bool greaterThan(const bignum &bn1, const bignum &bn2)
{
//if bases are different, convert the second and re-evaluate
if (bn1.getBase() != bn2.getBase())
return greaterThan(bn1, bn2.getConverted(bn1.getBase()));
if (bn1 == bn2)
return false;
if (bn1.isNegative() && !bn2.isNegative())
return false;
if (!bn1.isNegative() && bn2.isNegative())
return true;
if (bn1.isNegative() && bn2.isNegative())
return (lessThan(bn1.absolute(), bn2.absolute()));
if (bn1.getDigitCount() > bn2.getDigitCount())
return true;
if (bn1.getDigitCount() < bn2.getDigitCount())
return false;
for (int i = bn1.getDigitCount() - 1; i >= 0; i--)
{
if (bn1.getDigit(i) > bn2.getDigit(i))
return true;
if (bn1.getDigit(i) < bn2.getDigit(i))
return false;
}
return false;
}
bool lessThan(const bignum &bn1, const bignum &bn2)
{
if (bn1.getBase() != bn2.getBase())
return lessThan(bn1, bn2.getConverted(bn1.getBase()));
if (bn1 == bn2)
return false;
if (bn1.isNegative() && !bn2.isNegative())
return true;
if (!bn1.isNegative() && bn2.isNegative())
return false;
if (bn1.isNegative() && bn2.isNegative())
return (greaterThan(bn1.absolute(), bn2.absolute()));
if (bn1.getDigitCount() < bn2.getDigitCount())
return true;
if (bn1.getDigitCount() > bn2.getDigitCount())
return false;
for (int i = bn1.getDigitCount() - 1; i >= 0; i--)
{
if (bn1.getDigit(i) < bn2.getDigit(i))
return true;
if (bn1.getDigit(i) > bn2.getDigit(i))
return false;
}
return false;
}
bool equals(const bignum &bn1, const bignum &bn2)
{
if (bn1.getBase() != bn2.getBase())
return equals(bn1, bn2.getConverted(bn1.getBase()));
if (bn1.isNegative() != bn2.isNegative())
return false;
if (bn1.getDigitCount() != bn2.getDigitCount())
return false;
if (bn1.getDecimalCount() != bn2.getDecimalCount())
return false;
for (int i = bn1.getDigitCount(); i > 0; i--)
{
if (bn1.getDigit(i - 1) != bn2.getDigit(i - 1))
return false;
}
return true;
}
bignum multiplyNumbers(const bignum &bn1, const bignum &bn2)
{
if (bn1.getBase() != bn2.getBase())
return multiplyNumbers(bn1, bn2.getConverted(bn1.getBase()));
bignum temp(0);
temp.setBase(bn1.getBase());
if (bn1.isZero() || bn2.isZero())
return temp;
//multiply bn1 by each digit of bn2 independently, then add the values together
int counter = bn2.getDigitRange();
for (int i = 0; i < counter; i++)
{
int toMultiply = (ONES_PLACE - bn2.getDecimalCount()) + i;
//verify function isn't checking beyond bounds of the stored array
if (toMultiply >= 0)
{
if (toMultiply >= MAXDIGITS)
throw error_handler(__FILE__, __LINE__, "The value being calculated is too large for the settings provided");
bignum toAdd = multiplyNumbersSimple(bn1.absolute(), bn2.getDigit(toMultiply));
toAdd.leftShift(i);
temp += toAdd;
}
}
if (bn1.isNegative() != bn2.isNegative())
temp.setNegative();
//adjust for added decimal places during multiplication
temp.rightShift(bn2.getDecimalCount());
temp.updateDigits();
return temp;
}
bignum divideNumbers(const bignum &bn1, const bignum &bn2)
{
if (bn2.isZero())
throw error_handler(__FILE__, __LINE__, "Cannot divide a number by zero");
bignum temp;
bool negative_result = (bn1.isNegative() != bn2.isNegative());
if (bn1.getBase() != bn2.getBase())
return divideNumbers(bn1, bn2.getConverted(bn1.getBase()));
