src/cmd/compile/internal/ssa/_gen/generic.rules

// Copyright 2015 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.

// Simplifications that apply to all backend architectures. As an example, this
// Go source code
//
// y := 0 * x
//
// can be translated into y := 0 without losing any information, which saves a
// pointless multiplication instruction. Other .rules files in this directory
// (for example AMD64.rules) contain rules specific to the architecture in the
// filename. The rules here apply to every architecture.
//
// The code for parsing this file lives in rulegen.go; this file generates
// ssa/rewritegeneric.go.

// values are specified using the following format:
// (op <type> [auxint] {aux} arg0 arg1 ...)
// the type, aux, and auxint fields are optional
// on the matching side
//  - the type, aux, and auxint fields must match if they are specified.
//  - the first occurrence of a variable defines that variable.  Subsequent
//    uses must match (be == to) the first use.
//  - v is defined to be the value matched.
//  - an additional conditional can be provided after the match pattern with "&&".
// on the generated side
//  - the type of the top-level expression is the same as the one on the left-hand side.
//  - the type of any subexpressions must be specified explicitly (or
//    be specified in the op's type field).
//  - auxint will be 0 if not specified.
//  - aux will be nil if not specified.

// blocks are specified using the following format:
// (kind controlvalue succ0 succ1 ...)
// controlvalue must be "nil" or a value expression
// succ* fields must be variables
// For now, the generated successors must be a permutation of the matched successors.

// constant folding
(Trunc16to8  (Const16  [c])) => (Const8   [int8(c)])
(Trunc32to8  (Const32  [c])) => (Const8   [int8(c)])
(Trunc32to16 (Const32  [c])) => (Const16  [int16(c)])
(Trunc64to8  (Const64  [c])) => (Const8   [int8(c)])
(Trunc64to16 (Const64  [c])) => (Const16  [int16(c)])
(Trunc64to32 (Const64  [c])) => (Const32  [int32(c)])
(Cvt64Fto32F (Const64F [c])) => (Const32F [float32(c)])
(Cvt32Fto64F (Const32F [c])) => (Const64F [float64(c)])
(Cvt32to32F  (Const32  [c])) => (Const32F [float32(c)])
(Cvt32to64F  (Const32  [c])) => (Const64F [float64(c)])
(Cvt64to32F  (Const64  [c])) => (Const32F [float32(c)])
(Cvt64to64F  (Const64  [c])) => (Const64F [float64(c)])
(Cvt32Fto32  (Const32F [c])) => (Const32  [int32(c)])
(Cvt32Fto64  (Const32F [c])) => (Const64  [int64(c)])
(Cvt64Fto32  (Const64F [c])) => (Const32  [int32(c)])
(Cvt64Fto64  (Const64F [c])) => (Const64  [int64(c)])
(Round32F x:(Const32F)) => x
(Round64F x:(Const64F)) => x
(CvtBoolToUint8 (ConstBool [false])) => (Const8 [0])
(CvtBoolToUint8 (ConstBool [true])) => (Const8 [1])
(BitLen64 (Const64 [c])) && config.PtrSize == 8 => (Const64 [int64(bits.Len64(uint64(c)))])
(BitLen32 (Const32 [c])) && config.PtrSize == 8 => (Const64 [int64(bits.Len32(uint32(c)))])
(BitLen16 (Const16 [c])) && config.PtrSize == 8 => (Const64 [int64(bits.Len16(uint16(c)))])
(BitLen8  (Const8  [c])) && config.PtrSize == 8 => (Const64 [int64(bits.Len8(uint8(c)))])
(BitLen64 (Const64 [c])) && config.PtrSize == 4 => (Const32 [int32(bits.Len64(uint64(c)))])
(BitLen32 (Const32 [c])) && config.PtrSize == 4 => (Const32 [int32(bits.Len32(uint32(c)))])
(BitLen16 (Const16 [c])) && config.PtrSize == 4 => (Const32 [int32(bits.Len16(uint16(c)))])
(BitLen8  (Const8  [c])) && config.PtrSize == 4 => (Const32 [int32(bits.Len8(uint8(c)))])

(Trunc16to8  (ZeroExt8to16  x)) => x
(Trunc32to8  (ZeroExt8to32  x)) => x
(Trunc32to16 (ZeroExt8to32  x)) => (ZeroExt8to16  x)
(Trunc32to16 (ZeroExt16to32 x)) => x
(Trunc64to8  (ZeroExt8to64  x)) => x
(Trunc64to16 (ZeroExt8to64  x)) => (ZeroExt8to16  x)
(Trunc64to16 (ZeroExt16to64 x)) => x
(Trunc64to32 (ZeroExt8to64  x)) => (ZeroExt8to32  x)
(Trunc64to32 (ZeroExt16to64 x)) => (ZeroExt16to32 x)
(Trunc64to32 (ZeroExt32to64 x)) => x
(Trunc16to8  (SignExt8to16  x)) => x
(Trunc32to8  (SignExt8to32  x)) => x
(Trunc32to16 (SignExt8to32  x)) => (SignExt8to16  x)
(Trunc32to16 (SignExt16to32 x)) => x
(Trunc64to8  (SignExt8to64  x)) => x
(Trunc64to16 (SignExt8to64  x)) => (SignExt8to16  x)
(Trunc64to16 (SignExt16to64 x)) => x
(Trunc64to32 (SignExt8to64  x)) => (SignExt8to32  x)
(Trunc64to32 (SignExt16to64 x)) => (SignExt16to32 x)
(Trunc64to32 (SignExt32to64 x)) => x

(ZeroExt8to16  (Const8  [c])) => (Const16 [int16( uint8(c))])
(ZeroExt8to32  (Const8  [c])) => (Const32 [int32( uint8(c))])
(ZeroExt8to64  (Const8  [c])) => (Const64 [int64( uint8(c))])
(ZeroExt16to32 (Const16 [c])) => (Const32 [int32(uint16(c))])
(ZeroExt16to64 (Const16 [c])) => (Const64 [int64(uint16(c))])
(ZeroExt32to64 (Const32 [c])) => (Const64 [int64(uint32(c))])
(SignExt8to16  (Const8  [c])) => (Const16 [int16(c)])
(SignExt8to32  (Const8  [c])) => (Const32 [int32(c)])
(SignExt8to64  (Const8  [c])) => (Const64 [int64(c)])
(SignExt16to32 (Const16 [c])) => (Const32 [int32(c)])
(SignExt16to64 (Const16 [c])) => (Const64 [int64(c)])
(SignExt32to64 (Const32 [c])) => (Const64 [int64(c)])

(Neg8   (Const8   [c])) => (Const8   [-c])
(Neg16  (Const16  [c])) => (Const16  [-c])
(Neg32  (Const32  [c])) => (Const32  [-c])
(Neg64  (Const64  [c])) => (Const64  [-c])
(Neg32F (Const32F [c])) && c != 0 => (Const32F [-c])
(Neg64F (Const64F [c])) && c != 0 => (Const64F [-c])

(Add8   (Const8 [c])   (Const8 [d]))   => (Const8  [c+d])
(Add16  (Const16 [c])  (Const16 [d]))  => (Const16 [c+d])
(Add32  (Const32 [c])  (Const32 [d]))  => (Const32 [c+d])
(Add64  (Const64 [c])  (Const64 [d]))  => (Const64 [c+d])
(Add32F (Const32F [c]) (Const32F [d])) && c+d == c+d => (Const32F [c+d])
(Add64F (Const64F [c]) (Const64F [d])) && c+d == c+d => (Const64F [c+d])
(AddPtr <t> x (Const64 [c])) => (OffPtr <t> x [c])
(AddPtr <t> x (Const32 [c])) => (OffPtr <t> x [int64(c)])

(Sub8   (Const8 [c]) (Const8 [d]))     => (Const8 [c-d])
(Sub16  (Const16 [c]) (Const16 [d]))   => (Const16 [c-d])
(Sub32  (Const32 [c]) (Const32 [d]))   => (Const32 [c-d])
(Sub64  (Const64 [c]) (Const64 [d]))   => (Const64 [c-d])
(Sub32F (Const32F [c]) (Const32F [d])) && c-d == c-d => (Const32F [c-d])
(Sub64F (Const64F [c]) (Const64F [d])) && c-d == c-d => (Const64F [c-d])

(Mul8   (Const8 [c])   (Const8 [d]))   => (Const8  [c*d])
(Mul16  (Const16 [c])  (Const16 [d]))  => (Const16 [c*d])
(Mul32  (Const32 [c])  (Const32 [d]))  => (Const32 [c*d])
(Mul64  (Const64 [c])  (Const64 [d]))  => (Const64 [c*d])
(Mul32F (Const32F [c]) (Const32F [d])) && c*d == c*d => (Const32F [c*d])
(Mul64F (Const64F [c]) (Const64F [d])) && c*d == c*d => (Const64F [c*d])

(And8   (Const8 [c])   (Const8 [d]))   => (Const8  [c&d])
(And16  (Const16 [c])  (Const16 [d]))  => (Const16 [c&d])
(And32  (Const32 [c])  (Const32 [d]))  => (Const32 [c&d])
(And64  (Const64 [c])  (Const64 [d]))  => (Const64 [c&d])

(Or8   (Const8 [c])   (Const8 [d]))   => (Const8  [c|d])
(Or16  (Const16 [c])  (Const16 [d]))  => (Const16 [c|d])
(Or32  (Const32 [c])  (Const32 [d]))  => (Const32 [c|d])
(Or64  (Const64 [c])  (Const64 [d]))  => (Const64 [c|d])

(Xor8   (Const8 [c])   (Const8 [d]))   => (Const8  [c^d])
(Xor16  (Const16 [c])  (Const16 [d]))  => (Const16 [c^d])
(Xor32  (Const32 [c])  (Const32 [d]))  => (Const32 [c^d])
(Xor64  (Const64 [c])  (Const64 [d]))  => (Const64 [c^d])

(Ctz64 (Const64 [c])) && config.PtrSize == 4 => (Const32 [int32(ntz64(c))])
(Ctz32 (Const32 [c])) && config.PtrSize == 4 => (Const32 [int32(ntz32(c))])
(Ctz16 (Const16 [c])) && config.PtrSize == 4 => (Const32 [int32(ntz16(c))])
(Ctz8  (Const8  [c])) && config.PtrSize == 4 => (Const32 [int32(ntz8(c))])

(Ctz64 (Const64 [c])) && config.PtrSize == 8 => (Const64 [int64(ntz64(c))])
(Ctz32 (Const32 [c])) && config.PtrSize == 8 => (Const64 [int64(ntz32(c))])
(Ctz16 (Const16 [c])) && config.PtrSize == 8 => (Const64 [int64(ntz16(c))])
(Ctz8  (Const8  [c])) && config.PtrSize == 8 => (Const64 [int64(ntz8(c))])

(Div8   (Const8  [c])  (Const8  [d])) && d != 0 => (Const8  [c/d])
(Div16  (Const16 [c])  (Const16 [d])) && d != 0 => (Const16 [c/d])
(Div32  (Const32 [c])  (Const32 [d])) && d != 0 => (Const32 [c/d])
(Div64  (Const64 [c])  (Const64 [d])) && d != 0 => (Const64 [c/d])
(Div8u  (Const8  [c])  (Const8  [d])) && d != 0 => (Const8  [int8(uint8(c)/uint8(d))])
(Div16u (Const16 [c])  (Const16 [d])) && d != 0 => (Const16 [int16(uint16(c)/uint16(d))])
(Div32u (Const32 [c])  (Const32 [d])) && d != 0 => (Const32 [int32(uint32(c)/uint32(d))])
(Div64u (Const64 [c])  (Const64 [d])) && d != 0 => (Const64 [int64(uint64(c)/uint64(d))])
(Div32F (Const32F [c]) (Const32F [d])) && c/d == c/d => (Const32F [c/d])
(Div64F (Const64F [c]) (Const64F [d])) && c/d == c/d => (Const64F [c/d])
(Select0 (Div128u (Const64 [0]) lo y)) => (Div64u lo y)
(Select1 (Div128u (Const64 [0]) lo y)) => (Mod64u lo y)

(Not (ConstBool [c])) => (ConstBool [!c])

(Floor       (Const64F [c])) => (Const64F [math.Floor(c)])
(Ceil        (Const64F [c])) => (Const64F [math.Ceil(c)])
(Trunc       (Const64F [c])) => (Const64F [math.Trunc(c)])
(RoundToEven (Const64F [c])) => (Const64F [math.RoundToEven(c)])

// Convert x * 1 to x.
(Mul(8|16|32|64)  (Const(8|16|32|64)  [1]) x) => x
(Select0 (Mul(32|64)uover (Const(32|64) [1]) x)) => x
(Select1 (Mul(32|64)uover (Const(32|64) [1]) x)) => (ConstBool [false])

// Convert x * -1 to -x.
(Mul(8|16|32|64)  (Const(8|16|32|64)  [-1]) x) => (Neg(8|16|32|64)  x)

// DeMorgan's Laws
(And(8|16|32|64) <t> (Com(8|16|32|64) x) (Com(8|16|32|64) y)) => (Com(8|16|32|64) (Or(8|16|32|64) <t> x y))
(Or(8|16|32|64) <t> (Com(8|16|32|64) x) (Com(8|16|32|64) y)) => (Com(8|16|32|64) (And(8|16|32|64) <t> x y))

