void multiply_bignum(bignum *a, bignum *b, bignum *c)
{
bignum aCopy = *a;
bignum tmp;
int i, j;
int digit;
// TODO: compare a and b for the optimized performance.
if (compareBignum(a, b) < 0)
{
multiply_bignum(b, a, c);
return;
}
initializeBignum(c);
rightShift(&aCopy, b->numFractions);
// Multiple by the fractional numbers.
for (i = 0; i < b->numFractions; i++)
{
digit = b->integers[i];
// Add {digit} times.
for (j = 1; j <= digit; j++)
{
addBignum(c, &aCopy, &tmp);
*c = tmp;
}
leftShift(&aCopy, 1);
}
// Multiple by the integer numbers.
for (i = 0; i <= b->numIntegers; i++)
{
digit = b->integers[i];
for(j = 1; j <= digit; j++)
{
addBignum(c, &aCopy, &tmp);
*c = tmp;
}
leftShift(&aCopy, 1);
}
c->sign = (a->sign == b->sign) ? PLUS : MINUS;
optimizeBignum(c);
}
bignum::bignum(vector<int> n, int set_base, bool is_negative)
{
initializeBignum();
base = set_base;
int count = (ONES_PLACE - 1) + n.size();
for (vector<int>::iterator i = n.begin(); i != n.end() && count >= 0; i++)
{
if (count >= MAXDIGITS)
throw error_handler(__FILE__, __LINE__, "The value being calculated is too large for the settings provided");
if (*i >= base)
throw error_handler(__FILE__, __LINE__, "One of the values passed is beyond the given base");
digits[count] = (*i);
count--;
}
updateDigits();
negative = is_negative;
}
void addBignum(bignum *a, bignum *b, bignum *c)
{
int carry = 0;
int i = 0;
int maxNumFractions = getMax(a->numFractions, b->numFractions);
int maxNumDecimals = getMax(a->numIntegers, b->numIntegers);
int left, right;
int result;
// Determine if the two numbers are both positive. If not, call the substract function.
if (a->sign != b->sign)
{
// Call substract.
if (a->sign == MINUS)
{
a->sign = PLUS;
subtractBignum(b, a, c);
a->sign = MINUS;
}
else
{
b->sign = PLUS;
subtractBignum(a, b, c);
b->sign = MINUS;
}
return;
}
if (a->sign == MINUS)
{
a->sign = b->sign = PLUS;
addBignum(a, b, c);
a->sign = b->sign = MINUS;
c->sign = MINUS;
return;
}
initializeBignum(c);
c->numFractions = maxNumFractions;
c->numIntegers = maxNumDecimals;
// Adding the fractions.
for (i = maxNumFractions - 1; i >= 0; i--)
{
left = (i <= a->numFractions - 1) ? a->fractions[i] : 0;
right = (i <= b->numFractions - 1) ? b->fractions[i] : 0;
result = left + right + carry;
if (result >= 10)
{
carry = 1;
result -= 10;
}
else
{
carry = 0;
}
c->fractions[i] = result;
}
// Adding the integers.
for (i = 0; i < maxNumDecimals; i++)
{
left = (i < a->numIntegers) ? a->integers[i] : 0;
right = (i < b->numIntegers) ? b->integers[i] : 0;
result = left + right + carry;
if (result >= 10)
{
carry = 1;
result -= 10;
}
else
{
carry = 0;
}
c->integers[i] = result;
}
if (carry != 0)
{
c->integers[c->numIntegers] = 1;
c->numIntegers++;
}
optimizeBignum(c);
}
// Transfer the large number in the string to a big number.
// Return 0 if succeed, 1 if fail.
int stringToBignum(char* string, bignum *num) {
int i;
int j=0;
int k = 0;
int len = 0;
int hasFranction = 0;
char c;
int charInteger = 0;
int decimalsIndex = 0;
int fractionIndex = 0;
int numChars, numIntegers, numFractions;
analizeNumString(string, &numChars, &numIntegers, &numFractions);
decimalsIndex = numIntegers - 1;
initializeBignum(num);
num->numIntegers = 0;
for (i = 0, len = numChars; i <= len; i++) {
c = string[i];
if (isspace(c) || c == '\0')
{
break;
}
else if(isdigit(c))
{
charInteger = c - '0';
if (hasFranction == 0)
{
num->integers[decimalsIndex] = charInteger;
decimalsIndex--;
num->numIntegers++;
}
else if (hasFranction == 1)
{
num->fractions[k] = charInteger;
k++;
num->numFractions++;
}
}
else if(c == '-')
{
num->sign = MINUS;
}
else if(c == '.')
