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Hello to all, i have code karatsuba but it is not compute correctly after 6 decimal digits.

#include <iostream>
#include <vector>
#include <algorithm>
#include <limits>
#include <cmath>
#include <cctype>

// ================================================
using namespace std;

typedef unsigned long ulong;

void userInput(ulong&, ulong&);
int numberLength(ulong);

ulong leftSplit(ulong, int);
ulong rightSplit(ulong, int);

int numberPower(const ulong&, const ulong&, const ulong&);
ulong Karatsuba(const ulong&, const ulong&);

const int MINLENGTH = 5;

// =============================================
int main(int argc, char *argv[])
{
	ulong first(0), second(0);

 while (1)
 {
	 userInput(first, second);
	 cout << "The result of " << 
		 first << " * " << second << " : "
		 << Karatsuba(first, second);

 }
	return 0;
}
// =============================================
void userInput(ulong& first, ulong& second)
{
	cout << "\nEnter First Number : ";
	cin >> first;

	while (cin.fail())
	{
		cin.clear();
		cin.ignore(std::numeric_limits<int>::max(), '\n');

		cout << "\nEnter First Number : ";
		cin >> first;
	}

	cout << "\nEnter Second Number : ";
	cin >> second;

	while (cin.fail())
	{
		cin.clear();
		cin.ignore(std::numeric_limits<int>::max(), '\n');

		cout << "\nEnter Second Number : ";
		cin >> second;
	}
}
// =============================================
int numberLength(ulong number)
{
	int len(0);

	// Check length of integer algorithm
	// * 10 = To shift left 1 digit in number
	// % 10  = To get last digit of number
	while (number >= 1)
	{
		number /= 10;
		++len;
	}

	return len;
}
// =============================================
ulong leftSplit(ulong number, int length)
{
	int middle = length / 2;
	vector<int> remainder(0);

	// To get most significant digit
	while (number >= 10)
	{
		remainder.push_back(number % 10);
		number /= 10;
	}
	
	std::reverse(remainder.begin(), remainder.end());

	ulong result(number);int remLoop(0);
	for (int loop = 0;loop < middle - 1;++loop)
	{
		if (remLoop < static_cast<int>(remainder.size()))
		{
			result = result * 10 + remainder[remLoop];
		}
		++remLoop;
	}

	return result;
}
// =============================================
ulong rightSplit(ulong number, int length)
{
	int remainder(0), multiply(1);
	ulong result(0);
	for (int loop = 0; loop < length;++loop)
	{
		remainder = number % 10;
		number /= 10;
		result += remainder * multiply ;
		multiply *= 10;
	}

	return result;
}
// =============================================
int numberPower(const ulong& first, const ulong& x1, 
								const ulong& y1)
{
	int lengthPower(1);

	const int base(10);
	
	while (first - y1 != (x1 * (pow(static_cast<double>(base), 
		static_cast<int>(lengthPower)))) )
	{
		++lengthPower;
	}

	return lengthPower;
}
// =============================================
ulong Karatsuba(const ulong& first, const ulong& second)
{
	if (first != 0 && second != 0)
	{
		if (numberLength(first) > MINLENGTH 
			&& numberLength(second) > MINLENGTH)
		{
			ulong x1 = leftSplit(first, numberLength(first));
			ulong	y1 = leftSplit(second, numberLength(second));
			
			ulong x0 = rightSplit(first, numberLength(first) - numberLength(x1));
			ulong y0 = rightSplit(second, numberLength(second) - numberLength(y1));

			int lengthPower = numberPower(first, x1, x0);

			unsigned long X = Karatsuba(x1, y1);
			int length = numberLength(X);
			ulong Y = Karatsuba(x0, y0);
			ulong Z = Karatsuba(x1 + x0, y1 + y0);
			Z = Z - X - Y;

			return (X * static_cast<unsigned long>(pow(10.0, 2.0 * lengthPower))) +  
				(Z * static_cast<unsigned long>(pow(10.0, lengthPower))) + Y;
		}
		else
		{
			return first * second;
		}
	}
	else
	{
		return 0;
	}

}
// =============================================

For example, 123456 * 654321 * 80779853 but my program display wrong answer.

Thanks.

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Last Post by Peter_APIIT
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  • 1
    ArkM 1,090   7 Years Ago

    Take into account that [code] 123456 * 654321 * 80779853 == 6525384681074833728 [/code] but [icode]std::numeric_limits<long>::max()[/icode] is equal to 2147483647 on 32-bit processors (integer overflow is not detected). Try [icode]long long[/icode] type (it's supported by modern compilers now), its max value is 9223372036854775807. Otherwise try one of big int class libraries... Read More

1

Take into account that

123456 * 654321 * 80779853  == 6525384681074833728

but std::numeric_limits<long>::max() is equal to 2147483647 on 32-bit processors (integer overflow is not detected).
Try long long type (it's supported by modern compilers now), its max value is 9223372036854775807.
Otherwise try one of big int class libraries...

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Why will causing this value although it can fit that value ?

Do you have any good big integer library ?

I need those supports up to 512 bits ?

Thanks

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I do searching in google but i not sure which one is easy, popular.

How about GNU MP ?

Thanks.

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It seems you don't understand that no need in Karatsuba algorithm while you are trying to get unsigned long results: use built-in arithmetic - that's all. But if the result is greater than unsigned long max value you can't return unsigned long value from Karatsuba function! No need in Karatsuba algorithm if you have bigint library: there is bigint multiplication in every such library.

Therefore all your codes are senseless from the beginning. Start your design from the big int representation. See, for example, http://en.wikipedia.org/wiki/Karatsuba_algorithm.

Apropos: the simplest (but ineffective) arbitrary precision integer representation is a simple text string. Try to implement Karatsuba algorithm for this representation.

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Thanks for your help. In cases, iI don't want to create my own big int class since there are many outside. I just want some big int library which is template based, easy to use.
For instance,

bigInt<150> aBigInt;
150 is the number of bits.

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