// 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   [int64(int8(c))])
(Trunc32to8  (Const32 [c]))  -> (Const8   [int64(int8(c))])
(Trunc32to16 (Const32 [c]))  -> (Const16  [int64(int16(c))])
(Trunc64to8  (Const64 [c]))  -> (Const8   [int64(int8(c))])
(Trunc64to16 (Const64 [c]))  -> (Const16  [int64(int16(c))])
(Trunc64to32 (Const64 [c]))  -> (Const32  [int64(int32(c))])
(Cvt64Fto32F (Const64F [c])) -> (Const32F [f2i(float64(i2f32(c)))])
(Cvt32Fto64F (Const32F [c])) -> (Const64F [c]) // c is already a 64 bit float

(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 [int64( uint8(c))])
(ZeroExt8to32  (Const8  [c])) -> (Const32 [int64( uint8(c))])
(ZeroExt8to64  (Const8  [c])) -> (Const64 [int64( uint8(c))])
(ZeroExt16to32 (Const16 [c])) -> (Const32 [int64(uint16(c))])
(ZeroExt16to64 (Const16 [c])) -> (Const64 [int64(uint16(c))])
(ZeroExt32to64 (Const32 [c])) -> (Const64 [int64(uint32(c))])
(SignExt8to16  (Const8  [c])) -> (Const16 [int64(  int8(c))])
(SignExt8to32  (Const8  [c])) -> (Const32 [int64(  int8(c))])
(SignExt8to64  (Const8  [c])) -> (Const64 [int64(  int8(c))])
(SignExt16to32 (Const16 [c])) -> (Const32 [int64( int16(c))])
(SignExt16to64 (Const16 [c])) -> (Const64 [int64( int16(c))])
(SignExt32to64 (Const32 [c])) -> (Const64 [int64( int32(c))])

// const negation is currently handled by frontend
//(Neg8 (Const8 [c])) -> (Const8 [-c])
//(Neg16 (Const16 [c])) -> (Const16 [-c])
//(Neg32 (Const32 [c])) -> (Const32 [-c])
//(Neg64 (Const64 [c])) -> (Const64 [-c])
//(Neg32F (Const32F [c])) -> (Const32F [f2i(-i2f(c))])
//(Neg64F (Const64F [c])) -> (Const64F [f2i(-i2f(c))])

(Add8   (Const8 [c])   (Const8 [d]))   -> (Const8  [int64(int8(c+d))])
(Add16  (Const16 [c])  (Const16 [d]))  -> (Const16 [int64(int16(c+d))])
(Add32  (Const32 [c])  (Const32 [d]))  -> (Const32 [int64(int32(c+d))])
(Add64  (Const64 [c])  (Const64 [d]))  -> (Const64 [c+d])
(Add32F (Const32F [c]) (Const32F [d])) ->
        (Const32F [f2i(float64(i2f32(c) + i2f32(d)))]) // ensure we combine the operands with 32 bit precision
(Add64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) + i2f(d))])
(AddPtr <t> x (Const64 [c])) -> (OffPtr <t> x [c])

(Sub8   (Const8 [c]) (Const8 [d]))     -> (Const8 [int64(int8(c-d))])
(Sub16  (Const16 [c]) (Const16 [d]))   -> (Const16 [int64(int16(c-d))])
(Sub32  (Const32 [c]) (Const32 [d]))   -> (Const32 [int64(int32(c-d))])
(Sub64  (Const64 [c]) (Const64 [d]))   -> (Const64 [c-d])
(Sub32F (Const32F [c]) (Const32F [d])) ->
        (Const32F [f2i(float64(i2f32(c) - i2f32(d)))])
(Sub64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) - i2f(d))])

(Mul8   (Const8 [c])   (Const8 [d]))   -> (Const8  [int64(int8(c*d))])
(Mul16  (Const16 [c])  (Const16 [d]))  -> (Const16 [int64(int16(c*d))])
(Mul32  (Const32 [c])  (Const32 [d]))  -> (Const32 [int64(int32(c*d))])
(Mul64  (Const64 [c])  (Const64 [d]))  -> (Const64 [c*d])
(Mul32F (Const32F [c]) (Const32F [d])) ->
        (Const32F [f2i(float64(i2f32(c) * i2f32(d)))])
(Mul64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) * i2f(d))])

(Div8   (Const8  [c])  (Const8  [d])) && d != 0 -> (Const8  [int64(int8(c)/int8(d))])
(Div16  (Const16 [c])  (Const16 [d])) && d != 0 -> (Const16 [int64(int16(c)/int16(d))])
(Div32  (Const32 [c])  (Const32 [d])) && d != 0 -> (Const32 [int64(int32(c)/int32(d))])
(Div64  (Const64 [c])  (Const64 [d])) && d != 0 -> (Const64 [c/d])
(Div8u  (Const8  [c])  (Const8  [d])) && d != 0 -> (Const8  [int64(int8(uint8(c)/uint8(d)))])
(Div16u (Const16 [c])  (Const16 [d])) && d != 0 -> (Const16 [int64(int16(uint16(c)/uint16(d)))])
(Div32u (Const32 [c])  (Const32 [d])) && d != 0 -> (Const32 [int64(int32(uint32(c)/uint32(d)))])
(Div64u (Const64 [c])  (Const64 [d])) && d != 0 -> (Const64 [int64(uint64(c)/uint64(d))])
(Div32F (Const32F [c]) (Const32F [d])) -> (Const32F [f2i(float64(i2f32(c) / i2f32(d)))])
(Div64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) / i2f(d))])

// Convert x * 1 to x.
(Mul8  (Const8  [1]) x) -> x
(Mul16 (Const16 [1]) x) -> x
(Mul32 (Const32 [1]) x) -> x
(Mul64 (Const64 [1]) x) -> x

// Convert x * -1 to -x.
(Mul8  (Const8  [-1]) x) -> (Neg8  x)
(Mul16 (Const16 [-1]) x) -> (Neg16 x)
(Mul32 (Const32 [-1]) x) -> (Neg32 x)
(Mul64 (Const64 [-1]) x) -> (Neg64 x)

// Convert multiplication by a power of two to a shift.
(Mul8  <t> n (Const8  [c])) && isPowerOfTwo(c) -> (Lsh8x64  <t> n (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Mul16 <t> n (Const16 [c])) && isPowerOfTwo(c) -> (Lsh16x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Mul32 <t> n (Const32 [c])) && isPowerOfTwo(c) -> (Lsh32x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Mul64 <t> n (Const64 [c])) && isPowerOfTwo(c) -> (Lsh64x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Mul8  <t> n (Const8  [c])) && t.IsSigned() && isPowerOfTwo(-c) -> (Neg8  (Lsh8x64  <t> n (Const64 <config.fe.TypeUInt64()> [log2(-c)])))
(Mul16 <t> n (Const16 [c])) && t.IsSigned() && isPowerOfTwo(-c) -> (Neg16 (Lsh16x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(-c)])))
(Mul32 <t> n (Const32 [c])) && t.IsSigned() && isPowerOfTwo(-c) -> (Neg32 (Lsh32x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(-c)])))
(Mul64 <t> n (Const64 [c])) && t.IsSigned() && isPowerOfTwo(-c) -> (Neg64 (Lsh64x64 <t> n (Const64 <config.fe.TypeUInt64()> [log2(-c)])))

(Mod8  (Const8  [c]) (Const8  [d])) && d != 0 -> (Const8  [int64(int8(c % d))])
(Mod16 (Const16 [c]) (Const16 [d])) && d != 0 -> (Const16 [int64(int16(c % d))])
(Mod32 (Const32 [c]) (Const32 [d])) && d != 0 -> (Const32 [int64(int32(c % d))])
(Mod64 (Const64 [c]) (Const64 [d])) && d != 0 -> (Const64 [c % d])

