How to Implement a BigInt Class in C for Handling Arbitrarily Large Integers?

Implementing a BigInt Class in C

In C , when handling numbers larger than a long int, it is useful to create a custom "big int" class. Instead of relying on external implementations, consider creating your own to gain a deeper understanding of these concepts.

Data Structure

A straightforward approach involves storing the number as a string, breaking it down into smaller numbers (e.g., digits), and placing them in an array. This simplifies comparison operations but raises concerns for operations like addition and multiplication.

Algorithm Overview

For these operations, it is beneficial to consider the binary nature of integers. Implementing the addition operator ( =) as an example, iterate through each digit pair, and add them. If the result overflows the BaseType, carry over the excess into the next digit.

Code Example

template< class BaseType >
BigInt< BaseType >&amp; BigInt< BaseType >::operator += (BigInt< BaseType > const&amp; operand)
{
  BT count, carry = 0;
  for (count = 0; count < std::max(value_.size(), operand.value_.size(); count++)
  {
    BT op0 = count < value_.size() ? value_.at(count) : 0, 
       op1 = count < operand.value_.size() ? operand.value_.at(count) : 0;
    BT digits_result = op0 + op1 + carry;
    if (digits_result-carry < std::max(op0, op1)
    {
      BT carry_old = carry;
      carry = digits_result;
      digits_result = (op0 + op1 + carry) >> sizeof(BT)*8; // NOTE [1]
    }
    else carry = 0;
  }
 
  return *this;
}

Implementation Notes

• The BaseType is the underlying type of the BigInt, e.g., int or long.
• The value_ vector stores the individual digits of the number.
• carry tracks any overflow between digits.
• Overflow detection is done by comparing the result with the original digits.

Other Operators

Repeat this algorithmic approach for subtraction, multiplication, and division. Implement standard operators like << for output and < for comparison.

Conclusion

Building a custom BigInt class is a challenging but rewarding exercise. Following the steps outlined here can help you implement a functional and efficient class that handles arbitrarily large integers in C .

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