git @ Cat's Eye Technologies SixtyPical / 2be4406
Flesh out and describe the fallthru optimization algorithm. Chris Pressey 3 years ago
2 changed file(s) with 44 addition(s) and 10 deletion(s). Raw diff Collapse all Expand all
7777 Not because it saves 3 bytes, but because it's a neat trick. Doing it optimally
7878 is probably NP-complete. But doing it adequately is probably not that hard.
80 > Every routine is falled through to by zero or more routines.
81 > Don't consider the main routine.
82 > For each routine α that is finally-falled through to by a set of routines R(α),
83 > pick a movable routine β from R, move β in front of α, remove the `jmp` at the end of β and
84 > mark β as unmovable.
85 > Note this only works if β finally-falls through. If there are multiple tail
86 > positions, we can't eliminate all the `jmp`s.
87 > Note that if β finally-falls through to α it can't finally-fall through to anything
88 > else, so the sets R(α) should be disjoint for every α. (Right?)
9080 ### And at some point...
9282 * `low` and `high` address operators - to turn `word` type into `byte`.
33 This is a test suite, written in [Falderal][] format, for SixtyPical's
44 ability to detect which routines make tail calls to other routines,
55 and thus can be re-arranged to simply "fall through" to them.
7 The theory is as follows.
9 SixtyPical supports a `goto`, but it can only appear in tail position.
10 If a routine r1 ends with a unique `goto` to a fixed routine r2 it is said
11 to *potentially fall through* to r2.
13 A *unique* `goto` means that there are not multiple different `goto`s in
14 tail position (which can happen if, for example, an `if` is the last thing
15 in a routine, and each branch of that `if` ends with a different `goto`.)
17 A *fixed* routine means, a routine which is known at compile time, not a
18 `goto` through a vector.
20 Consider the set R of all routines in the program.
22 Every routine r1 ∈ R either potentially falls through to a single routine
23 r2 ∈ R (r2 ≠ r1) or it does not potentially fall through to any routine.
24 We can say out(r1) = {r2} or out(r1) = ∅.
26 Every routine r ∈ R in this set also has a set of zero or more
27 routines from which it is potentially falled through to by. Call this
28 in(r). It is the case that out(r1) = {r2} → r1 ∈ in(r2).
30 We can trace out the connections by following the in- or our- sets of
31 a given routine. Because each routine potentially falls through to only
32 a single routine, the structures we find will be tree-like, not DAG-like.
34 But they do permit cycles.
36 So, we first break those cycles. We will be left with out() sets which
37 are disjoint trees, i.e. if r1 ∈ in(r2), then r1 ∉ in(r3) for all r3 ≠ r2.
39 We then follow an algorithm something like this. Treat R as a mutable
40 set and start with an empty list L. Then,
42 - Pick a routine r from R where out(r) = ∅.
43 - Find the longest chain of routines r1,r2,...rn in R where out(r1) = {r2},
44 out(r2} = {r3}, ... out(rn-1) = {rn}, and rn = r.
45 - Remove (r1,r2,...,rn) from R and append them to L in that order.
46 Mark (r1,r2,...rn-1) as "will have their final `goto` removed."
47 - Repeat until R is empty.
49 When times comes to generate code, generate it in the order given by L.
751 [Falderal]: