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# SixtyPical Fallthru

This is a test suite, written in Falderal format, for SixtyPical's ability to detect which routines make tail calls to other routines, and thus can be re-arranged to simply "fall through" to them.

The theory is as follows.

SixtyPical supports a goto, but it can only appear in tail position. If a routine r1 ends with a unique goto to a fixed routine r2 it is said to potentially fall through to r2.

A unique goto means that there are not multiple different gotos in tail position (which can happen if, for example, an if is the last thing in a routine, and each branch of that if ends with a different goto.)

A fixed routine means, a routine which is known at compile time, not a goto through a vector.

Consider the set R of all available routines in the program.

Every routine either potentially falls through to a single other routine or it does not potentially fall through to any routine.

More formally, we can say

fall : R → R ∪ {nil}, fall(r) ≠ r

where nil is an atom that represents no routine.

Now consider an operation chain() vaguely similar to a transitive closure on fall(). Starting with r, we construct a list of r, fall(r), fall(fall(r)), ... with the following restrictions:

• we stop when we reach nil (because fall(nil) is not defined)
• we stop when we see an element that is not in R.
• we stop when we see an element that we have already added to the list (this is to prevent infinite lists due to cycles.)

With these definitions, our algorithm is something like this.

Treat R as a mutable set and start with an empty list of lists L. Then,

• For all r ∈ R, find all chain(r).
• Pick a longest such chain. Call it C.
• Append C to L.
• Remove all elements occurring in C, from R.
• Repeat until R is empty.

When time comes to generate code, generate it in the order given by L. In addition, each sublist in L represents a number of routines to generate; all except the final routine in such a sublist need not have any jump instruction generated for its final goto.

The tests in this document test against the list L.

Note that this optimization is a feature of the SixtyPical's reference compiler, not the language. So an implementation is not required to pass these tests to be considered an implementation of SixtyPical.

-> Tests for functionality "Dump fallthru info for SixtyPical program"

A single routine, obviously, falls through to nothing and has nothing fall through to it.

| define main routine
| {
| }
= [
=     [
=         "main"
=     ]
= ]

If main does a goto foo, then it can fall through to foo.

| define foo routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define main routine trashes a, z, n
| {
|     goto foo
| }
= [
=     [
=         "main",
=         "foo"
=     ]
= ]

More than one routine can fall through to a routine. We pick one of them to fall through, when selecting the order of routines.

| define foo routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 0
|     goto foo
| }
|
| define main routine trashes a, z, n
| {
|     goto foo
| }
= [
=     [
=         "main",
=         "foo"
=     ],
=     [
=         "bar"
=     ]
= ]

Because main is always serialized first (so that the entry point of the entire program appears at the beginning of the code), nothing ever falls through to main.

| define foo routine trashes a, z, n
| {
|     ld a, 0
|     goto main
| }
|
| define main routine trashes a, z, n
| {
|     ld a, 1
| }
= [
=     [
=         "main"
=     ],
=     [
=         "foo"
=     ]
= ]

There is nothing stopping two routines from tail-calling each other, but we will only be able to make one of them, at most, fall through to the other.

| define foo routine trashes a, z, n
| {
|     ld a, 0
|     goto bar
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 0
|     goto foo
| }
|
| define main routine trashes a, z, n
| {
| }
= [
=     [
=         "main"
=     ],
=     [
=         "foo",
=         "bar"
=     ]
= ]

If a routine does two tail calls (which is possible because they can be in different branches of an if) it cannot fall through to another routine.

| define foo routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define main routine inputs z trashes a, z, n
| {
|     if z {
|         goto foo
|     } else {
|         goto bar
|     }
| }
= [
=     [
=         "main"
=     ],
=     [
=         "foo"
=     ],
=     [
=         "bar"
=     ]
= ]

If, however, they are the same goto, one can be optimized away.

| define foo routine trashes a, z, n
| {
|     ld a, 0
|     if z {
|         ld a, 1
|         goto bar
|     } else {
|         ld a, 2
|         goto bar
|     }
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 255
| }
|
| define main routine trashes a, z, n
| {
| }
= [
=     [
=         "main"
=     ],
=     [
=         "foo",
=         "bar"
=     ]
= ]

Similarly, a tail call to a vector can't be turned into a fallthru, because we don't necessarily know what actual routine the vector contains.

| vector routine trashes a, z, n
|   vec
|
| define foo routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define main routine outputs vec trashes a, z, n
| {
|     copy bar, vec
|     goto vec
| }
= [
=     [
=         "main"
=     ],
=     [
=         "foo"
=     ],
=     [
=         "bar"
=     ]
= ]

Our algorithm might not be strictly optimal, but it does a good job.

| define r1 routine trashes a, z, n
| {
|     ld a, 0
|     goto r2
| }
|
| define r2 routine trashes a, z, n
| {
|     ld a, 0
|     goto r3
| }
|
| define r3 routine trashes a, z, n
| {
|     ld a, 0
|     goto r4
| }
|
| define r4 routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define r5 routine trashes a, z, n
| {
|     ld a, 0
|     goto r6
| }
|
| define r6 routine trashes a, z, n
| {
|     ld a, 0
|     goto r3
| }
|
| define main routine trashes a, z, n
| {
|     goto r1
| }
= [
=     [
=         "main",
=         "r1",
=         "r2",
=         "r3",
=         "r4"
=     ],
=     [
=         "r5",
=         "r6"
=     ]
= ]

-> Tests for functionality "Compile SixtyPical program with fallthru optimization"

Basic test for actually applying this optimization when compiling SixtyPical programs.

| define foo routine trashes a, z, n
| {
|     ld a, 0
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 255
|     goto foo
| }
|
| define main routine trashes a, z, n
| {
|     goto foo
| }
= \$080D   LDA #\$00
= \$080F   RTS
= \$0810   LDA #\$FF
= \$0812   JMP \$080D

It can optimize out one of the gotos if they are the same.

| define foo routine trashes a, z, n
| {
|     ld a, 0
|     if z {
|         ld a, 1
|         goto bar
|     } else {
|         ld a, 2
|         goto bar
|     }
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 255
| }
|
| define main routine trashes a, z, n
| {
| }
= \$080D   RTS
= \$080E   LDA #\$00
= \$0810   BNE \$0817
= \$0812   LDA #\$01
= \$0814   JMP \$0819
= \$0817   LDA #\$02
= \$0819   LDA #\$FF
= \$081B   RTS

It cannot optimize out the gotos if they are different.

| define foo routine trashes a, z, n
| {
|     ld a, 0
|     if z {
|         ld a, 1
|         goto bar
|     } else {
|         ld a, 2
|         goto main
|     }
| }
|
| define bar routine trashes a, z, n
| {
|     ld a, 255
| }
|
| define main routine trashes a, z, n
| {
| }
= \$080D   RTS
= \$080E   LDA #\$00
= \$0810   BNE \$0817
= \$0812   LDA #\$01
= \$0814   JMP \$081C
= \$0817   LDA #\$02
= \$0819   JMP \$080D
= \$081C   LDA #\$FF
= \$081E   RTS