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cmd/compile: implement loop BCE in prove

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Reuse findIndVar to discover induction variables, and then
register the facts we know about them into the facts table
when entering the loop block.

Moreover, handle "x+delta > w" while updating the facts table,
to be able to prove accesses to slices with constant offsets
such as slice[i-10].

Change-Id: I2a63d050ed58258136d54712ac7015b25c893d71
Reviewed-on: https://go-review.googlesource.com/104038
Run-TryBot: Giovanni Bajo <rasky@develer.com>
Reviewed-by: David Chase <drchase@google.com>
This commit is contained in:
Giovanni Bajo 2018-04-02 01:57:49 +02:00
parent 29162ec9a7
commit 7ec25d0acf
5 changed files with 163 additions and 44 deletions
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1
src/cmd/compile/fmt_test.go
View File

@ -646,6 +646,7 @@ var knownFormats = map[string]string{
"cmd/compile/internal/ssa.Op %s": "",
"cmd/compile/internal/ssa.Op %v": "",
"cmd/compile/internal/ssa.ValAndOff %s": "",
"cmd/compile/internal/ssa.domain %v": "",
"cmd/compile/internal/ssa.posetNode %v": "",
"cmd/compile/internal/ssa.posetTestOp %v": "",
"cmd/compile/internal/ssa.rbrank %d": "",

2
src/cmd/compile/internal/ssa/loopbce.go
View File

@ -137,7 +137,7 @@ nextb:
}
}
if f.pass.debug > 1 {
if f.pass.debug >= 1 {
if min.Op == OpConst64 {
b.Func.Warnl(b.Pos, "Induction variable with minimum %d and increment %d", min.AuxInt, inc.AuxInt)
} else {