// Convert multiplication by a power of two to a shift.
(Mul8  <t> n (Const8  [c])) && isPowerOfTwo8(c) => (Lsh8x64  <t> n (Const64 <typ.UInt64> [log8(c)]))
(Mul16 <t> n (Const16 [c])) && isPowerOfTwo16(c) => (Lsh16x64 <t> n (Const64 <typ.UInt64> [log16(c)]))
(Mul32 <t> n (Const32 [c])) && isPowerOfTwo32(c) => (Lsh32x64 <t> n (Const64 <typ.UInt64> [log32(c)]))
(Mul64 <t> n (Const64 [c])) && isPowerOfTwo64(c) => (Lsh64x64 <t> n (Const64 <typ.UInt64> [log64(c)]))
(Mul8  <t> n (Const8  [c])) && t.IsSigned() && isPowerOfTwo8(-c)  => (Neg8  (Lsh8x64  <t> n (Const64 <typ.UInt64> [log8(-c)])))
(Mul16 <t> n (Const16 [c])) && t.IsSigned() && isPowerOfTwo16(-c) => (Neg16 (Lsh16x64 <t> n (Const64 <typ.UInt64> [log16(-c)])))
(Mul32 <t> n (Const32 [c])) && t.IsSigned() && isPowerOfTwo32(-c) => (Neg32 (Lsh32x64 <t> n (Const64 <typ.UInt64> [log32(-c)])))
(Mul64 <t> n (Const64 [c])) && t.IsSigned() && isPowerOfTwo64(-c) => (Neg64 (Lsh64x64 <t> n (Const64 <typ.UInt64> [log64(-c)])))

(Mod8  (Const8  [c]) (Const8  [d])) && d != 0 => (Const8  [c % d])
(Mod16 (Const16 [c]) (Const16 [d])) && d != 0 => (Const16 [c % d])
(Mod32 (Const32 [c]) (Const32 [d])) && d != 0 => (Const32 [c % d])
(Mod64 (Const64 [c]) (Const64 [d])) && d != 0 => (Const64 [c % d])

(Mod8u  (Const8 [c])  (Const8  [d])) && d != 0 => (Const8  [int8(uint8(c) % uint8(d))])
(Mod16u (Const16 [c]) (Const16 [d])) && d != 0 => (Const16 [int16(uint16(c) % uint16(d))])
(Mod32u (Const32 [c]) (Const32 [d])) && d != 0 => (Const32 [int32(uint32(c) % uint32(d))])
(Mod64u (Const64 [c]) (Const64 [d])) && d != 0 => (Const64 [int64(uint64(c) % uint64(d))])

(Lsh64x64  (Const64 [c]) (Const64 [d])) => (Const64 [c << uint64(d)])
(Rsh64x64  (Const64 [c]) (Const64 [d])) => (Const64 [c >> uint64(d)])
(Rsh64Ux64 (Const64 [c]) (Const64 [d])) => (Const64 [int64(uint64(c) >> uint64(d))])
(Lsh32x64  (Const32 [c]) (Const64 [d])) => (Const32 [c << uint64(d)])
(Rsh32x64  (Const32 [c]) (Const64 [d])) => (Const32 [c >> uint64(d)])
(Rsh32Ux64 (Const32 [c]) (Const64 [d])) => (Const32 [int32(uint32(c) >> uint64(d))])
(Lsh16x64  (Const16 [c]) (Const64 [d])) => (Const16 [c << uint64(d)])
(Rsh16x64  (Const16 [c]) (Const64 [d])) => (Const16 [c >> uint64(d)])
(Rsh16Ux64 (Const16 [c]) (Const64 [d])) => (Const16 [int16(uint16(c) >> uint64(d))])
(Lsh8x64   (Const8  [c]) (Const64 [d])) => (Const8  [c << uint64(d)])
(Rsh8x64   (Const8  [c]) (Const64 [d])) => (Const8  [c >> uint64(d)])
(Rsh8Ux64  (Const8  [c]) (Const64 [d])) => (Const8  [int8(uint8(c) >> uint64(d))])

// Fold IsInBounds when the range of the index cannot exceed the limit.
(IsInBounds (ZeroExt8to32  _) (Const32 [c])) && (1 << 8)  <= c => (ConstBool [true])
(IsInBounds (ZeroExt8to64  _) (Const64 [c])) && (1 << 8)  <= c => (ConstBool [true])
(IsInBounds (ZeroExt16to32 _) (Const32 [c])) && (1 << 16) <= c => (ConstBool [true])
(IsInBounds (ZeroExt16to64 _) (Const64 [c])) && (1 << 16) <= c => (ConstBool [true])
(IsInBounds x x) => (ConstBool [false])
(IsInBounds                (And8  (Const8  [c]) _)  (Const8  [d])) && 0 <= c && c < d => (ConstBool [true])
(IsInBounds (ZeroExt8to16  (And8  (Const8  [c]) _)) (Const16 [d])) && 0 <= c && int16(c) < d => (ConstBool [true])
(IsInBounds (ZeroExt8to32  (And8  (Const8  [c]) _)) (Const32 [d])) && 0 <= c && int32(c) < d => (ConstBool [true])
(IsInBounds (ZeroExt8to64  (And8  (Const8  [c]) _)) (Const64 [d])) && 0 <= c && int64(c) < d => (ConstBool [true])
(IsInBounds                (And16 (Const16 [c]) _)  (Const16 [d])) && 0 <= c && c < d => (ConstBool [true])
(IsInBounds (ZeroExt16to32 (And16 (Const16 [c]) _)) (Const32 [d])) && 0 <= c && int32(c) < d => (ConstBool [true])
(IsInBounds (ZeroExt16to64 (And16 (Const16 [c]) _)) (Const64 [d])) && 0 <= c && int64(c) < d => (ConstBool [true])
(IsInBounds                (And32 (Const32 [c]) _)  (Const32 [d])) && 0 <= c && c < d => (ConstBool [true])
(IsInBounds (ZeroExt32to64 (And32 (Const32 [c]) _)) (Const64 [d])) && 0 <= c && int64(c) < d => (ConstBool [true])
(IsInBounds                (And64 (Const64 [c]) _)  (Const64 [d])) && 0 <= c && c < d => (ConstBool [true])
(IsInBounds (Const32 [c]) (Const32 [d])) => (ConstBool [0 <= c && c < d])
(IsInBounds (Const64 [c]) (Const64 [d])) => (ConstBool [0 <= c && c < d])
// (Mod64u x y) is always between 0 (inclusive) and y (exclusive).
(IsInBounds (Mod32u _ y) y) => (ConstBool [true])
(IsInBounds (Mod64u _ y) y) => (ConstBool [true])
// Right shifting an unsigned number limits its value.
(IsInBounds (ZeroExt8to64  (Rsh8Ux64  _ (Const64 [c]))) (Const64 [d])) && 0 < c && c <  8 && 1<<uint( 8-c)-1 < d => (ConstBool [true])
(IsInBounds (ZeroExt8to32  (Rsh8Ux64  _ (Const64 [c]))) (Const32 [d])) && 0 < c && c <  8 && 1<<uint( 8-c)-1 < d => (ConstBool [true])
(IsInBounds (ZeroExt8to16  (Rsh8Ux64  _ (Const64 [c]))) (Const16 [d])) && 0 < c && c <  8 && 1<<uint( 8-c)-1 < d => (ConstBool [true])
(IsInBounds                (Rsh8Ux64  _ (Const64 [c]))  (Const64 [d])) && 0 < c && c <  8 && 1<<uint( 8-c)-1 < d => (ConstBool [true])
(IsInBounds (ZeroExt16to64 (Rsh16Ux64 _ (Const64 [c]))) (Const64 [d])) && 0 < c && c < 16 && 1<<uint(16-c)-1 < d => (ConstBool [true])
(IsInBounds (ZeroExt16to32 (Rsh16Ux64 _ (Const64 [c]))) (Const64 [d])) && 0 < c && c < 16 && 1<<uint(16-c)-1 < d => (ConstBool [true])
(IsInBounds                (Rsh16Ux64 _ (Const64 [c]))  (Const64 [d])) && 0 < c && c < 16 && 1<<uint(16-c)-1 < d => (ConstBool [true])
(IsInBounds (ZeroExt32to64 (Rsh32Ux64 _ (Const64 [c]))) (Const64 [d])) && 0 < c && c < 32 && 1<<uint(32-c)-1 < d => (ConstBool [true])
(IsInBounds                (Rsh32Ux64 _ (Const64 [c]))  (Const64 [d])) && 0 < c && c < 32 && 1<<uint(32-c)-1 < d => (ConstBool [true])
(IsInBounds                (Rsh64Ux64 _ (Const64 [c]))  (Const64 [d])) && 0 < c && c < 64 && 1<<uint(64-c)-1 < d => (ConstBool [true])

(IsSliceInBounds x x) => (ConstBool [true])
(IsSliceInBounds (And32 (Const32 [c]) _) (Const32 [d])) && 0 <= c && c <= d => (ConstBool [true])
(IsSliceInBounds (And64 (Const64 [c]) _) (Const64 [d])) && 0 <= c && c <= d => (ConstBool [true])
(IsSliceInBounds (Const32 [0]) _) => (ConstBool [true])
(IsSliceInBounds (Const64 [0]) _) => (ConstBool [true])
(IsSliceInBounds (Const32 [c]) (Const32 [d])) => (ConstBool [0 <= c && c <= d])
(IsSliceInBounds (Const64 [c]) (Const64 [d])) => (ConstBool [0 <= c && c <= d])
(IsSliceInBounds (SliceLen x) (SliceCap x)) => (ConstBool [true])

(Eq(64|32|16|8) x x) => (ConstBool [true])
(EqB (ConstBool [c]) (ConstBool [d])) => (ConstBool [c == d])
(EqB (ConstBool [false]) x) => (Not x)
(EqB (ConstBool [true]) x) => x

(Neq(64|32|16|8) x x) => (ConstBool [false])
(NeqB (ConstBool [c]) (ConstBool [d])) => (ConstBool [c != d])
(NeqB (ConstBool [false]) x) => x
(NeqB (ConstBool [true]) x) => (Not x)
(NeqB (Not x) (Not y)) => (NeqB x y)

(Eq64 (Const64 <t> [c]) (Add64 (Const64 <t> [d]) x)) => (Eq64 (Const64 <t> [c-d]) x)
(Eq32 (Const32 <t> [c]) (Add32 (Const32 <t> [d]) x)) => (Eq32 (Const32 <t> [c-d]) x)
(Eq16 (Const16 <t> [c]) (Add16 (Const16 <t> [d]) x)) => (Eq16 (Const16 <t> [c-d]) x)
(Eq8  (Const8  <t> [c]) (Add8  (Const8  <t> [d]) x)) => (Eq8  (Const8  <t> [c-d]) x)

(Neq64 (Const64 <t> [c]) (Add64 (Const64 <t> [d]) x)) => (Neq64 (Const64 <t> [c-d]) x)
(Neq32 (Const32 <t> [c]) (Add32 (Const32 <t> [d]) x)) => (Neq32 (Const32 <t> [c-d]) x)
(Neq16 (Const16 <t> [c]) (Add16 (Const16 <t> [d]) x)) => (Neq16 (Const16 <t> [c-d]) x)
(Neq8  (Const8  <t> [c]) (Add8  (Const8  <t> [d]) x)) => (Neq8  (Const8  <t> [c-d]) x)

// signed integer range: ( c <= x && x (<|<=) d ) -> ( unsigned(x-c) (<|<=) unsigned(d-c) )
(AndB (Leq64 (Const64 [c]) x) ((Less|Leq)64 x (Const64 [d]))) && d >= c => ((Less|Leq)64U (Sub64 <x.Type> x (Const64 <x.Type> [c])) (Const64 <x.Type> [d-c]))
(AndB (Leq32 (Const32 [c]) x) ((Less|Leq)32 x (Const32 [d]))) && d >= c => ((Less|Leq)32U (Sub32 <x.Type> x (Const32 <x.Type> [c])) (Const32 <x.Type> [d-c]))
(AndB (Leq16 (Const16 [c]) x) ((Less|Leq)16 x (Const16 [d]))) && d >= c => ((Less|Leq)16U (Sub16 <x.Type> x (Const16 <x.Type> [c])) (Const16 <x.Type> [d-c]))
(AndB (Leq8  (Const8  [c]) x) ((Less|Leq)8  x (Const8  [d]))) && d >= c => ((Less|Leq)8U  (Sub8  <x.Type> x (Const8  <x.Type> [c])) (Const8  <x.Type> [d-c]))

// signed integer range: ( c < x && x (<|<=) d ) -> ( unsigned(x-(c+1)) (<|<=) unsigned(d-(c+1)) )
(AndB (Less64 (Const64 [c]) x) ((Less|Leq)64 x (Const64 [d]))) && d >= c+1 && c+1 > c => ((Less|Leq)64U (Sub64 <x.Type> x (Const64 <x.Type> [c+1])) (Const64 <x.Type> [d-c-1]))
(AndB (Less32 (Const32 [c]) x) ((Less|Leq)32 x (Const32 [d]))) && d >= c+1 && c+1 > c => ((Less|Leq)32U (Sub32 <x.Type> x (Const32 <x.Type> [c+1])) (Const32 <x.Type> [d-c-1]))
(AndB (Less16 (Const16 [c]) x) ((Less|Leq)16 x (Const16 [d]))) && d >= c+1 && c+1 > c => ((Less|Leq)16U (Sub16 <x.Type> x (Const16 <x.Type> [c+1])) (Const16 <x.Type> [d-c-1]))
(AndB (Less8  (Const8  [c]) x) ((Less|Leq)8  x (Const8  [d]))) && d >= c+1 && c+1 > c => ((Less|Leq)8U  (Sub8  <x.Type> x (Const8  <x.Type> [c+1])) (Const8  <x.Type> [d-c-1]))

