void BigNumber::subtract(const BigNumber& minuend, const BigNumber& subtrahend, BigNumber& result) {
//Corner case: subtrahend is zero.
if(subtrahend.is_zero()) {
result = minuend;
return;
}
//Equality check is required to subtract smaller number from larger.
equality_check compare_result = minuend.compare_to(subtrahend);
//Corner case: equal numbers.
if(compare_result == EQUAL) {
result = BigNumber();
return;
}
//Set result sign.
if(compare_result == SECOND_BIGGER) {
result.is_negative = true;
}
//Remember relation between subtracted numbers.
const BigNumber& greater_number = (result.is_negative == false) ? minuend : subtrahend;
const BigNumber& smaller_number = (&greater_number == &minuend) ? subtrahend : minuend;
//Set iterators to lowest bytes.
BigNumberIterator greater_it = greater_number.get_lowest_byte();
BigNumberIterator smaller_it = smaller_number.get_lowest_byte();
//Latest subtraction value.
ex_element_type operation_result = 0;
//Offset in last block where result may be stored.
int32_t offset = 0, max_offset = -1;
//Current block pointer - to avoid calls to list every time.
Block* block = NULL;
//Borrow flag - indicates if current computation is using "borrowed" values.
bool borrow = false;
uint64_t zero_elements = 0;
//Subtract smaller number from equal subset of higher number.
for(;smaller_it != ++smaller_number.get_highest_byte(); ++smaller_it, ++greater_it, operation_result = 0) { // TODO: AG: Should not count ++smaller_number.get_highest_byte() every time
//Copy current byte from greater number to result buffer.
operation_result = *greater_it;
if(borrow) {
if(*greater_it > 0) {
//Decrement value if this is the digit from which the borrow is taken (first non-zero digit before the loan taker).
--operation_result;
borrow = false;
} else {
//This digit is also beneficient of loan, enjoy it.
operation_result += ELEMENT_MAX;
}
}
//Enter "borrow mode" and take extra value.
if(operation_result < *smaller_it) {
borrow = true;
operation_result += ELEMENT_MAX + 1;
}
//Actual subtraction takes place here.
operation_result -= *smaller_it;
//Zero-results are counted, but not immedietaly appended to number.
//This is to avoid redundant blocks with arrays filled with zeros at the end of chain.
if(operation_result == 0) {
++zero_elements;
continue;
}
//If the result is non-zero, insert all preceeding zeros to number.
for(;zero_elements > 0; --zero_elements, ++offset) {
if(offset > max_offset) {
block = &result.push_back_new_block();
offset = 0;
max_offset = block->get_size() - 1;
}
block->get_bits_array()[offset] = 0;
}
if(offset > max_offset) {
block = &result.push_back_new_block();
offset = 0;
max_offset = block->get_size() - 1;
}
//Insert non-zero result into the chain.
block->get_bits_array()[offset++] = (element_type)operation_result;
block->trailing_zeros = block->get_size() - offset;
}
//Rewrite the rest of larger number into result.
for(;greater_it != ++greater_number.get_highest_byte(); ++greater_it) { // TODO: AG: Should not count ++greater_number.get_highest_byte() every time
//Copy current byte from greater number to result buffer.
operation_result = *greater_it;
if(borrow) {
if(*greater_it > 0) {
//Decrement value if this is the digit from which the borrow is taken (first non-zero digit before the loan taker).
--operation_result;
borrow = false;
} else {
//This digit is also beneficient of loan, enjoy it.
operation_result += ELEMENT_MAX;
}
}
//Zero-results are counted, but not immedietaly appended to number.
//This is to avoid redundant blocks with arrays filled with zeros at the end of chain.
if(operation_result == 0) {
++zero_elements;
continue;
}
//If the result is non-zero, insert all preceeding zeros to number.
for(;zero_elements > 0; --zero_elements, ++offset) {
if(offset > max_offset) {
block = &result.push_back_new_block();
offset = 0;
max_offset = block->get_size() - 1;
}
block->get_bits_array()[offset] = 0;
}
if(offset > max_offset) {
block = &result.push_back_new_block();
offset = 0;
max_offset = block->get_size() - 1;
}
//Insert non-zero result into the chain.
block->get_bits_array()[offset++] = (element_type)operation_result;
block->trailing_zeros = block->get_size() - offset;
}
}
