-// +build amd64
// errorcheck -0 -d=ssa/prove/debug=1
+//go:build amd64
+
// 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.
func f0(a []int) int {
a[0] = 1
- a[0] = 1 // ERROR "Proved boolean IsInBounds$"
+ a[0] = 1 // ERROR "Proved IsInBounds$"
a[6] = 1
- a[6] = 1 // ERROR "Proved boolean IsInBounds$"
+ a[6] = 1 // ERROR "Proved IsInBounds$"
+ a[5] = 1 // ERROR "Proved IsInBounds$"
a[5] = 1 // ERROR "Proved IsInBounds$"
- a[5] = 1 // ERROR "Proved boolean IsInBounds$"
return 13
}
if len(a) <= 5 {
return 18
}
- a[0] = 1 // ERROR "Proved non-negative bounds IsInBounds$"
- a[0] = 1 // ERROR "Proved boolean IsInBounds$"
+ a[0] = 1 // ERROR "Proved IsInBounds$"
+ a[0] = 1 // ERROR "Proved IsInBounds$"
a[6] = 1
- a[6] = 1 // ERROR "Proved boolean IsInBounds$"
+ a[6] = 1 // ERROR "Proved IsInBounds$"
+ a[5] = 1 // ERROR "Proved IsInBounds$"
a[5] = 1 // ERROR "Proved IsInBounds$"
- a[5] = 1 // ERROR "Proved boolean IsInBounds$"
return 26
}
func f1b(a []int, i int, j uint) int {
if i >= 0 && i < len(a) {
- return a[i] // ERROR "Proved non-negative bounds IsInBounds$"
+ return a[i] // ERROR "Proved IsInBounds$"
}
if i >= 10 && i < len(a) {
- return a[i] // ERROR "Proved non-negative bounds IsInBounds$"
+ return a[i] // ERROR "Proved IsInBounds$"
}
if i >= 10 && i < len(a) {
- return a[i] // ERROR "Proved non-negative bounds IsInBounds$"
+ return a[i] // ERROR "Proved IsInBounds$"
}
- if i >= 10 && i < len(a) { // todo: handle this case
- return a[i-10]
+ if i >= 10 && i < len(a) {
+ return a[i-10] // ERROR "Proved IsInBounds$"
}
if j < uint(len(a)) {
return a[j] // ERROR "Proved IsInBounds$"
}
func f2(a []int) int {
- for i := range a {
+ for i := range a { // ERROR "Induction variable: limits \[0,\?\), increment 1$"
a[i+1] = i
- a[i+1] = i // ERROR "Proved boolean IsInBounds$"
+ a[i+1] = i // ERROR "Proved IsInBounds$"
}
return 34
}
if a == b { // ERROR "Disproved Eq64$"
return 47
}
- if a > b { // ERROR "Disproved Greater64$"
+ if a > b { // ERROR "Disproved Less64$"
return 50
}
- if a < b { // ERROR "Proved boolean Less64$"
+ if a < b { // ERROR "Proved Less64$"
return 53
}
- if a == b { // ERROR "Disproved boolean Eq64$"
+ // We can't get to this point and prove knows that, so
+ // there's no message for the next (obvious) branch.