// unsigned integer range: ( c <= x && x (<|<=) d ) -> ( x-c (<|<=) d-c )
(AndB (Leq64U (Const64 [c]) x) ((Less|Leq)64U x (Const64 [d]))) && uint64(d) >= uint64(c) => ((Less|Leq)64U (Sub64 <x.Type> x (Const64 <x.Type> [c])) (Const64 <x.Type> [d-c]))
(AndB (Leq32U (Const32 [c]) x) ((Less|Leq)32U x (Const32 [d]))) && uint32(d) >= uint32(c) => ((Less|Leq)32U (Sub32 <x.Type> x (Const32 <x.Type> [c])) (Const32 <x.Type> [d-c]))
(AndB (Leq16U (Const16 [c]) x) ((Less|Leq)16U x (Const16 [d]))) && uint16(d) >= uint16(c) => ((Less|Leq)16U (Sub16 <x.Type> x (Const16 <x.Type> [c])) (Const16 <x.Type> [d-c]))
(AndB (Leq8U  (Const8  [c]) x) ((Less|Leq)8U  x (Const8  [d]))) && uint8(d)  >= uint8(c)  => ((Less|Leq)8U  (Sub8  <x.Type> x (Const8  <x.Type> [c])) (Const8  <x.Type> [d-c]))

// unsigned integer range: ( c < x && x (<|<=) d ) -> ( x-(c+1) (<|<=) d-(c+1) )
(AndB (Less64U (Const64 [c]) x) ((Less|Leq)64U x (Const64 [d]))) && uint64(d) >= uint64(c+1) && uint64(c+1) > uint64(c) => ((Less|Leq)64U (Sub64 <x.Type> x (Const64 <x.Type> [c+1])) (Const64 <x.Type> [d-c-1]))
(AndB (Less32U (Const32 [c]) x) ((Less|Leq)32U x (Const32 [d]))) && uint32(d) >= uint32(c+1) && uint32(c+1) > uint32(c) => ((Less|Leq)32U (Sub32 <x.Type> x (Const32 <x.Type> [c+1])) (Const32 <x.Type> [d-c-1]))
(AndB (Less16U (Const16 [c]) x) ((Less|Leq)16U x (Const16 [d]))) && uint16(d) >= uint16(c+1) && uint16(c+1) > uint16(c) => ((Less|Leq)16U (Sub16 <x.Type> x (Const16 <x.Type> [c+1])) (Const16 <x.Type> [d-c-1]))
(AndB (Less8U  (Const8  [c]) x) ((Less|Leq)8U  x (Const8  [d]))) && uint8(d)  >= uint8(c+1)  && uint8(c+1)  > uint8(c)  => ((Less|Leq)8U  (Sub8  <x.Type> x (Const8  <x.Type> [c+1]))  (Const8  <x.Type> [d-c-1]))

// signed integer range: ( c (<|<=) x || x < d ) -> ( unsigned(c-d) (<|<=) unsigned(x-d) )
(OrB ((Less|Leq)64 (Const64 [c]) x) (Less64 x (Const64 [d]))) && c >= d => ((Less|Leq)64U (Const64 <x.Type> [c-d]) (Sub64 <x.Type> x (Const64 <x.Type> [d])))
(OrB ((Less|Leq)32 (Const32 [c]) x) (Less32 x (Const32 [d]))) && c >= d => ((Less|Leq)32U (Const32 <x.Type> [c-d]) (Sub32 <x.Type> x (Const32 <x.Type> [d])))
(OrB ((Less|Leq)16 (Const16 [c]) x) (Less16 x (Const16 [d]))) && c >= d => ((Less|Leq)16U (Const16 <x.Type> [c-d]) (Sub16 <x.Type> x (Const16 <x.Type> [d])))
(OrB ((Less|Leq)8  (Const8  [c]) x) (Less8  x (Const8  [d]))) && c >= d => ((Less|Leq)8U  (Const8  <x.Type> [c-d]) (Sub8  <x.Type> x (Const8  <x.Type> [d])))

// signed integer range: ( c (<|<=) x || x <= d ) -> ( unsigned(c-(d+1)) (<|<=) unsigned(x-(d+1)) )
(OrB ((Less|Leq)64 (Const64 [c]) x) (Leq64 x (Const64 [d]))) && c >= d+1 && d+1 > d => ((Less|Leq)64U (Const64 <x.Type> [c-d-1]) (Sub64 <x.Type> x (Const64 <x.Type> [d+1])))
(OrB ((Less|Leq)32 (Const32 [c]) x) (Leq32 x (Const32 [d]))) && c >= d+1 && d+1 > d => ((Less|Leq)32U (Const32 <x.Type> [c-d-1]) (Sub32 <x.Type> x (Const32 <x.Type> [d+1])))
(OrB ((Less|Leq)16 (Const16 [c]) x) (Leq16 x (Const16 [d]))) && c >= d+1 && d+1 > d => ((Less|Leq)16U (Const16 <x.Type> [c-d-1]) (Sub16 <x.Type> x (Const16 <x.Type> [d+1])))
(OrB ((Less|Leq)8  (Const8  [c]) x) (Leq8  x (Const8  [d]))) && c >= d+1 && d+1 > d => ((Less|Leq)8U  (Const8  <x.Type> [c-d-1]) (Sub8  <x.Type> x (Const8  <x.Type> [d+1])))

// unsigned integer range: ( c (<|<=) x || x < d ) -> ( c-d (<|<=) x-d )
(OrB ((Less|Leq)64U (Const64 [c]) x) (Less64U x (Const64 [d]))) && uint64(c) >= uint64(d) => ((Less|Leq)64U (Const64 <x.Type> [c-d]) (Sub64 <x.Type> x (Const64 <x.Type> [d])))
(OrB ((Less|Leq)32U (Const32 [c]) x) (Less32U x (Const32 [d]))) && uint32(c) >= uint32(d) => ((Less|Leq)32U (Const32 <x.Type> [c-d]) (Sub32 <x.Type> x (Const32 <x.Type> [d])))
(OrB ((Less|Leq)16U (Const16 [c]) x) (Less16U x (Const16 [d]))) && uint16(c) >= uint16(d) => ((Less|Leq)16U (Const16 <x.Type> [c-d]) (Sub16 <x.Type> x (Const16 <x.Type> [d])))
(OrB ((Less|Leq)8U  (Const8  [c]) x) (Less8U  x (Const8  [d]))) && uint8(c)  >= uint8(d)  => ((Less|Leq)8U  (Const8  <x.Type> [c-d]) (Sub8  <x.Type> x (Const8  <x.Type> [d])))

// unsigned integer range: ( c (<|<=) x || x <= d ) -> ( c-(d+1) (<|<=) x-(d+1) )
(OrB ((Less|Leq)64U (Const64 [c]) x) (Leq64U x (Const64 [d]))) && uint64(c) >= uint64(d+1) && uint64(d+1) > uint64(d) => ((Less|Leq)64U (Const64 <x.Type> [c-d-1]) (Sub64 <x.Type> x (Const64 <x.Type> [d+1])))
(OrB ((Less|Leq)32U (Const32 [c]) x) (Leq32U x (Const32 [d]))) && uint32(c) >= uint32(d+1) && uint32(d+1) > uint32(d) => ((Less|Leq)32U (Const32 <x.Type> [c-d-1]) (Sub32 <x.Type> x (Const32 <x.Type> [d+1])))
(OrB ((Less|Leq)16U (Const16 [c]) x) (Leq16U x (Const16 [d]))) && uint16(c) >= uint16(d+1) && uint16(d+1) > uint16(d) => ((Less|Leq)16U (Const16 <x.Type> [c-d-1]) (Sub16 <x.Type> x (Const16 <x.Type> [d+1])))
(OrB ((Less|Leq)8U  (Const8  [c]) x) (Leq8U  x (Const8  [d]))) && uint8(c)  >= uint8(d+1)  && uint8(d+1)  > uint8(d)  => ((Less|Leq)8U  (Const8  <x.Type> [c-d-1]) (Sub8  <x.Type> x (Const8  <x.Type> [d+1])))

// Canonicalize x-const to x+(-const)
(Sub64 x (Const64 <t> [c])) && x.Op != OpConst64 => (Add64 (Const64 <t> [-c]) x)
(Sub32 x (Const32 <t> [c])) && x.Op != OpConst32 => (Add32 (Const32 <t> [-c]) x)
(Sub16 x (Const16 <t> [c])) && x.Op != OpConst16 => (Add16 (Const16 <t> [-c]) x)
(Sub8  x (Const8  <t> [c])) && x.Op != OpConst8  => (Add8  (Const8  <t> [-c]) x)

// fold negation into comparison operators
(Not (Eq(64|32|16|8|B|Ptr|64F|32F) x y)) => (Neq(64|32|16|8|B|Ptr|64F|32F) x y)
(Not (Neq(64|32|16|8|B|Ptr|64F|32F) x y)) => (Eq(64|32|16|8|B|Ptr|64F|32F) x y)

(Not (Less(64|32|16|8) x y)) => (Leq(64|32|16|8) y x)
(Not (Less(64|32|16|8)U x y)) => (Leq(64|32|16|8)U y x)
(Not (Leq(64|32|16|8) x y)) => (Less(64|32|16|8) y x)
(Not (Leq(64|32|16|8)U x y)) => (Less(64|32|16|8)U y x)

// Distribute multiplication c * (d+x) -> c*d + c*x. Useful for:
// a[i].b = ...; a[i+1].b = ...
(Mul64 (Const64 <t> [c]) (Add64 <t> (Const64 <t> [d]) x)) =>
  (Add64 (Const64 <t> [c*d]) (Mul64 <t> (Const64 <t> [c]) x))
(Mul32 (Const32 <t> [c]) (Add32 <t> (Const32 <t> [d]) x)) =>
  (Add32 (Const32 <t> [c*d]) (Mul32 <t> (Const32 <t> [c]) x))

// Rewrite x*y ± x*z  to  x*(y±z)
(Add(64|32|16|8) <t> (Mul(64|32|16|8) x y) (Mul(64|32|16|8) x z))
	=> (Mul(64|32|16|8) x (Add(64|32|16|8) <t> y z))
(Sub(64|32|16|8) <t> (Mul(64|32|16|8) x y) (Mul(64|32|16|8) x z))
	=> (Mul(64|32|16|8) x (Sub(64|32|16|8) <t> y z))

// rewrite shifts of 8/16/32 bit consts into 64 bit consts to reduce
// the number of the other rewrite rules for const shifts
(Lsh64x32  <t> x (Const32 [c])) => (Lsh64x64  x (Const64 <t> [int64(uint32(c))]))
(Lsh64x16  <t> x (Const16 [c])) => (Lsh64x64  x (Const64 <t> [int64(uint16(c))]))
(Lsh64x8   <t> x (Const8  [c])) => (Lsh64x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh64x32  <t> x (Const32 [c])) => (Rsh64x64  x (Const64 <t> [int64(uint32(c))]))
(Rsh64x16  <t> x (Const16 [c])) => (Rsh64x64  x (Const64 <t> [int64(uint16(c))]))
(Rsh64x8   <t> x (Const8  [c])) => (Rsh64x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh64Ux32 <t> x (Const32 [c])) => (Rsh64Ux64 x (Const64 <t> [int64(uint32(c))]))
(Rsh64Ux16 <t> x (Const16 [c])) => (Rsh64Ux64 x (Const64 <t> [int64(uint16(c))]))
(Rsh64Ux8  <t> x (Const8  [c])) => (Rsh64Ux64 x (Const64 <t> [int64(uint8(c))]))

(Lsh32x32  <t> x (Const32 [c])) => (Lsh32x64  x (Const64 <t> [int64(uint32(c))]))
(Lsh32x16  <t> x (Const16 [c])) => (Lsh32x64  x (Const64 <t> [int64(uint16(c))]))
(Lsh32x8   <t> x (Const8  [c])) => (Lsh32x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh32x32  <t> x (Const32 [c])) => (Rsh32x64  x (Const64 <t> [int64(uint32(c))]))
(Rsh32x16  <t> x (Const16 [c])) => (Rsh32x64  x (Const64 <t> [int64(uint16(c))]))
(Rsh32x8   <t> x (Const8  [c])) => (Rsh32x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh32Ux32 <t> x (Const32 [c])) => (Rsh32Ux64 x (Const64 <t> [int64(uint32(c))]))
(Rsh32Ux16 <t> x (Const16 [c])) => (Rsh32Ux64 x (Const64 <t> [int64(uint16(c))]))
(Rsh32Ux8  <t> x (Const8  [c])) => (Rsh32Ux64 x (Const64 <t> [int64(uint8(c))]))

(Lsh16x32  <t> x (Const32 [c])) => (Lsh16x64  x (Const64 <t> [int64(uint32(c))]))
(Lsh16x16  <t> x (Const16 [c])) => (Lsh16x64  x (Const64 <t> [int64(uint16(c))]))
(Lsh16x8   <t> x (Const8  [c])) => (Lsh16x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh16x32  <t> x (Const32 [c])) => (Rsh16x64  x (Const64 <t> [int64(uint32(c))]))
(Rsh16x16  <t> x (Const16 [c])) => (Rsh16x64  x (Const64 <t> [int64(uint16(c))]))
(Rsh16x8   <t> x (Const8  [c])) => (Rsh16x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh16Ux32 <t> x (Const32 [c])) => (Rsh16Ux64 x (Const64 <t> [int64(uint32(c))]))
(Rsh16Ux16 <t> x (Const16 [c])) => (Rsh16Ux64 x (Const64 <t> [int64(uint16(c))]))
(Rsh16Ux8  <t> x (Const8  [c])) => (Rsh16Ux64 x (Const64 <t> [int64(uint8(c))]))