119
src/cmd/compile/internal/ssa/prove.go
View File

@ -388,6 +388,77 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
}
}
}
// Process: x+delta > w (with delta,w constants)
//
// We want to derive: x+delta > w ⇒ x > w-delta
//
// We do this for signed numbers for now, as that allows to prove many
// accesses to slices in loops.
//
// From x+delta > w, we compute (using integers of the correct size):
// min = w - delta
// max = MaxInt - delta
//
// And we prove that:
// if min<max: min < x AND x <= max
// if min>max: min < x OR x <= max
//
// This is always correct, even in case of overflow.
//
// If the initial fact is x+delta >= w instead, the derived conditions are:
// if min<max: min <= x AND x <= max
// if min>max: min <= x OR x <= max
//
// Notice the conditions for max are still <=, as they handle overflows.
if r == gt || r == gt|eq {
if x, delta := isConstDelta(v); x != nil && w.isGenericIntConst() && d == signed {
if parent.Func.pass.debug > 1 {
parent.Func.Warnl(parent.Pos, "x+d >= w; x:%v %v delta:%v w:%v d:%v", x, parent.String(), delta, w.AuxInt, d)
}
var min, max int64
var vmin, vmax *Value
switch x.Type.Size() {
case 8:
min = w.AuxInt - delta
max = int64(^uint64(0)>>1) - delta
vmin = parent.NewValue0I(parent.Pos, OpConst64, parent.Func.Config.Types.Int64, min)
vmax = parent.NewValue0I(parent.Pos, OpConst64, parent.Func.Config.Types.Int64, max)
case 4:
min = int64(int32(w.AuxInt) - int32(delta))
max = int64(int32(^uint32(0)>>1) - int32(delta))
vmin = parent.NewValue0I(parent.Pos, OpConst32, parent.Func.Config.Types.Int32, min)
vmax = parent.NewValue0I(parent.Pos, OpConst32, parent.Func.Config.Types.Int32, max)
default:
panic("unimplemented")
}
if min < max {
// Record that x > min and max >= x
ft.update(parent, x, vmin, d, r)
ft.update(parent, vmax, x, d, r|eq)
} else {
// We know that either x>min OR x<=max. factsTable cannot record OR conditions,
// so let's see if we can already prove that one of them is false, in which case
// the other must be true
if l, has := ft.limits[x.ID]; has {
if l.max <= min {
// x>min is impossible, so it must be x<=max
ft.update(parent, vmax, x, d, r|eq)
} else if l.min > max {
// x<=max is impossible, so it must be x>min
ft.update(parent, x, vmin, d, r)
}
}
}
}
}
}
var opMin = map[Op]int64{
@ -405,8 +476,25 @@ func (ft *factsTable) isNonNegative(v *Value) bool {
if isNonNegative(v) {
return true
}
l, has := ft.limits[v.ID]
return has && (l.min >= 0 || l.umax <= math.MaxInt64)
// Check if the recorded limits can prove that the value is positive
if l, has := ft.limits[v.ID]; has && (l.min >= 0 || l.umax <= math.MaxInt64) {
return true
}
// Check if v = x+delta, and we can use x's limits to prove that it's positive
if x, delta := isConstDelta(v); x != nil {
if l, has := ft.limits[x.ID]; has {
if delta > 0 && l.min >= -delta && l.max <= math.MaxInt64-delta {
return true
}
if delta < 0 && l.min >= -delta {
return true
}
}
}
return false
}
// checkpoint saves the current state of known relations.
@ -595,6 +683,16 @@ func prove(f *Func) {
}
}
// Find induction variables. Currently, findIndVars
// is limited to one induction variable per block.
var indVars map[*Block]indVar
for _, v := range findIndVar(f) {
if indVars == nil {
indVars = make(map[*Block]indVar)
}
indVars[v.entry] = v
}
// current node state
type walkState int
const (
@ -634,6 +732,10 @@ func prove(f *Func) {
switch node.state {
case descend:
ft.checkpoint()
if iv, ok := indVars[node.block]; ok {
addIndVarRestrictions(ft, parent, iv)
}
if branch != unknown {
addBranchRestrictions(ft, parent, branch)
if ft.unsat {
@ -688,6 +790,19 @@ func getBranch(sdom SparseTree, p *Block, b *Block) branch {
return unknown
}
// addIndVarRestrictions updates the factsTables ft with the facts
// learned from the induction variable indVar which drives the loop
// starting in Block b.
func addIndVarRestrictions(ft *factsTable, b *Block, iv indVar) {
d := signed
if isNonNegative(iv.min) && isNonNegative(iv.max) {
d |= unsigned
}
addRestrictions(b, ft, d, iv.min, iv.ind, lt|eq)
addRestrictions(b, ft, d, iv.ind, iv.max, lt)
}
// addBranchRestrictions updates the factsTables ft with the facts learned when
// branching from Block b in direction br.
func addBranchRestrictions(ft *factsTable, b *Block, br branch) {

