[dev.ssa] cmd/compile/internal/ssa: remove proven redundant controls.

* It does very simple bounds checking elimination. E.g.
removes the second check in for i := range a { a[i]++; a[i++]; }
* Improves on the following redundant expression:
return a6 || (a6 || (a6 || a4)) || (a6 || (a4 || a6 || (false || a6)))
* Linear in the number of block edges.

I patched in CL 12960 that does bounds, nil and constant propagation
to make sure this CL is not just redundant. Size of pkg/tool/linux_amd64/*
(excluding compile which is affected by this change):

With IsInBounds and IsSliceInBounds
-this -12960 92285080
+this -12960 91947416
-this +12960 91978976
+this +12960 91923088

Gain is ~110% of 12960.

Without IsInBounds and IsSliceInBounds (older run)
-this -12960 95515512
+this -12960 95492536
-this +12960 95216920
+this +12960 95204440

Shaves 22k on its own.

* Can we handle IsInBounds better with this? In
for i := range a { a[i]++; } the bounds checking at a[i]
is not eliminated.

Change-Id: I98957427399145fb33693173fd4d5a8d71c7cc20
Reviewed-on: https://go-review.googlesource.com/19710
Reviewed-by: David Chase <drchase@google.com>
Reviewed-by: Keith Randall <khr@golang.org>
Run-TryBot: Alexandru Moșoi <alexandru@mosoi.ro>
TryBot-Result: Gobot Gobot <gobot@golang.org>

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

@@ -165,6 +165,7 @@ var passes = [...]pass{
 	{name: "opt deadcode", fn: deadcode},             // remove any blocks orphaned during opt
 	{name: "generic cse", fn: cse},
 	{name: "nilcheckelim", fn: nilcheckelim},
+	{name: "prove", fn: prove},
 	{name: "generic deadcode", fn: deadcode},
 	{name: "fuse", fn: fuse},
 	{name: "dse", fn: dse},
@@ -193,6 +194,10 @@ type constraint struct {
 }
 
 var passOrder = [...]constraint{
+	// prove reliese on common-subexpression elimination for maximum benefits.
+	{"generic cse", "prove"},
+	// deadcode after prove to eliminate all new dead blocks.
+	{"prove", "generic deadcode"},
 	// common-subexpression before dead-store elim, so that we recognize
 	// when two address expressions are the same.
 	{"generic cse", "dse"},

