It was a bit of a surprise seeing a test case fail and then succeed
after making a minor edit to help find the bug, but valgrind to the
rescue. I'm surprised nothing showed up earlier.
While it currently doesn't have any effect on generated code, it proved
to be necessary when experimenting with optimizing the operand of extend
expressions (which proved to produce worse code).
Along with some 0 -> nullptr changes.
This gets the types such that either there is only one definition, or C
sees the same name for what is essentially the same type despite there
being multiple local definitions.
Offset casts are used heavily in geometric algebra, but doing an offset
cast on a dereferenced pointer (array index) doesn't work well for
assignments. Fixes yet another bug in my test scene :)
There were a few places where some const-casts were needed, but they're
localized to code that's supposed to manipulate types (but I do want to
come up with something to clean that up).
When sum_expr gets a null expression as one of its args, it simply
returns the other arg, but that arg needs to have the correct type
applied.
Handle zero (null result) cross product in bivector geometric product.
Clean up types in bivector * vector geometric product.
I'm not sure the regressive product is right (overall sign), but that's
actually partly a problem in the math itself (duals and the regressive
product still get poked at, so it may be just a matter of
interpretation).
I'm not sure anything other than == or != has much meaning on anything
but scalars and pseudo scalars, but all comparisons are supported as a
simple boolean test. Any missing components are assumed to be 0. If
nothing else, it makes unit tests easier to write.
It turns out the algebra types make expression dag creation much more
difficult resulting in missed optimizations (eg, recognizing `a × a`).
This fixes the dead cross products in `⋆(s.B × ⋆s.B)`
I had wanted to do this earlier but shied away from the large edit. Now
it became more necessary (and will become even more necessary when I get
to the glsl front-end).
This allows them to be matched with cancelling factors. My fancy zero
test is now just that: a fancy zero:
typedef @algebra(float(3,0,1)) PGA;
typedef PGA.group_mask(0xa) bivector_t;
typedef PGA.group_mask(0x1e) motor_t;
typedef PGA.tvec point_t;
typedef PGA.vec plane_t;
plane_t
apply_motor (motor_t m, point_t p)
{
return (m * p * ~m).vec;
}
0000 nop there were plums...
0001 adjstk 0, 0
apply_motor:
motor.r:32:{
0002 with 2, 0, 1
motor.r:33: return (m * p * ~m).vec;
0003 return (<void>)
The motor-point.r test fails because it uses (m * p * ~m).tvec to get
the value but the type system is slightly broken in that a mono-group
algebra type does not have a structure associated with it and thus the
"missing" field results in 0. Yes, I spent too long chasing that one,
too.
I'd missed this in the previous commit, which was a good thing, really,
as it turns out this was the trigger of the bug that causes my fancy
zero test to become non-zero. It seems the bug is in either
component_sum or in the extend merging.
Or really, the implementers. This gets my fancy zero test down to just
unrecognized permutations of commutative multiplies and dot products
(with the multiplies above the dot products).
While this does "explode" the instruction count (I'll have to collect
like terms later), it does allow for many more opportunities for things
to cancel out to 0 (once (pseudo)commutativity is taken care of).
That is, dot(scale(A,a),scale(B,b)) -> (a*b)*dot(A,B). Does the right
thing when only one side is a scale. No change to the instruction count
in my fancy zero, but it does open more opportunities when I distribute
products.
That is, scale(scale(A,b),c) becomes scale(A,b*c), thus giving the
expression dag more opportunities to find common sub-expressions. My
fancy zero test is down to 20 total instructions (including overhead, or
16 for the actual algebra).
While splitting up the scaled vector into scaled xyz and scaled w does
cost an extra instruction, it allows for other optimizations to be
applied. For one, extends get all the way to the top now, and there are
at most two (in my test cases), thus either break-even or even a slight
reduction in instruction count. However, in the initial implementation,
I forgot to do the actual scaling, and 12 instructions were removed from
my fancy zero case, but real tests failed :P It looks like it's just
distributivity and commutativity holding things back (eg,
omega*gamma*sigma - gamma*omega*sigma: should be 0, but not recognized
as that).
This fixes the motor test :) It turns out that every lead I had
previously was due to the disabling of that feature "breaking" dags
(such that expressions wouldn't be found) and it was the dagged
multi-vector components getting linked by expr->next that made a mess of
things.
Or at least mostly so (there are a few casts). This doesn't fix the
motor bug, but I've wanted to do this for over twenty years and at least
I know what's not causing the bug. However, disabling fold_constants in
expr_algebra.c does "fix" things, so it's still a good place to look.
This doesn't fix the motor bug, but it doesn't make it worse. However,
it does simplify the trees quite a bit, so it should be easier to debug.
It seems the problem has something to do with fold_constants messing up
dagged aliases: in particular, const-folding multiplication by e0123 in
3d PGA as fold_constants sees it as 1.
They should be treated as such only when merging vector components. This
fixes a bug that doesn't actually exist (it's in experimental code),
where the sum of two 3-component vectors was getting lost.
For cross products: remove any a from a×(...+/-a...)
For dot products: remove any a×b from a•(...+/-a×b...) (or b×a)
This removed another 2 instructions :)
They don't have much effect that I've noticed, but the expression dags
code does check for commutative expressions. The algebra code uses the
anticommutative flag for cross, wedge and subtract (unconditional at
this stage). Integer ops that are commutative are always commutative (or
anticommutative). Floating point ops can be controlled (default to non),
but no way to set the options currently.
This takes advantage of the expression dag to detect when an expression
is on both sides of a cross product (which always results in 0). This
removes 3 instructions from my motor test (28 to go).
Finally, that little e. is cleaned up. convert_name was a bit of a pain
(in that it relied on modifying the expression rather than returning a
new one, or more that such behavior was relied on).
Sum expressions pull the negation through extend expressions allowing
them to switch to subtraction when appropriate, and offset_cast reaches
past negation to check for extend expressions. This has eliminated all
negation-only instructions from the motor-point, shaving off more
instructions (now 27 not including the return).
I don't know why I didn't think to do it this way before, but simply
recursing into each operand for + or - expressions makes it much easier
to generate correct code. Fixes the motor-point test.
This removes all the special cases and thus it should be more robust. It
did show up some out-by-one (or a factor of two!) errors elsewhere in
the group mask calculations.
