string addBitStrings( string first, string second )
{
string result; // To store the sum bits
// make the lengths same before adding
int length = makeEqualLength(first, second);
int carry = 0; // Initialize carry
// Add all bits one by one
for (int i = length-1 ; i >= 0 ; i--)
{
int firstBit = first.at(i) - '0';
int secondBit = second.at(i) - '0';
// boolean expression for sum of 3 bits
int sum = (firstBit ^ secondBit ^ carry)+'0';
result = (char)sum + result;
// boolean expression for 3-bit addition
carry = (firstBit&secondBit) | (secondBit&carry) | (firstBit&carry);
}
// if overflow, then add a leading 1
if (carry) result = '1' + result;
return result;
}
InfInt karatsubaMult(string x, string y)
{
InfInt *result = new InfInt(0);
int m = makeEqualLength(x, y);
if(m == 0)
return *result;
size_t sz = 0;
if( x.length() == 1 || y.length() == 1 ) {
result = new InfInt(stoull(x, &sz, 0) * stoull(y, &sz, 0));
return *result;
}
// m2 + m2Rest = m
int m2 = m/2;
int m2Rest = m - m2;
string xl = x.substr(0, m2);
string xr = x.substr(m2, m2Rest);
string yl = y.substr(0, m2);
string yr = y.substr(m2, m2Rest);
InfInt z0 = karatsubaMult(xr, yr);
InfInt z1 = karatsubaMult(add(xl, xr), add(yl, yr));
InfInt z2 = karatsubaMult(xl, yl);
*result = (z2 * basePower(*INFINTBASE10, 2*m2) + ((z1-z2-z0) * basePower(*INFINTBASE10, m2)) + z0);
return *result;
}
char *addBitStrings(char *n1,char *n2)
{
makeEqualLength(n1,n2);
// puts(n1);
// puts(n2);
int length = strlen(n1);
char *result = malloc(length + 2);
strcpy(result,"");
int carry = 0;
for(int i = length - 1;i >= 0; --i)
{
int first_bit = n1[i] - '0';
int second_bit = n2[i] - '0';
int sum = (first_bit ^ second_bit ^ carry) + '0';
char t[] = {sum,'\0'};
char *temp = malloc(length + 1);
strcpy(temp,"");
strcat(temp,t);
strcat(temp,result);
strcpy(result,temp);
carry = (first_bit & second_bit) | (second_bit & carry) | (first_bit & carry);
}
if(carry)
{
char *temp = malloc(length + 1);
strcpy(temp,"");
strcat(temp,"1");
strcat(temp,result);
strcpy(result,temp);
}
return result;
}
