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abacus: bignum: add division & modulo

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Like the C language, the `%` operator is rather the remainder, such that
`(a/b)*b + (a%b) = a`.

I still call it modulo though...
This commit is contained in:
Bruno BELANYI 2021-08-21 01:51:33 +02:00
parent 7cd0664e60
commit 4e3d53ecd4
3 changed files with 151 additions and 0 deletions
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63
src/bignum/bignum.cc
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@ -92,6 +92,37 @@ digits_type do_multiplication(digits_type const& lhs, digits_type const& rhs) {
return res;
}
std::pair<digits_type, digits_type> do_div_mod(digits_type const& lhs,
digits_type const& rhs) {
if (rhs.size() == 0) {
throw std::invalid_argument("attempt to divide by zero");
}
digits_type quotient;
digits_type remainder = lhs;
while (!do_less_than(remainder, rhs)) {
digits_type multiple = rhs;
digits_type rank;
rank.push_back(1);
digits_type prev_multiple = multiple;
digits_type prev_rank = rank;
while (!do_less_than(remainder, multiple)) {
prev_multiple = multiple;
prev_rank = rank;
multiple = do_addition(multiple, multiple);
rank = do_addition(rank, rank);
}
quotient = do_addition(quotient, prev_rank);
remainder = do_substraction(remainder, prev_multiple);
}
return std::make_pair(quotient, remainder);
}
} // namespace
BigNum::BigNum(std::int64_t number) {
@ -226,6 +257,14 @@ void BigNum::multiply(BigNum const& rhs) {
canonicalize();
}
void BigNum::divide(BigNum const& rhs) {
std::tie(*this, std::ignore) = div_mod(*this, rhs);
}
void BigNum::modulo(BigNum const& rhs) {
std::tie(std::ignore, *this) = div_mod(*this, rhs);
}
bool BigNum::equal(BigNum const& rhs) const {
assert(is_canonicalized());
assert(rhs.is_canonicalized());
@ -295,4 +334,28 @@ bool BigNum::is_negative() const {
return sign_ <= 0;
}
std::pair<BigNum, BigNum> div_mod(BigNum const& lhs, BigNum const& rhs) {
assert(lhs.is_canonicalized());
assert(rhs.is_canonicalized());
if (lhs.is_zero()) {
return std::make_pair(BigNum(), BigNum());
}
BigNum quotient;
BigNum remainder;
std::tie(quotient.digits_, remainder.digits_)
= do_div_mod(lhs.digits_, rhs.digits_);
// Respect the identity `(a/b)*b + (a%b) = a`
quotient.sign_ = lhs.sign_ * rhs.sign_;
remainder.sign_ = lhs.sign_;
quotient.canonicalize();
remainder.canonicalize();
return std::make_pair(quotient, remainder);
}
} // namespace abacus::bignum