cmd/compile: combine x*n + y*n into (x+y)*n

There are a few cases where this can be useful. Apart from the obvious
(and silly)

  100*n + 200*n

where we generate one IMUL instead of two, consider:

  15*n + 31*n

Currently, the compiler strength-reduces both imuls, generating:

    0x0000 00000	MOVQ	"".n+8(SP), AX
	0x0005 00005 	MOVQ	AX, CX
	0x0008 00008 	SHLQ	$4, AX
	0x000c 00012 	SUBQ	CX, AX
	0x000f 00015 	MOVQ	CX, DX
	0x0012 00018 	SHLQ	$5, CX
	0x0016 00022 	SUBQ	DX, CX
	0x0019 00025 	ADDQ	CX, AX
	0x001c 00028 	MOVQ	AX, "".~r1+16(SP)
	0x0021 00033 	RET

But combining the imuls is both faster and shorter:

	0x0000 00000	MOVQ	"".n+8(SP), AX
	0x0005 00005 	IMULQ	$46, AX
	0x0009 00009	MOVQ	AX, "".~r1+16(SP)
	0x000e 00014 	RET

even without strength-reduction.

Moreover, consider:

  5*n + 7*(n+1) + 11*(n+2)

We already have a rule that rewrites 7(n+1) into 7n+7, so the
generated code (without imuls merging) looks like this:

	0x0000 00000 	MOVQ	"".n+8(SP), AX
	0x0005 00005 	LEAQ	(AX)(AX*4), CX
	0x0009 00009 	MOVQ	AX, DX
	0x000c 00012 	NEGQ	AX
	0x000f 00015 	LEAQ	(AX)(DX*8), AX
	0x0013 00019 	ADDQ	CX, AX
	0x0016 00022 	LEAQ	(DX)(CX*2), CX
	0x001a 00026 	LEAQ	29(AX)(CX*1), AX
	0x001f 00031 	MOVQ	AX, "".~r1+16(SP)

But with imuls merging, the 5n, 7n and 11n factors get merged, and the
generated code looks like this:

	0x0000 00000 	MOVQ	"".n+8(SP), AX
	0x0005 00005 	IMULQ	$23, AX
	0x0009 00009 	ADDQ	$29, AX
	0x000d 00013 	MOVQ	AX, "".~r1+16(SP)
	0x0012 00018 	RET

Which is both faster and shorter; that's also the exact same code that
clang and the intel c compiler generate for the above expression.

Change-Id: Ib4d5503f05d2f2efe31a1be14e2fe6cac33730a9
Reviewed-on: https://go-review.googlesource.com/55143Reviewed-by: Keith Randall <khr@golang.org>

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

@@ -741,6 +741,29 @@ var linuxAMD64Tests = []*asmTest{
 		}`,
 		[]string{"\tPOPCNTQ\t", "support_popcnt"},
 	},
+	// multiplication merging tests
+	{
+		`
+		func mul1(n int) int {
+			return 15*n + 31*n
+		}`,
+		[]string{"\tIMULQ\t[$]46"}, // 46*n
+	},
+	{
+		`
+		func mul2(n int) int {
+			return 5*n + 7*(n+1) + 11*(n+2)
+		}`,
+		[]string{"\tIMULQ\t[$]23", "\tADDQ\t[$]29"}, // 23*n + 29
+	},
+	{
+		`
+		func mul3(a, n int) int {
+			return a*n + 19*n
+		}`,
+		[]string{"\tADDQ\t[$]19", "\tIMULQ"}, // (a+19)*n
+	},
+
 	// see issue 19595.
 	// We want to merge load+op in f58, but not in f59.
 	{
@@ -928,6 +951,21 @@ var linux386Tests = []*asmTest{
 		`,
 		[]string{"\tMOVL\t\\(.*\\)\\(.*\\*1\\),"},
 	},
+	// multiplication merging tests
+	{
+		`
+		func mul1(n int) int {
+			return 9*n + 14*n
+		}`,
+		[]string{"\tIMULL\t[$]23"}, // 23*n
+	},
+	{
+		`
+		func mul2(a, n int) int {
+			return 19*a + a*n
+		}`,
+		[]string{"\tADDL\t[$]19", "\tIMULL"}, // (n+19)*a
+	},
 }
 
