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cmd/compile: enhance induction variable detection for unrolled loops
Would suggest extending capabilities (32-bit, unsigned, etc) in separate CLs because prove bugs are so mystifying. This implements the suggestion in this comment https://go-review.googlesource.com/c/go/+/104041/10/src/cmd/compile/internal/ssa/loopbce.go#164 for inferring properly bounded iteration for loops of the form for i := K0; i < KNN-(K-1); i += K for i := K0; i <= KNN-K; i += K Where KNN is "known non negative" (i.e., len or cap) and K is also not negative. Because i <= KNN-K, i+K <= KNN and no overflow occurs. Also handles decreasing case (K1 > 0) for i := KNN; i >= K0; i -= K1 which works when MININT+K1 < K0 (i.e. MININT < K0-K1, no overflow) Signed only, also only 64 bit for now. Change-Id: I5da6015aba2f781ec76c4ad59c9c48d952325fdc Reviewed-on: https://go-review.googlesource.com/c/go/+/136375 Run-TryBot: David Chase <drchase@google.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Alexandru Moșoi <alexandru@mosoi.ro>
This commit is contained in:
David Chase
parent
c90f6dd496
commit
d8f60eea64
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@ -4,7 +4,10 @@
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package ssa
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import "fmt"
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import (
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"fmt"
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"math"
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)
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type indVarFlags uint8
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@ -59,6 +62,7 @@ func findIndVar(f *Func) []indVar {
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// Check thet the control if it either ind </<= max or max >/>= ind.
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// TODO: Handle 32-bit comparisons.
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// TODO: Handle unsigned comparisons?
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switch b.Control.Op {
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case OpLeq64:
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flags |= indVarMaxInc
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@ -165,15 +169,101 @@ func findIndVar(f *Func) []indVar {
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continue
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}
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// We can only guarantee that the loops runs within limits of induction variable
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// if the increment is ±1 or when the limits are constants.
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if step != 1 {
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// We can only guarantee that the loop runs within limits of induction variable
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// if (one of)
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// (1) the increment is ±1
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// (2) the limits are constants
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// (3) loop is of the form k0 upto Known_not_negative-k inclusive, step <= k
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// (4) loop is of the form k0 upto Known_not_negative-k exclusive, step <= k+1
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// (5) loop is of the form Known_not_negative downto k0, minint+step < k0
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if step > 1 {
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ok := false
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if min.Op == OpConst64 && max.Op == OpConst64 {
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if max.AuxInt > min.AuxInt && max.AuxInt%step == min.AuxInt%step { // handle overflow
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ok = true
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}
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}
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// Handle induction variables of these forms.
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// KNN is known-not-negative.
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// SIGNED ARITHMETIC ONLY. (see switch on b.Control.Op above)
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// Possibilitis for KNN are len and cap; perhaps we can infer others.
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// for i := 0; i <= KNN-k ; i += k
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// for i := 0; i < KNN-(k-1); i += k
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// Also handle decreasing.
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// "Proof" copied from https://go-review.googlesource.com/c/go/+/104041/10/src/cmd/compile/internal/ssa/loopbce.go#164
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//
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// In the case of
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// // PC is Positive Constant
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// L := len(A)-PC
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// for i := 0; i < L; i = i+PC
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//
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// we know:
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//
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// 0 + PC does not over/underflow.
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// len(A)-PC does not over/underflow
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// maximum value for L is MaxInt-PC
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// i < L <= MaxInt-PC means i + PC < MaxInt hence no overflow.
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// To match in SSA:
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// if (a) min.Op == OpConst64(k0)
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// and (b) k0 >= MININT + step
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// and (c) max.Op == OpSubtract(Op{StringLen,SliceLen,SliceCap}, k)
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// or (c) max.Op == OpAdd(Op{StringLen,SliceLen,SliceCap}, -k)
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// or (c) max.Op == Op{StringLen,SliceLen,SliceCap}
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// and (d) if upto loop, require indVarMaxInc && step <= k or !indVarMaxInc && step-1 <= k
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if min.Op == OpConst64 && min.AuxInt >= step+math.MinInt64 {
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knn := max
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k := int64(0)
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var kArg *Value
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switch max.Op {
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case OpSub64:
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knn = max.Args[0]
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kArg = max.Args[1]
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case OpAdd64:
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knn = max.Args[0]
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kArg = max.Args[1]
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if knn.Op == OpConst64 {
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knn, kArg = kArg, knn
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}
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}
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switch knn.Op {
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case OpSliceLen, OpStringLen, OpSliceCap:
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default:
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knn = nil
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}
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if kArg != nil && kArg.Op == OpConst64 {
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k = kArg.AuxInt
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if max.Op == OpAdd64 {
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k = -k
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}
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}
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if k >= 0 && knn != nil {
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if inc.AuxInt > 0 { // increasing iteration
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// The concern for the relation between step and k is to ensure that iv never exceeds knn
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// i.e., iv < knn-(K-1) ==> iv + K <= knn; iv <= knn-K ==> iv +K < knn
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if step <= k || flags&indVarMaxInc == 0 && step-1 == k {
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ok = true
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}
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} else { // decreasing iteration
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// Will be decrementing from max towards min; max is knn-k; will only attempt decrement if
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// knn-k >[=] min; underflow is only a concern if min-step is not smaller than min.