+ if a != a {
return 56
}
- if a > b { // ERROR "Disproved boolean Greater64$"
- return 59
- }
return 61
}
return 63
func f4d(a, b, c int) int {
if a < b {
if a < c {
- if a < b { // ERROR "Proved boolean Less64$"
- if a < c { // ERROR "Proved boolean Less64$"
+ if a < b { // ERROR "Proved Less64$"
+ if a < c { // ERROR "Proved Less64$"
return 87
}
return 89
func f4e(a, b, c int) int {
if a < b {
- if b > a { // ERROR "Proved Greater64$"
+ if b > a { // ERROR "Proved Less64$"
return 101
}
return 103
}
return 114
}
- if b >= a { // ERROR "Proved Geq64$"
+ if b >= a { // ERROR "Proved Leq64$"
if b == a { // ERROR "Proved Eq64$"
return 118
}
}
func f6x(a uint8) int {
- if a > a { // ERROR "Disproved Greater8U$"
+ if a > a { // ERROR "Disproved Less8U$"
return 143
}
return 151
}
func f6e(a uint8) int {
- if a >= a { // ERROR "Proved Geq8U$"
+ if a >= a { // ERROR "Proved Leq8U$"
return 149
}
return 151
func f7(a []int, b int) int {
if b < len(a) {
a[b] = 3
- if b < len(a) { // ERROR "Proved boolean Less64$"
- a[b] = 5 // ERROR "Proved boolean IsInBounds$"
+ if b < len(a) { // ERROR "Proved Less64$"
+ a[b] = 5 // ERROR "Proved IsInBounds$"
}
}
return 161
if a {
return 1
}
- if a || b { // ERROR "Disproved boolean Arg$"
+ if a || b { // ERROR "Disproved Arg$"
return 2
}
return 3
func f10(a string) int {
n := len(a)
- if a[:n>>1] == "aaaaaaaaaaaaaa" {
+ // We optimize comparisons with small constant strings (see cmd/compile/internal/gc/walk.go),
+ // so this string literal must be long.
+ if a[:n>>1] == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa" {
return 0
}
return 1
func f11a(a []int, i int) {
useInt(a[i])
- useInt(a[i]) // ERROR "Proved boolean IsInBounds$"
+ useInt(a[i]) // ERROR "Proved IsInBounds$"
}
func f11b(a []int, i int) {
useSlice(a[i:])
- useSlice(a[i:]) // ERROR "Proved boolean IsSliceInBounds$"
+ useSlice(a[i:]) // ERROR "Proved IsSliceInBounds$"
}
func f11c(a []int, i int) {
useSlice(a[:i])
- useSlice(a[:i]) // ERROR "Proved boolean IsSliceInBounds$"
+ useSlice(a[:i]) // ERROR "Proved IsSliceInBounds$"
}
func f11d(a []int, i int) {
useInt(a[2*i+7])
- useInt(a[2*i+7])
+ useInt(a[2*i+7]) // ERROR "Proved IsInBounds$"
}
func f12(a []int, b int) {
}
}
if x {
- if a >= 12 { // ERROR "Proved Geq64$"
+ if a >= 12 { // ERROR "Proved Leq64$"
return 4
}
}
if x {
- if a > 12 { // ERROR "Proved boolean Greater64$"
+ if a > 12 { // ERROR "Proved Less64$"
return 5
}
}
}
}
if x {
- if a == -9 { // ERROR "Proved boolean Eq64$"
+ if a == -9 { // ERROR "Proved Eq64$"
return 9
}
}
if x {
- if a >= -9 { // ERROR "Proved Geq64$"
+ if a >= -9 { // ERROR "Proved Leq64$"
return 10
}
}
if x {
- if a > -9 { // ERROR "Disproved Greater64$"
+ if a > -9 { // ERROR "Disproved Less64$"
return 11
}
}
func f13c(a int, x bool) int {
if a < 90 {
if x {
- if a < 90 { // ERROR "Proved boolean Less64$"
+ if a < 90 { // ERROR "Proved Less64$"
return 13
}
}
}
}
if x {
- if a >= 90 { // ERROR "Disproved Geq64$"
+ if a >= 90 { // ERROR "Disproved Leq64$"
return 16
}
}
if x {
- if a > 90 { // ERROR "Disproved Greater64$"
+ if a > 90 { // ERROR "Disproved Less64$"
return 17
}
}
func f13e(a int) int {
if a > 9 {
- if a > 5 { // ERROR "Proved Greater64$"
+ if a > 5 { // ERROR "Proved Less64$"
return 1
}
}
func f13f(a int64) int64 {
if a > math.MaxInt64 {
- // Unreachable, but prove doesn't know that.
- if a == 0 {
+ if a == 0 { // ERROR "Disproved Eq64$"
return 1
}
}
if a == 0 {
return 1
}
- if a > 0 { // ERROR "Proved Greater64U$"
+ if a > 0 { // ERROR "Proved Less64U$"
return 2
}
return 3
}
+func f14(p, q *int, a []int) {
+ // This crazy ordering usually gives i1 the lowest value ID,
+ // j the middle value ID, and i2 the highest value ID.
