477 lines
10 KiB
Go
477 lines
10 KiB
Go
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package vrp
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import (
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"fmt"
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"go/token"
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"go/types"
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"math/big"
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"honnef.co/go/tools/ssa"
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)
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type Zs []Z
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func (zs Zs) Len() int {
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return len(zs)
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}
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func (zs Zs) Less(i int, j int) bool {
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return zs[i].Cmp(zs[j]) == -1
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}
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func (zs Zs) Swap(i int, j int) {
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zs[i], zs[j] = zs[j], zs[i]
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}
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type Z struct {
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infinity int8
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integer *big.Int
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}
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func NewZ(n int64) Z {
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return NewBigZ(big.NewInt(n))
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}
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func NewBigZ(n *big.Int) Z {
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return Z{integer: n}
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}
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func (z1 Z) Infinite() bool {
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return z1.infinity != 0
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}
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func (z1 Z) Add(z2 Z) Z {
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if z2.Sign() == -1 {
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return z1.Sub(z2.Negate())
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}
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if z1 == NInfinity {
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return NInfinity
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}
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if z1 == PInfinity {
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return PInfinity
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}
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if z2 == PInfinity {
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return PInfinity
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}
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if !z1.Infinite() && !z2.Infinite() {
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n := &big.Int{}
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n.Add(z1.integer, z2.integer)
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return NewBigZ(n)
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}
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panic(fmt.Sprintf("%s + %s is not defined", z1, z2))
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}
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func (z1 Z) Sub(z2 Z) Z {
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if z2.Sign() == -1 {
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return z1.Add(z2.Negate())
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}
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if !z1.Infinite() && !z2.Infinite() {
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n := &big.Int{}
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n.Sub(z1.integer, z2.integer)
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return NewBigZ(n)
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}
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if z1 != PInfinity && z2 == PInfinity {
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return NInfinity
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}
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if z1.Infinite() && !z2.Infinite() {
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return Z{infinity: z1.infinity}
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}
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if z1 == PInfinity && z2 == PInfinity {
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return PInfinity
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}
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panic(fmt.Sprintf("%s - %s is not defined", z1, z2))
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}
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func (z1 Z) Mul(z2 Z) Z {
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if (z1.integer != nil && z1.integer.Sign() == 0) ||
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(z2.integer != nil && z2.integer.Sign() == 0) {
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return NewBigZ(&big.Int{})
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}
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if z1.infinity != 0 || z2.infinity != 0 {
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return Z{infinity: int8(z1.Sign() * z2.Sign())}
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}
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n := &big.Int{}
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n.Mul(z1.integer, z2.integer)
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return NewBigZ(n)
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}
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func (z1 Z) Negate() Z {
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if z1.infinity == 1 {
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return NInfinity
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}
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if z1.infinity == -1 {
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return PInfinity
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}
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n := &big.Int{}
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n.Neg(z1.integer)
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return NewBigZ(n)
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}
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func (z1 Z) Sign() int {
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if z1.infinity != 0 {
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return int(z1.infinity)
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}
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return z1.integer.Sign()
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}
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func (z1 Z) String() string {
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if z1 == NInfinity {
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return "-∞"
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}
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if z1 == PInfinity {
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return "∞"
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}
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return fmt.Sprintf("%d", z1.integer)
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}
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func (z1 Z) Cmp(z2 Z) int {
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if z1.infinity == z2.infinity && z1.infinity != 0 {
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return 0
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}
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if z1 == PInfinity {
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return 1
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}
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if z1 == NInfinity {
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return -1
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}