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

@@ -0,0 +1,359 @@
+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package ssa
+
+// rangeMask represents the possible relations between a pair of variables.
+type rangeMask uint
+
+const (
+	lt rangeMask = 1 << iota
+	eq
+	gt
+)
+
+// typeMask represents the universe of a variable pair in which
+// a set of relations is known.
+// For example, information learned for unsigned pairs cannot
+// be transfered to signed pairs because the same bit representation
+// can mean something else.
+type typeMask uint
+
+const (
+	signed typeMask = 1 << iota
+	unsigned
+	pointer
+)
+
+type typeRange struct {
+	t typeMask
+	r rangeMask
+}
+
+type control struct {
+	tm     typeMask
+	a0, a1 ID
+}
+
+var (
+	reverseBits = [...]rangeMask{0, 4, 2, 6, 1, 5, 3, 7}
+
+	// maps what we learn when the positive branch is taken.
+	// For example:
+	//      OpLess8:   {signed, lt},
+	//	v1 = (OpLess8 v2 v3).
+	// If v1 branch is taken than we learn that the rangeMaks
+	// can be at most lt.
+	typeRangeTable = map[Op]typeRange{
+		OpEq8:   {signed | unsigned, eq},
+		OpEq16:  {signed | unsigned, eq},
+		OpEq32:  {signed | unsigned, eq},
+		OpEq64:  {signed | unsigned, eq},
+		OpEqPtr: {pointer, eq},
+
+		OpNeq8:   {signed | unsigned, lt | gt},
+		OpNeq16:  {signed | unsigned, lt | gt},
+		OpNeq32:  {signed | unsigned, lt | gt},
+		OpNeq64:  {signed | unsigned, lt | gt},
+		OpNeqPtr: {pointer, lt | gt},
+
+		OpLess8:   {signed, lt},
+		OpLess8U:  {unsigned, lt},
+		OpLess16:  {signed, lt},
+		OpLess16U: {unsigned, lt},
+		OpLess32:  {signed, lt},
+		OpLess32U: {unsigned, lt},
+		OpLess64:  {signed, lt},
+		OpLess64U: {unsigned, lt},
+
+		OpLeq8:   {signed, lt | eq},
+		OpLeq8U:  {unsigned, lt | eq},
+		OpLeq16:  {signed, lt | eq},
+		OpLeq16U: {unsigned, lt | eq},
+		OpLeq32:  {signed, lt | eq},
+		OpLeq32U: {unsigned, lt | eq},
+		OpLeq64:  {signed, lt | eq},
+		OpLeq64U: {unsigned, lt | eq},
+
+		OpGeq8:   {signed, eq | gt},
+		OpGeq8U:  {unsigned, eq | gt},
+		OpGeq16:  {signed, eq | gt},
+		OpGeq16U: {unsigned, eq | gt},
+		OpGeq32:  {signed, eq | gt},
+		OpGeq32U: {unsigned, eq | gt},
+		OpGeq64:  {signed, eq | gt},
+		OpGeq64U: {unsigned, eq | gt},
+
+		OpGreater8:   {signed, gt},
+		OpGreater8U:  {unsigned, gt},
+		OpGreater16:  {signed, gt},
+		OpGreater16U: {unsigned, gt},
+		OpGreater32:  {signed, gt},
+		OpGreater32U: {unsigned, gt},
+		OpGreater64:  {signed, gt},
+		OpGreater64U: {unsigned, gt},
+
+		// TODO: OpIsInBounds actually test 0 <= a < b. This means
+		// that the positive branch learns signed/LT and unsigned/LT
+		// but the negative branch only learns unsigned/GE.
+		OpIsInBounds:      {unsigned, lt},
+		OpIsSliceInBounds: {unsigned, lt | eq},
+	}
+)
+
+// prove removes redundant BlockIf controls that can be inferred in a straight line.
+//
+// By far, the most common redundant control are generated by bounds checking.
+// For example for the code:
+//
+//    a[i] = 4
+//    foo(a[i])
+//
+// The compiler will generate the following code:
+//
+//    if i >= len(a) {
+//        panic("not in bounds")
+//    }
+//    a[i] = 4
+//    if i >= len(a) {
+//        panic("not in bounds")
+//    }
+//    foo(a[i])
+//
+// The second comparison i >= len(a) is clearly redundant because if the
