big: remove some unnecessary conversions

R=rsc
CC=golang-dev
https://golang.org/cl/4529110

src/pkg/big/arith.go

@@ -188,7 +188,7 @@ func subVW_g(z, x []Word, y Word) (c Word) {
 }
 
 
-func shlVW_g(z, x []Word, s Word) (c Word) {
+func shlVU_g(z, x []Word, s uint) (c Word) {
 	if n := len(z); n > 0 {
 		ŝ := _W - s
 		w1 := x[n-1]
@@ -204,7 +204,7 @@ func shlVW_g(z, x []Word, s Word) (c Word) {
 }
 
 
-func shrVW_g(z, x []Word, s Word) (c Word) {
+func shrVU_g(z, x []Word, s uint) (c Word) {
 	if n := len(z); n > 0 {
 		ŝ := _W - s
 		w1 := x[0]

src/pkg/big/arith_386.s

@@ -118,8 +118,8 @@ E4:	CMPL BX, BP		// i < n
 	RET
 
 
-// func shlVW(z, x []Word, s Word) (c Word)
-TEXT ·shlVW(SB),7,$0
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),7,$0
 	MOVL n+4(FP), BX	// i = n
 	SUBL $1, BX		// i--
 	JL X8b			// i < 0	(n <= 0)
@@ -153,8 +153,8 @@ X8b:	MOVL $0, c+28(FP)
 	RET
 
 
-// func shrVW(z, x []Word, s Word) (c Word)
-TEXT ·shrVW(SB),7,$0
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),7,$0
 	MOVL n+4(FP), BP
 	SUBL $1, BP		// n--
 	JL X9b			// n < 0	(n <= 0)

src/pkg/big/arith_amd64.s

@@ -120,8 +120,8 @@ E4:	CMPQ BX, R11		// i < n
 	RET
 
 
-// func shlVW(z, x []Word, s Word) (c Word)
-TEXT ·shlVW(SB),7,$0
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),7,$0
 	MOVL n+8(FP), BX	// i = n
 	SUBL $1, BX		// i--
 	JL X8b			// i < 0	(n <= 0)
@@ -129,7 +129,7 @@ TEXT ·shlVW(SB),7,$0
 	// n > 0
 	MOVQ z+0(FP), R10
 	MOVQ x+16(FP), R8
-	MOVQ s+32(FP), CX
+	MOVL s+32(FP), CX
 	MOVQ (R8)(BX*8), AX	// w1 = x[n-1]
 	MOVQ $0, DX
 	SHLQ CX, DX:AX		// w1>>ŝ
@@ -155,8 +155,8 @@ X8b:	MOVQ $0, c+40(FP)
 	RET
 
 
-// func shrVW(z, x []Word, s Word) (c Word)
-TEXT ·shrVW(SB),7,$0
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),7,$0
 	MOVL n+8(FP), R11
 	SUBL $1, R11		// n--
 	JL X9b			// n < 0	(n <= 0)
@@ -164,7 +164,7 @@ TEXT ·shrVW(SB),7,$0
 	// n > 0
 	MOVQ z+0(FP), R10
 	MOVQ x+16(FP), R8
-	MOVQ s+32(FP), CX
+	MOVL s+32(FP), CX
 	MOVQ (R8), AX		// w1 = x[0]
 	MOVQ $0, DX
 	SHRQ CX, DX:AX		// w1<<ŝ

src/pkg/big/arith_arm.s

@@ -97,6 +97,7 @@ E3:
 	RET
 
 
+// func subVW(z, x []Word, y Word) (c Word)
 TEXT ·subVW(SB),7,$0
 	MOVW	z+0(FP), R1
 	MOVW	x+12(FP), R2
@@ -131,8 +132,8 @@ E4:
 	RET
 
 
-// func shlVW(z, x []Word, s Word) (c Word)
-TEXT ·shlVW(SB),7,$0
+// func shlVU(z, x []Word, s uint) (c Word)
+TEXT ·shlVU(SB),7,$0
 	MOVW	n+4(FP), R5
 	CMP	$0, R5
 	BEQ	X7
@@ -180,7 +181,8 @@ X7:
 	RET
 
