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669db2cef5
go/test/prove.go
Austin Clements 669db2cef5 cmd/compile: make prove pass use unsatisfiability 
Currently the prove pass uses implication queries. For each block, it
collects the set of branch conditions leading to that block, and
queries this fact table for whether any of these facts imply the
block's own branch condition (or its inverse). This works remarkably
well considering it doesn't do any deduction on these facts, but it
has various downsides:

1. It requires an implementation both of adding facts to the table and
   determining implications. These are very nearly duals of each
   other, but require separate implementations. Likewise, the process
   of asserting facts of dominating branch conditions is very nearly
   the dual of the process of querying implied branch conditions.

2. It leads to less effective use of derived facts. For example, the
   prove pass currently derives facts about the relations between len
   and cap, but can't make use of these unless a branch condition is
   in the exact form of a derived fact. If one of these derived facts
   contradicts another fact, it won't notice or make use of this.

This CL changes the approach of the prove pass to instead use
*contradiction* instead of implication. Rather than ever querying a
branch condition, it simply adds branch conditions to the fact table.
If this leads to a contradiction (specifically, it makes the fact set
unsatisfiable), that branch is impossible and can be cut. As a result,

1. We can eliminate the code for determining implications
   (factsTable.get disappears entirely). Also, there is now a single
   implementation of visiting and asserting branch conditions, since
   we don't have to flip them around to treat them as facts in one
   place and queries in another.

2. Derived facts can be used effectively. It doesn't matter *why* the
   fact table is unsatisfiable; a contradiction in any of the facts is
   enough.

3. As an added benefit, it's now quite easy to avoid traversing beyond
   provably-unreachable blocks. In contrast, the current
   implementation always visits all blocks.

The prove pass already has nearly all of the mechanism necessary to
compute unsatisfiability, which means this both simplifies the code
and makes it more powerful.

The only complication is that the current implication procedure has a
hack for dealing with the 0 <= Args[0] condition of OpIsInBounds and
OpIsSliceInBounds. We replace this with asserting the appropriate fact
when we process one of these conditions. This seems much cleaner
anyway, and works because we can now take advantage of derived facts.

This has no measurable effect on compiler performance.

Effectiveness:

There is exactly one condition in all of std and cmd that this fails
to prove that the old implementation could: (int64(^uint(0)>>1) < x)
in encoding/gob. This can never be true because x is an int, and it's
basically coincidence that the old code gets this. (For example, it
fails to prove the similar (x < ^int64(^uint(0)>>1)) condition that
immediately precedes it, and even though the conditions are logically
unrelated, it wouldn't get the second one if it hadn't first processed
the first!)

It does, however, prove a few dozen additional branches. These come
from facts that are added to the fact table about the relations
between len and cap. These were almost never queried directly before,
but could lead to contradictions, which the unsat-based approach is
able to use.

There are exactly two branches in std and cmd that this implementation
proves in the *other* direction. This sounds scary, but is okay
because both occur in already-unreachable blocks, so it doesn't matter
what we chose. Because the fact table logic is sound but incomplete,
it fails to prove that the block isn't reachable, even though it is
able to prove that both outgoing branches are impossible. We could
turn these blocks into BlockExit blocks, but it doesn't seem worth the
trouble of the extra proof effort for something that happens twice in
all of std and cmd.

Tests:

This CL updates test/prove.go to change the expected messages because
it can no longer give a "reason" why it proved or disproved a
condition. It also adds a new test of a branch it couldn't prove
before.

It mostly guts test/sliceopt.go, removing everything related to slice
bounds optimizations and moving a few relevant tests to test/prove.go.
Much of this test is actually unreachable. The new prove pass figures
this out and doesn't try to prove anything about the unreachable
parts. The output on the unreachable parts is already suspect because
anything can be proved at that point, so it's really just a regression
test for an algorithm the compiler no longer uses.

This is a step toward fixing #23354. That issue is quite easy to fix
once we can use derived facts effectively.

Change-Id: Ia48a1b9ee081310579fe474e4a61857424ff8ce8
Reviewed-on: https://go-review.googlesource.com/87478
Reviewed-by: Keith Randall <khr@golang.org>
2018-03-08 22:25:25 +00:00