+// else branch of the first comparison is executed, we already know that i < len(a).
+// The code for the second panic can be removed.
+func prove(f *Func) {
+	idom := dominators(f)
+	sdom := newSparseTree(f, idom)
+	domTree := make([][]*Block, f.NumBlocks())
+
+	// Create a block ID -> [dominees] mapping
+	for _, b := range f.Blocks {
+		if dom := idom[b.ID]; dom != nil {
+			domTree[dom.ID] = append(domTree[dom.ID], b)
+		}
+	}
+
+	// current node state
+	type walkState int
+	const (
+		descend walkState = iota
+		simplify
+	)
+	// work maintains the DFS stack.
+	type bp struct {
+		block *Block      // current handled block
+		state walkState   // what's to do
+		saved []typeRange // save previous map entries modified by node
+	}
+	work := make([]bp, 0, 256)
+	work = append(work, bp{
+		block: f.Entry,
+		state: descend,
+	})
+
+	// mask keep tracks of restrictions for each pair of values in
+	// the dominators for the current node.
+	// Invariant: a0.ID <= a1.ID
+	// For example {unsigned, a0, a1} -> eq|gt means that from
+	// predecessors we know that a0 must be greater or equal to
+	// a1.
+	mask := make(map[control]rangeMask)
+
+	// DFS on the dominator tree.
+	for len(work) > 0 {
+		node := work[len(work)-1]
+		work = work[:len(work)-1]
+
+		switch node.state {
+		case descend:
+			parent := idom[node.block.ID]
+			tr := getRestrict(sdom, parent, node.block)
+			saved := updateRestrictions(mask, parent, tr)
+
+			work = append(work, bp{
+				block: node.block,
+				state: simplify,
+				saved: saved,
+			})
+
+			for _, s := range domTree[node.block.ID] {
+				work = append(work, bp{
+					block: s,
+					state: descend,
+				})
+			}
+
+		case simplify:
+			simplifyBlock(mask, node.block)
+			restoreRestrictions(mask, idom[node.block.ID], node.saved)
+		}
+	}
+}
+
+// getRestrict returns the range restrictions added by p
+// when reaching b. p is the immediate dominator or b.
+func getRestrict(sdom sparseTree, p *Block, b *Block) typeRange {
+	if p == nil || p.Kind != BlockIf {
+		return typeRange{}
+	}
+	tr, has := typeRangeTable[p.Control.Op]
+	if !has {
+		return typeRange{}
+	}
+	// If p and p.Succs[0] are dominators it means that every path
+	// from entry to b passes through p and p.Succs[0]. We care that
+	// no path from entry to b passes through p.Succs[1]. If p.Succs[0]
+	// has one predecessor then (apart from the degenerate case),
+	// there is no path from entry that can reach b through p.Succs[1].
+	// TODO: how about p->yes->b->yes, i.e. a loop in yes.
+	if sdom.isAncestorEq(p.Succs[0], b) && len(p.Succs[0].Preds) == 1 {
+		return tr
+	} else if sdom.isAncestorEq(p.Succs[1], b) && len(p.Succs[1].Preds) == 1 {
+		tr.r = (lt | eq | gt) ^ tr.r
+		return tr
+	}
+	return typeRange{}
+}
+
+// updateRestrictions updates restrictions from the previous block (p) based on tr.
+// normally tr was calculated with getRestrict.
+func updateRestrictions(mask map[control]rangeMask, p *Block, tr typeRange) []typeRange {
+	if tr.t == 0 {
+		return nil
+	}
+
+	// p modifies the restrictions for (a0, a1).
+	// save and return the previous state.
+	a0 := p.Control.Args[0]
+	a1 := p.Control.Args[1]
+	if a0.ID > a1.ID {
+		tr.r = reverseBits[tr.r]
+		a0, a1 = a1, a0
+	}
+
+	saved := make([]typeRange, 0, 2)
+	for t := typeMask(1); t <= tr.t; t <<= 1 {