(Mod8u  (Const8 [c])  (Const8  [d])) && d != 0 -> (Const8  [int64(uint8(c) % uint8(d))])
(Mod16u (Const16 [c]) (Const16 [d])) && d != 0 -> (Const16 [int64(uint16(c) % uint16(d))])
(Mod32u (Const32 [c]) (Const32 [d])) && d != 0 -> (Const32 [int64(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 [int64(int32(c) << uint64(d))])
(Rsh32x64  (Const32 [c]) (Const64 [d])) -> (Const32 [int64(int32(c) >> uint64(d))])
(Rsh32Ux64 (Const32 [c]) (Const64 [d])) -> (Const32 [int64(int32(uint32(c) >> uint64(d)))])
(Lsh16x64  (Const16 [c]) (Const64 [d])) -> (Const16 [int64(int16(c) << uint64(d))])
(Rsh16x64  (Const16 [c]) (Const64 [d])) -> (Const16 [int64(int16(c) >> uint64(d))])
(Rsh16Ux64 (Const16 [c]) (Const64 [d])) -> (Const16 [int64(int16(uint16(c) >> uint64(d)))])
(Lsh8x64   (Const8  [c]) (Const64 [d])) -> (Const8  [int64(int8(c) << uint64(d))])
(Rsh8x64   (Const8  [c]) (Const64 [d])) -> (Const8  [int64(int8(c) >> uint64(d))])
(Rsh8Ux64  (Const8  [c]) (Const64 [d])) -> (Const8  [int64(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 [1])
(IsInBounds (ZeroExt8to64  _) (Const64 [c])) && (1 << 8)  <= c -> (ConstBool [1])
(IsInBounds (ZeroExt16to32 _) (Const32 [c])) && (1 << 16) <= c -> (ConstBool [1])
(IsInBounds (ZeroExt16to64 _) (Const64 [c])) && (1 << 16) <= c -> (ConstBool [1])
(IsInBounds x x) -> (ConstBool [0])
(IsInBounds (And32 (Const32 [c]) _) (Const32 [d])) && 0 <= c && c < d -> (ConstBool [1])
(IsInBounds (And64 (Const64 [c]) _) (Const64 [d])) && 0 <= c && c < d -> (ConstBool [1])
(IsInBounds (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(0 <= c && c < d)])
(IsInBounds (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(0 <= c && c < d)])
// (Mod64u x y) is always between 0 (inclusive) and y (exclusive).
(IsInBounds (Mod32u _ y) y) -> (ConstBool [1])
(IsInBounds (Mod64u _ y) y) -> (ConstBool [1])

(IsSliceInBounds x x) -> (ConstBool [1])
(IsSliceInBounds (And32 (Const32 [c]) _) (Const32 [d])) && 0 <= c && c <= d -> (ConstBool [1])
(IsSliceInBounds (And64 (Const64 [c]) _) (Const64 [d])) && 0 <= c && c <= d -> (ConstBool [1])
(IsSliceInBounds (Const32 [0]) _) -> (ConstBool [1])
(IsSliceInBounds (Const64 [0]) _) -> (ConstBool [1])
(IsSliceInBounds (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(0 <= c && c <= d)])
(IsSliceInBounds (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(0 <= c && c <= d)])
(IsSliceInBounds (SliceLen x) (SliceCap x)) -> (ConstBool [1])

(Eq64 x x) -> (ConstBool [1])
(Eq32 x x) -> (ConstBool [1])
(Eq16 x x) -> (ConstBool [1])
(Eq8  x x) -> (ConstBool [1])
(EqB (ConstBool [c]) (ConstBool [d])) -> (ConstBool [b2i(c == d)])
(EqB (ConstBool [0]) x) -> (Not x)
(EqB (ConstBool [1]) x) -> x

(Neq64 x x) -> (ConstBool [0])
(Neq32 x x) -> (ConstBool [0])
(Neq16 x x) -> (ConstBool [0])
(Neq8  x x) -> (ConstBool [0])
(NeqB (ConstBool [c]) (ConstBool [d])) -> (ConstBool [b2i(c != d)])
(NeqB (ConstBool [0]) x) -> x
(NeqB (ConstBool [1]) x) -> (Not x)

(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> [int64(int32(c-d))]) x)
(Eq16 (Const16 <t> [c]) (Add16 (Const16 <t> [d]) x)) -> (Eq16 (Const16 <t> [int64(int16(c-d))]) x)
(Eq8  (Const8  <t> [c]) (Add8  (Const8  <t> [d]) x)) -> (Eq8  (Const8 <t> [int64(int8(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> [int64(int32(c-d))]) x)
(Neq16 (Const16 <t> [c]) (Add16 (Const16 <t> [d]) x)) -> (Neq16 (Const16 <t> [int64(int16(c-d))]) x)
(Neq8  (Const8  <t> [c]) (Add8  (Const8  <t> [d]) x)) -> (Neq8 (Const8 <t> [int64(int8(c-d))]) x)

// canonicalize: swap arguments for commutative operations when one argument is a constant.
(Eq64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Eq64 (Const64 <t> [c]) x)
(Eq32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Eq32 (Const32 <t> [c]) x)
(Eq16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Eq16 (Const16 <t> [c]) x)
(Eq8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Eq8  (Const8  <t> [c]) x)

(Neq64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Neq64 (Const64 <t> [c]) x)
(Neq32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Neq32 (Const32 <t> [c]) x)
(Neq16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Neq16 (Const16 <t> [c]) x)
(Neq8  x (Const8 <t>  [c])) && x.Op != OpConst8  -> (Neq8  (Const8  <t> [c]) x)

// AddPtr is not canonicalized because nilcheck ptr checks the first argument to be non-nil.
(Add64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Add64 (Const64 <t> [c]) x)
(Add32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Add32 (Const32 <t> [c]) x)
(Add16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Add16 (Const16 <t> [c]) x)
(Add8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Add8  (Const8  <t> [c]) x)

(Mul64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Mul64 (Const64 <t> [c]) x)
(Mul32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Mul32 (Const32 <t> [c]) x)
(Mul16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Mul16 (Const16 <t> [c]) x)
(Mul8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Mul8  (Const8  <t> [c]) x)

(Sub64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Add64 (Const64 <t> [-c]) x)
(Sub32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Add32 (Const32 <t> [int64(int32(-c))]) x)
(Sub16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Add16 (Const16 <t> [int64(int16(-c))]) x)
(Sub8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Add8  (Const8  <t> [int64(int8(-c))]) x)

(And64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (And64 (Const64 <t> [c]) x)
(And32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (And32 (Const32 <t> [c]) x)
(And16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (And16 (Const16 <t> [c]) x)
(And8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (And8  (Const8  <t> [c]) x)

(Or64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Or64 (Const64 <t> [c]) x)
(Or32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Or32 (Const32 <t> [c]) x)
(Or16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Or16 (Const16 <t> [c]) x)
(Or8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Or8  (Const8  <t> [c]) x)

(Xor64 x (Const64 <t> [c])) && x.Op != OpConst64 -> (Xor64 (Const64 <t> [c]) x)
(Xor32 x (Const32 <t> [c])) && x.Op != OpConst32 -> (Xor32 (Const32 <t> [c]) x)
(Xor16 x (Const16 <t> [c])) && x.Op != OpConst16 -> (Xor16 (Const16 <t> [c]) x)
(Xor8  x (Const8  <t> [c])) && x.Op != OpConst8  -> (Xor8  (Const8  <t> [c]) x)