//set base of the return value to match that of the passed values
int baseSet = bn1.getBase();
temp.setBase(baseSet);
bool remainder = false;
bool end = false;
int index = bn1.getDigitCount() - 1;
//starting with the left-most digit, create a bignumber of that digit that matches the set base
bignum number_to_compare(bn1.getDigit(index));
number_to_compare.convertBase(baseSet);
//ignore decimal places when comparing dividend to digits of the divisor
bignum nextNumber = divideNumbersSimple(number_to_compare, bn2.absolute().noDecimal(), remainder);
bignum number_to_subtract;
number_to_subtract.setBase(baseSet);
while (!end && index >= 0)
{
if (index >= MAXDIGITS)
throw error_handler(__FILE__, __LINE__, "The value being calculated is too large for the settings provided");
if (remainder == false && index < ONES_PLACE - bn1.getDecimalCount())
end = true;
temp.setDigit(index, nextNumber.getDigit(ONES_PLACE));
index--;
number_to_subtract = bn2.absolute().noDecimal() * nextNumber;
number_to_subtract.updateDigits();
number_to_compare -= number_to_subtract;
number_to_compare.leftShift(1);
if (index >= 0)
{
bignum digit(bn1.getDigit(index));
digit.convertBaseSimple(number_to_compare.getBase());
number_to_compare += digit;
}
nextNumber = divideNumbersSimple(number_to_compare, bn2.absolute().noDecimal(), remainder);
if (index < 0)
end = true;
}
if (negative_result && temp != 0)
temp.setNegative();
temp.leftShift(bn2.getDecimalCount());
return temp;
}
bignum subtractNumbers(const bignum &bn1, const bignum &bn2)
{
if (bn1.getBase() != bn2.getBase())
return subtractNumbers(bn1, bn2.getConverted(bn1.getBase()));
int base = bn1.getBase();
bignum difference;
difference.setBase(base);
//evaluate the numbers being of equal absolute value
if (bn1.absolute() == bn2.absolute())
{
// -12 - 12 ---> -(12 + 12)
if (bn1.isNegative() && !bn2.isNegative())
{
bignum temp = addNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
// 12 - -12 ---> 12 + 12
if (!bn1.isNegative() && bn2.isNegative())
return addNumbers(bn1.absolute(), bn2.absolute());
// -12 - -12 ---> 0
if (bn1.isNegative() && bn2.isNegative())
{
bignum temp;
temp.setBase(base);
return temp;
}
}
//evaluate the numbers if absolute first is larger than absolute second
if (bn1.absolute() > bn2.absolute())
{
// -12 - 8 ---> -(12 + 8)
if (bn1.isNegative() && !bn2.isNegative())
{
bignum temp = addNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
// 12 - -8 ---> 12 + 8
if (!bn1.isNegative()&& bn2.isNegative())
return addNumbers(bn1.absolute(), bn2.absolute());
// -12 - -8 ---> -(12 - 8)
if (bn1.isNegative() && bn2.isNegative())
{
bignum temp = subtractNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
}
//evaluate the numbers if absolute first is smaller than absolute second
if (bn1.absolute() < bn2.absolute())
{
// 8 - 12 ---> -(12 - 8)
if (!bn1.isNegative()&& !bn2.isNegative())
{
bignum temp = subtractNumbers(bn2.absolute(), bn1.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
// -8 - 12 ---> -(8 + 12)
if (bn1.isNegative() && !bn2.isNegative())
{
bignum temp = addNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
// 8 - -12 ---> 8 + 12
if (!bn1.isNegative() && bn2.isNegative())
return addNumbers(bn1.absolute(), bn2.absolute());