+		if t&tr.t == 0 {
+			continue
+		}
+
+		i := control{t, a0.ID, a1.ID}
+		oldRange, ok := mask[i]
+		if !ok {
+			if a1 != a0 {
+				oldRange = lt | eq | gt
+			} else { // sometimes happens after cse
+				oldRange = eq
+			}
+		}
+		// if i was not already in the map we save the full range
+		// so that when we restore it we properly keep track of it.
+		saved = append(saved, typeRange{t, oldRange})
+		// mask[i] contains the possible relations between a0 and a1.
+		// When we branched from parent we learned that the possible
+		// relations cannot be more than tr.r. We compute the new set of
+		// relations as the intersection betwee the old and the new set.
+		mask[i] = oldRange & tr.r
+	}
+	return saved
+}
+
+func restoreRestrictions(mask map[control]rangeMask, p *Block, saved []typeRange) {
+	if p == nil || p.Kind != BlockIf || len(saved) == 0 {
+		return
+	}
+
+	a0 := p.Control.Args[0].ID
+	a1 := p.Control.Args[1].ID
+	if a0 > a1 {
+		a0, a1 = a1, a0
+	}
+
+	for _, tr := range saved {
+		i := control{tr.t, a0, a1}
+		if tr.r != lt|eq|gt {
+			mask[i] = tr.r
+		} else {
+			delete(mask, i)
+		}
+	}
+}
+
+// simplifyBlock simplifies block known the restrictions in mask.
+func simplifyBlock(mask map[control]rangeMask, b *Block) {
+	if b.Kind != BlockIf {
+		return
+	}
+
+	tr, has := typeRangeTable[b.Control.Op]
+	if !has {
+		return
+	}
+
+	succ := -1
+	a0 := b.Control.Args[0].ID
+	a1 := b.Control.Args[1].ID
+	if a0 > a1 {
+		tr.r = reverseBits[tr.r]
+		a0, a1 = a1, a0
+	}
+
+	for t := typeMask(1); t <= tr.t; t <<= 1 {
+		if t&tr.t == 0 {
+			continue
+		}
+
+		// tr.r represents in which case the positive branch is taken.
+		// m.r represents which cases are possible because of previous relations.
+		// If the set of possible relations m.r is included in the set of relations
+		// need to take the positive branch (or negative) then that branch will
+		// always be taken.
+		// For shortcut, if m.r == 0 then this block is dead code.
+		i := control{t, a0, a1}
+		m := mask[i]
+		if m != 0 && tr.r&m == m {
+			if b.Func.pass.debug > 0 {
+				b.Func.Config.Warnl(int(b.Line), "Proved %s", b.Control.Op)
+			}
+			b.Logf("proved positive branch of %s, block %s in %s\n", b.Control, b, b.Func.Name)
+			succ = 0
+			break
+		}
+		if m != 0 && ((lt|eq|gt)^tr.r)&m == m {
+			if b.Func.pass.debug > 0 {
+				b.Func.Config.Warnl(int(b.Line), "Disproved %s", b.Control.Op)
+			}
+			b.Logf("proved negative branch of %s, block %s in %s\n", b.Control, b, b.Func.Name)
+			succ = 1
+			break
+		}
+	}
+
+	if succ == -1 {
+		// HACK: If the first argument of IsInBounds or IsSliceInBounds
+		// is a constant and we already know that constant is smaller (or equal)
+		// to the upper bound than this is proven. Most useful in cases such as:
+		// if len(a) <= 1 { return }
+		// do something with a[1]
+		c := b.Control
+		if (c.Op == OpIsInBounds || c.Op == OpIsSliceInBounds) &&
+			c.Args[0].Op == OpConst64 && c.Args[0].AuxInt >= 0 {
+			m := mask[control{signed, a0, a1}]
+			if m != 0 && tr.r&m == m {
+				if b.Func.pass.debug > 0 {
+					b.Func.Config.Warnl(int(b.Line), "Proved constant %s", c.Op)
+				}
+				succ = 0
+			}
+		}
+	}
+
+	if succ != -1 {
+		b.Kind = BlockFirst
+		b.Control = nil
+		b.Succs[0], b.Succs[1] = b.Succs[succ], b.Succs[1-succ]
+	}
+}