80
test/loopbce.go
View File

@ -1,12 +1,12 @@
// +build amd64
// errorcheck -0 -d=ssa/loopbce/debug=3
// errorcheck -0 -d=ssa/prove/debug=1
package main
func f0a(a []int) int {
x := 0
for i := range a { // ERROR "Induction variable with minimum 0 and increment 1$"
x += a[i] // ERROR "Found redundant IsInBounds$"
x += a[i] // ERROR "Proved IsInBounds$"
}
return x
}
@ -14,7 +14,7 @@ func f0a(a []int) int {
func f0b(a []int) int {
x := 0
for i := range a { // ERROR "Induction variable with minimum 0 and increment 1$"
b := a[i:] // ERROR "Found redundant IsSliceInBounds$"
b := a[i:] // ERROR "Proved IsSliceInBounds$"
x += b[0]
}
return x
@ -23,7 +23,7 @@ func f0b(a []int) int {
func f0c(a []int) int {
x := 0
for i := range a { // ERROR "Induction variable with minimum 0 and increment 1$"
b := a[:i+1] // ERROR "Found redundant IsSliceInBounds \(len promoted to cap\)$"
b := a[:i+1] // ERROR "Proved IsSliceInBounds$"
x += b[0]
}
return x
@ -40,7 +40,7 @@ func f1(a []int) int {
func f2(a []int) int {
x := 0
for i := 1; i < len(a); i++ { // ERROR "Induction variable with minimum 1 and increment 1$"
x += a[i] // ERROR "Found redundant IsInBounds$"
x += a[i] // ERROR "Proved IsInBounds$"
}
return x
}
@ -48,7 +48,7 @@ func f2(a []int) int {
func f4(a [10]int) int {
x := 0
for i := 0; i < len(a); i += 2 { // ERROR "Induction variable with minimum 0 and increment 2$"
x += a[i] // ERROR "Found redundant IsInBounds$"
x += a[i] // ERROR "Proved IsInBounds$"
}
return x
}
@ -63,7 +63,7 @@ func f5(a [10]int) int {
func f6(a []int) {
for i := range a { // ERROR "Induction variable with minimum 0 and increment 1$"
b := a[0:i] // ERROR "Found redundant IsSliceInBounds \(len promoted to cap\)$"
b := a[0:i] // ERROR "Proved IsSliceInBounds$"
f6(b)
}
}
@ -71,7 +71,7 @@ func f6(a []int) {
func g0a(a string) int {
x := 0
for i := 0; i < len(a); i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
x += int(a[i]) // ERROR "Found redundant IsInBounds$"
x += int(a[i]) // ERROR "Proved IsInBounds$"
}
return x
}
@ -79,7 +79,7 @@ func g0a(a string) int {
func g0b(a string) int {
x := 0
for i := 0; len(a) > i; i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
x += int(a[i]) // ERROR "Found redundant IsInBounds$"
x += int(a[i]) // ERROR "Proved IsInBounds$"
}
return x
}
@ -88,7 +88,7 @@ func g1() int {
a := "evenlength"
x := 0
for i := 0; i < len(a); i += 2 { // ERROR "Induction variable with minimum 0 and increment 2$"
x += int(a[i]) // ERROR "Found redundant IsInBounds$"
x += int(a[i]) // ERROR "Proved IsInBounds$"
}
return x
}
@ -98,7 +98,7 @@ func g2() int {
x := 0
for i := 0; i < len(a); i += 2 { // ERROR "Induction variable with minimum 0 and increment 2$"
j := i
if a[i] == 'e' { // ERROR "Found redundant IsInBounds$"
if a[i] == 'e' { // ERROR "Proved IsInBounds$"
j = j + 1
}
x += int(a[j])
@ -109,27 +109,27 @@ func g2() int {
func g3a() {
a := "this string has length 25"
for i := 0; i < len(a); i += 5 { // ERROR "Induction variable with minimum 0 and increment 5$"
useString(a[i:]) // ERROR "Found redundant IsSliceInBounds$"
useString(a[i:]) // ERROR "Proved IsSliceInBounds$"
useString(a[:i+3])
}
}
func g3b(a string) {
for i := 0; i < len(a); i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
useString(a[i+1:]) // ERROR "Found redundant IsSliceInBounds$"
useString(a[i+1:]) // ERROR "Proved IsSliceInBounds$"
}
}
func g3c(a string) {
for i := 0; i < len(a); i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
useString(a[:i+1]) // ERROR "Found redundant IsSliceInBounds$"
useString(a[:i+1]) // ERROR "Proved IsSliceInBounds$"
}
}
func h1(a []byte) {
c := a[:128]
for i := range c { // ERROR "Induction variable with minimum 0 and increment 1$"
c[i] = byte(i) // ERROR "Found redundant IsInBounds$"
c[i] = byte(i) // ERROR "Proved IsInBounds$"
}
}
@ -142,11 +142,11 @@ func h2(a []byte) {
func k0(a [100]int) [100]int {
for i := 10; i < 90; i++ { // ERROR "Induction variable with minimum 10 and increment 1$"
a[i-11] = i
a[i-10] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 80$"
a[i-5] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 85$"
a[i] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 90$"
a[i+5] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 95$"
a[i+10] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 100$"
a[i-10] = i // ERROR "Proved IsInBounds$"
a[i-5] = i // ERROR "Proved IsInBounds$"
a[i] = i // ERROR "Proved IsInBounds$"
