cmd/compile: in poset, implement path collapsing

Sometimes, poset needs to collapse a path making all nodes in
the path aliases. For instance, we know that A<=N1<=B and we
learn that B<=A, we can deduce A==N1==B, and thus we can
collapse all paths from A to B into a single aliased node.

Currently, this is a TODO. This CL implements the path-collapsing
primitive by doing a DFS walk to build a bitset of all nodes
across all paths, and then calling the new aliasnodes that allow
to mark multiple nodes as aliases of a single master node.

This helps only 4 times in std+cmd, but it will be fundamental
when we will rely on poset to calculate numerical limits, to
calculate the correct values.

This also fixes #35157, a bug uncovered by a previous CL in this
serie. A testcase will be added soon.

Change-Id: I5fc54259711769d7bd7c2d166a5abc1cddc26350
Reviewed-on: https://go-review.googlesource.com/c/go/+/200861
Run-TryBot: Giovanni Bajo <rasky@develer.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>

src/cmd/compile/internal/ssa/poset.go

@@ -629,27 +629,56 @@ func (po *poset) mergeroot(r1, r2 uint32) uint32 {
 	return r
 }
 
-// collapsepath marks i1 and i2 as equal and collapses as equal all
-// nodes across all paths between i1 and i2. If a strict edge is
+// collapsepath marks n1 and n2 as equal and collapses as equal all
+// nodes across all paths between n1 and n2. If a strict edge is
 // found, the function does not modify the DAG and returns false.
+// Complexity is O(n).
 func (po *poset) collapsepath(n1, n2 *Value) bool {
 	i1, i2 := po.values[n1.ID], po.values[n2.ID]
 	if po.reaches(i1, i2, true) {
 		return false
 	}
 
-	// TODO: for now, only handle the simple case of i2 being child of i1
-	l, r := po.children(i1)
-	if l.Target() == i2 || r.Target() == i2 {
-		i2s := newBitset(int(po.lastidx) + 1)
-		i2s.Set(i2)
-		po.aliasnodes(n1, i2s)
-		po.addchild(i1, i2, false)
-		return true
-	}
+	// Find all the paths from i1 to i2
+	paths := po.findpaths(i1, i2)
+	// Mark all nodes in all the paths as aliases of n1
+	// (excluding n1 itself)
+	paths.Clear(i1)
+	po.aliasnodes(n1, paths)
 	return true
 }
 
+// findpaths is a recursive function that calculates all paths from cur to dst
+// and return them as a bitset (the index of a node is set in the bitset if
+// that node is on at least one path from cur to dst).
+// We do a DFS from cur (stopping going deep any time we reach dst, if ever),
+// and mark as part of the paths any node that has a children which is already
+// part of the path (or is dst itself).
+func (po *poset) findpaths(cur, dst uint32) bitset {
+	seen := newBitset(int(po.lastidx + 1))
+	path := newBitset(int(po.lastidx + 1))
+	path.Set(dst)
+	po.findpaths1(cur, dst, seen, path)
+	return path
+}
+
+func (po *poset) findpaths1(cur, dst uint32, seen bitset, path bitset) {
+	if cur == dst {
+		return
+	}
+	seen.Set(cur)
+	l, r := po.chl(cur), po.chr(cur)
+	if !seen.Test(l) {
+		po.findpaths1(l, dst, seen, path)
+	}
+	if !seen.Test(r) {
+		po.findpaths1(r, dst, seen, path)
+	}
+	if path.Test(l) || path.Test(r) {
+		path.Set(cur)
+	}
+}
+
 // Check whether it is recorded that i1!=i2
 func (po *poset) isnoneq(i1, i2 uint32) bool {
 	if i1 == i2 {