 var linuxS390XTests = []*asmTest{

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

@@ -322,6 +322,12 @@
 (Mul32 (Const32 <t> [c]) (Add32 <t> (Const32 <t> [d]) x)) ->
   (Add32 (Const32 <t> [int64(int32(c*d))]) (Mul32 <t> (Const32 <t> [c]) x))
 
+// Rewrite x*y + x*z  to  x*(y+z)
+(Add64 <t> (Mul64 x y) (Mul64 x z)) -> (Mul64 x (Add64 <t> y z))
+(Add32 <t> (Mul32 x y) (Mul32 x z)) -> (Mul32 x (Add32 <t> y z))
+(Add16 <t> (Mul16 x y) (Mul16 x z)) -> (Mul16 x (Add16 <t> y z))
+(Add8  <t> (Mul8  x y) (Mul8  x z)) -> (Mul8  x (Add8  <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))]))

test/mergemul.go

+// runoutput
+
+// Copyright 2017 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"
+
+// Check that expressions like (c*n + d*(n+k)) get correctly merged by
+// the compiler into (c+d)*n + d*k (with c+d and d*k computed at
+// compile time).
+//
+// The merging is performed by a combination of the multiplication
+// merge rules
+//  (c*n + d*n) -> (c+d)*n
+// and the distributive multiplication rules
+//  c * (d+x)  ->  c*d + c*x
+
+// Generate a MergeTest that looks like this:
+//
+//   a8, b8 = m1*n8 + m2*(n8+k), (m1+m2)*n8 + m2*k
+//   if a8 != b8 {
+// 	   // print error msg and panic
+//   }
+func makeMergeTest(m1, m2, k int, size string) string {
+
+	model := "    a" + size + ", b" + size
+	model += fmt.Sprintf(" = %%d*n%s + %%d*(n%s+%%d), (%%d+%%d)*n%s + (%%d*%%d)", size, size, size)
+
+	test := fmt.Sprintf(model, m1, m2, k, m1, m2, m2, k)
+	test += fmt.Sprintf(`
+    if a%s != b%s {
+        fmt.Printf("MergeTest(%d, %d, %d, %s) failed\n")
+        fmt.Printf("%%d != %%d\n", a%s, b%s)
+        panic("FAIL")
+    }
+`, size, size, m1, m2, k, size, size, size)
+	return test + "\n"
+}
+
+func makeAllSizes(m1, m2, k int) string {
+	var tests string
+	tests += makeMergeTest(m1, m2, k, "8")
+	tests += makeMergeTest(m1, m2, k, "16")
+	tests += makeMergeTest(m1, m2, k, "32")
+	tests += makeMergeTest(m1, m2, k, "64")
+	tests += "\n"
+	return tests
+}
+
+func main() {
+	fmt.Println(`package main
+
+import "fmt"
+
+var n8 int8 = 42
+var n16 int16 = 42
+var n32 int32 = 42
+var n64 int64 = 42
+
+func main() {
+    var a8, b8 int8
+    var a16, b16 int16
+    var a32, b32 int32
+    var a64, b64 int64
+`)
+
+	fmt.Println(makeAllSizes(03, 05, 0)) // 3*n + 5*n
+	fmt.Println(makeAllSizes(17, 33, 0))
+	fmt.Println(makeAllSizes(80, 45, 0))
+	fmt.Println(makeAllSizes(32, 64, 0))
+
+	fmt.Println(makeAllSizes(7, 11, +1)) // 7*n + 11*(n+1)
+	fmt.Println(makeAllSizes(9, 13, +2))
+	fmt.Println(makeAllSizes(11, 16, -1))
+	fmt.Println(makeAllSizes(17, 9, -2))
+
+	fmt.Println("}")
+}