(Lsh8x32  <t> x (Const32 [c])) => (Lsh8x64  x (Const64 <t> [int64(uint32(c))]))
(Lsh8x16  <t> x (Const16 [c])) => (Lsh8x64  x (Const64 <t> [int64(uint16(c))]))
(Lsh8x8   <t> x (Const8  [c])) => (Lsh8x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh8x32  <t> x (Const32 [c])) => (Rsh8x64  x (Const64 <t> [int64(uint32(c))]))
(Rsh8x16  <t> x (Const16 [c])) => (Rsh8x64  x (Const64 <t> [int64(uint16(c))]))
(Rsh8x8   <t> x (Const8  [c])) => (Rsh8x64  x (Const64 <t> [int64(uint8(c))]))
(Rsh8Ux32 <t> x (Const32 [c])) => (Rsh8Ux64 x (Const64 <t> [int64(uint32(c))]))
(Rsh8Ux16 <t> x (Const16 [c])) => (Rsh8Ux64 x (Const64 <t> [int64(uint16(c))]))
(Rsh8Ux8  <t> x (Const8  [c])) => (Rsh8Ux64 x (Const64 <t> [int64(uint8(c))]))

// shifts by zero
(Lsh(64|32|16|8)x64  x (Const64 [0])) => x
(Rsh(64|32|16|8)x64  x (Const64 [0])) => x
(Rsh(64|32|16|8)Ux64 x (Const64 [0])) => x

// rotates by multiples of register width
(RotateLeft64 x (Const64 [c])) && c%64 == 0 => x
(RotateLeft32 x (Const32 [c])) && c%32 == 0 => x
(RotateLeft16 x (Const16 [c])) && c%16 == 0 => x
(RotateLeft8  x (Const8 [c]))  && c%8  == 0 => x

// zero shifted
(Lsh64x(64|32|16|8)  (Const64 [0]) _) => (Const64 [0])
(Rsh64x(64|32|16|8)  (Const64 [0]) _) => (Const64 [0])
(Rsh64Ux(64|32|16|8) (Const64 [0]) _) => (Const64 [0])
(Lsh32x(64|32|16|8)  (Const32 [0]) _) => (Const32 [0])
(Rsh32x(64|32|16|8)  (Const32 [0]) _) => (Const32 [0])
(Rsh32Ux(64|32|16|8) (Const32 [0]) _) => (Const32 [0])
(Lsh16x(64|32|16|8)  (Const16 [0]) _) => (Const16 [0])
(Rsh16x(64|32|16|8)  (Const16 [0]) _) => (Const16 [0])
(Rsh16Ux(64|32|16|8) (Const16 [0]) _) => (Const16 [0])
(Lsh8x(64|32|16|8)   (Const8  [0]) _) => (Const8  [0])
(Rsh8x(64|32|16|8)   (Const8  [0]) _) => (Const8  [0])
(Rsh8Ux(64|32|16|8)  (Const8  [0]) _) => (Const8  [0])

// large left shifts of all values, and right shifts of unsigned values
((Lsh64|Rsh64U)x64  _ (Const64 [c])) && uint64(c) >= 64 => (Const64 [0])
((Lsh32|Rsh32U)x64  _ (Const64 [c])) && uint64(c) >= 32 => (Const32 [0])
((Lsh16|Rsh16U)x64  _ (Const64 [c])) && uint64(c) >= 16 => (Const16 [0])
((Lsh8|Rsh8U)x64    _ (Const64 [c])) && uint64(c) >= 8  => (Const8  [0])

// combine const shifts
(Lsh64x64 <t> (Lsh64x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Lsh64x64 x (Const64 <t> [c+d]))
(Lsh32x64 <t> (Lsh32x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Lsh32x64 x (Const64 <t> [c+d]))
(Lsh16x64 <t> (Lsh16x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Lsh16x64 x (Const64 <t> [c+d]))
(Lsh8x64  <t> (Lsh8x64  x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Lsh8x64  x (Const64 <t> [c+d]))

(Rsh64x64 <t> (Rsh64x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh64x64 x (Const64 <t> [c+d]))
(Rsh32x64 <t> (Rsh32x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh32x64 x (Const64 <t> [c+d]))
(Rsh16x64 <t> (Rsh16x64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh16x64 x (Const64 <t> [c+d]))
(Rsh8x64  <t> (Rsh8x64  x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh8x64  x (Const64 <t> [c+d]))

(Rsh64Ux64 <t> (Rsh64Ux64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh64Ux64 x (Const64 <t> [c+d]))
(Rsh32Ux64 <t> (Rsh32Ux64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh32Ux64 x (Const64 <t> [c+d]))
(Rsh16Ux64 <t> (Rsh16Ux64 x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh16Ux64 x (Const64 <t> [c+d]))
(Rsh8Ux64  <t> (Rsh8Ux64  x (Const64 [c])) (Const64 [d])) && !uaddOvf(c,d) => (Rsh8Ux64  x (Const64 <t> [c+d]))

// Remove signed right shift before an unsigned right shift that extracts the sign bit.
(Rsh8Ux64  (Rsh8x64  x _) (Const64 <t> [7] )) => (Rsh8Ux64  x (Const64 <t> [7] ))
(Rsh16Ux64 (Rsh16x64 x _) (Const64 <t> [15])) => (Rsh16Ux64 x (Const64 <t> [15]))
(Rsh32Ux64 (Rsh32x64 x _) (Const64 <t> [31])) => (Rsh32Ux64 x (Const64 <t> [31]))
(Rsh64Ux64 (Rsh64x64 x _) (Const64 <t> [63])) => (Rsh64Ux64 x (Const64 <t> [63]))

// Convert x>>c<<c to x&^(1<<c-1)
(Lsh64x64 i:(Rsh(64|64U)x64  x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 64 && i.Uses == 1 => (And64 x (Const64 <v.Type> [int64(-1) << c]))
(Lsh32x64 i:(Rsh(32|32U)x64  x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 32 && i.Uses == 1 => (And32 x (Const32 <v.Type> [int32(-1) << c]))
(Lsh16x64 i:(Rsh(16|16U)x64  x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 16 && i.Uses == 1 => (And16 x (Const16 <v.Type> [int16(-1) << c]))
(Lsh8x64  i:(Rsh(8|8U)x64    x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 8  && i.Uses == 1 => (And8  x (Const8  <v.Type> [int8(-1)  << c]))
// similarly for x<<c>>c
(Rsh64Ux64 i:(Lsh64x64 x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 64 && i.Uses == 1 => (And64 x (Const64 <v.Type> [int64(^uint64(0)>>c)]))
(Rsh32Ux64 i:(Lsh32x64 x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 32 && i.Uses == 1 => (And32 x (Const32 <v.Type> [int32(^uint32(0)>>c)]))
(Rsh16Ux64 i:(Lsh16x64 x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 16 && i.Uses == 1 => (And16 x (Const16 <v.Type> [int16(^uint16(0)>>c)]))
(Rsh8Ux64  i:(Lsh8x64  x (Const64 [c])) (Const64 [c])) && c >= 0 && c < 8  && i.Uses == 1 => (And8  x (Const8  <v.Type> [int8 (^uint8 (0)>>c)]))

// ((x >> c1) << c2) >> c3
(Rsh(64|32|16|8)Ux64 (Lsh(64|32|16|8)x64 (Rsh(64|32|16|8)Ux64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  => (Rsh(64|32|16|8)Ux64 x (Const64 <typ.UInt64> [c1-c2+c3]))

// ((x << c1) >> c2) << c3
(Lsh(64|32|16|8)x64 (Rsh(64|32|16|8)Ux64 (Lsh(64|32|16|8)x64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  => (Lsh(64|32|16|8)x64 x (Const64 <typ.UInt64> [c1-c2+c3]))

// (x >> c) & uppermask = 0
(And64 (Const64 [m]) (Rsh64Ux64 _ (Const64 [c]))) && c >= int64(64-ntz64(m)) => (Const64 [0])
(And32 (Const32 [m]) (Rsh32Ux64 _ (Const64 [c]))) && c >= int64(32-ntz32(m)) => (Const32 [0])
(And16 (Const16 [m]) (Rsh16Ux64 _ (Const64 [c]))) && c >= int64(16-ntz16(m)) => (Const16 [0])
(And8  (Const8  [m]) (Rsh8Ux64  _ (Const64 [c]))) && c >= int64(8-ntz8(m))  => (Const8  [0])

// (x << c) & lowermask = 0
(And64 (Const64 [m]) (Lsh64x64  _ (Const64 [c]))) && c >= int64(64-nlz64(m)) => (Const64 [0])
(And32 (Const32 [m]) (Lsh32x64  _ (Const64 [c]))) && c >= int64(32-nlz32(m)) => (Const32 [0])
(And16 (Const16 [m]) (Lsh16x64  _ (Const64 [c]))) && c >= int64(16-nlz16(m)) => (Const16 [0])
(And8  (Const8  [m]) (Lsh8x64   _ (Const64 [c]))) && c >= int64(8-nlz8(m))  => (Const8  [0])

// replace shifts with zero extensions
(Rsh16Ux64 (Lsh16x64 x (Const64  [8])) (Const64  [8])) => (ZeroExt8to16  (Trunc16to8  <typ.UInt8>  x))
(Rsh32Ux64 (Lsh32x64 x (Const64 [24])) (Const64 [24])) => (ZeroExt8to32  (Trunc32to8  <typ.UInt8>  x))
(Rsh64Ux64 (Lsh64x64 x (Const64 [56])) (Const64 [56])) => (ZeroExt8to64  (Trunc64to8  <typ.UInt8>  x))
(Rsh32Ux64 (Lsh32x64 x (Const64 [16])) (Const64 [16])) => (ZeroExt16to32 (Trunc32to16 <typ.UInt16> x))
(Rsh64Ux64 (Lsh64x64 x (Const64 [48])) (Const64 [48])) => (ZeroExt16to64 (Trunc64to16 <typ.UInt16> x))
(Rsh64Ux64 (Lsh64x64 x (Const64 [32])) (Const64 [32])) => (ZeroExt32to64 (Trunc64to32 <typ.UInt32> x))

// replace shifts with sign extensions
(Rsh16x64 (Lsh16x64 x (Const64  [8])) (Const64  [8])) => (SignExt8to16  (Trunc16to8  <typ.Int8>  x))
(Rsh32x64 (Lsh32x64 x (Const64 [24])) (Const64 [24])) => (SignExt8to32  (Trunc32to8  <typ.Int8>  x))
(Rsh64x64 (Lsh64x64 x (Const64 [56])) (Const64 [56])) => (SignExt8to64  (Trunc64to8  <typ.Int8>  x))
(Rsh32x64 (Lsh32x64 x (Const64 [16])) (Const64 [16])) => (SignExt16to32 (Trunc32to16 <typ.Int16> x))
(Rsh64x64 (Lsh64x64 x (Const64 [48])) (Const64 [48])) => (SignExt16to64 (Trunc64to16 <typ.Int16> x))
(Rsh64x64 (Lsh64x64 x (Const64 [32])) (Const64 [32])) => (SignExt32to64 (Trunc64to32 <typ.Int32> x))

// constant comparisons
(Eq(64|32|16|8)   (Const(64|32|16|8) [c]) (Const(64|32|16|8) [d])) => (ConstBool [c == d])
(Neq(64|32|16|8)  (Const(64|32|16|8) [c]) (Const(64|32|16|8) [d])) => (ConstBool [c != d])
(Less(64|32|16|8) (Const(64|32|16|8) [c]) (Const(64|32|16|8) [d])) => (ConstBool [c < d])
(Leq(64|32|16|8)  (Const(64|32|16|8) [c]) (Const(64|32|16|8) [d])) => (ConstBool [c <= d])

(Less64U (Const64 [c]) (Const64 [d])) => (ConstBool [uint64(c) < uint64(d)])
(Less32U (Const32 [c]) (Const32 [d])) => (ConstBool [uint32(c) < uint32(d)])
(Less16U (Const16 [c]) (Const16 [d])) => (ConstBool [uint16(c) < uint16(d)])
(Less8U  (Const8  [c]) (Const8  [d])) => (ConstBool [ uint8(c) <  uint8(d)])

(Leq64U (Const64 [c]) (Const64 [d])) => (ConstBool [uint64(c) <= uint64(d)])
(Leq32U (Const32 [c]) (Const32 [d])) => (ConstBool [uint32(c) <= uint32(d)])
(Leq16U (Const16 [c]) (Const16 [d])) => (ConstBool [uint16(c) <= uint16(d)])
(Leq8U  (Const8  [c]) (Const8  [d])) => (ConstBool [ uint8(c) <=  uint8(d)])

(Leq8  (Const8  [0]) (And8  _ (Const8  [c]))) && c >= 0 => (ConstBool [true])
(Leq16 (Const16 [0]) (And16 _ (Const16 [c]))) && c >= 0 => (ConstBool [true])
(Leq32 (Const32 [0]) (And32 _ (Const32 [c]))) && c >= 0 => (ConstBool [true])
(Leq64 (Const64 [0]) (And64 _ (Const64 [c]))) && c >= 0 => (ConstBool [true])

(Leq8  (Const8  [0]) (Rsh8Ux64  _ (Const64 [c]))) && c > 0 => (ConstBool [true])
(Leq16 (Const16 [0]) (Rsh16Ux64 _ (Const64 [c]))) && c > 0 => (ConstBool [true])
(Leq32 (Const32 [0]) (Rsh32Ux64 _ (Const64 [c]))) && c > 0 => (ConstBool [true])
(Leq64 (Const64 [0]) (Rsh64Ux64 _ (Const64 [c]))) && c > 0 => (ConstBool [true])