// fold negation into comparison operators
(Not (Eq64 x y)) -> (Neq64 x y)
(Not (Eq32 x y)) -> (Neq32 x y)
(Not (Eq16 x y)) -> (Neq16 x y)
(Not (Eq8  x y)) -> (Neq8  x y)
(Not (EqB  x y)) -> (NeqB  x y)

(Not (Neq64 x y)) -> (Eq64 x y)
(Not (Neq32 x y)) -> (Eq32 x y)
(Not (Neq16 x y)) -> (Eq16 x y)
(Not (Neq8  x y)) -> (Eq8  x y)
(Not (NeqB  x y)) -> (EqB  x y)

(Not (Greater64 x y)) -> (Leq64 x y)
(Not (Greater32 x y)) -> (Leq32 x y)
(Not (Greater16 x y)) -> (Leq16 x y)
(Not (Greater8  x y)) -> (Leq8  x y)

(Not (Greater64U x y)) -> (Leq64U x y)
(Not (Greater32U x y)) -> (Leq32U x y)
(Not (Greater16U x y)) -> (Leq16U x y)
(Not (Greater8U  x y)) -> (Leq8U  x y)

(Not (Geq64 x y)) -> (Less64 x y)
(Not (Geq32 x y)) -> (Less32 x y)
(Not (Geq16 x y)) -> (Less16 x y)
(Not (Geq8  x y)) -> (Less8  x y)

(Not (Geq64U x y)) -> (Less64U x y)
(Not (Geq32U x y)) -> (Less32U x y)
(Not (Geq16U x y)) -> (Less16U x y)
(Not (Geq8U  x y)) -> (Less8U  x y)

(Not (Less64 x y)) -> (Geq64 x y)
(Not (Less32 x y)) -> (Geq32 x y)
(Not (Less16 x y)) -> (Geq16 x y)
(Not (Less8  x y)) -> (Geq8  x y)

(Not (Less64U x y)) -> (Geq64U x y)
(Not (Less32U x y)) -> (Geq32U x y)
(Not (Less16U x y)) -> (Geq16U x y)
(Not (Less8U  x y)) -> (Geq8U  x y)

(Not (Leq64 x y)) -> (Greater64 x y)
(Not (Leq32 x y)) -> (Greater32 x y)
(Not (Leq16 x y)) -> (Greater16 x y)
(Not (Leq8  x y)) -> (Greater8 x y)

(Not (Leq64U x y)) -> (Greater64U x y)
(Not (Leq32U x y)) -> (Greater32U x y)
(Not (Leq16U x y)) -> (Greater16U x y)
(Not (Leq8U  x y)) -> (Greater8U  x y)

// 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> [int64(int32(c*d))]) (Mul32 <t> (Const32 <t> [c]) x))

// 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
(Lsh64x64  x (Const64 [0])) -> x
(Rsh64x64  x (Const64 [0])) -> x
(Rsh64Ux64 x (Const64 [0])) -> x
(Lsh32x64  x (Const64 [0])) -> x
(Rsh32x64  x (Const64 [0])) -> x
(Rsh32Ux64 x (Const64 [0])) -> x
(Lsh16x64  x (Const64 [0])) -> x
(Rsh16x64  x (Const64 [0])) -> x
(Rsh16Ux64 x (Const64 [0])) -> x
(Lsh8x64   x (Const64 [0])) -> x
(Rsh8x64   x (Const64 [0])) -> x
(Rsh8Ux64  x (Const64 [0])) -> x

// zero shifted.
(Lsh64x64  (Const64 [0]) _) -> (Const64 [0])
(Lsh64x32  (Const64 [0]) _) -> (Const64 [0])
(Lsh64x16  (Const64 [0]) _) -> (Const64 [0])
(Lsh64x8  (Const64 [0]) _) -> (Const64 [0])
(Rsh64x64  (Const64 [0]) _) -> (Const64 [0])
(Rsh64x32  (Const64 [0]) _) -> (Const64 [0])
(Rsh64x16  (Const64 [0]) _) -> (Const64 [0])
(Rsh64x8  (Const64 [0]) _) -> (Const64 [0])
(Rsh64Ux64 (Const64 [0]) _) -> (Const64 [0])
(Rsh64Ux32 (Const64 [0]) _) -> (Const64 [0])
(Rsh64Ux16 (Const64 [0]) _) -> (Const64 [0])
(Rsh64Ux8 (Const64 [0]) _) -> (Const64 [0])
(Lsh32x64  (Const32 [0]) _) -> (Const32 [0])
(Lsh32x32  (Const32 [0]) _) -> (Const32 [0])
(Lsh32x16  (Const32 [0]) _) -> (Const32 [0])
(Lsh32x8  (Const32 [0]) _) -> (Const32 [0])
(Rsh32x64  (Const32 [0]) _) -> (Const32 [0])
(Rsh32x32  (Const32 [0]) _) -> (Const32 [0])
(Rsh32x16  (Const32 [0]) _) -> (Const32 [0])
(Rsh32x8  (Const32 [0]) _) -> (Const32 [0])
(Rsh32Ux64 (Const32 [0]) _) -> (Const32 [0])
(Rsh32Ux32 (Const32 [0]) _) -> (Const32 [0])
(Rsh32Ux16 (Const32 [0]) _) -> (Const32 [0])
(Rsh32Ux8 (Const32 [0]) _) -> (Const32 [0])
(Lsh16x64  (Const16 [0]) _) -> (Const16 [0])
(Lsh16x32  (Const16 [0]) _) -> (Const16 [0])
(Lsh16x16  (Const16 [0]) _) -> (Const16 [0])
(Lsh16x8  (Const16 [0]) _) -> (Const16 [0])
(Rsh16x64  (Const16 [0]) _) -> (Const16 [0])
(Rsh16x32  (Const16 [0]) _) -> (Const16 [0])
(Rsh16x16  (Const16 [0]) _) -> (Const16 [0])
(Rsh16x8  (Const16 [0]) _) -> (Const16 [0])
(Rsh16Ux64 (Const16 [0]) _) -> (Const16 [0])
(Rsh16Ux32 (Const16 [0]) _) -> (Const16 [0])
(Rsh16Ux16 (Const16 [0]) _) -> (Const16 [0])
(Rsh16Ux8 (Const16 [0]) _) -> (Const16 [0])
(Lsh8x64   (Const8 [0]) _) -> (Const8  [0])
(Lsh8x32   (Const8 [0]) _) -> (Const8  [0])
(Lsh8x16   (Const8 [0]) _) -> (Const8  [0])
(Lsh8x8   (Const8 [0]) _) -> (Const8  [0])
(Rsh8x64   (Const8 [0]) _) -> (Const8  [0])
(Rsh8x32   (Const8 [0]) _) -> (Const8  [0])
(Rsh8x16   (Const8 [0]) _) -> (Const8  [0])
(Rsh8x8   (Const8 [0]) _) -> (Const8  [0])
(Rsh8Ux64  (Const8 [0]) _) -> (Const8  [0])
(Rsh8Ux32  (Const8 [0]) _) -> (Const8  [0])
(Rsh8Ux16  (Const8 [0]) _) -> (Const8  [0])
(Rsh8Ux8  (Const8 [0]) _) -> (Const8  [0])

