Replace shifts with enforced byte dropping in special cases about fixedpointsarduino HOT 1 OPEN

I started investigating this today to see if I could work out a way to make it viable.

Out of the techniques I've tried so far, the only one that both produced the correct result and resulted in a saving was:

template< unsigned Integer >
SFixed<Integer, 8> operator *(const SFixed<Integer, 8> & left, const SFixed<Integer, 8> & right)
{
	static_assert(((Integer + 1) * 2 + 8 * 2) <= FIXED_POINTS_DETAILS::BitSize<intmax_t>::Value, "Multiplication cannot be performed, the intermediary type would be too large");	
	
	using InternalType = typename SFixed<Integer, 8>::InternalType;
	using PrecisionType = typename SFixed<Integer * 2, 8 * 2>::InternalType;

	const auto intermediary = (static_cast<PrecisionType>(left.getInternal()) * static_cast<PrecisionType>(right.getInternal()));

	char buffer[sizeof(PrecisionType)];
	
	for(size_t index = 0; index < sizeof(PrecisionType); ++index)
		buffer[index] = reinterpret_cast<const char *>(&intermediary)[index];

	const InternalType result = *reinterpret_cast<const InternalType *>(&buffer[1]);

	return SFixed<Integer, 8>::fromInternal(result);
}

But this only appeared to result in an 8 byte saving in progmem, and I'm not 100% sure if it's 'legal'.

I may look into creating an AVR assembly implementation, and if that creates a significant enough saving then I'll consider adding it in, but most likely only when enabled using conditional compilation via an opt-in macro.

Regardless of which result I come up with, I won't be making this a general feature, it will be specifically for AVR because:

• Creating a version that works with big endian CPUs will be double the work
• Testing it on other CPUs (most of which I don't own) would be another hurdle

And I'd make it an opt-in feature because any solution is probably going to require the constexpr to be dropped because Arduino only targets C++11 and it's unlikely that the operations required to pull this off without creeping into the land of undefined behaviour will be usable under C++11's constexpr restrictions (which outlaw both variables and loops).

from fixedpointsarduino.