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// This all assumes signed integer arithmetic
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// This is already assured by the test above: min.AuxInt >= step+math.MinInt64
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ok = true
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}
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}
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}
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// TODO: other unrolling idioms
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// for i := 0; i < KNN - KNN % k ; i += k
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// for i := 0; i < KNN&^(k-1) ; i += k // k a power of 2
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// for i := 0; i < KNN&(-k) ; i += k // k a power of 2
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if !ok {
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continue
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}
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117
test/prove.go
117
test/prove.go
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@ -726,6 +726,123 @@ func signHint2(b []byte, n int) {
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}
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}
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// Induction variable in unrolled loop.
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func unrollUpExcl(a []int) int {
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var i, x int
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for i = 0; i < len(a)-1; i += 2 { // ERROR "Induction variable: limits \[0,\?\), increment 2$"
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x += a[i] // ERROR "Proved IsInBounds$"
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x += a[i+1]
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}
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if i == len(a)-1 {
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x += a[i]
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}
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return x
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}
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// Induction variable in unrolled loop.
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func unrollUpIncl(a []int) int {
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var i, x int
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for i = 0; i <= len(a)-2; i += 2 { // ERROR "Induction variable: limits \[0,\?\], increment 2$"
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x += a[i]
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x += a[i+1]
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}
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if i == len(a)-1 {
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x += a[i]
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}
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return x
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}
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// Induction variable in unrolled loop.
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func unrollDownExcl0(a []int) int {
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var i, x int
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for i = len(a) - 1; i > 0; i -= 2 { // ERROR "Induction variable: limits \(0,\?\], increment 2$"
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x += a[i] // ERROR "Proved IsInBounds$"
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x += a[i-1] // ERROR "Proved IsInBounds$"
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}
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if i == 0 {
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x += a[i]
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}
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return x
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}
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// Induction variable in unrolled loop.
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func unrollDownExcl1(a []int) int {
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var i, x int
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for i = len(a) - 1; i >= 1; i -= 2 { // ERROR "Induction variable: limits \[1,\?\], increment 2$"
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x += a[i] // ERROR "Proved IsInBounds$"
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x += a[i-1] // ERROR "Proved IsInBounds$"
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}
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if i == 0 {
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x += a[i]
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}
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return x
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}
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// Induction variable in unrolled loop.
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func unrollDownInclStep(a []int) int {
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var i, x int
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for i = len(a); i >= 2; i -= 2 { // ERROR "Induction variable: limits \[2,\?\], increment 2$"
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x += a[i-1] // ERROR "Proved IsInBounds$"
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x += a[i-2]
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}
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if i == 1 {
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x += a[i-1]
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}
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return x
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}
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// Not an induction variable (step too large)
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func unrollExclStepTooLarge(a []int) int {
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var i, x int
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for i = 0; i < len(a)-1; i += 3 {
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x += a[i]
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x += a[i+1]
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}
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if i == len(a)-1 {
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x += a[i]
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}
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return x
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}
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// Not an induction variable (step too large)
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func unrollInclStepTooLarge(a []int) int {
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var i, x int
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for i = 0; i <= len(a)-2; i += 3 {
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x += a[i]
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x += a[i+1]
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}
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if i == len(a)-1 {
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x += a[i]
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}
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return x
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}
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// Not an induction variable (min too small, iterating down)
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func unrollDecMin(a []int) int {
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var i, x int
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for i = len(a); i >= math.MinInt64; i -= 2 {
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x += a[i-1]
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x += a[i-2]
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}
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if i == 1 { // ERROR "Disproved Eq64$"
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x += a[i-1]
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}
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return x
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}
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// Not an induction variable (min too small, iterating up -- perhaps could allow, but why bother?)
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func unrollIncMin(a []int) int {
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var i, x int
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for i = len(a); i >= math.MinInt64; i += 2 {
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x += a[i-1]
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x += a[i-2]
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}
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if i == 1 { // ERROR "Disproved Eq64$"
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x += a[i-1]
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}
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return x
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}
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//go:noinline
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func useInt(a int) {
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}
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