// large left shifts of all values, and right shifts of unsigned values
(Lsh64x64  _ (Const64 [c])) && uint64(c) >= 64 -> (Const64 [0])
(Rsh64Ux64 _ (Const64 [c])) && uint64(c) >= 64 -> (Const64 [0])
(Lsh32x64  _ (Const64 [c])) && uint64(c) >= 32 -> (Const32 [0])
(Rsh32Ux64 _ (Const64 [c])) && uint64(c) >= 32 -> (Const32 [0])
(Lsh16x64  _ (Const64 [c])) && uint64(c) >= 16 -> (Const16 [0])
(Rsh16Ux64 _ (Const64 [c])) && uint64(c) >= 16 -> (Const16 [0])
(Lsh8x64   _ (Const64 [c])) && uint64(c) >= 8  -> (Const8  [0])
(Rsh8Ux64  _ (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]))

// ((x >> c1) << c2) >> c3
(Rsh64Ux64 (Lsh64x64 (Rsh64Ux64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Rsh64Ux64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Rsh32Ux64 (Lsh32x64 (Rsh32Ux64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Rsh32Ux64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Rsh16Ux64 (Lsh16x64 (Rsh16Ux64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Rsh16Ux64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Rsh8Ux64 (Lsh8x64 (Rsh8Ux64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Rsh8Ux64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))

// ((x << c1) >> c2) << c3
(Lsh64x64 (Rsh64Ux64 (Lsh64x64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Lsh64x64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Lsh32x64 (Rsh32Ux64 (Lsh32x64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Lsh32x64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Lsh16x64 (Rsh16Ux64 (Lsh16x64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Lsh16x64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))
(Lsh8x64 (Rsh8Ux64 (Lsh8x64 x (Const64 [c1])) (Const64 [c2])) (Const64 [c3]))
  && uint64(c1) >= uint64(c2) && uint64(c3) >= uint64(c2) && !uaddOvf(c1-c2, c3)
  -> (Lsh8x64 x (Const64 <config.fe.TypeUInt64()> [c1-c2+c3]))

// constant comparisons
(Eq64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c == d)])
(Eq32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c == d)])
(Eq16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c == d)])
(Eq8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c == d)])

(Neq64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c != d)])
(Neq32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c != d)])
(Neq16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c != d)])
(Neq8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c != d)])

(Greater64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c > d)])
(Greater32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c > d)])
(Greater16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c > d)])
(Greater8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c > d)])

(Greater64U (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(uint64(c) > uint64(d))])
(Greater32U (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(uint32(c) > uint32(d))])
(Greater16U (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(uint16(c) > uint16(d))])
(Greater8U  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(uint8(c)  > uint8(d))])

(Geq64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c >= d)])
(Geq32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c >= d)])
(Geq16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c >= d)])
(Geq8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c >= d)])

(Geq64U (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(uint64(c) >= uint64(d))])
(Geq32U (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(uint32(c) >= uint32(d))])
(Geq16U (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(uint16(c) >= uint16(d))])
(Geq8U  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(uint8(c)  >= uint8(d))])

(Less64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c < d)])
(Less32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c < d)])
(Less16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c < d)])
(Less8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c < d)])

(Less64U (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(uint64(c) < uint64(d))])
(Less32U (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(uint32(c) < uint32(d))])
(Less16U (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(uint16(c) < uint16(d))])
(Less8U  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(uint8(c)  < uint8(d))])

(Leq64 (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(c <= d)])
(Leq32 (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(c <= d)])
(Leq16 (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(c <= d)])
(Leq8  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(c <= d)])

(Leq64U (Const64 [c]) (Const64 [d])) -> (ConstBool [b2i(uint64(c) <= uint64(d))])
(Leq32U (Const32 [c]) (Const32 [d])) -> (ConstBool [b2i(uint32(c) <= uint32(d))])
(Leq16U (Const16 [c]) (Const16 [d])) -> (ConstBool [b2i(uint16(c) <= uint16(d))])
(Leq8U  (Const8  [c]) (Const8  [d])) -> (ConstBool [b2i(uint8(c)  <= uint8(d))])

// simplifications
(Or64 x x) -> x
(Or32 x x) -> x
(Or16 x x) -> x
(Or8  x x) -> x
(Or64 (Const64 [0]) x) -> x
(Or32 (Const32 [0]) x) -> x
(Or16 (Const16 [0]) x) -> x
(Or8  (Const8  [0]) x) -> x
(Or64 (Const64 [-1]) _) -> (Const64 [-1])
(Or32 (Const32 [-1]) _) -> (Const32 [-1])
(Or16 (Const16 [-1]) _) -> (Const16 [-1])
(Or8  (Const8  [-1]) _) -> (Const8  [-1])
(And64 x x) -> x
(And32 x x) -> x
(And16 x x) -> x
(And8  x x) -> x
(And64 (Const64 [-1]) x) -> x
(And32 (Const32 [-1]) x) -> x
(And16 (Const16 [-1]) x) -> x
(And8  (Const8  [-1]) x) -> x
(And64 (Const64 [0]) _) -> (Const64 [0])
(And32 (Const32 [0]) _) -> (Const32 [0])
(And16 (Const16 [0]) _) -> (Const16 [0])
(And8  (Const8  [0]) _) -> (Const8  [0])
(Xor64 x x) -> (Const64 [0])
(Xor32 x x) -> (Const32 [0])
(Xor16 x x) -> (Const16 [0])
(Xor8  x x) -> (Const8  [0])
(Xor64 (Const64 [0]) x) -> x
(Xor32 (Const32 [0]) x) -> x
(Xor16 (Const16 [0]) x) -> x
(Xor8  (Const8  [0]) x) -> x
(Add64 (Const64 [0]) x) -> x
(Add32 (Const32 [0]) x) -> x
(Add16 (Const16 [0]) x) -> x
(Add8  (Const8  [0]) x) -> x
(Sub64 x x) -> (Const64 [0])
(Sub32 x x) -> (Const32 [0])
(Sub16 x x) -> (Const16 [0])
(Sub8  x x) -> (Const8  [0])
(Mul64 (Const64 [0]) _) -> (Const64 [0])
(Mul32 (Const32 [0]) _) -> (Const32 [0])
(Mul16 (Const16 [0]) _) -> (Const16 [0])
(Mul8  (Const8  [0]) _) -> (Const8  [0])
(Com8  (Com8  x)) -> x
(Com16 (Com16 x)) -> x
(Com32 (Com32 x)) -> x
(Com64 (Com64 x)) -> x
(Neg8  (Sub8  x y)) -> (Sub8  y x)
(Neg16 (Sub16 x y)) -> (Sub16 y x)
(Neg32 (Sub32 x y)) -> (Sub32 y x)
(Neg64 (Sub64 x y)) -> (Sub64 y x)

