template <class Element, class Iterator> Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group, Iterator begin, Iterator end)
{
if (end-begin == 1)
return group.ScalarMultiply(begin->base, begin->exponent);
else if (end-begin == 2)
return group.CascadeScalarMultiply(begin->base, begin->exponent, (begin+1)->base, (begin+1)->exponent);
else
{
Integer q, t;
Iterator last = end;
--last;
std::make_heap(begin, end);
std::pop_heap(begin, end);
while (!!begin->exponent)
{
// last->exponent is largest exponent, begin->exponent is next largest
t = last->exponent;
Integer::Divide(last->exponent, q, t, begin->exponent);
if (q == Integer::One())
group.Accumulate(begin->base, last->base); // avoid overhead of ScalarMultiply()
else
group.Accumulate(begin->base, group.ScalarMultiply(last->base, q));
std::push_heap(begin, end);
std::pop_heap(begin, end);
}
return group.ScalarMultiply(last->base, last->exponent);
}
}
