big: potential bug fix, cleanups

- implemented setWord, use it where setUint64 is wrong
- divLarge: use fast mulWW, divWW; implemented mulWW, divWW
- better assembly code for addMulVVW

R=rsc
CC=golang-dev
https://golang.org/cl/1258042

src/pkg/big/arith.go

@@ -56,6 +56,7 @@ func subWW_g(x, y, c Word) (z1, z0 Word) {
 
 
 // z1<<_W + z0 = x*y
+func mulWW(x, y Word) (z1, z0 Word)
 func mulWW_g(x, y Word) (z1, z0 Word) {
 	// Split x and y into 2 halfWords each, multiply
 	// the halfWords separately while avoiding overflow,
@@ -242,6 +243,7 @@ func leadingZeros(x Word) uint {
 
 
 // q = (x1<<_W + x0 - r)/y
+func divWW(x1, x0, y Word) (q, r Word)
 func divWW_g(x1, x0, y Word) (q, r Word) {
 	if x1 == 0 {
 		q, r = x0/y, x0%y

src/pkg/big/arith_386.s

@@ -5,6 +5,25 @@
 // This file provides fast assembly versions for the elementary
 // arithmetic operations on vectors implemented in arith.go.
 
+// func mulWW(x, y Word) (z1, z0 Word)
+TEXT ·mulWW(SB),7,$0
+	MOVL x+0(FP), AX
+	MULL y+4(FP)
+	MOVL DX, z1+8(FP)
+	MOVL AX, z0+12(FP)
+	RET
+
+
+// func divWW(x1, x0, y Word) (q, r Word)
+TEXT ·divWW(SB),7,$0
+	MOVL x1+0(FP), DX
+	MOVL x0+4(FP), AX
+	DIVL y+8(FP)
+	MOVL AX, q+12(FP)
+	MOVL DX, r+16(FP)
+	RET
+
+
 // func addVV(z, x, y []Word) (c Word)
 TEXT ·addVV(SB),7,$0
 	MOVL z+0(FP), DI
@@ -212,11 +231,10 @@ TEXT ·addMulVVW(SB),7,$0
 
 L6:	MOVL (SI)(BX*4), AX
 	MULL BP
-	ADDL (DI)(BX*4), AX
-	ADCL $0, DX
 	ADDL CX, AX
 	ADCL $0, DX
-	MOVL AX, (DI)(BX*4)
+	ADDL AX, (DI)(BX*4)
+	ADCL $0, DX
 	MOVL DX, CX
 	ADDL $1, BX		// i++
 

src/pkg/big/arith_amd64.s

@@ -7,6 +7,25 @@
 
 // TODO(gri) - experiment with unrolled loops for faster execution
 
+// func mulWW(x, y Word) (z1, z0 Word)
+TEXT ·mulWW(SB),7,$0
+	MOVQ x+0(FP), AX
+	MULQ y+8(FP)
+	MOVQ DX, z1+16(FP)
+	MOVQ AX, z0+24(FP)
+	RET
+
+
+// func divWW(x1, x0, y Word) (q, r Word)
+TEXT ·divWW(SB),7,$0
+	MOVQ x1+0(FP), DX
+	MOVQ x0+8(FP), AX
+	DIVQ y+16(FP)
+	MOVQ AX, q+24(FP)
+	MOVQ DX, r+32(FP)
+	RET
+
+
 // func addVV(z, x, y []Word) (c Word)
 TEXT ·addVV(SB),7,$0
 	MOVQ z+0(FP), R10
@@ -210,11 +229,10 @@ TEXT ·addMulVVW(SB),7,$0
 
 L6:	MOVQ (R8)(BX*8), AX
 	MULQ R9
-	ADDQ (R10)(BX*8), AX
-	ADCQ $0, DX
 	ADDQ CX, AX
 	ADCQ $0, DX
-	MOVQ AX, (R10)(BX*8)
+	ADDQ AX, (R10)(BX*8)
+	ADCQ $0, DX
 	MOVQ DX, CX
 	ADDL $1, BX		// i++
 

src/pkg/big/nat.go

@@ -69,16 +69,20 @@ func (z nat) make(n int) nat {
 }
 
 
-func (z nat) setUint64(x uint64) nat {
+func (z nat) setWord(x Word) nat {
 	if x == 0 {
 		return z.make(0)
 	}
+	z = z.make(1)
+	z[0] = x
+	return z
+}
+
 
+func (z nat) setUint64(x uint64) nat {
 	// single-digit values
-	if x == uint64(Word(x)) {
-		z = z.make(1)
-		z[0] = Word(x)
-		return z
+	if w := Word(x); uint64(w) == x {
+		return z.setWord(w)
 	}
 
 	// compute number of words n required to represent x
@@ -194,7 +198,7 @@ func (x nat) cmp(y nat) (r int) {
 func (z nat) mulAddWW(x nat, y, r Word) nat {
 	m := len(x)
 	if m == 0 || y == 0 {
-		return z.setUint64(uint64(r)) // result is r
+		return z.setWord(r) // result is r
 	}
 	// m > 0
 
@@ -529,6 +533,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	m := len(uIn) - n
 
 	// determine if z can be reused
+	// TODO(gri) should find a better solution - this if statement
+	//           is very costly (see e.g. time pidigits -s -n 10000)
 	if alias(z, uIn) || alias(z, v) {
 		z = nil // z is an alias for uIn or v - cannot reuse
 	}
@@ -549,15 +555,13 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	// D2.
 	for j := m; j >= 0; j-- {
 		// D3.
-		var qhat Word
-		if u[j+n] == v[n-1] {
-			qhat = _B - 1
-		} else {
+		qhat := Word(_M)
+		if u[j+n] != v[n-1] {
 			var rhat Word
-			qhat, rhat = divWW_g(u[j+n], u[j+n-1], v[n-1])
+			qhat, rhat = divWW(u[j+n], u[j+n-1], v[n-1])
 
 			// x1 | x2 = q̂v_{n-2}
-			x1, x2 := mulWW_g(qhat, v[n-2])
+			x1, x2 := mulWW(qhat, v[n-2])
 			// test if q̂v_{n-2} > br̂ + u_{j+n-2}
 			for greaterThan(x1, x2, rhat, u[j+n-2]) {
 				qhat--
@@ -567,7 +571,7 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 				if rhat < prevRhat {
 					break
 				}
-				x1, x2 = mulWW_g(qhat, v[n-2])
+				x1, x2 = mulWW(qhat, v[n-2])
 			}
 		}