{
hasFranction = 1;
}
else
{
return EXIT_FAILURE;
}
}
optimizeBignum(num);
return EXIT_SUCCESS;
}
bignum getZeroBignum()
{
bignum num;
initializeBignum(&num);
return num;
}
int divide_bignum(bignum *a, bignum *b, bignum *c)
{
int aSign, bSign; /* temporary signs */
int i; /* counters */
int numShiftRequired;
int answerIndex;
bignum aCopy, bCopy, tempNum;
int compareResult;
int count = 0;
int isExiting = 0;
int isIntegersDone = 0;
if (isBignumZero(b))
{
// Divided by zero.
return 0;
}
initializeBignum(c);
if (isBignumZero(a))
{
return 1;
}
c->sign = (a->sign == b->sign) ? PLUS : MINUS;
aSign = a->sign;
bSign = b->sign;
a->sign = b->sign = PLUS;
aCopy = *a;
bCopy = *b;
if (b->numIntegers == 1 && b->integers[0] == 0)
{
for (i = 0; i < MAX_NUM_DIGITS; i++)
{
if (b->fractions[i] != 0)
{
break;
}
}
numShiftRequired = (a->numIntegers - b->numIntegers) + i + 1;
}
else
{
numShiftRequired = (a->numIntegers > b->numIntegers) ? a->numIntegers - b->numIntegers : 0;
}
c->numIntegers = numShiftRequired + 1;
leftShift(&bCopy, numShiftRequired);
answerIndex = numShiftRequired;
// Fill up the integers.
while (answerIndex >= 0)
{
while (1)
{
if (isBignumZero(&aCopy))
{
isExiting = 1;
break;
}
compareResult = compareBignum(&aCopy, &bCopy);
if (compareResult < 0)
{
if (--answerIndex < 0)
{
isIntegersDone = 1;
break;
}
leftShift(&aCopy, 1);
continue;
}
subtractBignum(&aCopy, &bCopy, &tempNum);
aCopy = tempNum;
c->integers[answerIndex]++;
}
if (isIntegersDone || isExiting)
{
break;
}
}
if (!isExiting)
{
answerIndex = 0;
leftShift(&aCopy, 1);
c->numFractions++;
// Fill up the fractions.
while (answerIndex < MAX_NUM_DIGITS - 1)
{
while (1)
{
if (isBignumZero(&aCopy))
{
isExiting = 1;
break;
}
compareResult = compareBignum(&aCopy, &bCopy);
if (compareResult < 0)
{
if (++answerIndex >= MAX_NUM_DIGITS - 1)
{
isExiting = 1;
break;
}
leftShift(&aCopy, 1);
c->numFractions++;
continue;
}
subtractBignum(&aCopy, &bCopy, &tempNum);
aCopy = tempNum;
c->fractions[answerIndex]++;
}
if (isExiting)
{
break;
}
}
}
optimizeBignum(c);
a->sign = aSign;
b->sign = bSign;
return 1;
}
bignum::bignum(float f, int decimal_places)
{
initializeBignum();
vector<int> exponent, mantissa;
bool sign = false;
//based on 32-bit system architecture
static int float_bits = 32, mantissa_delim = 23, exponent_delim = 31, exponent_bias = 127;
union float_converter
{
float f;
unsigned int u;
};
float_converter converter;
converter.f = f;
unsigned int compare = 1;
//iterate through bits of the stored value, push bit value to appropriate container
for (int i = 0; i < float_bits; i++)
{
if (i < mantissa_delim)
mantissa.push_back(converter.u & compare == compare);
else if (i < exponent_delim)
exponent.push_back(converter.u & compare == compare);
else sign = (converter.u & compare == compare);
converter.u = converter.u >> 1;
}
//reversed to compensate for endianess
std::reverse(mantissa.begin(), mantissa.end());
std::reverse(exponent.begin(), exponent.end());
//create the mantissa as a binary bignum
bignum big_mantissa(mantissa, 2, false);
big_mantissa.rightShift(mantissa_delim);
//create the exponent as a binary bignum, adjust based on exponent bias
bignum big_exponent(exponent, 2, false);
bignum big_exponent_bias(exponent_bias);
big_exponent_bias.convertBase(2);
big_exponent -= big_exponent_bias;
//generates multiplier of the floating format based on mantissa and exponent
bignum mantissa_multiplier(10);
mantissa_multiplier.setBase(2);
mantissa_multiplier = jep::exponent(mantissa_multiplier, big_exponent);
mantissa_multiplier.convertBase(2);
//increment, since system architecture does not incorporate the 1 by default
big_mantissa += 1;
bignum temp = big_mantissa * mantissa_multiplier;
if (sign)
temp.setNegative();
temp.convertBase(10);
*this = temp;
roundToIndex(ONES_PLACE - decimal_places);
}
bignum::bignum(double d, int decimal_places)
{
initializeBignum();
vector<int> exponent;
vector<int> mantissa;
bool sign = false;
static int double_bits = 64, mantissa_delim = 52, exponent_delim = 63, exponent_bias = 1023;
union double_converter
{
double d;
unsigned long long int u;
};
double_converter converter;
converter.d = d;
unsigned int compare = 1;
for (int i = 0; i < double_bits; i++)
{
if (i < mantissa_delim)
mantissa.push_back(converter.u & compare == compare);
else if (i < exponent_delim)
exponent.push_back(converter.u & compare == compare);
else sign = (converter.u & compare == compare);
converter.u = converter.u >> 1;
}
std::reverse(mantissa.begin(), mantissa.end());
std::reverse(exponent.begin(), exponent.end());
bignum big_mantissa(mantissa, 2, false);