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if z2 == NInfinity {
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return 1
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}
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if z2 == PInfinity {
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return -1
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}
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return z1.integer.Cmp(z2.integer)
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}
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func MaxZ(zs ...Z) Z {
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if len(zs) == 0 {
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panic("Max called with no arguments")
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}
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if len(zs) == 1 {
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return zs[0]
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}
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ret := zs[0]
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for _, z := range zs[1:] {
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if z.Cmp(ret) == 1 {
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ret = z
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}
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}
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return ret
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}
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func MinZ(zs ...Z) Z {
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if len(zs) == 0 {
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panic("Min called with no arguments")
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}
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if len(zs) == 1 {
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return zs[0]
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}
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ret := zs[0]
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for _, z := range zs[1:] {
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if z.Cmp(ret) == -1 {
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ret = z
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}
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}
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return ret
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}
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var NInfinity = Z{infinity: -1}
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var PInfinity = Z{infinity: 1}
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var EmptyIntInterval = IntInterval{true, PInfinity, NInfinity}
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func InfinityFor(v ssa.Value) IntInterval {
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if b, ok := v.Type().Underlying().(*types.Basic); ok {
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if (b.Info() & types.IsUnsigned) != 0 {
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return NewIntInterval(NewZ(0), PInfinity)
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}
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}
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return NewIntInterval(NInfinity, PInfinity)
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}
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type IntInterval struct {
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known bool
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Lower Z
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Upper Z
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}
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func NewIntInterval(l, u Z) IntInterval {
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if u.Cmp(l) == -1 {
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return EmptyIntInterval
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}
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return IntInterval{known: true, Lower: l, Upper: u}
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}
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func (i IntInterval) IsKnown() bool {
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return i.known
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}
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func (i IntInterval) Empty() bool {
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return i.Lower == PInfinity && i.Upper == NInfinity
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}
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func (i IntInterval) IsMaxRange() bool {
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return i.Lower == NInfinity && i.Upper == PInfinity
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}
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func (i1 IntInterval) Intersection(i2 IntInterval) IntInterval {
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if !i1.IsKnown() {
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return i2
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}
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if !i2.IsKnown() {
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return i1
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}
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if i1.Empty() || i2.Empty() {
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return EmptyIntInterval
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}
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i3 := NewIntInterval(MaxZ(i1.Lower, i2.Lower), MinZ(i1.Upper, i2.Upper))
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if i3.Lower.Cmp(i3.Upper) == 1 {
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return EmptyIntInterval
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}
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return i3
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}
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func (i1 IntInterval) Union(other Range) Range {
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i2, ok := other.(IntInterval)
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if !ok {
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i2 = EmptyIntInterval
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}
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if i1.Empty() || !i1.IsKnown() {
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return i2
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}
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if i2.Empty() || !i2.IsKnown() {
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return i1
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}
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return NewIntInterval(MinZ(i1.Lower, i2.Lower), MaxZ(i1.Upper, i2.Upper))
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}
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func (i1 IntInterval) Add(i2 IntInterval) IntInterval {
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if i1.Empty() || i2.Empty() {
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return EmptyIntInterval
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}
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l1, u1, l2, u2 := i1.Lower, i1.Upper, i2.Lower, i2.Upper
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return NewIntInterval(l1.Add(l2), u1.Add(u2))
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}
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func (i1 IntInterval) Sub(i2 IntInterval) IntInterval {
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if i1.Empty() || i2.Empty() {
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return EmptyIntInterval
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}
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l1, u1, l2, u2 := i1.Lower, i1.Upper, i2.Lower, i2.Upper
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return NewIntInterval(l1.Sub(u2), u1.Sub(l2))
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}
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func (i1 IntInterval) Mul(i2 IntInterval) IntInterval {
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if i1.Empty() || i2.Empty() {