(And64 x (And64 x y)) -> (And64 x y)
(And32 x (And32 x y)) -> (And32 x y)
(And16 x (And16 x y)) -> (And16 x y)
(And8  x (And8  x y)) -> (And8  x y)
(And64 x (And64 y x)) -> (And64 x y)
(And32 x (And32 y x)) -> (And32 x y)
(And16 x (And16 y x)) -> (And16 x y)
(And8  x (And8  y x)) -> (And8  x y)
(And64 (And64 x y) x) -> (And64 x y)
(And32 (And32 x y) x) -> (And32 x y)
(And16 (And16 x y) x) -> (And16 x y)
(And8  (And8  x y) x) -> (And8  x y)
(And64 (And64 x y) y) -> (And64 x y)
(And32 (And32 x y) y) -> (And32 x y)
(And16 (And16 x y) y) -> (And16 x y)
(And8  (And8  x y) y) -> (And8  x y)
(Or64 x (Or64 x y)) -> (Or64 x y)
(Or32 x (Or32 x y)) -> (Or32 x y)
(Or16 x (Or16 x y)) -> (Or16 x y)
(Or8  x (Or8  x y)) -> (Or8  x y)
(Or64 x (Or64 y x)) -> (Or64 x y)
(Or32 x (Or32 y x)) -> (Or32 x y)
(Or16 x (Or16 y x)) -> (Or16 x y)
(Or8  x (Or8  y x)) -> (Or8  x y)
(Or64 (Or64 x y) x) -> (Or64 x y)
(Or32 (Or32 x y) x) -> (Or32 x y)
(Or16 (Or16 x y) x) -> (Or16 x y)
(Or8  (Or8  x y) x) -> (Or8  x y)
(Or64 (Or64 x y) y) -> (Or64 x y)
(Or32 (Or32 x y) y) -> (Or32 x y)
(Or16 (Or16 x y) y) -> (Or16 x y)
(Or8  (Or8  x y) y) -> (Or8  x y)
(Xor64 x (Xor64 x y)) -> y
(Xor32 x (Xor32 x y)) -> y
(Xor16 x (Xor16 x y)) -> y
(Xor8  x (Xor8  x y)) -> y
(Xor64 x (Xor64 y x)) -> y
(Xor32 x (Xor32 y x)) -> y
(Xor16 x (Xor16 y x)) -> y
(Xor8  x (Xor8  y x)) -> y
(Xor64 (Xor64 x y) x) -> y
(Xor32 (Xor32 x y) x) -> y
(Xor16 (Xor16 x y) x) -> y
(Xor8  (Xor8  x y) x) -> y
(Xor64 (Xor64 x y) y) -> x
(Xor32 (Xor32 x y) y) -> x
(Xor16 (Xor16 x y) y) -> x
(Xor8  (Xor8  x y) y) -> 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])

// Rewrite AND of consts as shifts if possible, slightly faster for 64 bit operands
// leading zeros can be shifted left, then right
(And64 <t> (Const64 [y]) x) && nlz(y) + nto(y) == 64 && nto(y) >= 32
  -> (Rsh64Ux64 (Lsh64x64 <t> x (Const64 <t> [nlz(y)])) (Const64 <t> [nlz(y)]))
// trailing zeros can be shifted right, then left
(And64 <t> (Const64 [y]) x) && nlo(y) + ntz(y) == 64 && ntz(y) >= 32
  -> (Lsh64x64 (Rsh64Ux64 <t> x (Const64 <t> [ntz(y)])) (Const64 <t> [ntz(y)]))

// simplifications often used for lengths.  e.g. len(s[i:i+5])==5
(Sub64 (Add64 x y) x) -> y
(Sub64 (Add64 x y) y) -> x
(Sub32 (Add32 x y) x) -> y
(Sub32 (Add32 x y) y) -> x
(Sub16 (Add16 x y) x) -> y
(Sub16 (Add16 x y) y) -> x
(Sub8  (Add8  x y) x) -> y
(Sub8  (Add8  x y) y) -> x

// 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])

// user nil checks
(NeqPtr p (ConstNil)) -> (IsNonNil p)
(NeqPtr (ConstNil) p) -> (IsNonNil p)
(EqPtr p (ConstNil)) -> (Not (IsNonNil p))
(EqPtr (ConstNil) p) -> (Not (IsNonNil p))
(IsNonNil (ConstNil)) -> (ConstBool [0])

// 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 [w] p2 x _)) && isSamePtr(p1,p2) && t1.Compare(x.Type)==CMPeq && w == t1.Size() -> x

// Collapse OffPtr
(OffPtr (OffPtr p [b]) [a]) -> (OffPtr p [a+b])
(OffPtr p [0]) && v.Type.Compare(p.Type) == CMPeq -> p

// indexing operations
// Note: bounds check has already been done
(PtrIndex <t> ptr idx) && config.PtrSize == 4 -> (AddPtr ptr (Mul32 <config.fe.TypeInt()> idx (Const32 <config.fe.TypeInt()> [t.ElemType().Size()])))
(PtrIndex <t> ptr idx) && config.PtrSize == 8 -> (AddPtr ptr (Mul64 <config.fe.TypeInt()> idx (Const64 <config.fe.TypeInt()> [t.ElemType().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 && config.fe.CanSSA(t) ->
  (StructMake0)
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 1 && config.fe.CanSSA(t) ->
  (StructMake1
    (Load <t.FieldType(0)> ptr mem))
(Load <t> ptr mem) && t.IsStruct() && t.NumFields() == 2 && config.fe.CanSSA(t) ->
  (StructMake2
    (Load <t.FieldType(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 && config.fe.CanSSA(t) ->
  (StructMake3
    (Load <t.FieldType(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 && config.fe.CanSSA(t) ->
  (StructMake4
    (Load <t.FieldType(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)) && !config.fe.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).Size()] dst f0 mem)
(Store dst (StructMake2 <t> f0 f1) mem) ->
  (Store [t.FieldType(1).Size()]
    (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
    f1
    (Store [t.FieldType(0).Size()] dst f0 mem))
(Store dst (StructMake3 <t> f0 f1 f2) mem) ->
  (Store [t.FieldType(2).Size()]
    (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] dst)
    f2
    (Store [t.FieldType(1).Size()]
      (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
      f1
      (Store [t.FieldType(0).Size()] dst f0 mem)))
(Store dst (StructMake4 <t> f0 f1 f2 f3) mem) ->
  (Store [t.FieldType(3).Size()]
    (OffPtr <t.FieldType(3).PtrTo()> [t.FieldOff(3)] dst)
    f3
    (Store [t.FieldType(2).Size()]
      (OffPtr <t.FieldType(2).PtrTo()> [t.FieldOff(2)] dst)
      f2
      (Store [t.FieldType(1).Size()]
        (OffPtr <t.FieldType(1).PtrTo()> [t.FieldOff(1)] dst)
        f1
        (Store [t.FieldType(0).Size()] dst f0 mem))))

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

// un-SSAable values use mem->mem copies
(Store [size] dst (Load <t> src mem) mem) && !config.fe.CanSSA(t) ->
	(Move [MakeSizeAndAlign(size, t.Alignment()).Int64()] dst src mem)
(Store [size] dst (Load <t> src mem) (VarDef {x} mem)) && !config.fe.CanSSA(t) ->
	(Move [MakeSizeAndAlign(size, t.Alignment()).Int64()] 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 && config.fe.CanSSA(t) ->
  (ArrayMake1 (Load <t.ElemType()> ptr mem))

(Store _ (ArrayMake0) mem) -> mem
(Store [size] dst (ArrayMake1 e) mem) -> (Store [size] dst e mem)

(ArraySelect [0] (Load ptr mem)) -> (Load ptr mem)

// Putting [1]{*byte} and similar into direct interfaces.
(IMake typ (ArrayMake1 val)) -> (IMake typ val)
(ArraySelect [0] 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 (Const64 <t> [c]) _)) -> (Const64 <t> [c])
(StringLen (StringMake _ (Const64 <t> [c]))) -> (Const64 <t> [c])
(ConstString {s}) && config.PtrSize == 4 && s.(string) == "" ->
  (StringMake (ConstNil) (Const32 <config.fe.TypeInt()> [0]))
(ConstString {s}) && config.PtrSize == 8 && s.(string) == "" ->
  (StringMake (ConstNil) (Const64 <config.fe.TypeInt()> [0]))
(ConstString {s}) && config.PtrSize == 4 && s.(string) != "" ->
  (StringMake
    (Addr <config.fe.TypeBytePtr()> {config.fe.StringData(s.(string))}
      (SB))
    (Const32 <config.fe.TypeInt()> [int64(len(s.(string)))]))
(ConstString {s}) && config.PtrSize == 8 && s.(string) != "" ->
  (StringMake
    (Addr <config.fe.TypeBytePtr()> {config.fe.StringData(s.(string))}
      (SB))
    (Const64 <config.fe.TypeInt()> [int64(len(s.(string)))]))