// prefer equalities with zero
(Less(64|32|16|8) (Const(64|32|16|8) <t> [0]) x) && isNonNegative(x) => (Neq(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)
(Less(64|32|16|8) x (Const(64|32|16|8) <t> [1])) && isNonNegative(x) => (Eq(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)
(Less(64|32|16|8)U x (Const(64|32|16|8) <t> [1])) => (Eq(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)
(Leq(64|32|16|8)U (Const(64|32|16|8) <t> [1]) x) => (Neq(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)

// prefer comparisons with zero
(Less(64|32|16|8) x (Const(64|32|16|8) <t> [1])) => (Leq(64|32|16|8) x (Const(64|32|16|8) <t> [0]))
(Leq(64|32|16|8) x (Const(64|32|16|8) <t> [-1])) => (Less(64|32|16|8) x (Const(64|32|16|8) <t> [0]))
(Leq(64|32|16|8) (Const(64|32|16|8) <t> [1]) x) => (Less(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)
(Less(64|32|16|8) (Const(64|32|16|8) <t> [-1]) x) => (Leq(64|32|16|8) (Const(64|32|16|8) <t> [0]) x)

// constant floating point comparisons
(Eq32F   (Const32F [c]) (Const32F [d])) => (ConstBool [c == d])
(Eq64F   (Const64F [c]) (Const64F [d])) => (ConstBool [c == d])
(Neq32F  (Const32F [c]) (Const32F [d])) => (ConstBool [c != d])
(Neq64F  (Const64F [c]) (Const64F [d])) => (ConstBool [c != d])
(Less32F (Const32F [c]) (Const32F [d])) => (ConstBool [c < d])
(Less64F (Const64F [c]) (Const64F [d])) => (ConstBool [c < d])
(Leq32F  (Const32F [c]) (Const32F [d])) => (ConstBool [c <= d])
(Leq64F  (Const64F [c]) (Const64F [d])) => (ConstBool [c <= d])

// simplifications
(Or(64|32|16|8) x x) => x
(Or(64|32|16|8) (Const(64|32|16|8)  [0]) x) => x
(Or(64|32|16|8) (Const(64|32|16|8) [-1]) _) => (Const(64|32|16|8) [-1])
(Or(64|32|16|8) (Com(64|32|16|8)     x)  x) => (Const(64|32|16|8) [-1])

(And(64|32|16|8) x x) => x
(And(64|32|16|8) (Const(64|32|16|8) [-1]) x) => x
(And(64|32|16|8) (Const(64|32|16|8)  [0]) _) => (Const(64|32|16|8) [0])
(And(64|32|16|8) (Com(64|32|16|8)     x)  x) => (Const(64|32|16|8) [0])

(Xor(64|32|16|8) x x) => (Const(64|32|16|8) [0])
(Xor(64|32|16|8) (Const(64|32|16|8) [0]) x) => x
(Xor(64|32|16|8) (Com(64|32|16|8)    x)  x) => (Const(64|32|16|8) [-1])

(Add(64|32|16|8) (Const(64|32|16|8) [0]) x) => x
(Sub(64|32|16|8) x x) => (Const(64|32|16|8) [0])
(Mul(64|32|16|8) (Const(64|32|16|8) [0]) _) => (Const(64|32|16|8) [0])
(Select0 (Mul(64|32)uover (Const(64|32) [0]) x)) => (Const(64|32) [0])
(Select1 (Mul(64|32)uover (Const(64|32) [0]) x)) => (ConstBool [false])

(Com(64|32|16|8) (Com(64|32|16|8)  x)) => x
(Com(64|32|16|8) (Const(64|32|16|8) [c])) => (Const(64|32|16|8) [^c])

(Neg(64|32|16|8) (Sub(64|32|16|8) x y)) => (Sub(64|32|16|8) y x)
(Add(64|32|16|8) x (Neg(64|32|16|8) y)) => (Sub(64|32|16|8) x y)

(Xor(64|32|16|8) (Const(64|32|16|8) [-1]) x) => (Com(64|32|16|8) x)

(Sub(64|32|16|8) (Neg(64|32|16|8) x) (Com(64|32|16|8) x)) => (Const(64|32|16|8) [1])
(Sub(64|32|16|8) (Com(64|32|16|8) x) (Neg(64|32|16|8) x)) => (Const(64|32|16|8) [-1])
(Add(64|32|16|8) (Com(64|32|16|8) x)                  x)  => (Const(64|32|16|8) [-1])

// Simplification when involving common integer
// (t + x) - (t + y) == x - y
// (t + x) - (y + t) == x - y
// (x + t) - (y + t) == x - y
// (x + t) - (t + y) == x - y
// (x - t) + (t + y) == x + y
// (x - t) + (y + t) == x + y
(Sub(64|32|16|8) (Add(64|32|16|8) t x) (Add(64|32|16|8) t y)) => (Sub(64|32|16|8) x y)
(Add(64|32|16|8) (Sub(64|32|16|8) x t) (Add(64|32|16|8) t y)) => (Add(64|32|16|8) x y)

// ^(x-1) == ^x+1 == -x
(Add(64|32|16|8) (Const(64|32|16|8) [1]) (Com(64|32|16|8) x)) => (Neg(64|32|16|8) x)
(Com(64|32|16|8) (Add(64|32|16|8) (Const(64|32|16|8) [-1]) x)) => (Neg(64|32|16|8) x)

// -(-x) == x
(Neg(64|32|16|8) (Neg(64|32|16|8) x)) => x

// -^x == x+1
(Neg(64|32|16|8) <t> (Com(64|32|16|8) x)) => (Add(64|32|16|8) (Const(64|32|16|8) <t> [1]) x)

(And(64|32|16|8) x (And(64|32|16|8) x y)) => (And(64|32|16|8) x y)
(Or(64|32|16|8) x (Or(64|32|16|8) x y)) => (Or(64|32|16|8) x y)
(Xor(64|32|16|8) x (Xor(64|32|16|8) x y)) => y

// Fold comparisons with numeric bounds
(Less(64|32|16|8)U _ (Const(64|32|16|8) [0]))  => (ConstBool [false])
(Leq(64|32|16|8)U (Const(64|32|16|8) [0]) _)   => (ConstBool [true])
(Less(64|32|16|8)U (Const(64|32|16|8) [-1]) _) => (ConstBool [false])
(Leq(64|32|16|8)U _ (Const(64|32|16|8) [-1]))  => (ConstBool [true])
(Less64 _ (Const64 [math.MinInt64])) => (ConstBool [false])
(Less32 _ (Const32 [math.MinInt32])) => (ConstBool [false])
(Less16 _ (Const16 [math.MinInt16])) => (ConstBool [false])
(Less8  _ (Const8  [math.MinInt8 ])) => (ConstBool [false])
(Leq64 (Const64 [math.MinInt64]) _)  => (ConstBool [true])
(Leq32 (Const32 [math.MinInt32]) _)  => (ConstBool [true])
(Leq16 (Const16 [math.MinInt16]) _)  => (ConstBool [true])
(Leq8  (Const8  [math.MinInt8 ]) _)  => (ConstBool [true])
(Less64 (Const64 [math.MaxInt64]) _) => (ConstBool [false])
(Less32 (Const32 [math.MaxInt32]) _) => (ConstBool [false])
(Less16 (Const16 [math.MaxInt16]) _) => (ConstBool [false])
(Less8  (Const8  [math.MaxInt8 ]) _) => (ConstBool [false])
(Leq64 _ (Const64 [math.MaxInt64]))  => (ConstBool [true])
(Leq32 _ (Const32 [math.MaxInt32]))  => (ConstBool [true])
(Leq16 _ (Const16 [math.MaxInt16]))  => (ConstBool [true])
(Leq8  _ (Const8  [math.MaxInt8 ]))  => (ConstBool [true])

// Canonicalize <= on numeric bounds and < near numeric bounds to ==
(Leq(64|32|16|8)U x c:(Const(64|32|16|8) [0]))     => (Eq(64|32|16|8) x c)
(Leq(64|32|16|8)U c:(Const(64|32|16|8) [-1]) x)    => (Eq(64|32|16|8) x c)
(Less(64|32|16|8)U x (Const(64|32|16|8) <t> [1]))  => (Eq(64|32|16|8) x (Const(64|32|16|8) <t> [0]))
(Less(64|32|16|8)U (Const(64|32|16|8) <t> [-2]) x) => (Eq(64|32|16|8) x (Const(64|32|16|8) <t> [-1]))
(Leq64 x c:(Const64 [math.MinInt64])) => (Eq64 x c)
(Leq32 x c:(Const32 [math.MinInt32])) => (Eq32 x c)
(Leq16 x c:(Const16 [math.MinInt16])) => (Eq16 x c)
(Leq8  x c:(Const8  [math.MinInt8 ])) => (Eq8  x c)
(Leq64 c:(Const64 [math.MaxInt64]) x) => (Eq64 x c)
(Leq32 c:(Const32 [math.MaxInt32]) x) => (Eq32 x c)
(Leq16 c:(Const16 [math.MaxInt16]) x) => (Eq16 x c)
(Leq8  c:(Const8  [math.MaxInt8 ]) x) => (Eq8  x c)
(Less64 x (Const64 <t> [math.MinInt64+1])) => (Eq64 x (Const64 <t> [math.MinInt64]))
(Less32 x (Const32 <t> [math.MinInt32+1])) => (Eq32 x (Const32 <t> [math.MinInt32]))
(Less16 x (Const16 <t> [math.MinInt16+1])) => (Eq16 x (Const16 <t> [math.MinInt16]))
(Less8  x (Const8  <t> [math.MinInt8 +1])) => (Eq8  x (Const8  <t> [math.MinInt8 ]))
(Less64 (Const64 <t> [math.MaxInt64-1]) x) => (Eq64 x (Const64 <t> [math.MaxInt64]))
(Less32 (Const32 <t> [math.MaxInt32-1]) x) => (Eq32 x (Const32 <t> [math.MaxInt32]))
(Less16 (Const16 <t> [math.MaxInt16-1]) x) => (Eq16 x (Const16 <t> [math.MaxInt16]))
(Less8  (Const8  <t> [math.MaxInt8 -1]) x) => (Eq8  x (Const8  <t> [math.MaxInt8 ]))

// Ands clear bits. Ors set bits.
// If a subsequent Or will set all the bits
// that an And cleared, we can skip the And.
// This happens in bitmasking code like:
//   x &^= 3 << shift // clear two old bits
//   x  |= v << shift // set two new bits
// when shift is a small constant and v ends up a constant 3.
(Or8  (And8  x (Const8  [c2])) (Const8  <t> [c1])) && ^(c1 | c2) == 0 => (Or8  (Const8  <t> [c1]) x)
(Or16 (And16 x (Const16 [c2])) (Const16 <t> [c1])) && ^(c1 | c2) == 0 => (Or16 (Const16 <t> [c1]) x)
(Or32 (And32 x (Const32 [c2])) (Const32 <t> [c1])) && ^(c1 | c2) == 0 => (Or32 (Const32 <t> [c1]) x)
(Or64 (And64 x (Const64 [c2])) (Const64 <t> [c1])) && ^(c1 | c2) == 0 => (Or64 (Const64 <t> [c1]) x)

(Trunc64to8  (And64 (Const64 [y]) x)) && y&0xFF == 0xFF => (Trunc64to8 x)
(Trunc64to16 (And64 (Const64 [y]) x)) && y&0xFFFF == 0xFFFF => (Trunc64to16 x)
(Trunc64to32 (And64 (Const64 [y]) x)) && y&0xFFFFFFFF == 0xFFFFFFFF => (Trunc64to32 x)
(Trunc32to8  (And32 (Const32 [y]) x)) && y&0xFF == 0xFF => (Trunc32to8 x)
(Trunc32to16 (And32 (Const32 [y]) x)) && y&0xFFFF == 0xFFFF => (Trunc32to16 x)
(Trunc16to8  (And16 (Const16 [y]) x)) && y&0xFF == 0xFF => (Trunc16to8 x)

(ZeroExt8to64  (Trunc64to8  x:(Rsh64Ux64 _ (Const64 [s])))) && s >= 56 => x
(ZeroExt16to64 (Trunc64to16 x:(Rsh64Ux64 _ (Const64 [s])))) && s >= 48 => x
(ZeroExt32to64 (Trunc64to32 x:(Rsh64Ux64 _ (Const64 [s])))) && s >= 32 => x
(ZeroExt8to32  (Trunc32to8  x:(Rsh32Ux64 _ (Const64 [s])))) && s >= 24 => x
(ZeroExt16to32 (Trunc32to16 x:(Rsh32Ux64 _ (Const64 [s])))) && s >= 16 => x
(ZeroExt8to16  (Trunc16to8  x:(Rsh16Ux64 _ (Const64 [s])))) && s >= 8 => x

(SignExt8to64  (Trunc64to8  x:(Rsh64x64 _ (Const64 [s])))) && s >= 56 => x
(SignExt16to64 (Trunc64to16 x:(Rsh64x64 _ (Const64 [s])))) && s >= 48 => x
(SignExt32to64 (Trunc64to32 x:(Rsh64x64 _ (Const64 [s])))) && s >= 32 => x
(SignExt8to32  (Trunc32to8  x:(Rsh32x64 _ (Const64 [s])))) && s >= 24 => x
(SignExt16to32 (Trunc32to16 x:(Rsh32x64 _ (Const64 [s])))) && s >= 16 => x
(SignExt8to16  (Trunc16to8  x:(Rsh16x64 _ (Const64 [s])))) && s >= 8 => x