+ // That used to confuse CSE because it ordered the args
+ // of the two + ops below differently.
+ // That in turn foiled bounds check elimination.
+ i1 := *p
+ j := *q
+ i2 := *p
+ useInt(a[i1+j])
+ useInt(a[i2+j]) // ERROR "Proved IsInBounds$"
+}
+
+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++ { // ERROR "Induction variable: limits \[0,\?\), increment 1$"
+ // This tests for i <= cap, which we can only prove
+ // using the derived relation between len and cap.
+ // This depends on finding the contradiction, since we
+ // don't query this condition directly.
+ useSlice(b[:i]) // ERROR "Proved IsSliceInBounds$"
+ }
+}
+
+func f18(b []int, x int, y uint) {
+ _ = b[x]
+ _ = b[y]
+
+ if x > len(b) { // ERROR "Disproved Less64$"
+ return
+ }
+ if y > uint(len(b)) { // ERROR "Disproved Less64U$"
+ return
+ }
+ if int(y) > len(b) { // ERROR "Disproved Less64$"
+ return
+ }
+}
+
+func f19() (e int64, err error) {
+ // Issue 29502: slice[:0] is incorrectly disproved.
+ var stack []int64
+ stack = append(stack, 123)
+ if len(stack) > 1 {
+ panic("too many elements")
+ }
+ last := len(stack) - 1
+ e = stack[last]
+ // Buggy compiler prints "Disproved Leq64" for the next line.
+ stack = stack[:last]
+ return e, nil
+}
+
+func sm1(b []int, x int) {
+ // Test constant argument to slicemask.
+ useSlice(b[2:8]) // ERROR "Proved slicemask not needed$"
+ // Test non-constant argument with known limits.
+ if cap(b) > 10 {
+ useSlice(b[2:])
+ }
+}
+
+func lim1(x, y, z int) {
+ // Test relations between signed and unsigned limits.
+ if x > 5 {
+ if uint(x) > 5 { // ERROR "Proved Less64U$"
+ return
+ }
+ }
+ if y >= 0 && y < 4 {
+ if uint(y) > 4 { // ERROR "Disproved Less64U$"
+ return
+ }
+ if uint(y) < 5 { // ERROR "Proved Less64U$"
+ return
+ }
+ }
+ if z < 4 {
+ if uint(z) > 4 { // Not provable without disjunctions.
+ return
+ }
+ }
+}
+
+// fence1–4 correspond to the four fence-post implications.
+
+func fence1(b []int, x, y int) {
+ // Test proofs that rely on fence-post implications.
+ if x+1 > y {
+ if x < y { // ERROR "Disproved Less64$"
+ return
+ }
+ }
+ if len(b) < cap(b) {
+ // This eliminates the growslice path.
+ b = append(b, 1) // ERROR "Disproved Less64U$"
+ }
+}
+
+func fence2(x, y int) {
+ if x-1 < y {
+ if x > y { // ERROR "Disproved Less64$"
+ return
+ }
+ }
+}
+
+func fence3(b, c []int, x, y int64) {
+ if x-1 >= y {
+ if x <= y { // Can't prove because x may have wrapped.
+ return
+ }
+ }
+
+ if x != math.MinInt64 && x-1 >= y {
+ if x <= y { // ERROR "Disproved Leq64$"
+ return
+ }
+ }
+
+ c[len(c)-1] = 0 // Can't prove because len(c) might be 0
+
+ if n := len(b); n > 0 {
+ b[n-1] = 0 // ERROR "Proved IsInBounds$"
+ }
+}
+
+func fence4(x, y int64) {
+ if x >= y+1 {
+ if x <= y {
+ return
+ }
+ }
+ if y != math.MaxInt64 && x >= y+1 {
+ if x <= y { // ERROR "Disproved Leq64$"
+ return
+ }
+ }
+}
+
+// Check transitive relations
+func trans1(x, y int64) {
+ if x > 5 {
+ if y > x {
+ if y > 2 { // ERROR "Proved Less64$"
+ return
+ }
+ } else if y == x {
+ if y > 5 { // ERROR "Proved Less64$"
+ return
+ }
+ }
+ }
+ if x >= 10 {
+ if y > x {
+ if y > 10 { // ERROR "Proved Less64$"
+ return
+ }
+ }
+ }
+}
+
+func trans2(a, b []int, i int) {
+ if len(a) != len(b) {
+ return
+ }
+
+ _ = a[i]
+ _ = b[i] // ERROR "Proved IsInBounds$"
+}
+
+func trans3(a, b []int, i int) {
+ if len(a) > len(b) {
+ return
+ }
+
+ _ = a[i]
+ _ = b[i] // ERROR "Proved IsInBounds$"
+}
+
+func trans4(b []byte, x int) {
+ // Issue #42603: slice len/cap transitive relations.
