, and provides math operations on them. All the source code is included, you could transfer it, but this really isn't the kind of thing C++ is best at--I'd use a JVM based language and use one of the Big libraries.

I don't think I'd use ruby for this unless you wanted it to be slow, and I'm assuming that since you are talking about C++, speed is somewhat of a design consideration.


Solution:8

As others have already pointed out, there are various bignum/arbitrary precision libraries in C++ that you would likely find useful. If speed isn't necessary, I'm under the impression that Python and Lisp both use bignums by default.


Solution:9

Well I think the best way to do such arithmetic calculation is by using strings. Give input as command line arguments and then manipulate the whole logic using string functions like atoi() and itoa()! But, hey can this be done for multiplication and Division? I think in this way strlen of strings entered doesn't matter for programming for compiler until the logic is fine.


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