Also, correct the handling of scalars in dot and wedge products: it
turns out s.v and s^v both scale. However, it seems the CSE code loses
things sometimes.
I guess Hamish's suggestion made sense at the time, but I found that
with the current instructions, the reversed bivector wasn't so nice to
implement it would need a swizzle as well as the cross-product.
This makes working with them much easier, and the type system reflects
what's in the multi-vector. Unfortunately, that does mean that large
algebras will wind up having a LOT of types, but it allows for efficient
storage of sparse multi-vectors:
auto v = 4*(e1 + e032 + e123);
results in:
0005 0213 1:0008<00000008>4:void 0:0000<00000000>?:invalid
0:0044<00000044>4:void assign (<void>), v
0006 0213 1:000c<0000000c>4:void 0:0000<00000000>?:invalid
0:0048<00000048>4:void assign (<void>), {v + 4}
Where the two source vectors are:
44:1 0 .imm float:18e [4, 0, 0, 0]
48:1 0 .imm float:1aa [4, 0, 0, 4]
They just happen to be adjacent, but don't need to be.
This gets only some very basics working:
* Algebra (multi-vector) types: eg @algebra(float(3,0,1)).
* Algebra scopes (using either the above or @algebra(TYPE_NAME) where
the above was used in a typedef.
* Basis blades (eg, e12) done via procedural symbols that evaluate to
suitable constants based on the basis group for the blade.
* Addition and subtraction of multi-vectors (only partially tested).
* Assignment of sub-algebra multi-vectors to full-algebra multi-vectors
(missing elements zeroed).
There's still much work to be done, but I thought it time to get
something into git.