(Slicemask (Const32 [x])) && x > 0 => (Const32 [-1])
(Slicemask (Const32 [0]))          => (Const32 [0])
(Slicemask (Const64 [x])) && x > 0 => (Const64 [-1])
(Slicemask (Const64 [0]))          => (Const64 [0])

// simplifications often used for lengths.  e.g. len(s[i:i+5])==5
(Sub(64|32|16|8) (Add(64|32|16|8) x y) x) => y
(Sub(64|32|16|8) (Add(64|32|16|8) x y) y) => x
(Sub(64|32|16|8) (Sub(64|32|16|8) x y) x) => (Neg(64|32|16|8) y)
(Sub(64|32|16|8) x (Add(64|32|16|8) x y)) => (Neg(64|32|16|8) y)
(Add(64|32|16|8) x (Sub(64|32|16|8) y x)) => y
(Add(64|32|16|8) x (Add(64|32|16|8) y (Sub(64|32|16|8) z x))) => (Add(64|32|16|8) y z)

// basic phi simplifications
(Phi (Const8  [c]) (Const8  [c])) => (Const8  [c])
(Phi (Const16 [c]) (Const16 [c])) => (Const16 [c])
(Phi (Const32 [c]) (Const32 [c])) => (Const32 [c])
(Phi (Const64 [c]) (Const64 [c])) => (Const64 [c])

// slice and interface comparisons
// The frontend ensures that we can only compare against nil,
// so we need only compare the first word (interface type or slice ptr).
(EqInter x y)  => (EqPtr  (ITab x) (ITab y))
(NeqInter x y) => (NeqPtr (ITab x) (ITab y))
(EqSlice x y)  => (EqPtr  (SlicePtr x) (SlicePtr y))
(NeqSlice x y) => (NeqPtr (SlicePtr x) (SlicePtr y))

// Load of store of same address, with compatibly typed value and same size
(Load <t1> p1 (Store {t2} p2 x _))
	&& isSamePtr(p1, p2)
	&& t1.Compare(x.Type) == types.CMPeq
	&& t1.Size() == t2.Size()
	=> x
(Load <t1> p1 (Store {t2} p2 _ (Store {t3} p3 x _)))
	&& isSamePtr(p1, p3)
	&& t1.Compare(x.Type) == types.CMPeq
	&& t1.Size() == t2.Size()
	&& disjoint(p3, t3.Size(), p2, t2.Size())
	=> x
(Load <t1> p1 (Store {t2} p2 _ (Store {t3} p3 _ (Store {t4} p4 x _))))
	&& isSamePtr(p1, p4)
	&& t1.Compare(x.Type) == types.CMPeq
	&& t1.Size() == t2.Size()
	&& disjoint(p4, t4.Size(), p2, t2.Size())
	&& disjoint(p4, t4.Size(), p3, t3.Size())
	=> x
(Load <t1> p1 (Store {t2} p2 _ (Store {t3} p3 _ (Store {t4} p4 _ (Store {t5} p5 x _)))))
	&& isSamePtr(p1, p5)
	&& t1.Compare(x.Type) == types.CMPeq
	&& t1.Size() == t2.Size()
	&& disjoint(p5, t5.Size(), p2, t2.Size())
	&& disjoint(p5, t5.Size(), p3, t3.Size())
	&& disjoint(p5, t5.Size(), p4, t4.Size())
	=> x

// Pass constants through math.Float{32,64}bits and math.Float{32,64}frombits
(Load <t1> p1 (Store {t2} p2 (Const64  [x]) _)) && isSamePtr(p1,p2) && sizeof(t2) == 8 && is64BitFloat(t1) && !math.IsNaN(math.Float64frombits(uint64(x))) => (Const64F [math.Float64frombits(uint64(x))])
(Load <t1> p1 (Store {t2} p2 (Const32  [x]) _)) && isSamePtr(p1,p2) && sizeof(t2) == 4 && is32BitFloat(t1) && !math.IsNaN(float64(math.Float32frombits(uint32(x)))) => (Const32F [math.Float32frombits(uint32(x))])
(Load <t1> p1 (Store {t2} p2 (Const64F [x]) _)) && isSamePtr(p1,p2) && sizeof(t2) == 8 && is64BitInt(t1)   => (Const64  [int64(math.Float64bits(x))])
(Load <t1> p1 (Store {t2} p2 (Const32F [x]) _)) && isSamePtr(p1,p2) && sizeof(t2) == 4 && is32BitInt(t1)   => (Const32  [int32(math.Float32bits(x))])

// Float Loads up to Zeros so they can be constant folded.
(Load <t1> op:(OffPtr [o1] p1)
	(Store {t2} p2 _
		mem:(Zero [n] p3 _)))
	&& o1 >= 0 && o1+t1.Size() <= n && isSamePtr(p1, p3)
	&& CanSSA(t1)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	=> @mem.Block (Load <t1> (OffPtr <op.Type> [o1] p3) mem)
(Load <t1> op:(OffPtr [o1] p1)
	(Store {t2} p2 _
		(Store {t3} p3 _
			mem:(Zero [n] p4 _))))
	&& o1 >= 0 && o1+t1.Size() <= n && isSamePtr(p1, p4)
	&& CanSSA(t1)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	&& disjoint(op, t1.Size(), p3, t3.Size())
	=> @mem.Block (Load <t1> (OffPtr <op.Type> [o1] p4) mem)
(Load <t1> op:(OffPtr [o1] p1)
	(Store {t2} p2 _
		(Store {t3} p3 _
			(Store {t4} p4 _
				mem:(Zero [n] p5 _)))))
	&& o1 >= 0 && o1+t1.Size() <= n && isSamePtr(p1, p5)
	&& CanSSA(t1)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	&& disjoint(op, t1.Size(), p3, t3.Size())
	&& disjoint(op, t1.Size(), p4, t4.Size())
	=> @mem.Block (Load <t1> (OffPtr <op.Type> [o1] p5) mem)
(Load <t1> op:(OffPtr [o1] p1)
	(Store {t2} p2 _
		(Store {t3} p3 _
			(Store {t4} p4 _
				(Store {t5} p5 _
					mem:(Zero [n] p6 _))))))
	&& o1 >= 0 && o1+t1.Size() <= n && isSamePtr(p1, p6)
	&& CanSSA(t1)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	&& disjoint(op, t1.Size(), p3, t3.Size())
	&& disjoint(op, t1.Size(), p4, t4.Size())
	&& disjoint(op, t1.Size(), p5, t5.Size())
	=> @mem.Block (Load <t1> (OffPtr <op.Type> [o1] p6) mem)

// Zero to Load forwarding.
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& t1.IsBoolean()
	&& isSamePtr(p1, p2)
	&& n >= o + 1
	=> (ConstBool [false])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is8BitInt(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 1
	=> (Const8 [0])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is16BitInt(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 2
	=> (Const16 [0])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is32BitInt(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 4
	=> (Const32 [0])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is64BitInt(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 8
	=> (Const64 [0])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is32BitFloat(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 4
	=> (Const32F [0])
(Load <t1> (OffPtr [o] p1) (Zero [n] p2 _))
	&& is64BitFloat(t1)
	&& isSamePtr(p1, p2)
	&& n >= o + 8
	=> (Const64F [0])

// Eliminate stores of values that have just been loaded from the same location.
// We also handle the common case where there are some intermediate stores.
(Store {t1} p1 (Load <t2> p2 mem) mem)
	&& isSamePtr(p1, p2)
	&& t2.Size() == t1.Size()
	=> mem
(Store {t1} p1 (Load <t2> p2 oldmem) mem:(Store {t3} p3 _ oldmem))
	&& isSamePtr(p1, p2)
	&& t2.Size() == t1.Size()
	&& disjoint(p1, t1.Size(), p3, t3.Size())
	=> mem
(Store {t1} p1 (Load <t2> p2 oldmem) mem:(Store {t3} p3 _ (Store {t4} p4 _ oldmem)))
	&& isSamePtr(p1, p2)
	&& t2.Size() == t1.Size()
	&& disjoint(p1, t1.Size(), p3, t3.Size())
	&& disjoint(p1, t1.Size(), p4, t4.Size())
	=> mem
(Store {t1} p1 (Load <t2> p2 oldmem) mem:(Store {t3} p3 _ (Store {t4} p4 _ (Store {t5} p5 _ oldmem))))
	&& isSamePtr(p1, p2)
	&& t2.Size() == t1.Size()
	&& disjoint(p1, t1.Size(), p3, t3.Size())
	&& disjoint(p1, t1.Size(), p4, t4.Size())
	&& disjoint(p1, t1.Size(), p5, t5.Size())
	=> mem

// Don't Store zeros to cleared variables.
(Store {t} (OffPtr [o] p1) x mem:(Zero [n] p2 _))
	&& isConstZero(x)
	&& o >= 0 && t.Size() + o <= n && isSamePtr(p1, p2)
	=> mem
(Store {t1} op:(OffPtr [o1] p1) x mem:(Store {t2} p2 _ (Zero [n] p3 _)))
	&& isConstZero(x)
	&& o1 >= 0 && t1.Size() + o1 <= n && isSamePtr(p1, p3)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	=> mem
(Store {t1} op:(OffPtr [o1] p1) x mem:(Store {t2} p2 _ (Store {t3} p3 _ (Zero [n] p4 _))))
	&& isConstZero(x)
	&& o1 >= 0 && t1.Size() + o1 <= n && isSamePtr(p1, p4)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	&& disjoint(op, t1.Size(), p3, t3.Size())
	=> mem
(Store {t1} op:(OffPtr [o1] p1) x mem:(Store {t2} p2 _ (Store {t3} p3 _ (Store {t4} p4 _ (Zero [n] p5 _)))))
	&& isConstZero(x)
	&& o1 >= 0 && t1.Size() + o1 <= n && isSamePtr(p1, p5)
	&& disjoint(op, t1.Size(), p2, t2.Size())
	&& disjoint(op, t1.Size(), p3, t3.Size())
	&& disjoint(op, t1.Size(), p4, t4.Size())
	=> mem

// Collapse OffPtr
(OffPtr (OffPtr p [y]) [x]) => (OffPtr p [x+y])
(OffPtr p [0]) && v.Type.Compare(p.Type) == types.CMPeq => p

// indexing operations
// Note: bounds check has already been done
(PtrIndex <t> ptr idx) && config.PtrSize == 4 && is32Bit(t.Elem().Size()) => (AddPtr ptr (Mul32 <typ.Int> idx (Const32 <typ.Int> [int32(t.Elem().Size())])))
(PtrIndex <t> ptr idx) && config.PtrSize == 8 => (AddPtr ptr (Mul64 <typ.Int> idx (Const64 <typ.Int> [t.Elem().Size()])))

// struct operations
(StructSelect (StructMake1 x)) => x
(StructSelect [0] (StructMake2 x _)) => x
(StructSelect [1] (StructMake2 _ x)) => x
(StructSelect [0] (StructMake3 x _ _)) => x
(StructSelect [1] (StructMake3 _ x _)) => x
(StructSelect [2] (StructMake3 _ _ x)) => x
(StructSelect [0] (StructMake4 x _ _ _)) => x
(StructSelect [1] (StructMake4 _ x _ _)) => x
(StructSelect [2] (StructMake4 _ _ x _)) => x
(StructSelect [3] (StructMake4 _ _ _ x)) => x

(Load <t> _ _) && t.IsStruct() && t.NumFields() == 0 && CanSSA(t) =>
  (StructMake0)
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 1 && CanSSA(t) =>
  (StructMake1
    (Load <t.FieldType(0)> (OffPtr <t.FieldType(0).PtrTo()> [0] ptr) mem))
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 2 && CanSSA(t) =>
  (StructMake2
    (Load <t.FieldType(0)> (OffPtr <t.FieldType(0).PtrTo()> [0]             ptr) mem)
    (Load <t.FieldType(1)> (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] ptr) mem))
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 3 && CanSSA(t) =>
  (StructMake3
    (Load <t.FieldType(0)> (OffPtr <t.FieldType(0).PtrTo()> [0]             ptr) mem)
    (Load <t.FieldType(1)> (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] ptr) mem)
    (Load <t.FieldType(2)> (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] ptr) mem))
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 4 && CanSSA(t) =>
  (StructMake4
    (Load <t.FieldType(0)> (OffPtr <t.FieldType(0).PtrTo()> [0]             ptr) mem)
    (Load <t.FieldType(1)> (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] ptr) mem)
    (Load <t.FieldType(2)> (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] ptr) mem)
    (Load <t.FieldType(3)> (OffPtr <t.FieldType(3).PtrTo()> [t.FieldOff(3)] ptr) mem))

(StructSelect [i] x:(Load <t> ptr mem)) && !CanSSA(t) =>
  @x.Block (Load <v.Type> (OffPtr <v.Type.PtrTo()> [t.FieldOff(int(i))] ptr) mem)

