Failing to promote ints to the algebra type results in a segfault in
assignment of a multi-vector due to the symbol pointer walking off the
end of the list of symbols.
And convert addition to subtraction when extend expressions are not
involved. This has taken my little test down to 56 instructions total
(21 for `l p ~l`), down from 74 (39).
This takes care of chained sums of extend expressions. Now `l p ~l` has
only four extend instructions which is expected for the code not
detecting the cross product that always produces 0.
This goes a ways towards minimizing extend expressions, even finding
zeros and thus eliminating whole branches of expressions, but shows the
need for better handling of chained sums of extends.
Any geometric algebra product of two negatives cancels out the negative,
and if the result is negative (because only one operand was negative),
the negation is migrated to above the operation. This resulted in
removing 2 instructions from one if my mini-tests (went from 74 to 78
with the addition/subtraction change, but this takes it back to 76
instructions).
Summed extend expressions are used for merging a sub-vector with a
scalar. Putting the vector first in the sum will simplify checks later
on (it really doesn't matter which is first so long as it's consistent).
Subtraction is implemented as adding a negative (with the plan of
optimizing it later). The idea is to give tree inspection and
manipulation a more consistent view without having to worry about
addition vs subtraction.
Negation is moved as high as possible in the expression, but is always
below an extend expression. The plane here is that the manipulation code
can bypass an alias-add-extend combo and see the negation.
This doesn't affect the generated code (aliases are free), but does
simplify the dag significantly, thus optimizing the compiler somewhat,
but also makes reading dags much easier and therefore optimizing the
debugging process.
Because the aliases were treated as live, every alias of a temp resulted
in an assignment, which proved to be quite significant (4-5 assignments
in some simple GA expressions). By using an alias node in the dag, the
unaliased temp can be marked live while the alias is treated as an
operation rather than an operand. Now my GA expressions have no
superfluous assignments (generally no assignments at all).
VM side of the work needed for #58. Tests are still only 4-component,
but the geometric algebra tests seem to have 2-component covered at
least a little bit.
While it could be emulated using a 3d cross-product, it was a hack and
required the use of a swizzle (or alias) to extract the scalar value.
This will make 2d PGA a little nicer when I get to modifying qfcc for it
Simple k-vectors don't use structs for their layout since they're just
an array of scalars, but having the structs for group sets or full
multi-vectors makes the system alignment agnostic.
And geometric algebra vectors. This does break things a little in GA,
but it does bring qfcc's C closer to standard C in that sizeof respects
the alignment of the type (very important for arrays).
It's implemented as the Hodge dual, which is probably reasonable until
people complain. Both ⋆ and ! are supported, though the former is a
little hard to see in Consola.
That was surprisingly harder than expected due to recursion and a
not-so-good implementation in expr_negate (it went too high-level thus
resulting in multivec expressions getting to the code generator).
But only for scalar divisors. The simple method of AB†/(BB†) works only
if B is a versor and there's also the problem of left and right
division. Thanks to sudgy for making me stop and think before I actually
implemented anything (though he mentioned only that it doesn't work for
general mutli-vector divisors).
That was tedious. I can't say I'm looking forward to writing the tests
for 3d. And even though trivector . bivector and bivector . trivector
give the same answer, they're not really commutative when it comes to
the code.
Meaning vec3 is aligned to 4 components instead of 1. 2-component ops
use vec2 in the VM thus requiring alignment to boundaries of 2, but 4
seems better as it conforms with OpenGL and Vulkan (and, I imagine,
DirectX, but I doubt QF will ever use DirectX).