// -8 - -12 ---> (12 - 8)
if (bn1.isNegative() && bn2.isNegative())
return subtractNumbers(bn2.absolute(), bn1.absolute());
}
int carry = 0;
int digits = 0;
int decimal = 0;
//bool carry_negative = false;
//sets decimal and digit values to the highest of each number
decimal = (bn1.getDecimalCount() > bn2.getDecimalCount() ? bn1.getDecimalCount() : bn2.getDecimalCount());
digits = (bn1.getDigitCount() > bn2.getDigitCount() ? bn1.getDigitCount() + 1 : bn2.getDigitCount() + 1);
for (int i = (ONES_PLACE - decimal); i < digits + 1 && i >= 0; i++)
{
if (i >= MAXDIGITS)
throw error_handler(__FILE__, __LINE__, "The value being calculated is too large for the settings provided");
int tempNumber = bn1.getDigit(i) - bn2.getDigit(i);
tempNumber -= carry;
if (tempNumber < 0)
{
tempNumber += base;
carry = 1;
}
else carry = 0;
difference.setDigit(i, tempNumber);
}
difference.updateDigits();
difference.setBase(base);
return difference;
}
bignum addNumbers(const bignum &bn1, const bignum &bn2)
{
if (bn1.getBase() != bn2.getBase())
return addNumbers(bn1, bn2.getConverted(bn1.getBase()));
if (bn1.absolute() == bn2.absolute())
{
// -12 + 12 or 12 + -12 ---> 0
if (bn1.isNegative() != bn2.isNegative())
{
bignum temp;
temp.setBase(bn1.getBase());
return temp;
}
// -12 + -12 ---> -(12 + 12)
if (bn1.isNegative() && bn2.isNegative())
{
bignum temp(addNumbers(bn1.absolute(), bn2.absolute()));
temp.setNegative();
temp.updateDigits();
return temp;
}
}
if (bn1.absolute() > bn2.absolute())
{
// -12 + 8 ---> -(12 - 8)
if (bn1.isNegative() && !bn2.isNegative())
{
bignum temp = subtractNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
// 12 + -8 ---> 12 - 8
if (!bn1.isNegative() && bn2.isNegative())
return subtractNumbers(bn1.absolute(), bn2.absolute());
// -12 + -8 ---> -(12 + 8)
if (bn1.isNegative()&& bn2.isNegative())
{
bignum temp = addNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
}
if (bn1.absolute() < bn2.absolute())
{
// -8 + 12 ---> 12 - 8
if (bn1.isNegative() && !bn2.isNegative())
{
bignum temp = subtractNumbers(bn2.absolute(), bn1.absolute());
temp.updateDigits();
return temp;
}
// 8 + -12 ---> 8 - 12
if (!bn1.isNegative() && bn2.isNegative())
return subtractNumbers(bn1.absolute(), bn2.absolute());
// -8 + -12 ---> -(8 + 12)
if (bn1.isNegative() && bn2.isNegative())
{
bignum temp = addNumbers(bn1.absolute(), bn2.absolute());
temp.setNegative();
temp.updateDigits();
return temp;
}
}
int carry = 0;
int digits = 0;
int decimal = 0;
//sets decimal and digit values to the highest of each number
decimal = (bn1.getDecimalCount() > bn2.getDecimalCount() ? bn1.getDecimalCount() : bn2.getDecimalCount());
digits = (bn1.getDigitCount() > bn2.getDigitCount() ? bn1.getDigitCount() + 1 : bn2.getDigitCount() + 1);
bignum sum;
int base = bn1.getBase();
for (int i = (ONES_PLACE - decimal); i < digits + 1 ; i++)
{
if (i >= MAXDIGITS)
throw error_handler(__FILE__, __LINE__, "The value being calculated is too large for the settings provided");
int tempNumber = bn1.getDigit(i) + bn2.getDigit(i);
tempNumber += carry;
if (tempNumber>(base - 1))
{
tempNumber -= base;
carry = 1;
}
else carry = 0;
sum.setDigit(i, tempNumber);
}
sum.updateDigits();
sum.setBase(base);
return sum;
}