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return EmptyIntInterval
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}
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x1, x2 := i1.Lower, i1.Upper
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y1, y2 := i2.Lower, i2.Upper
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return NewIntInterval(
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MinZ(x1.Mul(y1), x1.Mul(y2), x2.Mul(y1), x2.Mul(y2)),
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MaxZ(x1.Mul(y1), x1.Mul(y2), x2.Mul(y1), x2.Mul(y2)),
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)
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}
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func (i1 IntInterval) String() string {
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if !i1.IsKnown() {
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return "[⊥, ⊥]"
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}
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if i1.Empty() {
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return "{}"
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}
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return fmt.Sprintf("[%s, %s]", i1.Lower, i1.Upper)
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}
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type IntArithmeticConstraint struct {
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aConstraint
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A ssa.Value
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B ssa.Value
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Op token.Token
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Fn func(IntInterval, IntInterval) IntInterval
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}
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type IntAddConstraint struct{ *IntArithmeticConstraint }
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type IntSubConstraint struct{ *IntArithmeticConstraint }
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type IntMulConstraint struct{ *IntArithmeticConstraint }
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type IntConversionConstraint struct {
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aConstraint
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X ssa.Value
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}
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type IntIntersectionConstraint struct {
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aConstraint
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ranges Ranges
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A ssa.Value
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B ssa.Value
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Op token.Token
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I IntInterval
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resolved bool
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}
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type IntIntervalConstraint struct {
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aConstraint
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I IntInterval
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}
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func NewIntArithmeticConstraint(a, b, y ssa.Value, op token.Token, fn func(IntInterval, IntInterval) IntInterval) *IntArithmeticConstraint {
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return &IntArithmeticConstraint{NewConstraint(y), a, b, op, fn}
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}
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func NewIntAddConstraint(a, b, y ssa.Value) Constraint {
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return &IntAddConstraint{NewIntArithmeticConstraint(a, b, y, token.ADD, IntInterval.Add)}
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}
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func NewIntSubConstraint(a, b, y ssa.Value) Constraint {
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return &IntSubConstraint{NewIntArithmeticConstraint(a, b, y, token.SUB, IntInterval.Sub)}
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}
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func NewIntMulConstraint(a, b, y ssa.Value) Constraint {
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return &IntMulConstraint{NewIntArithmeticConstraint(a, b, y, token.MUL, IntInterval.Mul)}
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}
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func NewIntConversionConstraint(x, y ssa.Value) Constraint {
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return &IntConversionConstraint{NewConstraint(y), x}
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}
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func NewIntIntersectionConstraint(a, b ssa.Value, op token.Token, ranges Ranges, y ssa.Value) Constraint {
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return &IntIntersectionConstraint{
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aConstraint: NewConstraint(y),
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ranges: ranges,
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A: a,
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B: b,
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Op: op,
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}
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}
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func NewIntIntervalConstraint(i IntInterval, y ssa.Value) Constraint {
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return &IntIntervalConstraint{NewConstraint(y), i}
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}
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func (c *IntArithmeticConstraint) Operands() []ssa.Value { return []ssa.Value{c.A, c.B} }
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func (c *IntConversionConstraint) Operands() []ssa.Value { return []ssa.Value{c.X} }
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func (c *IntIntersectionConstraint) Operands() []ssa.Value { return []ssa.Value{c.A} }
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func (s *IntIntervalConstraint) Operands() []ssa.Value { return nil }
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func (c *IntArithmeticConstraint) String() string {
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return fmt.Sprintf("%s = %s %s %s", c.Y().Name(), c.A.Name(), c.Op, c.B.Name())
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}
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func (c *IntConversionConstraint) String() string {
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return fmt.Sprintf("%s = %s(%s)", c.Y().Name(), c.Y().Type(), c.X.Name())
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}
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func (c *IntIntersectionConstraint) String() string {
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return fmt.Sprintf("%s = %s %s %s (%t branch)", c.Y().Name(), c.A.Name(), c.Op, c.B.Name(), c.Y().(*ssa.Sigma).Branch)
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}
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func (c *IntIntervalConstraint) String() string { return fmt.Sprintf("%s = %s", c.Y().Name(), c.I) }
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func (c *IntArithmeticConstraint) Eval(g *Graph) Range {
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i1, i2 := g.Range(c.A).(IntInterval), g.Range(c.B).(IntInterval)
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if !i1.IsKnown() || !i2.IsKnown() {
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return IntInterval{}
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}
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return c.Fn(i1, i2)
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}
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func (c *IntConversionConstraint) Eval(g *Graph) Range {
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s := &types.StdSizes{
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// XXX is it okay to assume the largest word size, or do we
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// need to be platform specific?