(Store _ (StructMake0) mem) => mem
(Store dst (StructMake1 <t> f0) mem) =>
  (Store {t.FieldType(0)} (OffPtr <t.FieldType(0).PtrTo()> [0] dst) f0 mem)
(Store dst (StructMake2 <t> f0 f1) mem) =>
  (Store {t.FieldType(1)}
    (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
    f1
    (Store {t.FieldType(0)}
      (OffPtr <t.FieldType(0).PtrTo()> [0] dst)
        f0 mem))
(Store dst (StructMake3 <t> f0 f1 f2) mem) =>
  (Store {t.FieldType(2)}
    (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] dst)
    f2
    (Store {t.FieldType(1)}
      (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
      f1
      (Store {t.FieldType(0)}
        (OffPtr <t.FieldType(0).PtrTo()> [0] dst)
          f0 mem)))
(Store dst (StructMake4 <t> f0 f1 f2 f3) mem) =>
  (Store {t.FieldType(3)}
    (OffPtr <t.FieldType(3).PtrTo()> [t.FieldOff(3)] dst)
    f3
    (Store {t.FieldType(2)}
      (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] dst)
      f2
      (Store {t.FieldType(1)}
        (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
        f1
        (Store {t.FieldType(0)}
          (OffPtr <t.FieldType(0).PtrTo()> [0] dst)
            f0 mem))))

// Putting struct{*byte} and similar into direct interfaces.
(IMake _typ (StructMake1 val)) => (IMake _typ val)
(StructSelect [0] (IData x)) => (IData x)

// un-SSAable values use mem->mem copies
(Store {t} dst (Load src mem) mem) && !CanSSA(t) =>
	(Move {t} [t.Size()] dst src mem)
(Store {t} dst (Load src mem) (VarDef {x} mem)) && !CanSSA(t) =>
	(Move {t} [t.Size()] dst src (VarDef {x} mem))

// array ops
(ArraySelect (ArrayMake1 x)) => x

(Load <t> _ _) && t.IsArray() && t.NumElem() == 0 =>
  (ArrayMake0)

(Load <t> ptr mem) && t.IsArray() && t.NumElem() == 1 && CanSSA(t) =>
  (ArrayMake1 (Load <t.Elem()> ptr mem))

(Store _ (ArrayMake0) mem) => mem
(Store dst (ArrayMake1 e) mem) => (Store {e.Type} dst e mem)

// Putting [1]*byte and similar into direct interfaces.
(IMake _typ (ArrayMake1 val)) => (IMake _typ val)
(ArraySelect [0] (IData x)) => (IData x)

// string ops
// Decomposing StringMake and lowering of StringPtr and StringLen
// happens in a later pass, dec, so that these operations are available
// to other passes for optimizations.
(StringPtr (StringMake (Addr <t> {s} base) _)) => (Addr <t> {s} base)
(StringLen (StringMake _ (Const64 <t> [c]))) => (Const64 <t> [c])
(ConstString {str}) && config.PtrSize == 4 && str == "" =>
  (StringMake (ConstNil) (Const32 <typ.Int> [0]))
(ConstString {str}) && config.PtrSize == 8 && str == "" =>
  (StringMake (ConstNil) (Const64 <typ.Int> [0]))
(ConstString {str}) && config.PtrSize == 4 && str != "" =>
  (StringMake
    (Addr <typ.BytePtr> {fe.StringData(str)}
      (SB))
    (Const32 <typ.Int> [int32(len(str))]))
(ConstString {str}) && config.PtrSize == 8 && str != "" =>
  (StringMake
    (Addr <typ.BytePtr> {fe.StringData(str)}
      (SB))
    (Const64 <typ.Int> [int64(len(str))]))

// slice ops
// Only a few slice rules are provided here.  See dec.rules for
// a more comprehensive set.
(SliceLen (SliceMake _ (Const64 <t> [c]) _)) => (Const64 <t> [c])
(SliceCap (SliceMake _ _ (Const64 <t> [c]))) => (Const64 <t> [c])
(SliceLen (SliceMake _ (Const32 <t> [c]) _)) => (Const32 <t> [c])
(SliceCap (SliceMake _ _ (Const32 <t> [c]))) => (Const32 <t> [c])
(SlicePtr (SliceMake (SlicePtr x) _ _)) => (SlicePtr x)
(SliceLen (SliceMake _ (SliceLen x) _)) => (SliceLen x)
(SliceCap (SliceMake _ _ (SliceCap x))) => (SliceCap x)
(SliceCap (SliceMake _ _ (SliceLen x))) => (SliceLen x)
(ConstSlice) && config.PtrSize == 4 =>
  (SliceMake
    (ConstNil <v.Type.Elem().PtrTo()>)
    (Const32 <typ.Int> [0])
    (Const32 <typ.Int> [0]))
(ConstSlice) && config.PtrSize == 8 =>
  (SliceMake
    (ConstNil <v.Type.Elem().PtrTo()>)
    (Const64 <typ.Int> [0])
    (Const64 <typ.Int> [0]))

// interface ops
(ConstInterface) =>
  (IMake
    (ConstNil <typ.Uintptr>)
    (ConstNil <typ.BytePtr>))

(NilCheck ptr:(GetG mem) mem) => ptr

(If (Not cond) yes no) => (If cond no yes)
(If (ConstBool [c]) yes no) && c => (First yes no)
(If (ConstBool [c]) yes no) && !c => (First no yes)

(Phi <t> nx:(Not x) ny:(Not y)) && nx.Uses == 1 && ny.Uses == 1 => (Not (Phi <t> x y))

// Get rid of Convert ops for pointer arithmetic on unsafe.Pointer.
(Convert (Add(64|32) (Convert ptr mem) off) mem) => (AddPtr ptr off)
(Convert (Convert ptr mem) mem) => ptr

// strength reduction of divide by a constant.
// See ../magic.go for a detailed description of these algorithms.

// Unsigned divide by power of 2.  Strength reduce to a shift.
(Div8u  n (Const8  [c])) && isPowerOfTwo8(c)  => (Rsh8Ux64  n (Const64 <typ.UInt64> [log8(c)]))
(Div16u n (Const16 [c])) && isPowerOfTwo16(c) => (Rsh16Ux64 n (Const64 <typ.UInt64> [log16(c)]))
(Div32u n (Const32 [c])) && isPowerOfTwo32(c) => (Rsh32Ux64 n (Const64 <typ.UInt64> [log32(c)]))
(Div64u n (Const64 [c])) && isPowerOfTwo64(c) => (Rsh64Ux64 n (Const64 <typ.UInt64> [log64(c)]))
(Div64u n (Const64 [-1<<63]))                 => (Rsh64Ux64 n (Const64 <typ.UInt64> [63]))

// Signed non-negative divide by power of 2.
(Div8  n (Const8  [c])) && isNonNegative(n) && isPowerOfTwo8(c)  => (Rsh8Ux64  n (Const64 <typ.UInt64> [log8(c)]))
(Div16 n (Const16 [c])) && isNonNegative(n) && isPowerOfTwo16(c) => (Rsh16Ux64 n (Const64 <typ.UInt64> [log16(c)]))
(Div32 n (Const32 [c])) && isNonNegative(n) && isPowerOfTwo32(c) => (Rsh32Ux64 n (Const64 <typ.UInt64> [log32(c)]))
(Div64 n (Const64 [c])) && isNonNegative(n) && isPowerOfTwo64(c) => (Rsh64Ux64 n (Const64 <typ.UInt64> [log64(c)]))
(Div64 n (Const64 [-1<<63])) && isNonNegative(n)                 => (Const64 [0])

// Unsigned divide, not a power of 2.  Strength reduce to a multiply.
// For 8-bit divides, we just do a direct 9-bit by 8-bit multiply.
(Div8u x (Const8 [c])) && umagicOK8(c) =>
  (Trunc32to8
    (Rsh32Ux64 <typ.UInt32>
      (Mul32 <typ.UInt32>
        (Const32 <typ.UInt32> [int32(1<<8+umagic8(c).m)])
        (ZeroExt8to32 x))
      (Const64 <typ.UInt64> [8+umagic8(c).s])))

// For 16-bit divides on 64-bit machines, we do a direct 17-bit by 16-bit multiply.
(Div16u x (Const16 [c])) && umagicOK16(c) && config.RegSize == 8 =>
  (Trunc64to16
    (Rsh64Ux64 <typ.UInt64>
      (Mul64 <typ.UInt64>
        (Const64 <typ.UInt64> [int64(1<<16+umagic16(c).m)])
        (ZeroExt16to64 x))
      (Const64 <typ.UInt64> [16+umagic16(c).s])))

// For 16-bit divides on 32-bit machines
(Div16u x (Const16 [c])) && umagicOK16(c) && config.RegSize == 4 && umagic16(c).m&1 == 0 =>
  (Trunc32to16
    (Rsh32Ux64 <typ.UInt32>
      (Mul32 <typ.UInt32>
        (Const32 <typ.UInt32> [int32(1<<15+umagic16(c).m/2)])
        (ZeroExt16to32 x))
      (Const64 <typ.UInt64> [16+umagic16(c).s-1])))
(Div16u x (Const16 [c])) && umagicOK16(c) && config.RegSize == 4 && c&1 == 0 =>
  (Trunc32to16
    (Rsh32Ux64 <typ.UInt32>
      (Mul32 <typ.UInt32>
        (Const32 <typ.UInt32> [int32(1<<15+(umagic16(c).m+1)/2)])
        (Rsh32Ux64 <typ.UInt32> (ZeroExt16to32 x) (Const64 <typ.UInt64> [1])))
      (Const64 <typ.UInt64> [16+umagic16(c).s-2])))
(Div16u x (Const16 [c])) && umagicOK16(c) && config.RegSize == 4 && config.useAvg =>
  (Trunc32to16
    (Rsh32Ux64 <typ.UInt32>
      (Avg32u
        (Lsh32x64 <typ.UInt32> (ZeroExt16to32 x) (Const64 <typ.UInt64> [16]))
        (Mul32 <typ.UInt32>
          (Const32 <typ.UInt32> [int32(umagic16(c).m)])
          (ZeroExt16to32 x)))
      (Const64 <typ.UInt64> [16+umagic16(c).s-1])))

// For 32-bit divides on 32-bit machines
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 4 && umagic32(c).m&1 == 0 && config.useHmul =>
  (Rsh32Ux64 <typ.UInt32>
    (Hmul32u <typ.UInt32>
      (Const32 <typ.UInt32> [int32(1<<31+umagic32(c).m/2)])
      x)
    (Const64 <typ.UInt64> [umagic32(c).s-1]))
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 4 && c&1 == 0 && config.useHmul =>
  (Rsh32Ux64 <typ.UInt32>
    (Hmul32u <typ.UInt32>
      (Const32 <typ.UInt32> [int32(1<<31+(umagic32(c).m+1)/2)])
      (Rsh32Ux64 <typ.UInt32> x (Const64 <typ.UInt64> [1])))
    (Const64 <typ.UInt64> [umagic32(c).s-2]))
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 4 && config.useAvg && config.useHmul =>
  (Rsh32Ux64 <typ.UInt32>
    (Avg32u
      x
      (Hmul32u <typ.UInt32>
        (Const32 <typ.UInt32> [int32(umagic32(c).m)])
        x))
    (Const64 <typ.UInt64> [umagic32(c).s-1]))

// For 32-bit divides on 64-bit machines
// We'll use a regular (non-hi) multiply for this case.
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 8 && umagic32(c).m&1 == 0 =>
  (Trunc64to32
    (Rsh64Ux64 <typ.UInt64>
      (Mul64 <typ.UInt64>
        (Const64 <typ.UInt64> [int64(1<<31+umagic32(c).m/2)])
        (ZeroExt32to64 x))
      (Const64 <typ.UInt64> [32+umagic32(c).s-1])))
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 8 && c&1 == 0 =>
  (Trunc64to32
    (Rsh64Ux64 <typ.UInt64>
      (Mul64 <typ.UInt64>
        (Const64 <typ.UInt64> [int64(1<<31+(umagic32(c).m+1)/2)])
        (Rsh64Ux64 <typ.UInt64> (ZeroExt32to64 x) (Const64 <typ.UInt64> [1])))
      (Const64 <typ.UInt64> [32+umagic32(c).s-2])))
(Div32u x (Const32 [c])) && umagicOK32(c) && config.RegSize == 8 && config.useAvg =>
  (Trunc64to32
    (Rsh64Ux64 <typ.UInt64>
      (Avg64u
        (Lsh64x64 <typ.UInt64> (ZeroExt32to64 x) (Const64 <typ.UInt64> [32]))
        (Mul64 <typ.UInt64>
          (Const64 <typ.UInt32> [int64(umagic32(c).m)])
          (ZeroExt32to64 x)))
      (Const64 <typ.UInt64> [32+umagic32(c).s-1])))