src/cmd/compile/internal/ssa/poset_test.go

@@ -438,7 +438,127 @@ func TestPosetStrict(t *testing.T) {
 	})
 }
 
-func TestSetEqual(t *testing.T) {
+func TestPosetCollapse(t *testing.T) {
+	testPosetOps(t, false, []posetTestOp{
+		{Checkpoint, 0, 0},
+		// Create a complex graph of <= relations among nodes between 10 and 25.
+		{SetOrderOrEqual, 10, 15},
+		{SetOrderOrEqual, 15, 20},
+		{SetOrderOrEqual, 20, vconst(20)},
+		{SetOrderOrEqual, vconst(20), 25},
+		{SetOrderOrEqual, 10, 12},
+		{SetOrderOrEqual, 12, 16},
+		{SetOrderOrEqual, 16, vconst(20)},
+		{SetOrderOrEqual, 10, 17},
+		{SetOrderOrEqual, 17, 25},
+		{SetOrderOrEqual, 15, 18},
+		{SetOrderOrEqual, 18, vconst(20)},
+		{SetOrderOrEqual, 15, 19},
+		{SetOrderOrEqual, 19, 25},
+
+		// These are other paths not part of the main collapsing path
+		{SetOrderOrEqual, 10, 11},
+		{SetOrderOrEqual, 11, 26},
+		{SetOrderOrEqual, 13, 25},
+		{SetOrderOrEqual, 100, 25},
+		{SetOrderOrEqual, 101, 15},
+		{SetOrderOrEqual, 102, 10},
+		{SetOrderOrEqual, 25, 103},
+		{SetOrderOrEqual, 20, 104},
+
+		{Checkpoint, 0, 0},
+		// Collapse everything by setting 10 >= 25: this should make everything equal
+		{SetOrderOrEqual, 25, 10},
+
+		// Check that all nodes are pairwise equal now
+		{Equal, 10, 12},
+		{Equal, 10, 15},
+		{Equal, 10, 16},
+		{Equal, 10, 17},
+		{Equal, 10, 18},
+		{Equal, 10, 19},
+		{Equal, 10, vconst(20)},
+		{Equal, 10, vconst2(20)},
+		{Equal, 10, 25},
+
+		{Equal, 12, 15},
+		{Equal, 12, 16},
+		{Equal, 12, 17},
+		{Equal, 12, 18},
+		{Equal, 12, 19},
+		{Equal, 12, vconst(20)},
+		{Equal, 12, vconst2(20)},
+		{Equal, 12, 25},
+
+		{Equal, 15, 16},
+		{Equal, 15, 17},
+		{Equal, 15, 18},
+		{Equal, 15, 19},
+		{Equal, 15, vconst(20)},
+		{Equal, 15, vconst2(20)},
+		{Equal, 15, 25},
+
+		{Equal, 16, 17},
+		{Equal, 16, 18},
+		{Equal, 16, 19},
+		{Equal, 16, vconst(20)},
+		{Equal, 16, vconst2(20)},
+		{Equal, 16, 25},
+
+		{Equal, 17, 18},
+		{Equal, 17, 19},
+		{Equal, 17, vconst(20)},
+		{Equal, 17, vconst2(20)},
+		{Equal, 17, 25},
+
+		{Equal, 18, 19},
+		{Equal, 18, vconst(20)},
+		{Equal, 18, vconst2(20)},
+		{Equal, 18, 25},
+
+		{Equal, 19, vconst(20)},
+		{Equal, 19, vconst2(20)},
+		{Equal, 19, 25},
+
+		{Equal, vconst(20), vconst2(20)},
+		{Equal, vconst(20), 25},
+
+		{Equal, vconst2(20), 25},
+
+		// ... but not 11/26/100/101/102, which were on a different path
+		{Equal_Fail, 10, 11},
+		{Equal_Fail, 10, 26},
+		{Equal_Fail, 10, 100},
+		{Equal_Fail, 10, 101},
+		{Equal_Fail, 10, 102},
+		{OrderedOrEqual, 10, 26},
+		{OrderedOrEqual, 25, 26},
+		{OrderedOrEqual, 13, 25},
+		{OrderedOrEqual, 13, 10},
+
+		{Undo, 0, 0},
+		{OrderedOrEqual, 10, 25},
+		{Equal_Fail, 10, 12},
+		{Equal_Fail, 10, 15},
+		{Equal_Fail, 10, 25},
+
+		{Undo, 0, 0},
+	})
+
+	testPosetOps(t, false, []posetTestOp{
+		{Checkpoint, 0, 0},
+		{SetOrderOrEqual, 10, 15},
+		{SetOrderOrEqual, 15, 20},
+		{SetOrderOrEqual, 20, 25},
+		{SetOrder, 10, 16},
+		{SetOrderOrEqual, 16, 20},
+		// Check that we cannot collapse here because of the strict relation 10<16
+		{SetOrderOrEqual_Fail, 20, 10},
+		{Undo, 0, 0},
+	})
+}
+
+func TestPosetSetEqual(t *testing.T) {
 	testPosetOps(t, false, []posetTestOp{
 		// 10<=20<=30<40,  20<=100<110
 		{Checkpoint, 0, 0},