a[i+5] = i // ERROR "Proved IsInBounds$"
a[i+10] = i // ERROR "Proved IsInBounds$"
a[i+11] = i
}
return a
@ -155,12 +155,13 @@ func k0(a [100]int) [100]int {
func k1(a [100]int) [100]int {
for i := 10; i < 90; i++ { // ERROR "Induction variable with minimum 10 and increment 1$"
useSlice(a[:i-11])
useSlice(a[:i-10]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 80$"
useSlice(a[:i-5]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 85$"
useSlice(a[:i]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 90$"
useSlice(a[:i+5]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 95$"
useSlice(a[:i+10]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 100$"
useSlice(a[:i+11]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 101$"
useSlice(a[:i-10]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i-5]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i+5]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i+10]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i+11]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[:i+12])
}
return a
@ -169,19 +170,22 @@ func k1(a [100]int) [100]int {
func k2(a [100]int) [100]int {
for i := 10; i < 90; i++ { // ERROR "Induction variable with minimum 10 and increment 1$"
useSlice(a[i-11:])
useSlice(a[i-10:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 80$"
useSlice(a[i-5:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 85$"
useSlice(a[i:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 90$"
useSlice(a[i+5:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 95$"
useSlice(a[i+10:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 100$"
useSlice(a[i+11:]) // ERROR "Found redundant \(IsSliceInBounds ind 100\), ind < 101$"
useSlice(a[i-10:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i-5:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i+5:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i+10:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i+11:]) // ERROR "Proved IsSliceInBounds$"
useSlice(a[i+12:])
}
return a
}
func k3(a [100]int) [100]int {
for i := -10; i < 90; i++ { // ERROR "Induction variable with minimum -10 and increment 1$"
a[i+10] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 100$"
a[i+9] = i
a[i+10] = i // ERROR "Proved IsInBounds$"
a[i+11] = i
}
return a
}
@ -189,7 +193,7 @@ func k3(a [100]int) [100]int {
func k4(a [100]int) [100]int {
min := (-1) << 63
for i := min; i < min+50; i++ { // ERROR "Induction variable with minimum -9223372036854775808 and increment 1$"
a[i-min] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 50$"
a[i-min] = i // ERROR "Proved IsInBounds$"
}
return a
}
@ -197,8 +201,8 @@ func k4(a [100]int) [100]int {
func k5(a [100]int) [100]int {
max := (1 << 63) - 1
for i := max - 50; i < max; i++ { // ERROR "Induction variable with minimum 9223372036854775757 and increment 1$"
a[i-max+50] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 50$"
a[i-(max-70)] = i // ERROR "Found redundant \(IsInBounds ind 100\), ind < 70$"
a[i-max+50] = i // ERROR "Proved IsInBounds$"
a[i-(max-70)] = i // ERROR "Proved IsInBounds$"
}
return a
}
@ -221,10 +225,10 @@ func nobce1() {
func nobce2(a string) {
for i := int64(0); i < int64(len(a)); i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
useString(a[i:]) // ERROR "Found redundant IsSliceInBounds$"
useString(a[i:]) // ERROR "Proved IsSliceInBounds$"
}
for i := int64(0); i < int64(len(a))-31337; i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
useString(a[i:]) // ERROR "Found redundant IsSliceInBounds$"
useString(a[i:]) // ERROR "Proved IsSliceInBounds$"
}
for i := int64(0); i < int64(len(a))+int64(-1<<63); i++ { // ERROR "Induction variable with minimum 0 and increment 1$"
// tests an overflow of StringLen-MinInt64

5
test/prove.go
View File

@ -62,7 +62,7 @@ func f1c(a []int, i int64) int {
}
func f2(a []int) int {
for i := range a {
for i := range a { // ERROR "Induction variable with minimum 0 and increment 1"
a[i+1] = i
a[i+1] = i // ERROR "Proved IsInBounds$"
}
@ -464,8 +464,7 @@ func f16(s []int) []int {
}
func f17(b []int) {
for i := 0; i < len(b); i++ {
useSlice(b[i:]) // Learns i <= len
for i := 0; i < len(b); i++ { // ERROR "Induction variable with minimum 0 and increment 1"
// This tests for i <= cap, which we can only prove
// using the derived relation between len and cap.
// This depends on finding the contradiction, since we