// For unsigned 64-bit divides on 32-bit machines,
// if the constant fits in 16 bits (so that the last term
// fits in 32 bits), convert to three 32-bit divides by a constant.
//
// If 1<<32 = Q * c + R
// and    x = hi << 32 + lo
//
// Then x = (hi/c*c + hi%c) << 32 + lo
//        = hi/c*c<<32 + hi%c<<32 + lo
//        = hi/c*c<<32 + (hi%c)*(Q*c+R) + lo/c*c + lo%c
//        = hi/c*c<<32 + (hi%c)*Q*c + lo/c*c + (hi%c*R+lo%c)
// and x / c = (hi/c)<<32 + (hi%c)*Q + lo/c + (hi%c*R+lo%c)/c
(Div64u x (Const64 [c])) && c > 0 && c <= 0xFFFF && umagicOK32(int32(c)) && config.RegSize == 4 && config.useHmul =>
  (Add64
    (Add64 <typ.UInt64>
      (Add64 <typ.UInt64>
        (Lsh64x64 <typ.UInt64>
          (ZeroExt32to64
            (Div32u <typ.UInt32>
              (Trunc64to32 <typ.UInt32> (Rsh64Ux64 <typ.UInt64> x (Const64 <typ.UInt64> [32])))
              (Const32 <typ.UInt32> [int32(c)])))
          (Const64 <typ.UInt64> [32]))
        (ZeroExt32to64 (Div32u <typ.UInt32> (Trunc64to32 <typ.UInt32> x) (Const32 <typ.UInt32> [int32(c)]))))
      (Mul64 <typ.UInt64>
        (ZeroExt32to64 <typ.UInt64>
          (Mod32u <typ.UInt32>
            (Trunc64to32 <typ.UInt32> (Rsh64Ux64 <typ.UInt64> x (Const64 <typ.UInt64> [32])))
            (Const32 <typ.UInt32> [int32(c)])))
        (Const64 <typ.UInt64> [int64((1<<32)/c)])))
      (ZeroExt32to64
        (Div32u <typ.UInt32>
          (Add32 <typ.UInt32>
            (Mod32u <typ.UInt32> (Trunc64to32 <typ.UInt32> x) (Const32 <typ.UInt32> [int32(c)]))
            (Mul32 <typ.UInt32>
              (Mod32u <typ.UInt32>
                (Trunc64to32 <typ.UInt32> (Rsh64Ux64 <typ.UInt64> x (Const64 <typ.UInt64> [32])))
                (Const32 <typ.UInt32> [int32(c)]))
              (Const32 <typ.UInt32> [int32((1<<32)%c)])))
          (Const32 <typ.UInt32> [int32(c)]))))

// For 64-bit divides on 64-bit machines
// (64-bit divides on 32-bit machines are lowered to a runtime call by the walk pass.)
(Div64u x (Const64 [c])) && umagicOK64(c) && config.RegSize == 8 && umagic64(c).m&1 == 0 && config.useHmul =>
  (Rsh64Ux64 <typ.UInt64>
    (Hmul64u <typ.UInt64>
      (Const64 <typ.UInt64> [int64(1<<63+umagic64(c).m/2)])
      x)
    (Const64 <typ.UInt64> [umagic64(c).s-1]))
(Div64u x (Const64 [c])) && umagicOK64(c) && config.RegSize == 8 && c&1 == 0 && config.useHmul =>
  (Rsh64Ux64 <typ.UInt64>
    (Hmul64u <typ.UInt64>
      (Const64 <typ.UInt64> [int64(1<<63+(umagic64(c).m+1)/2)])
      (Rsh64Ux64 <typ.UInt64> x (Const64 <typ.UInt64> [1])))
    (Const64 <typ.UInt64> [umagic64(c).s-2]))
(Div64u x (Const64 [c])) && umagicOK64(c) && config.RegSize == 8 && config.useAvg && config.useHmul =>
  (Rsh64Ux64 <typ.UInt64>
    (Avg64u
      x
      (Hmul64u <typ.UInt64>
        (Const64 <typ.UInt64> [int64(umagic64(c).m)])
        x))
    (Const64 <typ.UInt64> [umagic64(c).s-1]))

// Signed divide by a negative constant.  Rewrite to divide by a positive constant.
(Div8  <t> n (Const8  [c])) && c < 0 && c != -1<<7  => (Neg8  (Div8  <t> n (Const8  <t> [-c])))
(Div16 <t> n (Const16 [c])) && c < 0 && c != -1<<15 => (Neg16 (Div16 <t> n (Const16 <t> [-c])))
(Div32 <t> n (Const32 [c])) && c < 0 && c != -1<<31 => (Neg32 (Div32 <t> n (Const32 <t> [-c])))
(Div64 <t> n (Const64 [c])) && c < 0 && c != -1<<63 => (Neg64 (Div64 <t> n (Const64 <t> [-c])))

// Dividing by the most-negative number.  Result is always 0 except
// if the input is also the most-negative number.
// We can detect that using the sign bit of x & -x.
(Div8  <t> x (Const8  [-1<<7 ])) => (Rsh8Ux64  (And8  <t> x (Neg8  <t> x)) (Const64 <typ.UInt64> [7 ]))
(Div16 <t> x (Const16 [-1<<15])) => (Rsh16Ux64 (And16 <t> x (Neg16 <t> x)) (Const64 <typ.UInt64> [15]))
(Div32 <t> x (Const32 [-1<<31])) => (Rsh32Ux64 (And32 <t> x (Neg32 <t> x)) (Const64 <typ.UInt64> [31]))
(Div64 <t> x (Const64 [-1<<63])) => (Rsh64Ux64 (And64 <t> x (Neg64 <t> x)) (Const64 <typ.UInt64> [63]))

// Signed divide by power of 2.
// n / c =       n >> log(c) if n >= 0
//       = (n+c-1) >> log(c) if n < 0
// We conditionally add c-1 by adding n>>63>>(64-log(c)) (first shift signed, second shift unsigned).
(Div8  <t> n (Const8  [c])) && isPowerOfTwo8(c) =>
  (Rsh8x64
    (Add8  <t> n (Rsh8Ux64  <t> (Rsh8x64  <t> n (Const64 <typ.UInt64> [ 7])) (Const64 <typ.UInt64> [int64( 8-log8(c))])))
    (Const64 <typ.UInt64> [int64(log8(c))]))
(Div16 <t> n (Const16 [c])) && isPowerOfTwo16(c) =>
  (Rsh16x64
    (Add16 <t> n (Rsh16Ux64 <t> (Rsh16x64 <t> n (Const64 <typ.UInt64> [15])) (Const64 <typ.UInt64> [int64(16-log16(c))])))
    (Const64 <typ.UInt64> [int64(log16(c))]))
(Div32 <t> n (Const32 [c])) && isPowerOfTwo32(c) =>
  (Rsh32x64
    (Add32 <t> n (Rsh32Ux64 <t> (Rsh32x64 <t> n (Const64 <typ.UInt64> [31])) (Const64 <typ.UInt64> [int64(32-log32(c))])))
    (Const64 <typ.UInt64> [int64(log32(c))]))
(Div64 <t> n (Const64 [c])) && isPowerOfTwo64(c) =>
  (Rsh64x64
    (Add64 <t> n (Rsh64Ux64 <t> (Rsh64x64 <t> n (Const64 <typ.UInt64> [63])) (Const64 <typ.UInt64> [int64(64-log64(c))])))
    (Const64 <typ.UInt64> [int64(log64(c))]))

// Signed divide, not a power of 2.  Strength reduce to a multiply.
(Div8 <t> x (Const8 [c])) && smagicOK8(c) =>
  (Sub8 <t>
    (Rsh32x64 <t>
      (Mul32 <typ.UInt32>
        (Const32 <typ.UInt32> [int32(smagic8(c).m)])
        (SignExt8to32 x))
      (Const64 <typ.UInt64> [8+smagic8(c).s]))
    (Rsh32x64 <t>
      (SignExt8to32 x)
      (Const64 <typ.UInt64> [31])))
(Div16 <t> x (Const16 [c])) && smagicOK16(c) =>
  (Sub16 <t>
    (Rsh32x64 <t>
      (Mul32 <typ.UInt32>
        (Const32 <typ.UInt32> [int32(smagic16(c).m)])
        (SignExt16to32 x))
      (Const64 <typ.UInt64> [16+smagic16(c).s]))
    (Rsh32x64 <t>
      (SignExt16to32 x)
      (Const64 <typ.UInt64> [31])))
(Div32 <t> x (Const32 [c])) && smagicOK32(c) && config.RegSize == 8 =>
  (Sub32 <t>
    (Rsh64x64 <t>
      (Mul64 <typ.UInt64>
        (Const64 <typ.UInt64> [int64(smagic32(c).m)])
        (SignExt32to64 x))
      (Const64 <typ.UInt64> [32+smagic32(c).s]))
    (Rsh64x64 <t>
      (SignExt32to64 x)
      (Const64 <typ.UInt64> [63])))
(Div32 <t> x (Const32 [c])) && smagicOK32(c) && config.RegSize == 4 && smagic32(c).m&1 == 0 && config.useHmul =>
  (Sub32 <t>
    (Rsh32x64 <t>
      (Hmul32 <t>
        (Const32 <typ.UInt32> [int32(smagic32(c).m/2)])
        x)
      (Const64 <typ.UInt64> [smagic32(c).s-1]))
    (Rsh32x64 <t>
      x
      (Const64 <typ.UInt64> [31])))
(Div32 <t> x (Const32 [c])) && smagicOK32(c) && config.RegSize == 4 && smagic32(c).m&1 != 0 && config.useHmul =>
  (Sub32 <t>
    (Rsh32x64 <t>
      (Add32 <t>
        (Hmul32 <t>
          (Const32 <typ.UInt32> [int32(smagic32(c).m)])
          x)
        x)
      (Const64 <typ.UInt64> [smagic32(c).s]))
    (Rsh32x64 <t>
      x
      (Const64 <typ.UInt64> [31])))
(Div64 <t> x (Const64 [c])) && smagicOK64(c) && smagic64(c).m&1 == 0 && config.useHmul =>
  (Sub64 <t>
    (Rsh64x64 <t>
      (Hmul64 <t>
        (Const64 <typ.UInt64> [int64(smagic64(c).m/2)])
        x)
      (Const64 <typ.UInt64> [smagic64(c).s-1]))
    (Rsh64x64 <t>
      x
      (Const64 <typ.UInt64> [63])))
(Div64 <t> x (Const64 [c])) && smagicOK64(c) && smagic64(c).m&1 != 0 && config.useHmul =>
  (Sub64 <t>
    (Rsh64x64 <t>
      (Add64 <t>
        (Hmul64 <t>
          (Const64 <typ.UInt64> [int64(smagic64(c).m)])
          x)
        x)
      (Const64 <typ.UInt64> [smagic64(c).s]))
    (Rsh64x64 <t>
      x
      (Const64 <typ.UInt64> [63])))

// Unsigned mod by power of 2 constant.
(Mod8u  <t> n (Const8  [c])) && isPowerOfTwo8(c)  => (And8  n (Const8  <t> [c-1]))
(Mod16u <t> n (Const16 [c])) && isPowerOfTwo16(c) => (And16 n (Const16 <t> [c-1]))
(Mod32u <t> n (Const32 [c])) && isPowerOfTwo32(c) => (And32 n (Const32 <t> [c-1]))
(Mod64u <t> n (Const64 [c])) && isPowerOfTwo64(c) => (And64 n (Const64 <t> [c-1]))
(Mod64u <t> n (Const64 [-1<<63]))                 => (And64 n (Const64 <t> [1<<63-1]))

// Signed non-negative mod by power of 2 constant.
(Mod8  <t> n (Const8  [c])) && isNonNegative(n) && isPowerOfTwo8(c)  => (And8  n (Const8  <t> [c-1]))
(Mod16 <t> n (Const16 [c])) && isNonNegative(n) && isPowerOfTwo16(c) => (And16 n (Const16 <t> [c-1]))
(Mod32 <t> n (Const32 [c])) && isNonNegative(n) && isPowerOfTwo32(c) => (And32 n (Const32 <t> [c-1]))
(Mod64 <t> n (Const64 [c])) && isNonNegative(n) && isPowerOfTwo64(c) => (And64 n (Const64 <t> [c-1]))
(Mod64 n (Const64 [-1<<63])) && isNonNegative(n)                   => n

// Signed mod by negative constant.
(Mod8  <t> n (Const8  [c])) && c < 0 && c != -1<<7  => (Mod8  <t> n (Const8  <t> [-c]))
(Mod16 <t> n (Const16 [c])) && c < 0 && c != -1<<15 => (Mod16 <t> n (Const16 <t> [-c]))
(Mod32 <t> n (Const32 [c])) && c < 0 && c != -1<<31 => (Mod32 <t> n (Const32 <t> [-c]))
(Mod64 <t> n (Const64 [c])) && c < 0 && c != -1<<63 => (Mod64 <t> n (Const64 <t> [-c]))

// All other mods by constants, do A%B = A-(A/B*B).
// This implements % with two * and a bunch of ancillary ops.
// One of the * is free if the user's code also computes A/B.
(Mod8   <t> x (Const8  [c])) && x.Op != OpConst8  && (c > 0 || c == -1<<7)
  => (Sub8  x (Mul8  <t> (Div8   <t> x (Const8  <t> [c])) (Const8  <t> [c])))
(Mod16  <t> x (Const16 [c])) && x.Op != OpConst16 && (c > 0 || c == -1<<15)
  => (Sub16 x (Mul16 <t> (Div16  <t> x (Const16 <t> [c])) (Const16 <t> [c])))
(Mod32  <t> x (Const32 [c])) && x.Op != OpConst32 && (c > 0 || c == -1<<31)
  => (Sub32 x (Mul32 <t> (Div32  <t> x (Const32 <t> [c])) (Const32 <t> [c])))
(Mod64  <t> x (Const64 [c])) && x.Op != OpConst64 && (c > 0 || c == -1<<63)
  => (Sub64 x (Mul64 <t> (Div64  <t> x (Const64 <t> [c])) (Const64 <t> [c])))
(Mod8u  <t> x (Const8  [c])) && x.Op != OpConst8  && c > 0 && umagicOK8( c)
  => (Sub8  x (Mul8  <t> (Div8u  <t> x (Const8  <t> [c])) (Const8  <t> [c])))
(Mod16u <t> x (Const16 [c])) && x.Op != OpConst16 && c > 0 && umagicOK16(c)
  => (Sub16 x (Mul16 <t> (Div16u <t> x (Const16 <t> [c])) (Const16 <t> [c])))
(Mod32u <t> x (Const32 [c])) && x.Op != OpConst32 && c > 0 && umagicOK32(c)
  => (Sub32 x (Mul32 <t> (Div32u <t> x (Const32 <t> [c])) (Const32 <t>