cmd/compile: optimize signed non-negative div/mod by a power of 2

This CL optimizes assembly for len() or cap() division
by a power of 2 constants:

    func lenDiv(s []int) int {
        return len(s) / 16
    }

amd64 assembly before the CL:

    MOVQ    "".s+16(SP), AX
    MOVQ    AX, CX
    SARQ    $63, AX
    SHRQ    $60, AX
    ADDQ    CX, AX
    SARQ    $4, AX
    MOVQ    AX, "".~r1+32(SP)
    RET

amd64 assembly after the CL:

    MOVQ    "".s+16(SP), AX
    SHRQ    $4, AX
    MOVQ    AX, "".~r1+32(SP)
    RET

The CL relies on the fact that len() and cap() result cannot
be negative.

Trigger stats for the added SSA rules on linux/amd64 when running
make.bash:

     46 Div64
     12 Mod64

The added SSA rules may trigger on more cases in the future
when SSA values will be populated with the info on their
lower bounds.

For instance:

    func f(i int16) int16 {
        if i < 3 {
            return -1
        }

        // Lower bound of i is 3 here -> i is non-negative,
        // so unsigned arithmetics may be used here.
        return i % 16
    }

Change-Id: I8bc6be5a03e71157ced533c01416451ff6f1a7f0
Reviewed-on: https://go-review.googlesource.com/65530Reviewed-by: Keith Randall <khr@golang.org>

src/cmd/compile/internal/gc/asm_test.go

@@ -1140,6 +1140,58 @@ var linuxAMD64Tests = []*asmTest{
 		`,
 		pos: []string{"\tSETHI\t\\("},
 	},
+	// Check that len() and cap() div by a constant power of two
+	// are compiled into SHRQ.
+	{
+		fn: `
+		func $(a []int) int {
+			return len(a) / 1024
+		}
+		`,
+		pos: []string{"\tSHRQ\t\\$10,"},
+	},
+	{
+		fn: `
+		func $(s string) int {
+			return len(s) / (4097 >> 1)
+		}
+		`,
+		pos: []string{"\tSHRQ\t\\$11,"},
+	},
+	{
+		fn: `
+		func $(a []int) int {
+			return cap(a) / ((1 << 11) + 2048)
+		}
+		`,
+		pos: []string{"\tSHRQ\t\\$12,"},
+	},
+	// Check that len() and cap() mod by a constant power of two
+	// are compiled into ANDQ.
+	{
+		fn: `
+		func $(a []int) int {
+			return len(a) % 1024
+		}
+		`,
+		pos: []string{"\tANDQ\t\\$1023,"},
+	},
+	{
+		fn: `
+		func $(s string) int {
+			return len(s) % (4097 >> 1)
+		}
+		`,
+		pos: []string{"\tANDQ\t\\$2047,"},
+	},
+	{
+		fn: `
+		func $(a []int) int {
+			return cap(a) % ((1 << 11) + 2048)
+		}
+		`,
+		pos: []string{"\tANDQ\t\\$4095,"},
+	},
 }
 
 var linux386Tests = []*asmTest{
@@ -1219,6 +1271,58 @@ var linux386Tests = []*asmTest{
 		}`,
 		pos: []string{"\tADDL\t[$]-19", "\tIMULL"}, // (n-19)*a
 	},
+	// Check that len() and cap() div by a constant power of two
+	// are compiled into SHRL.
+	{
+		fn: `
+		func $(a []int) int {
+			return len(a) / 1024
+		}
+		`,
+		pos: []string{"\tSHRL\t\\$10,"},
+	},
+	{
+		fn: `
+		func $(s string) int {
+			return len(s) / (4097 >> 1)
+		}
+		`,
+		pos: []string{"\tSHRL\t\\$11,"},
+	},
+	{
+		fn: `
+		func $(a []int) int {
+			return cap(a) / ((1 << 11) + 2048)
+		}
+		`,
+		pos: []string{"\tSHRL\t\\$12,"},
+	},
+	// Check that len() and cap() mod by a constant power of two
+	// are compiled into ANDL.
+	{
+		fn: `
+		func $(a []int) int {
+			return len(a) % 1024
+		}
+		`,
+		pos: []string{"\tANDL\t\\$1023,"},
+	},
+	{
+		fn: `
+		func $(s string) int {
+			return len(s) % (4097 >> 1)
+		}
+		`,
+		pos: []string{"\tANDL\t\\$2047,"},
+	},
+	{
+		fn: `
+		func $(a []int) int {
+			return cap(a) % ((1 << 11) + 2048)
+		}
+		`,
+		pos: []string{"\tANDL\t\\$4095,"},
+	},
 }
 