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WordSize: 8,
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MaxAlign: 1,
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}
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fromI := g.Range(c.X).(IntInterval)
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toI := g.Range(c.Y()).(IntInterval)
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fromT := c.X.Type().Underlying().(*types.Basic)
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|
|
toT := c.Y().Type().Underlying().(*types.Basic)
|
||
|
|
fromB := s.Sizeof(c.X.Type())
|
||
|
|
toB := s.Sizeof(c.Y().Type())
|
||
|
|
|
||
|
|
if !fromI.IsKnown() {
|
||
|
|
return toI
|
||
|
|
}
|
||
|
|
if !toI.IsKnown() {
|
||
|
|
return fromI
|
||
|
|
}
|
||
|
|
|
||
|
|
// uint<N> -> sint/uint<M>, M > N: [max(0, l1), min(2**N-1, u2)]
|
||
|
|
if (fromT.Info()&types.IsUnsigned != 0) &&
|
||
|
|
toB > fromB {
|
||
|
|
|
||
|
|
n := big.NewInt(1)
|
||
|
|
n.Lsh(n, uint(fromB*8))
|
||
|
|
n.Sub(n, big.NewInt(1))
|
||
|
|
return NewIntInterval(
|
||
|
|
MaxZ(NewZ(0), fromI.Lower),
|
||
|
|
MinZ(NewBigZ(n), toI.Upper),
|
||
|
|
)
|
||
|
|
}
|
||
|
|
|
||
|
|
// sint<N> -> sint<M>, M > N; [max(-∞, l1), min(2**N-1, u2)]
|
||
|
|
if (fromT.Info()&types.IsUnsigned == 0) &&
|
||
|
|
(toT.Info()&types.IsUnsigned == 0) &&
|
||
|
|
toB > fromB {
|
||
|
|
|
||
|
|
n := big.NewInt(1)
|
||
|
|
n.Lsh(n, uint(fromB*8))
|
||
|
|
n.Sub(n, big.NewInt(1))
|
||
|
|
return NewIntInterval(
|
||
|
|
MaxZ(NInfinity, fromI.Lower),
|
||
|
|
MinZ(NewBigZ(n), toI.Upper),
|
||
|
|
)
|
||
|
|
}
|
||
|
|
|
||
|
|
return fromI
|
||
|
|
}
|
||
|
|
func (c *IntIntersectionConstraint) Eval(g *Graph) Range {
|
||
|
|
xi := g.Range(c.A).(IntInterval)
|
||
|
|
if !xi.IsKnown() {
|
||
|
|
return c.I
|
||
|
|
}
|
||
|
|
return xi.Intersection(c.I)
|
||
|
|
}
|
||
|
|
func (c *IntIntervalConstraint) Eval(*Graph) Range { return c.I }
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) Futures() []ssa.Value {
|
||
|
|
return []ssa.Value{c.B}
|
||
|
|
}
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) Resolve() {
|
||
|
|
r, ok := c.ranges[c.B].(IntInterval)
|
||
|
|
if !ok {
|
||
|
|
c.I = InfinityFor(c.Y())
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
switch c.Op {
|
||
|
|
case token.EQL:
|
||
|
|
c.I = r
|
||
|
|
case token.GTR:
|
||
|
|
c.I = NewIntInterval(r.Lower.Add(NewZ(1)), PInfinity)
|
||
|
|
case token.GEQ:
|
||
|
|
c.I = NewIntInterval(r.Lower, PInfinity)
|
||
|
|
case token.LSS:
|
||
|
|
// TODO(dh): do we need 0 instead of NInfinity for uints?
|
||
|
|
c.I = NewIntInterval(NInfinity, r.Upper.Sub(NewZ(1)))
|
||
|
|
case token.LEQ:
|
||
|
|
c.I = NewIntInterval(NInfinity, r.Upper)
|
||
|
|
case token.NEQ:
|
||
|
|
c.I = InfinityFor(c.Y())
|
||
|
|
default:
|
||
|
|
panic("unsupported op " + c.Op.String())
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) IsKnown() bool {
|
||
|
|
return c.I.IsKnown()
|
||
|
|
}
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) MarkUnresolved() {
|
||
|
|
c.resolved = false
|
||
|
|
}
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) MarkResolved() {
|
||
|
|
c.resolved = true
|
||
|
|
}
|
||
|
|
|
||
|
|
func (c *IntIntersectionConstraint) IsResolved() bool {
|
||
|
|
return c.resolved
|
||
|
|
}
|