+ switch x {
+ case 0:
+ if len(b) < 20 {
+ return
+ }
+ _ = b[:2] // ERROR "Proved IsSliceInBounds$"
+ case 1:
+ if len(b) < 40 {
+ return
+ }
+ _ = b[:2] // ERROR "Proved IsSliceInBounds$"
+ }
+}
+
+// Derived from nat.cmp
+func natcmp(x, y []uint) (r int) {
+ m := len(x)
+ n := len(y)
+ if m != n || m == 0 {
+ return
+ }
+
+ i := m - 1
+ for i > 0 && // ERROR "Induction variable: limits \(0,\?\], increment 1$"
+ x[i] == // ERROR "Proved IsInBounds$"
+ y[i] { // ERROR "Proved IsInBounds$"
+ i--
+ }
+
+ switch {
+ case x[i] < // todo, cannot prove this because it's dominated by i<=0 || x[i]==y[i]
+ y[i]: // ERROR "Proved IsInBounds$"
+ r = -1
+ case x[i] > // ERROR "Proved IsInBounds$"
+ y[i]: // ERROR "Proved IsInBounds$"
+ r = 1
+ }
+ return
+}
+
+func suffix(s, suffix string) bool {
+ // todo, we're still not able to drop the bound check here in the general case
+ return len(s) >= len(suffix) && s[len(s)-len(suffix):] == suffix
+}
+
+func constsuffix(s string) bool {
+ return suffix(s, "abc") // ERROR "Proved IsSliceInBounds$"
+}
+
+// oforuntil tests the pattern created by OFORUNTIL blocks. These are
+// handled by addLocalInductiveFacts rather than findIndVar.
+func oforuntil(b []int) {
+ i := 0
+ if len(b) > i {
+ top:
+ println(b[i]) // ERROR "Induction variable: limits \[0,\?\), increment 1$" "Proved IsInBounds$"
+ i++
+ if i < len(b) {
+ goto top
+ }
+ }
+}
+
+func atexit(foobar []func()) {
+ for i := len(foobar) - 1; i >= 0; i-- { // ERROR "Induction variable: limits \[0,\?\], increment 1"
+ f := foobar[i]
+ foobar = foobar[:i] // ERROR "IsSliceInBounds"
+ f()
+ }
+}
+
+func make1(n int) []int {
+ s := make([]int, n)
+ for i := 0; i < n; i++ { // ERROR "Induction variable: limits \[0,\?\), increment 1"
+ s[i] = 1 // ERROR "Proved IsInBounds$"
+ }
+ return s
+}
+
+func make2(n int) []int {
+ s := make([]int, n)
+ for i := range s { // ERROR "Induction variable: limits \[0,\?\), increment 1"
+ s[i] = 1 // ERROR "Proved IsInBounds$"
+ }
+ return s
+}
+
+// The range tests below test the index variable of range loops.
+
+// range1 compiles to the "efficiently indexable" form of a range loop.
+func range1(b []int) {
+ for i, v := range b { // ERROR "Induction variable: limits \[0,\?\), increment 1$"
+ b[i] = v + 1 // ERROR "Proved IsInBounds$"
+ if i < len(b) { // ERROR "Proved Less64$"
+ println("x")
+ }
+ if i >= 0 { // ERROR "Proved Leq64$"
+ println("x")
+ }
+ }
+}
+
+// range2 elements are larger, so they use the general form of a range loop.