 var linuxS390XTests = []*asmTest{

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

@@ -1003,6 +1003,13 @@
 (Div64u n (Const64 [c])) && isPowerOfTwo(c)            -> (Rsh64Ux64 n (Const64 <typ.UInt64> [log2(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) && isPowerOfTwo(c&0xff)       -> (Rsh8Ux64 n  (Const64 <typ.UInt64> [log2(c&0xff)]))
+(Div16 n (Const16 [c])) && isNonNegative(n) && isPowerOfTwo(c&0xffff)     -> (Rsh16Ux64 n (Const64 <typ.UInt64> [log2(c&0xffff)]))
+(Div32 n (Const32 [c])) && isNonNegative(n) && isPowerOfTwo(c&0xffffffff) -> (Rsh32Ux64 n (Const64 <typ.UInt64> [log2(c&0xffffffff)]))
+(Div64 n (Const64 [c])) && isNonNegative(n) && isPowerOfTwo(c)            -> (Rsh64Ux64 n (Const64 <typ.UInt64> [log2(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])) && umagicOK(8, c) ->
@@ -1236,6 +1243,13 @@
 (Mod64u <t> n (Const64 [c])) && isPowerOfTwo(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) && isPowerOfTwo(c&0xff)       -> (And8 n (Const8 <t> [(c&0xff)-1]))
+(Mod16 <t> n (Const16 [c])) && isNonNegative(n) && isPowerOfTwo(c&0xffff)     -> (And16 n (Const16 <t> [(c&0xffff)-1]))
+(Mod32 <t> n (Const32 [c])) && isNonNegative(n) && isPowerOfTwo(c&0xffffffff) -> (And32 n (Const32 <t> [(c&0xffffffff)-1]))
+(Mod64 <t> n (Const64 [c])) && isNonNegative(n) && isPowerOfTwo(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]))