// 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.ElemType().PtrTo()>)
    (Const32 <config.fe.TypeInt()> [0])
    (Const32 <config.fe.TypeInt()> [0]))
(ConstSlice) && config.PtrSize == 8 ->
  (SliceMake
    (ConstNil <v.Type.ElemType().PtrTo()>)
    (Const64 <config.fe.TypeInt()> [0])
    (Const64 <config.fe.TypeInt()> [0]))

// interface ops
(ConstInterface) ->
  (IMake
    (ConstNil <config.fe.TypeBytePtr()>)
    (ConstNil <config.fe.TypeBytePtr()>))

(NilCheck (GetG mem) mem) -> mem

(If (Not cond) yes no) -> (If cond no yes)
(If (ConstBool [c]) yes no) && c == 1 -> (First nil yes no)
(If (ConstBool [c]) yes no) && c == 0 -> (First nil no yes)

// Get rid of Convert ops for pointer arithmetic on unsafe.Pointer.
(Convert (Add64 (Convert ptr mem) off) mem) -> (Add64 ptr off)
(Convert (Add64 off (Convert ptr mem)) mem) -> (Add64 ptr off)
(Convert (Convert ptr mem) mem) -> ptr

// Decompose compound argument values
(Arg {n} [off]) && v.Type.IsString() ->
  (StringMake
    (Arg <config.fe.TypeBytePtr()> {n} [off])
    (Arg <config.fe.TypeInt()> {n} [off+config.PtrSize]))

(Arg {n} [off]) && v.Type.IsSlice() ->
  (SliceMake
    (Arg <v.Type.ElemType().PtrTo()> {n} [off])
    (Arg <config.fe.TypeInt()> {n} [off+config.PtrSize])
    (Arg <config.fe.TypeInt()> {n} [off+2*config.PtrSize]))

(Arg {n} [off]) && v.Type.IsInterface() ->
  (IMake
    (Arg <config.fe.TypeBytePtr()> {n} [off])
    (Arg <config.fe.TypeBytePtr()> {n} [off+config.PtrSize]))

(Arg {n} [off]) && v.Type.IsComplex() && v.Type.Size() == 16 ->
  (ComplexMake
    (Arg <config.fe.TypeFloat64()> {n} [off])
    (Arg <config.fe.TypeFloat64()> {n} [off+8]))

(Arg {n} [off]) && v.Type.IsComplex() && v.Type.Size() == 8 ->
  (ComplexMake
    (Arg <config.fe.TypeFloat32()> {n} [off])
    (Arg <config.fe.TypeFloat32()> {n} [off+4]))

(Arg <t>) && t.IsStruct() && t.NumFields() == 0 && config.fe.CanSSA(t) ->
  (StructMake0)
(Arg <t> {n} [off]) && t.IsStruct() && t.NumFields() == 1 && config.fe.CanSSA(t) ->
  (StructMake1
    (Arg <t.FieldType(0)> {n} [off+t.FieldOff(0)]))
(Arg <t> {n} [off]) && t.IsStruct() && t.NumFields() == 2 && config.fe.CanSSA(t) ->
  (StructMake2
    (Arg <t.FieldType(0)> {n} [off+t.FieldOff(0)])
    (Arg <t.FieldType(1)> {n} [off+t.FieldOff(1)]))
(Arg <t> {n} [off]) && t.IsStruct() && t.NumFields() == 3 && config.fe.CanSSA(t) ->
  (StructMake3
    (Arg <t.FieldType(0)> {n} [off+t.FieldOff(0)])
    (Arg <t.FieldType(1)> {n} [off+t.FieldOff(1)])
    (Arg <t.FieldType(2)> {n} [off+t.FieldOff(2)]))
(Arg <t> {n} [off]) && t.IsStruct() && t.NumFields() == 4 && config.fe.CanSSA(t) ->
  (StructMake4
    (Arg <t.FieldType(0)> {n} [off+t.FieldOff(0)])
    (Arg <t.FieldType(1)> {n} [off+t.FieldOff(1)])
    (Arg <t.FieldType(2)> {n} [off+t.FieldOff(2)])
    (Arg <t.FieldType(3)> {n} [off+t.FieldOff(3)]))

(Arg <t>) && t.IsArray() && t.NumElem() == 0 ->
  (ArrayMake0)
(Arg <t> {n} [off]) && t.IsArray() && t.NumElem() == 1 && config.fe.CanSSA(t) ->
  (ArrayMake1 (Arg <t.ElemType()> {n} [off]))

// 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])) && isPowerOfTwo(c&0xff)       -> (Rsh8Ux64 n  (Const64 <config.fe.TypeUInt64()> [log2(c&0xff)]))
(Div16u n (Const16 [c])) && isPowerOfTwo(c&0xffff)     -> (Rsh16Ux64 n (Const64 <config.fe.TypeUInt64()> [log2(c&0xffff)]))
(Div32u n (Const32 [c])) && isPowerOfTwo(c&0xffffffff) -> (Rsh32Ux64 n (Const64 <config.fe.TypeUInt64()> [log2(c&0xffffffff)]))
(Div64u n (Const64 [c])) && isPowerOfTwo(c)            -> (Rsh64Ux64 n (Const64 <config.fe.TypeUInt64()> [log2(c)]))

// 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])) && umagicOK(8, c) ->
  (Trunc32to8
    (Rsh32Ux64 <config.fe.TypeUInt32()>
      (Mul32 <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(1<<8+umagic(8,c).m)])
        (ZeroExt8to32 x))
      (Const64 <config.fe.TypeUInt64()> [8+umagic(8,c).s])))

// For 16-bit divides on 64-bit machines, we do a direct 17-bit by 16-bit multiply.
(Div16u x (Const16 [c])) && umagicOK(16, c) && config.RegSize == 8 ->
  (Trunc64to16
    (Rsh64Ux64 <config.fe.TypeUInt64()>
      (Mul64 <config.fe.TypeUInt64()>
        (Const64 <config.fe.TypeUInt64()> [int64(1<<16+umagic(16,c).m)])
        (ZeroExt16to64 x))
      (Const64 <config.fe.TypeUInt64()> [16+umagic(16,c).s])))

// For 16-bit divides on 32-bit machines
(Div16u x (Const16 [c])) && umagicOK(16, c) && config.RegSize == 4 && umagic(16,c).m&1 == 0 ->
  (Trunc32to16
    (Rsh32Ux64 <config.fe.TypeUInt32()>
      (Mul32 <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(1<<15+umagic(16,c).m/2)])
        (ZeroExt16to32 x))
      (Const64 <config.fe.TypeUInt64()> [16+umagic(16,c).s-1])))
(Div16u x (Const16 [c])) && umagicOK(16, c) && config.RegSize == 4 && c&1 == 0 ->
  (Trunc32to16
    (Rsh32Ux64 <config.fe.TypeUInt32()>
      (Mul32 <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(1<<15+(umagic(16,c).m+1)/2)])
        (Rsh32Ux64 <config.fe.TypeUInt32()> (ZeroExt16to32 x) (Const64 <config.fe.TypeUInt64()> [1])))
      (Const64 <config.fe.TypeUInt64()> [16+umagic(16,c).s-2])))
(Div16u x (Const16 [c])) && umagicOK(16, c) && config.RegSize == 4 ->
  (Trunc32to16
    (Rsh32Ux64 <config.fe.TypeUInt32()>
      (Avg32u
        (Lsh32x64 <config.fe.TypeUInt32()> (ZeroExt16to32 x) (Const64 <config.fe.TypeUInt64()> [16]))
        (Mul32 <config.fe.TypeUInt32()>
          (Const32 <config.fe.TypeUInt32()> [int64(umagic(16,c).m)])
          (ZeroExt16to32 x)))
      (Const64 <config.fe.TypeUInt64()> [16+umagic(16,c).s-1])))