big_mantissa.rightShift(mantissa_delim);
bignum big_exponent(exponent, 2, false);
bignum big_exponent_bias(exponent_bias);
big_exponent_bias.convertBase(2);
big_exponent -= big_exponent_bias;
//generates multiplier of the floating format
bignum mantissa_multiplier(10);
mantissa_multiplier.setBase(2);
mantissa_multiplier = jep::exponent(mantissa_multiplier, big_exponent);
mantissa_multiplier.convertBase(2);
big_mantissa += 1;
bignum temp = big_mantissa * mantissa_multiplier;
if (sign)
temp.setNegative();
temp.convertBase(10);
*this = temp;
roundToIndex(ONES_PLACE - decimal_places);
}
bignum::bignum(string s, int baseGiven)
{
initializeBignum();
base = baseGiven;
vector <int> numbersToAdd;
int numbersAdded = 0;
int decimalNumbers = 0;
for (int i = 0; i < s.length(); i++)
{
bool decimal = false;
switch (s[i])
{
case ',': break;
case '.':
if (decimal == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, number contains multiple decimal points");
else decimal = true;
break;
case '-':
if (negative == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, number contains multiple negative symbols");
else negative = true;
break;
default:
char zero = '0';
char letter = 'A';
if (s[i] >= zero && s[i] <= zero + 9)
{
int digitToAdd = s[i] - zero;
if (digitToAdd >= base)
throw error_handler(__FILE__, __LINE__, "constructor failed, digit exceeds base desired");
if (decimal == true)
decimalNumbers++;
numbersAdded++;
numbersToAdd.push_back(digitToAdd);
break;
}
else if (s[i] >= letter && s[i] <= letter + 27)
{
int digitToAdd = s[i] - letter + 10;
if (digitToAdd >= base)
throw error_handler(__FILE__, __LINE__, "constructor failed, digit exceeds base desired");
if (decimal == true)
decimalNumbers++;
numbersAdded++;
numbersToAdd.push_back(digitToAdd);
break;
}
else throw error_handler(__FILE__, __LINE__, "constructor failed, invalid character(s) included");
break;
}
}
if (decimalNumbers > ONES_PLACE)
throw error_handler(__FILE__, __LINE__, "constructor failed, number has too many decimal places");
int startingPoint = ONES_PLACE + (numbersAdded - decimalNumbers) - 1;
for (int i = 0; i < numbersToAdd.size(); i++)
{
int digitToAdd = numbersToAdd.at(i);
int locationToSet = startingPoint - i;
digits[locationToSet] = digitToAdd;
}
updateDigits();
}
bignum::bignum(string s)
{
initializeBignum();
vector <int> numbersToAdd;
int numbersAdded = 0;
int decimalNumbers = 0;
bool decimal = false;
int commaNumbers = 0;
bool comma = false;
for (int i = 0; i < s.length(); i++)
{
switch (s[i])
{
case ',':
if (decimal == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, comma included after decimal point");
else if (comma == true && commaNumbers != 3)
throw error_handler(__FILE__, __LINE__, "constructor failed, improper use of commas");
else if (comma == false && numbersAdded > 3)
throw error_handler(__FILE__, __LINE__, "constructor failed, improper use of commas");
else if (numbersAdded == 0)
throw error_handler(__FILE__, __LINE__, "constructor failed, improper use of commas");
comma = true;
commaNumbers = 0;
break;
case '.':
if (decimal == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, number contains multiple decimal points");
else decimal = true;
break;
case '-':
if (decimal == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, negative symbol included after a decimal point");
if (numbersAdded > 0)
throw error_handler(__FILE__, __LINE__, "constructor failed, negative symbol included after a number");
if (comma == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, negative sign included after a comma");
if (negative == true)
throw error_handler(__FILE__, __LINE__, "constructor failed, number contains multiple negative symbols");
else negative = true;
break;
default:
char zero = '0';
if (s[i] >= zero && s[i] <= zero + 9)
{
int digitToAdd = s[i] - zero;
if (digitToAdd >= base)
throw error_handler(__FILE__, __LINE__, "constructor failed, digit exceeds base desired");
if (decimal == true)
decimalNumbers++;
if (comma == true)
commaNumbers++;
numbersAdded++;
numbersToAdd.push_back(digitToAdd);
break;
}
else throw error_handler(__FILE__, __LINE__, "constructor failed, invalid character(s) included");
break;
}
}
if (decimalNumbers > ONES_PLACE)
throw error_handler(__FILE__, __LINE__, "constructor failed, number has too many decimal places");
int startingPoint = ONES_PLACE + (numbersAdded - decimalNumbers) - 1;
for (int i = 0; i < numbersToAdd.size(); i++)
{
int digitToAdd = numbersToAdd.at(i);
int locationToSet = startingPoint - i;
digits[locationToSet] = digitToAdd;
}
updateDigits();
}