src/cmd/compile/internal/ssa/rewritegeneric.go

@@ -7266,6 +7266,27 @@ func rewriteValuegeneric_OpDiv16_0(v *Value) bool {
 		v.AuxInt = int64(int16(c) / int16(d))
 		return true
 	}
+	// match: (Div16 n (Const16 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xffff)
+	// result: (Rsh16Ux64 n (Const64 <typ.UInt64> [log2(c&0xffff)]))
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst16 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xffff)) {
+			break
+		}
+		v.reset(OpRsh16Ux64)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst64, typ.UInt64)
+		v0.AuxInt = log2(c & 0xffff)
+		v.AddArg(v0)
+		return true
+	}
 	// match: (Div16 <t> n (Const16 [c]))
 	// cond: c < 0 && c != -1<<15
 	// result: (Neg16 (Div16 <t> n (Const16 <t> [-c])))
@@ -7609,6 +7630,27 @@ func rewriteValuegeneric_OpDiv32_0(v *Value) bool {
 		v.AuxInt = int64(int32(c) / int32(d))
 		return true
 	}
+	// match: (Div32 n (Const32 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xffffffff)
+	// result: (Rsh32Ux64 n (Const64 <typ.UInt64> [log2(c&0xffffffff)]))
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst32 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xffffffff)) {
+			break
+		}
+		v.reset(OpRsh32Ux64)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst64, typ.UInt64)
+		v0.AuxInt = log2(c & 0xffffffff)
+		v.AddArg(v0)
+		return true
+	}
 	// match: (Div32 <t> n (Const32 [c]))
 	// cond: c < 0 && c != -1<<31
 	// result: (Neg32 (Div32 <t> n (Const32 <t> [-c])))
@@ -8130,6 +8172,47 @@ func rewriteValuegeneric_OpDiv64_0(v *Value) bool {
 		v.AuxInt = c / d
 		return true
 	}
+	// match: (Div64 n (Const64 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c)
+	// result: (Rsh64Ux64 n (Const64 <typ.UInt64> [log2(c)]))
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst64 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c)) {
+			break
+		}
+		v.reset(OpRsh64Ux64)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst64, typ.UInt64)
+		v0.AuxInt = log2(c)
+		v.AddArg(v0)
+		return true
+	}
+	// match: (Div64 n (Const64 [-1<<63]))
+	// cond: isNonNegative(n)
+	// result: (Const64 [0])
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst64 {
+			break
+		}
+		if v_1.AuxInt != -1<<63 {
+			break
+		}
+		if !(isNonNegative(n)) {
+			break
+		}
+		v.reset(OpConst64)
+		v.AuxInt = 0
+		return true
+	}
 	// match: (Div64 <t> n (Const64 [c]))
 	// cond: c < 0 && c != -1<<63
 	// result: (Neg64 (Div64 <t> n (Const64 <t> [-c])))
@@ -8526,6 +8609,27 @@ func rewriteValuegeneric_OpDiv8_0(v *Value) bool {
 		v.AuxInt = int64(int8(c) / int8(d))
 		return true
 	}
+	// match: (Div8 n (Const8 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xff)
+	// result: (Rsh8Ux64 n  (Const64 <typ.UInt64> [log2(c&0xff)]))
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst8 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xff)) {
+			break
+		}
+		v.reset(OpRsh8Ux64)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst64, typ.UInt64)
+		v0.AuxInt = log2(c & 0xff)
+		v.AddArg(v0)
+		return true
+	}
 	// match: (Div8 <t> n (Const8 [c]))
 	// cond: c < 0 && c != -1<<7
 	// result: (Neg8  (Div8  <t> n (Const8  <t> [-c])))
@@ -13476,6 +13580,28 @@ func rewriteValuegeneric_OpMod16_0(v *Value) bool {
 		return true
 	}
 	// match: (Mod16 <t> n (Const16 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xffff)
+	// result: (And16 n (Const16 <t> [(c&0xffff)-1]))
+	for {
+		t := v.Type
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst16 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xffff)) {
+			break
+		}
+		v.reset(OpAnd16)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst16, t)
+		v0.AuxInt = (c & 0xffff) - 1
+		v.AddArg(v0)
+		return true
+	}
+	// match: (Mod16 <t> n (Const16 [c]))
 	// cond: c < 0 && c != -1<<15
 	// result: (Mod16 <t> n (Const16 <t> [-c]))
 	for {
@@ -13635,6 +13761,28 @@ func rewriteValuegeneric_OpMod32_0(v *Value) bool {
 		return true
 	}
 	// match: (Mod32 <t> n (Const32 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xffffffff)
+	// result: (And32 n (Const32 <t> [(c&0xffffffff)-1]))
+	for {
+		t := v.Type
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst32 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xffffffff)) {
+			break
+		}
+		v.reset(OpAnd32)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst32, t)
+		v0.AuxInt = (c & 0xffffffff) - 1
+		v.AddArg(v0)
+		return true
+	}
+	// match: (Mod32 <t> n (Const32 [c]))
 	// cond: c < 0 && c != -1<<31
 	// result: (Mod32 <t> n (Const32 <t> [-c]))
 	for {
@@ -13794,6 +13942,49 @@ func rewriteValuegeneric_OpMod64_0(v *Value) bool {
 		return true
 	}
 	// match: (Mod64 <t> n (Const64 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c)
+	// result: (And64 n (Const64 <t> [c-1]))
+	for {
+		t := v.Type
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst64 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c)) {
+			break
+		}
+		v.reset(OpAnd64)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst64, t)
+		v0.AuxInt = c - 1
+		v.AddArg(v0)
+		return true
+	}
+	// match: (Mod64 n (Const64 [-1<<63]))
+	// cond: isNonNegative(n)
+	// result: n
+	for {
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst64 {
+			break
+		}
+		if v_1.AuxInt != -1<<63 {
+			break
+		}
+		if !(isNonNegative(n)) {
+			break
+		}
+		v.reset(OpCopy)
+		v.Type = n.Type
+		v.AddArg(n)
+		return true
+	}
+	// match: (Mod64 <t> n (Const64 [c]))
 	// cond: c < 0 && c != -1<<63
 	// result: (Mod64 <t> n (Const64 <t> [-c]))
 	for {
@@ -13974,6 +14165,28 @@ func rewriteValuegeneric_OpMod8_0(v *Value) bool {
 		return true
 	}
 	// match: (Mod8 <t> n (Const8 [c]))
+	// cond: isNonNegative(n) && isPowerOfTwo(c&0xff)
+	// result: (And8 n (Const8 <t> [(c&0xff)-1]))
+	for {
+		t := v.Type
+		_ = v.Args[1]
+		n := v.Args[0]
+		v_1 := v.Args[1]
+		if v_1.Op != OpConst8 {
+			break
+		}
+		c := v_1.AuxInt
+		if !(isNonNegative(n) && isPowerOfTwo(c&0xff)) {
+			break
+		}
+		v.reset(OpAnd8)
+		v.AddArg(n)
+		v0 := b.NewValue0(v.Pos, OpConst8, t)
+		v0.AuxInt = (c & 0xff) - 1
+		v.AddArg(v0)
+		return true
+	}
+	// match: (Mod8 <t> n (Const8 [c]))
 	// cond: c < 0 && c != -1<<7
 	// result: (Mod8  <t> n (Const8  <t> [-c]))
 	for {