// For 32-bit divides on 32-bit machines
(Div32u x (Const32 [c])) && umagicOK(32, c) && config.RegSize == 4 && umagic(32,c).m&1 == 0 ->
  (Rsh32Ux64 <config.fe.TypeUInt32()>
    (Hmul32u <config.fe.TypeUInt32()>
      (Const32 <config.fe.TypeUInt32()> [int64(int32(1<<31+umagic(32,c).m/2))])
      x)
    (Const64 <config.fe.TypeUInt64()> [umagic(32,c).s-1]))
(Div32u x (Const32 [c])) && umagicOK(32, c) && config.RegSize == 4 && c&1 == 0 ->
  (Rsh32Ux64 <config.fe.TypeUInt32()>
    (Hmul32u <config.fe.TypeUInt32()>
      (Const32 <config.fe.TypeUInt32()> [int64(int32(1<<31+(umagic(32,c).m+1)/2))])
      (Rsh32Ux64 <config.fe.TypeUInt32()> x (Const64 <config.fe.TypeUInt64()> [1])))
    (Const64 <config.fe.TypeUInt64()> [umagic(32,c).s-2]))
(Div32u x (Const32 [c])) && umagicOK(32, c) && config.RegSize == 4 ->
  (Rsh32Ux64 <config.fe.TypeUInt32()>
    (Avg32u
      x
      (Hmul32u <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(int32(umagic(32,c).m))])
        x))
    (Const64 <config.fe.TypeUInt64()> [umagic(32,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])) && umagicOK(32, c) && config.RegSize == 8 && umagic(32,c).m&1 == 0 ->
  (Trunc64to32
    (Rsh64Ux64 <config.fe.TypeUInt64()>
      (Mul64 <config.fe.TypeUInt64()>
        (Const64 <config.fe.TypeUInt64()> [int64(1<<31+umagic(32,c).m/2)])
        (ZeroExt32to64 x))
      (Const64 <config.fe.TypeUInt64()> [32+umagic(32,c).s-1])))
(Div32u x (Const32 [c])) && umagicOK(32, c) && config.RegSize == 8 && c&1 == 0 ->
  (Trunc64to32
    (Rsh64Ux64 <config.fe.TypeUInt64()>
      (Mul64 <config.fe.TypeUInt64()>
        (Const64 <config.fe.TypeUInt64()> [int64(1<<31+(umagic(32,c).m+1)/2)])
        (Rsh64Ux64 <config.fe.TypeUInt64()> (ZeroExt32to64 x) (Const64 <config.fe.TypeUInt64()> [1])))
      (Const64 <config.fe.TypeUInt64()> [32+umagic(32,c).s-2])))
(Div32u x (Const32 [c])) && umagicOK(32, c) && config.RegSize == 8 ->
  (Trunc64to32
    (Rsh64Ux64 <config.fe.TypeUInt64()>
      (Avg64u
        (Lsh64x64 <config.fe.TypeUInt64()> (ZeroExt32to64 x) (Const64 <config.fe.TypeUInt64()> [32]))
        (Mul64 <config.fe.TypeUInt64()>
          (Const64 <config.fe.TypeUInt32()> [int64(umagic(32,c).m)])
          (ZeroExt32to64 x)))
      (Const64 <config.fe.TypeUInt64()> [32+umagic(32,c).s-1])))

// 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])) && umagicOK(64, c) && config.RegSize == 8 && umagic(64,c).m&1 == 0 ->
  (Rsh64Ux64 <config.fe.TypeUInt64()>
    (Hmul64u <config.fe.TypeUInt64()>
      (Const64 <config.fe.TypeUInt64()> [int64(1<<63+umagic(64,c).m/2)])
      x)
    (Const64 <config.fe.TypeUInt64()> [umagic(64,c).s-1]))
(Div64u x (Const64 [c])) && umagicOK(64, c) && config.RegSize == 8 && c&1 == 0 ->
  (Rsh64Ux64 <config.fe.TypeUInt64()>
    (Hmul64u <config.fe.TypeUInt64()>
      (Const64 <config.fe.TypeUInt64()> [int64(1<<63+(umagic(64,c).m+1)/2)])
      (Rsh64Ux64 <config.fe.TypeUInt64()> x (Const64 <config.fe.TypeUInt64()> [1])))
    (Const64 <config.fe.TypeUInt64()> [umagic(64,c).s-2]))
(Div64u x (Const64 [c])) && umagicOK(64, c) && config.RegSize == 8 ->
  (Rsh64Ux64 <config.fe.TypeUInt64()>
    (Avg64u
      x
      (Hmul64u <config.fe.TypeUInt64()>
        (Const64 <config.fe.TypeUInt64()> [int64(umagic(64,c).m)])
        x))
    (Const64 <config.fe.TypeUInt64()> [umagic(64,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 <config.fe.TypeUInt64()> [7 ]))
(Div16 <t> x (Const16 [-1<<15])) -> (Rsh16Ux64 (And16 <t> x (Neg16 <t> x)) (Const64 <config.fe.TypeUInt64()> [15]))
(Div32 <t> x (Const32 [-1<<31])) -> (Rsh32Ux64 (And32 <t> x (Neg32 <t> x)) (Const64 <config.fe.TypeUInt64()> [31]))
(Div64 <t> x (Const64 [-1<<63])) -> (Rsh64Ux64 (And64 <t> x (Neg64 <t> x)) (Const64 <config.fe.TypeUInt64()> [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])) && isPowerOfTwo(c) ->
  (Rsh8x64
    (Add8  <t> n (Rsh8Ux64  <t> (Rsh8x64  <t> n (Const64 <config.fe.TypeUInt64()> [ 7])) (Const64 <config.fe.TypeUInt64()> [ 8-log2(c)])))
    (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Div16 <t> n (Const16 [c])) && isPowerOfTwo(c) ->
  (Rsh16x64
    (Add16 <t> n (Rsh16Ux64 <t> (Rsh16x64 <t> n (Const64 <config.fe.TypeUInt64()> [15])) (Const64 <config.fe.TypeUInt64()> [16-log2(c)])))
    (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Div32 <t> n (Const32 [c])) && isPowerOfTwo(c) ->
  (Rsh32x64
    (Add32 <t> n (Rsh32Ux64 <t> (Rsh32x64 <t> n (Const64 <config.fe.TypeUInt64()> [31])) (Const64 <config.fe.TypeUInt64()> [32-log2(c)])))
    (Const64 <config.fe.TypeUInt64()> [log2(c)]))
(Div64 <t> n (Const64 [c])) && isPowerOfTwo(c) ->
  (Rsh64x64
    (Add64 <t> n (Rsh64Ux64 <t> (Rsh64x64 <t> n (Const64 <config.fe.TypeUInt64()> [63])) (Const64 <config.fe.TypeUInt64()> [64-log2(c)])))
    (Const64 <config.fe.TypeUInt64()> [log2(c)]))

