cmd/compile: precompute constant square roots

If a program wants to evaluate math.Sqrt for any constant value
(for example, math.Sqrt(3)), we can replace that expression with
its evaluation (1.7320508075688772) at compile time, instead of
generating a SQRT assembly command or equivalent.

Adds tests that math.Sqrt generates the correct values. I also
compiled a short program and verified that the Sqrt expression was
replaced by a constant value in the "after opt" step.

Adds a short doc to the top of generic.rules explaining what the file
does and how other files interact with it.

Fixes #15543.

Change-Id: I6b6e63ac61cec50763a09ba581024adeee03d4fa
Reviewed-on: https://go-review.googlesource.com/27457
Reviewed-by: Josh Bleecher Snyder <josharian@gmail.com>
Reviewed-by: Keith Randall <khr@golang.org>

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

@@ -103,3 +103,5 @@ func TestSlice(t *testing.T) { runTest(t, "slice.go") }
 func TestNamedReturn(t *testing.T) { runTest(t, "namedReturn.go") }
 
 func TestDuplicateLoad(t *testing.T) { runTest(t, "dupLoad.go") }
+
+func TestSqrt(t *testing.T) { runTest(t, "sqrt_const.go") }

src/cmd/compile/internal/gc/testdata/sqrt_const.go

@@ -0,0 +1,59 @@
+// Copyright 2016 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.
+
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+var tests = [...]struct {
+	name string
+	in   float64 // used for error messages, not an input
+	got  float64
+	want float64
+}{
+	{"sqrt0", 0, math.Sqrt(0), 0},
+	{"sqrt1", 1, math.Sqrt(1), 1},
+	{"sqrt2", 2, math.Sqrt(2), math.Sqrt2},
+	{"sqrt4", 4, math.Sqrt(4), 2},
+	{"sqrt100", 100, math.Sqrt(100), 10},
+	{"sqrt101", 101, math.Sqrt(101), 10.04987562112089},
+}
+
+var nanTests = [...]struct {
+	name string
+	in   float64 // used for error messages, not an input
+	got  float64
+}{
+	{"sqrtNaN", math.NaN(), math.Sqrt(math.NaN())},
+	{"sqrtNegative", -1, math.Sqrt(-1)},
+	{"sqrtNegInf", math.Inf(-1), math.Sqrt(math.Inf(-1))},
+}
+
+var failed = false
+
+func main() {
+	for _, test := range tests {
+		if test.got != test.want {
+			fmt.Printf("%s: math.Sqrt(%f): got %f, want %f\n", test.name, test.in, test.got, test.want)
+			failed = true
+		}
+	}
+	for _, test := range nanTests {
+		if math.IsNaN(test.got) != true {
+			fmt.Printf("%s: math.Sqrt(%f): got %f, want NaN\n", test.name, test.in, test.got)
+			failed = true
+		}
+	}
+	if got := math.Sqrt(math.Inf(1)); !math.IsInf(got, 1) {
+		fmt.Printf("math.Sqrt(+Inf), got %f, want +Inf\n", got)
+		failed = true
+	}
+
+	if failed {
+		panic("failed")
+	}
+}

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

@@ -2,6 +2,19 @@
 // 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
@@ -46,7 +59,7 @@
 (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])) -> 
+(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])
@@ -55,7 +68,7 @@
 (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])) -> 
+(Sub32F (Const32F [c]) (Const32F [d])) ->
         (Const32F [f2i(float64(i2f32(c) - i2f32(d)))])
 (Sub64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) - i2f(d))])
 
@@ -63,7 +76,7 @@
 (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])) -> 
+(Mul32F (Const32F [c]) (Const32F [d])) ->
         (Const32F [f2i(float64(i2f32(c) * i2f32(d)))])
 (Mul64F (Const64F [c]) (Const64F [d])) -> (Const64F [f2i(i2f(c) * i2f(d))])
 
@@ -860,3 +873,5 @@
 (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)))])

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

@@ -316,6 +316,8 @@ func rewriteValuegeneric(v *Value, config *Config) bool {
 		return rewriteValuegeneric_OpSliceLen(v, config)
 	case OpSlicePtr:
 		return rewriteValuegeneric_OpSlicePtr(v, config)
+	case OpSqrt:
+		return rewriteValuegeneric_OpSqrt(v, config)
 	case OpStore:
 		return rewriteValuegeneric_OpStore(v, config)
 	case OpStringLen:
@@ -9032,6 +9034,24 @@ func rewriteValuegeneric_OpSlicePtr(v *Value, config *Config) bool {
 	}
 	return false
 }
+func rewriteValuegeneric_OpSqrt(v *Value, config *Config) bool {
+	b := v.Block
+	_ = b
+	// match: (Sqrt (Const64F [c]))
+	// cond:
+	// result: (Const64F [f2i(math.Sqrt(i2f(c)))])
+	for {
+		v_0 := v.Args[0]
+		if v_0.Op != OpConst64F {
+			break
+		}
+		c := v_0.AuxInt
+		v.reset(OpConst64F)
+		v.AuxInt = f2i(math.Sqrt(i2f(c)))
+		return true
+	}
+	return false
+}
 func rewriteValuegeneric_OpStore(v *Value, config *Config) bool {
 	b := v.Block
 	_ = b

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

@@ -26,6 +26,7 @@ type Value struct {
 
 	// Auxiliary info for this value. The type of this information depends on the opcode and type.
 	// AuxInt is used for integer values, Aux is used for other values.
+	// Floats are stored in AuxInt using math.Float64bits(f).
 	AuxInt int64
 	Aux    interface{}