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// +build amd64
// errorcheck -0 -d=ssa/prove/debug=1
// 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 main
import "math"
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 // ERROR "Proved IsInBounds$"
a[5] = 1 // ERROR "Proved IsInBounds$"
return 13
}
func f1(a []int) int {
if len(a) <= 5 {
return 18
}
a[0] = 1 // ERROR "Proved IsInBounds$"
a[0] = 1 // ERROR "Proved IsInBounds$"
a[6] = 1
a[6] = 1 // ERROR "Proved IsInBounds$"
a[5] = 1 // ERROR "Proved IsInBounds$"
a[5] = 1 // ERROR "Proved IsInBounds$"
return 26
}
func f1b(a []int, i int, j uint) int {
if i >= 0 && i < len(a) {
return a[i] // ERROR "Proved IsInBounds$"
}
if i >= 10 && i < len(a) {
return a[i] // ERROR "Proved IsInBounds$"
}
if i >= 10 && i < len(a) {
return a[i] // ERROR "Proved IsInBounds$"
}
if i >= 10 && i < len(a) { // todo: handle this case
return a[i-10]
}
if j < uint(len(a)) {
return a[j] // ERROR "Proved IsInBounds$"
}
return 0
}
func f1c(a []int, i int64) int {
c := uint64(math.MaxInt64 + 10) // overflows int
d := int64(c)
if i >= d && i < int64(len(a)) {
// d overflows, should not be handled.
return a[i]
}
return 0
}
func f2(a []int) int {
for i := range a {
a[i+1] = i
a[i+1] = i // ERROR "Proved IsInBounds$"
}
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
}
// We can't get to this point and prove knows that, so
// there's no message for the next (obvious) branch.
if a != a {
return 56
}
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$"
return 172
}
return 174
}
func f9(a, b bool) int {
if a {
return 1
}
if a || b { // ERROR "Disproved Arg$"
return 2
}
return 3
}
func f10(a string) int {
n := len(a)
// We optimize comparisons with small constant strings (see cmd/compile/internal/gc/walk.go),
// so this string literal must be long.
if a[:n>>1] == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa" {
return 0
}
return 1
}
func f11a(a []int, i int) {
useInt(a[i])
useInt(a[i]) // ERROR "Proved IsInBounds$"
}
func f11b(a []int, i int) {
useSlice(a[i:])
useSlice(a[i:]) // ERROR "Proved IsSliceInBounds$"
}
func f11c(a []int, i int) {
useSlice(a[:i])
useSlice(a[:i]) // ERROR "Proved IsSliceInBounds$"
}
func f11d(a []int, i int) {
useInt(a[2*i+7])
useInt(a[2*i+7]) // ERROR "Proved IsInBounds$"
}
func f12(a []int, b int) {
useSlice(a[:b])
}
func f13a(a, b, c int, x bool) int {
if a > 12 {
if x {
if a < 12 { // ERROR "Disproved Less64$"
return 1
}
}
if x {
if a <= 12 { // ERROR "Disproved Leq64$"
return 2
}
}
if x {
if a == 12 { // ERROR "Disproved Eq64$"
return 3
}
}
if x {
if a >= 12 { // ERROR "Proved Geq64$"
return 4
}
}
if x {
if a > 12 { // ERROR "Proved Greater64$"
return 5
}
}
return 6
}
return 0
}
func f13b(a int, x bool) int {
if a == -9 {
if x {
if a < -9 { // ERROR "Disproved Less64$"
return 7
}
}
if x {
if a <= -9 { // ERROR "Proved Leq64$"
return 8
}
}
if x {
if a == -9 { // ERROR "Proved Eq64$"
return 9
}
}
if x {
if a >= -9 { // ERROR "Proved Geq64$"
return 10
}
}
if x {
if a > -9 { // ERROR "Disproved Greater64$"
return 11
}
}
return 12
}
return 0
}
func f13c(a int, x bool) int {
if a < 90 {
if x {
if a < 90 { // ERROR "Proved Less64$"
return 13
}
}
if x {
if a <= 90 { // ERROR "Proved Leq64$"
return 14
}
}
if x {
if a == 90 { // ERROR "Disproved Eq64$"
return 15
}
}
if x {
if a >= 90 { // ERROR "Disproved Geq64$"
return 16
}
}
if x {
if a > 90 { // ERROR "Disproved Greater64$"
return 17
}
}
return 18
}
return 0
}
func f13d(a int) int {
if a < 5 {
if a < 9 { // ERROR "Proved Less64$"
return 1
}
}
return 0
}
func f13e(a int) int {
if a > 9 {
if a > 5 { // ERROR "Proved Greater64$"
return 1
}
}
return 0
}
func f13f(a int64) int64 {
if a > math.MaxInt64 {
// Unreachable, but prove doesn't know that.
if a == 0 {
return 1
}
}
return 0
}
func f13g(a int) int {
if a < 3 {
return 5
}
if a > 3 {
return 6
}
if a == 3 { // ERROR "Proved Eq64$"
return 7
}
return 8
}
func f13h(a int) int {
if a < 3 {
if a > 1 {
if a == 2 { // ERROR "Proved Eq64$"
return 5
}
}
}
return 0
}
func f13i(a uint) int {
if a == 0 {
return 1
}
if a > 0 { // ERROR "Proved Greater64U$"
return 2
}
return 3
}
func f14(p, q *int, a []int) {
// This crazy ordering usually gives i1 the lowest value ID,
// j the middle value ID, and i2 the highest value ID.
// That used to confuse CSE because it ordered the args
// of the two + ops below differently.
// That in turn foiled bounds check elimination.
i1 := *p
j := *q
i2 := *p
useInt(a[i1+j])
useInt(a[i2+j]) // ERROR "Proved IsInBounds$"
}
func f15(s []int, x int) {
useSlice(s[x:])
useSlice(s[:x]) // ERROR "Proved IsSliceInBounds$"
}
func f16(s []int) []int {
if len(s) >= 10 {
return s[:10] // ERROR "Proved IsSliceInBounds$"
}
return nil
}
func f17(b []int) {
for i := 0; i < len(b); i++ {
useSlice(b[i:]) // Learns i <= len
// This tests for i <= cap, which we can only prove
// using the derived relation between len and cap.
// This depends on finding the contradiction, since we
// don't query this condition directly.
useSlice(b[:i]) // ERROR "Proved IsSliceInBounds$"
}
}
func sm1(b []int, x int) {
// Test constant argument to slicemask.
useSlice(b[2:8]) // ERROR "Proved slicemask not needed$"
// Test non-constant argument with known limits.
// Right now prove only uses the unsigned limit.
if uint(cap(b)) > 10 {
useSlice(b[2:]) // ERROR "Proved slicemask not needed$"
}
}
//go:noinline
func useInt(a int) {
}
//go:noinline
func useSlice(a []int) {
}
func main() {
}
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