// Signed divide, not a power of 2.  Strength reduce to a multiply.
(Div8 <t> x (Const8 [c])) && smagicOK(8,c) ->
  (Sub8 <t>
    (Rsh32x64 <t>
      (Mul32 <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(smagic(8,c).m)])
        (SignExt8to32 x))
      (Const64 <config.fe.TypeUInt64()> [8+smagic(8,c).s]))
    (Rsh32x64 <t>
      (SignExt8to32 x)
      (Const64 <config.fe.TypeUInt64()> [31])))
(Div16 <t> x (Const16 [c])) && smagicOK(16,c) ->
  (Sub16 <t>
    (Rsh32x64 <t>
      (Mul32 <config.fe.TypeUInt32()>
        (Const32 <config.fe.TypeUInt32()> [int64(smagic(16,c).m)])
        (SignExt16to32 x))
      (Const64 <config.fe.TypeUInt64()> [16+smagic(16,c).s]))
    (Rsh32x64 <t>
      (SignExt16to32 x)
      (Const64 <config.fe.TypeUInt64()> [31])))
(Div32 <t> x (Const32 [c])) && smagicOK(32,c) && config.RegSize == 8 ->
  (Sub32 <t>
    (Rsh64x64 <t>
      (Mul64 <config.fe.TypeUInt64()>
        (Const64 <config.fe.TypeUInt64()> [int64(smagic(32,c).m)])
        (SignExt32to64 x))
      (Const64 <config.fe.TypeUInt64()> [32+smagic(32,c).s]))
    (Rsh64x64 <t>
      (SignExt32to64 x)
      (Const64 <config.fe.TypeUInt64()> [63])))
(Div32 <t> x (Const32 [c])) && smagicOK(32,c) && config.RegSize == 4 && smagic(32,c).m&1 == 0 ->
  (Sub32 <t>
    (Rsh32x64 <t>
      (Hmul32 <t>
        (Const32 <config.fe.TypeUInt32()> [int64(int32(smagic(32,c).m/2))])
        x)
      (Const64 <config.fe.TypeUInt64()> [smagic(32,c).s-1]))
    (Rsh32x64 <t>
      x
      (Const64 <config.fe.TypeUInt64()> [31])))
(Div32 <t> x (Const32 [c])) && smagicOK(32,c) && config.RegSize == 4 && smagic(32,c).m&1 != 0 ->
  (Sub32 <t>
    (Rsh32x64 <t>
      (Add32 <t>
        (Hmul32 <t>
          (Const32 <config.fe.TypeUInt32()> [int64(int32(smagic(32,c).m))])
          x)
        x)
      (Const64 <config.fe.TypeUInt64()> [smagic(32,c).s]))
    (Rsh32x64 <t>
      x
      (Const64 <config.fe.TypeUInt64()> [31])))
(Div64 <t> x (Const64 [c])) && smagicOK(64,c) && smagic(64,c).m&1 == 0 ->
  (Sub64 <t>
    (Rsh64x64 <t>
      (Hmul64 <t>
        (Const64 <config.fe.TypeUInt64()> [int64(smagic(64,c).m/2)])
        x)
      (Const64 <config.fe.TypeUInt64()> [smagic(64,c).s-1]))
    (Rsh64x64 <t>
      x
      (Const64 <config.fe.TypeUInt64()> [63])))
(Div64 <t> x (Const64 [c])) && smagicOK(64,c) && smagic(64,c).m&1 != 0 ->
  (Sub64 <t>
    (Rsh64x64 <t>
      (Add64 <t>
        (Hmul64 <t>
          (Const64 <config.fe.TypeUInt64()> [int64(smagic(64,c).m)])
          x)
        x)
      (Const64 <config.fe.TypeUInt64()> [smagic(64,c).s]))
    (Rsh64x64 <t>
      x
      (Const64 <config.fe.TypeUInt64()> [63])))

// Unsigned mod by power of 2 constant.
(Mod8u  <t> n (Const8  [c])) && isPowerOfTwo(c&0xff)       -> (And8 n (Const8 <t> [(c&0xff)-1]))
(Mod16u <t> n (Const16 [c])) && isPowerOfTwo(c&0xffff)     -> (And16 n (Const16 <t> [(c&0xffff)-1]))
(Mod32u <t> n (Const32 [c])) && isPowerOfTwo(c&0xffffffff) -> (And32 n (Const32 <t> [(c&0xffffffff)-1]))
(Mod64u <t> n (Const64 [c])) && isPowerOfTwo(c)            -> (And64 n (Const64 <t> [c-1]))

// 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 && umagicOK(8 ,c)
  -> (Sub8  x (Mul8  <t> (Div8u  <t> x (Const8  <t> [c])) (Const8  <t> [c])))
(Mod16u <t> x (Const16 [c])) && x.Op != OpConst16 && c > 0 && umagicOK(16,c)
  -> (Sub16 x (Mul16 <t> (Div16u <t> x (Const16 <t> [c])) (Const16 <t> [c])))
(Mod32u <t> x (Const32 [c])) && x.Op != OpConst32 && c > 0 && umagicOK(32,c)
  -> (Sub32 x (Mul32 <t> (Div32u <t> x (Const32 <t> [c])) (Const32 <t> [c])))
(Mod64u <t> x (Const64 [c])) && x.Op != OpConst64 && c > 0 && umagicOK(64,c)
  -> (Sub64 x (Mul64 <t> (Div64u <t> x (Const64 <t> [c])) (Const64 <t> [c])))

// floating point optimizations
(Add32F x (Const32F [0])) -> x
(Add32F (Const32F [0]) x) -> x
(Add64F x (Const64F [0])) -> x
(Add64F (Const64F [0]) x) -> x
(Sub32F x (Const32F [0])) -> x
(Sub64F x (Const64F [0])) -> x
(Mul32F x (Const32F [f2i(1)])) -> x
(Mul32F (Const32F [f2i(1)]) x) -> x
(Mul64F x (Const64F [f2i(1)])) -> x
(Mul64F (Const64F [f2i(1)]) x) -> x
(Mul32F x (Const32F [f2i(-1)])) -> (Neg32F x)
(Mul32F (Const32F [f2i(-1)]) x) -> (Neg32F x)
(Mul64F x (Const64F [f2i(-1)])) -> (Neg64F x)
(Mul64F (Const64F [f2i(-1)]) x) -> (Neg64F x)
(Div32F x (Const32F [f2i(1)])) -> x
(Div64F x (Const64F [f2i(1)])) -> x
(Div32F x (Const32F [f2i(-1)])) -> (Neg32F x)
(Div64F x (Const64F [f2i(-1)])) -> (Neg32F x)

(Sqrt (Const64F [c])) -> (Const64F [f2i(math.Sqrt(i2f(c)))])

// recognize runtime.newobject and don't Zero/Nilcheck it
(Zero (Load (OffPtr [c] (SP)) mem) mem)
        && mem.Op == OpStaticCall
	&& isSameSym(mem.Aux, "runtime.newobject")
	&& c == config.ctxt.FixedFrameSize() + config.PtrSize // offset of return value
	-> mem
// nil checks just need to rewrite to something useless.
// they will be deadcode eliminated soon afterwards.
(NilCheck (Load (OffPtr [c] (SP)) mem) mem)
	&& mem.Op == OpStaticCall
	&& isSameSym(mem.Aux, "runtime.newobject")
	&& c == config.ctxt.FixedFrameSize() + config.RegSize // offset of return value
	&& warnRule(config.Debug_checknil() && v.Pos.Line() > 1, v, "removed nil check")
	-> (Invalid)
(NilCheck (OffPtr (Load (OffPtr [c] (SP)) mem)) mem)
	&& mem.Op == OpStaticCall
	&& isSameSym(mem.Aux, "runtime.newobject")
	&& c == config.ctxt.FixedFrameSize() + config.RegSize // offset of return value
	&& warnRule(config.Debug_checknil() && v.Pos.Line() > 1, v, "removed nil check")
	-> (Invalid)