test/prove.go

@@ -0,0 +1,207 @@
+// +build amd64
+// errorcheck -0 -d=ssa/prove/debug=3
+
+package main
+
+func f0(a []int) int {
+	a[0] = 1
+	a[0] = 1 // ERROR "Proved IsInBounds$"
+	a[6] = 1
+	a[6] = 1 // ERROR "Proved IsInBounds$"
+	a[5] = 1
+	a[5] = 1 // ERROR "Proved IsInBounds$"
+	return 13
+}
+
+func f1(a []int) int {
+	if len(a) <= 5 {
+		return 18
+	}
+	a[0] = 1
+	a[0] = 1 // ERROR "Proved IsInBounds$"
+	a[6] = 1
+	a[6] = 1 // ERROR "Proved IsInBounds$"
+	a[5] = 1 // ERROR "Proved constant IsInBounds$"
+	a[5] = 1 // ERROR "Proved IsInBounds$"
+	return 26
+}
+
+func f2(a []int) int {
+	for i := range a {
+		a[i] = i
+		a[i] = i // ERROR "Proved IsInBounds$"
+	}
+	return 34
+}
+
+func f3(a []uint) int {
+	for i := uint(0); i < uint(len(a)); i++ {
+		a[i] = i // ERROR "Proved IsInBounds$"
+	}
+	return 41
+}
+
+func f4a(a, b, c int) int {
+	if a < b {
+		if a == b { // ERROR "Disproved Eq64$"
+			return 47
+		}
+		if a > b { // ERROR "Disproved Greater64$"
+			return 50
+		}
+		if a < b { // ERROR "Proved Less64$"
+			return 53
+		}
+		if a == b { // ERROR "Disproved Eq64$"
+			return 56
+		}
+		if a > b {
+			return 59
+		}
+		return 61
+	}
+	return 63
+}
+
+func f4b(a, b, c int) int {
+	if a <= b {
+		if a >= b {
+			if a == b { // ERROR "Proved Eq64$"
+				return 70
+			}
+			return 75
+		}
+		return 77
+	}
+	return 79
+}
+
+func f4c(a, b, c int) int {
+	if a <= b {
+		if a >= b {
+			if a != b { // ERROR "Disproved Neq64$"
+				return 73
+			}
+			return 75
+		}
+		return 77
+	}
+	return 79
+}
+
+func f4d(a, b, c int) int {
+	if a < b {
+		if a < c {
+			if a < b { // ERROR "Proved Less64$"
+				if a < c { // ERROR "Proved Less64$"
+					return 87
+				}
+				return 89
+			}
+			return 91
+		}
+		return 93
+	}
+	return 95
+}
+
+func f4e(a, b, c int) int {
+	if a < b {
+		if b > a { // ERROR "Proved Greater64$"
+			return 101
+		}
+		return 103
+	}
+	return 105
+}
+
+func f4f(a, b, c int) int {
+	if a <= b {
+		if b > a {
+			if b == a { // ERROR "Disproved Eq64$"
+				return 112
+			}
+			return 114
+		}
+		if b >= a { // ERROR "Proved Geq64$"
+			if b == a { // ERROR "Proved Eq64$"
+				return 118
+			}
+			return 120
+		}
+		return 122
+	}
+	return 124
+}
+
+func f5(a, b uint) int {
+	if a == b {
+		if a <= b { // ERROR "Proved Leq64U$"
+			return 130
+		}
+		return 132
+	}
+	return 134
+}
+
+// These comparisons are compile time constants.
+func f6a(a uint8) int {
+	if a < a { // ERROR "Disproved Less8U$"
+		return 140
+	}
+	return 151
+}
+
+func f6b(a uint8) int {
+	if a < a { // ERROR "Disproved Less8U$"
+		return 140
+	}
+	return 151
+}
+
+func f6x(a uint8) int {
+	if a > a { // ERROR "Disproved Greater8U$"
+		return 143
+	}
+	return 151
+}
+
+func f6d(a uint8) int {
+	if a <= a { // ERROR "Proved Leq8U$"
+		return 146
+	}
+	return 151
+}
+
+func f6e(a uint8) int {
+	if a >= a { // ERROR "Proved Geq8U$"
+		return 149
+	}
+	return 151
+}
+
+func f7(a []int, b int) int {
+	if b < len(a) {
+		a[b] = 3
+		if b < len(a) { // ERROR "Proved Less64$"
+			a[b] = 5 // ERROR "Proved IsInBounds$"
+		}
+	}
+	return 161
+}
+
+func f8(a, b uint) int {
+	if a == b {
+		return 166
+	}
+	if a > b {
+		return 169
+	}
+	if a < b { // ERROR "Proved Less64U$"
+		return 172
+	}
+	return 174
+}
+
+func main() {
+}