+func range2(b [][32]int) {
+ for i, v := range b { // ERROR "Induction variable: limits \[0,\?\), increment 1$"
+ b[i][0] = v[0] + 1 // ERROR "Proved IsInBounds$"
+ if i < len(b) { // ERROR "Proved Less64$"
+ println("x")
+ }
+ if i >= 0 { // ERROR "Proved Leq64$"
+ println("x")
+ }
+ }
+}
+
+// signhint1-2 test whether the hint (int >= 0) is propagated into the loop.
+func signHint1(i int, data []byte) {
+ if i >= 0 {
+ for i < len(data) { // ERROR "Induction variable: limits \[\?,\?\), increment 1$"
+ _ = data[i] // ERROR "Proved IsInBounds$"
+ i++
+ }
+ }
+}
+
+func signHint2(b []byte, n int) {
+ if n < 0 {
+ panic("")
+ }
+ _ = b[25]
+ for i := n; i <= 25; i++ { // ERROR "Induction variable: limits \[\?,25\], increment 1$"
+ b[i] = 123 // ERROR "Proved IsInBounds$"
+ }
+}
+
+// indexGT0 tests whether prove learns int index >= 0 from bounds check.
+func indexGT0(b []byte, n int) {
+ _ = b[n]
+ _ = b[25]
+
+ for i := n; i <= 25; i++ { // ERROR "Induction variable: limits \[\?,25\], increment 1$"
+ b[i] = 123 // ERROR "Proved IsInBounds$"
+ }
+}
+
+// Induction variable in unrolled loop.
+func unrollUpExcl(a []int) int {
+ var i, x int
+ for i = 0; i < len(a)-1; i += 2 { // ERROR "Induction variable: limits \[0,\?\), increment 2$"
+ x += a[i] // ERROR "Proved IsInBounds$"
+ x += a[i+1]
+ }
+ if i == len(a)-1 {
+ x += a[i]
+ }
+ return x
+}
+
+// Induction variable in unrolled loop.
+func unrollUpIncl(a []int) int {
+ var i, x int
+ for i = 0; i <= len(a)-2; i += 2 { // ERROR "Induction variable: limits \[0,\?\], increment 2$"
+ x += a[i] // ERROR "Proved IsInBounds$"
+ x += a[i+1]
+ }
+ if i == len(a)-1 {
+ x += a[i]
+ }
+ return x
+}
+
+// Induction variable in unrolled loop.
+func unrollDownExcl0(a []int) int {
+ var i, x int
+ for i = len(a) - 1; i > 0; i -= 2 { // ERROR "Induction variable: limits \(0,\?\], increment 2$"
+ x += a[i] // ERROR "Proved IsInBounds$"
+ x += a[i-1] // ERROR "Proved IsInBounds$"
+ }
+ if i == 0 {
+ x += a[i]
+ }
+ return x
+}
+
+// Induction variable in unrolled loop.
+func unrollDownExcl1(a []int) int {
+ var i, x int
+ for i = len(a) - 1; i >= 1; i -= 2 { // ERROR "Induction variable: limits \(0,\?\], increment 2$"
+ x += a[i] // ERROR "Proved IsInBounds$"
+ x += a[i-1] // ERROR "Proved IsInBounds$"
+ }
+ if i == 0 {
+ x += a[i]
+ }
+ return x
+}
+
+// Induction variable in unrolled loop.
+func unrollDownInclStep(a []int) int {
+ var i, x int
+ for i = len(a); i >= 2; i -= 2 { // ERROR "Induction variable: limits \[2,\?\], increment 2$"
+ x += a[i-1] // ERROR "Proved IsInBounds$"
+ x += a[i-2] // ERROR "Proved IsInBounds$"
+ }
+ if i == 1 {
+ x += a[i-1]
+ }
+ return x
+}
+
+// Not an induction variable (step too large)
+func unrollExclStepTooLarge(a []int) int {
+ var i, x int
+ for i = 0; i < len(a)-1; i += 3 {
+ x += a[i]
+ x += a[i+1]
+ }
+ if i == len(a)-1 {
+ x += a[i]
+ }
+ return x
+}
+
+// Not an induction variable (step too large)
+func unrollInclStepTooLarge(a []int) int {
+ var i, x int
+ for i = 0; i <= len(a)-2; i += 3 {
+ x += a[i]
+ x += a[i+1]
+ }
+ if i == len(a)-1 {
+ x += a[i]
+ }
+ return x
+}
+
+// Not an induction variable (min too small, iterating down)
+func unrollDecMin(a []int) int {
+ var i, x int
+ for i = len(a); i >= math.MinInt64; i -= 2 {
+ x += a[i-1]
+ x += a[i-2]
+ }
+ if i == 1 { // ERROR "Disproved Eq64$"
+ x += a[i-1]
+ }
+ return x
+}
+
+// Not an induction variable (min too small, iterating up -- perhaps could allow, but why bother?)
+func unrollIncMin(a []int) int {
+ var i, x int
+ for i = len(a); i >= math.MinInt64; i += 2 {
+ x += a[i-1]
+ x += a[i-2]
+ }
+ if i == 1 { // ERROR "Disproved Eq64$"
+ x += a[i-1]
+ }
+ return x
+}
+
+// The 4 xxxxExtNto64 functions below test whether prove is looking
+// through value-preserving sign/zero extensions of index values (issue #26292).
+
+// Look through all extensions
+func signExtNto64(x []int, j8 int8, j16 int16, j32 int32) int {
+ if len(x) < 22 {
+ return 0
+ }
+ if j8 >= 0 && j8 < 22 {
+ return x[j8] // ERROR "Proved IsInBounds$"
+ }
+ if j16 >= 0 && j16 < 22 {
+ return x[j16] // ERROR "Proved IsInBounds$"
+ }
+ if j32 >= 0 && j32 < 22 {
+ return x[j32] // ERROR "Proved IsInBounds$"
+ }
+ return 0
+}
+
+func zeroExtNto64(x []int, j8 uint8, j16 uint16, j32 uint32) int {
+ if len(x) < 22 {
+ return 0
+ }
+ if j8 >= 0 && j8 < 22 {
+ return x[j8] // ERROR "Proved IsInBounds$"
+ }
+ if j16 >= 0 && j16 < 22 {
+ return x[j16] // ERROR "Proved IsInBounds$"
+ }
+ if j32 >= 0 && j32 < 22 {
+ return x[j32] // ERROR "Proved IsInBounds$"
+ }
+ return 0
+}
+
+// Process fence-post implications through 32to64 extensions (issue #29964)
+func signExt32to64Fence(x []int, j int32) int {
+ if x[j] != 0 {
+ return 1
+ }
+ if j > 0 && x[j-1] != 0 { // ERROR "Proved IsInBounds$"
+ return 1
+ }
+ return 0
+}
+
+func zeroExt32to64Fence(x []int, j uint32) int {
+ if x[j] != 0 {
+ return 1
+ }
+ if j > 0 && x[j-1] != 0 { // ERROR "Proved IsInBounds$"
+ return 1
+ }
+ return 0
+}
+
+// Ensure that bounds checks with negative indexes are not incorrectly removed.
+func negIndex() {
+ n := make([]int, 1)
+ for i := -1; i <= 0; i++ { // ERROR "Induction variable: limits \[-1,0\], increment 1$"
+ n[i] = 1
+ }
+}
+func negIndex2(n int) {
+ a := make([]int, 5)
+ b := make([]int, 5)
+ c := make([]int, 5)
+ for i := -1; i <= 0; i-- {
+ b[i] = i
+ n++
+ if n > 10 {
+ break
+ }
+ }
+ useSlice(a)
+ useSlice(c)
+}
+
+// Check that prove is zeroing these right shifts of positive ints by bit-width - 1.
+// e.g (Rsh64x64 <t> n (Const64 <typ.UInt64> [63])) && ft.isNonNegative(n) -> 0
+func sh64(n int64) int64 {
+ if n < 0 {
+ return n
+ }
+ return n >> 63 // ERROR "Proved Rsh64x64 shifts to zero"
+}
+
+func sh32(n int32) int32 {
+ if n < 0 {
+ return n
+ }
+ return n >> 31 // ERROR "Proved Rsh32x64 shifts to zero"
+}
+
+func sh32x64(n int32) int32 {
+ if n < 0 {
+ return n
+ }
+ return n >> uint64(31) // ERROR "Proved Rsh32x64 shifts to zero"
+}
+
+func sh16(n int16) int16 {
+ if n < 0 {
+ return n
+ }
+ return n >> 15 // ERROR "Proved Rsh16x64 shifts to zero"
+}
+
+func sh64noopt(n int64) int64 {
+ return n >> 63 // not optimized; n could be negative
+}
+
+// These cases are division of a positive signed integer by a power of 2.
+// The opt pass doesnt have sufficient information to see that n is positive.
+// So, instead, opt rewrites the division with a less-than-optimal replacement.
+// Prove, which can see that n is nonnegative, cannot see the division because
+// opt, an earlier pass, has already replaced it.
+// The fix for this issue allows prove to zero a right shift that was added as
+// part of the less-than-optimal reqwrite. That change by prove then allows
+// lateopt to clean up all the unnecessary parts of the original division
+// replacement. See issue #36159.
+func divShiftClean(n int) int {
+ if n < 0 {
+ return n
+ }
+ return n / int(8) // ERROR "Proved Rsh64x64 shifts to zero"
+}
+
+func divShiftClean64(n int64) int64 {
+ if n < 0 {
+ return n
+ }
+ return n / int64(16) // ERROR "Proved Rsh64x64 shifts to zero"
+}
+
+func divShiftClean32(n int32) int32 {
+ if n < 0 {
+ return n
+ }
+ return n / int32(16) // ERROR "Proved Rsh32x64 shifts to zero"
+}
+
+// Bounds check elimination
+
+func sliceBCE1(p []string, h uint) string {
+ if len(p) == 0 {
+ return ""
+ }
+
+ i := h & uint(len(p)-1)
+ return p[i] // ERROR "Proved IsInBounds$"
+}
+
+func sliceBCE2(p []string, h int) string {
+ if len(p) == 0 {
+ return ""
+ }
+ i := h & (len(p) - 1)
+ return p[i] // ERROR "Proved IsInBounds$"
+}
+
+func and(p []byte) ([]byte, []byte) { // issue #52563
+ const blocksize = 16
+ fullBlocks := len(p) &^ (blocksize - 1)
+ blk := p[:fullBlocks] // ERROR "Proved IsSliceInBounds$"
+ rem := p[fullBlocks:] // ERROR "Proved IsSliceInBounds$"
+ return blk, rem
+}
+
+func rshu(x, y uint) int {
+ z := x >> y
+ if z <= x { // ERROR "Proved Leq64U$"
+ return 1
+ }
+ return 0
+}
+
+func divu(x, y uint) int {
+ z := x / y
+ if z <= x { // ERROR "Proved Leq64U$"
+ return 1
+ }
+ return 0
+}
+
+func modu1(x, y uint) int {
+ z := x % y
+ if z < y { // ERROR "Proved Less64U$"
+ return 1
+ }
+ return 0
+}
+
+func modu2(x, y uint) int {
+ z := x % y
+ if z <= x { // ERROR "Proved Leq64U$"
+ return 1
+ }
+ return 0
+}
+
+func issue57077(s []int) (left, right []int) {
+ middle := len(s) / 2
+ left = s[:middle] // ERROR "Proved IsSliceInBounds$"
+ right = s[middle:] // ERROR "Proved IsSliceInBounds$"
+ return
+}
+
+func issue51622(b []byte) int {
+ if len(b) >= 3 && b[len(b)-3] == '#' { // ERROR "Proved IsInBounds$"
+ return len(b)
+ }
+ return 0
+}
+
+func issue45928(x int) {
+ combinedFrac := x / (x | (1 << 31)) // ERROR "Proved Neq64$"
+ useInt(combinedFrac)
+}
+
//go:noinline
func useInt(a int) {
}