 
-TEXT ·shrVW(SB),7,$0
+// func shrVU(z, x []Word, s uint) (c Word)
+TEXT ·shrVU(SB),7,$0
 	MOVW	n+4(FP), R5
 	CMP	$0, R5
 	BEQ	X6
@@ -229,6 +231,7 @@ X6:
 	RET
 
 
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
 TEXT ·mulAddVWW(SB),7,$0
 	MOVW	$0, R0
 	MOVW	z+0(FP), R1
@@ -256,6 +259,7 @@ E8:
 	RET
 
 
+// func addMulVVW(z, x []Word, y Word) (c Word)
 TEXT ·addMulVVW(SB),7,$0
 	MOVW	$0, R0
 	MOVW	z+0(FP), R1
@@ -286,11 +290,13 @@ E9:
 	RET
 
 
+// divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
 TEXT ·divWVW(SB),7,$0
 	// ARM has no multiword division, so use portable code.
 	B ·divWVW_g(SB)
 
 
+// func divWW(x1, x0, y Word) (q, r Word)
 TEXT ·divWW(SB),7,$0
 	// ARM has no multiword division, so use portable code.
 	B ·divWW_g(SB)

src/pkg/big/arith_decl.go

@@ -11,8 +11,8 @@ func addVV(z, x, y []Word) (c Word)
 func subVV(z, x, y []Word) (c Word)
 func addVW(z, x []Word, y Word) (c Word)
 func subVW(z, x []Word, y Word) (c Word)
-func shlVW(z, x []Word, s Word) (c Word)
-func shrVW(z, x []Word, s Word) (c Word)
+func shlVU(z, x []Word, s uint) (c Word)
+func shrVU(z, x []Word, s uint) (c Word)
 func mulAddVWW(z, x []Word, y, r Word) (c Word)
 func addMulVVW(z, x []Word, y Word) (c Word)
 func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)

src/pkg/big/arith_test.go

@@ -185,6 +185,13 @@ func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
 }
 
 
+func makeFunVW(f func(z, x []Word, s uint) (c Word)) funVW {
+	return func(z, x []Word, s Word) (c Word) {
+		return f(z, x, uint(s))
+	}
+}
+
+
 func TestFunVW(t *testing.T) {
 	for _, a := range sumVW {
 		arg := a
@@ -196,16 +203,20 @@ func TestFunVW(t *testing.T) {
 		testFunVW(t, "subVW", subVW, arg)
 	}
 
+	shlVW_g := makeFunVW(shlVU_g)
+	shlVW := makeFunVW(shlVU)
 	for _, a := range lshVW {
 		arg := a
-		testFunVW(t, "shlVW_g", shlVW_g, arg)
-		testFunVW(t, "shlVW", shlVW, arg)
+		testFunVW(t, "shlVU_g", shlVW_g, arg)
+		testFunVW(t, "shlVU", shlVW, arg)
 	}
 
+	shrVW_g := makeFunVW(shrVU_g)
+	shrVW := makeFunVW(shrVU)
 	for _, a := range rshVW {
 		arg := a
-		testFunVW(t, "shrVW_g", shrVW_g, arg)
-		testFunVW(t, "shrVW", shrVW, arg)
+		testFunVW(t, "shrVU_g", shrVW_g, arg)
+		testFunVW(t, "shrVU", shrVW, arg)
 	}
 }
 

src/pkg/big/nat.go

@@ -550,14 +550,14 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	u.clear()
 
 	// D1.
-	shift := Word(leadingZeros(v[n-1]))
+	shift := leadingZeros(v[n-1])
 	if shift > 0 {
 		// do not modify v, it may be used by another goroutine simultaneously
 		v1 := make(nat, n)
-		shlVW(v1, v, shift)
+		shlVU(v1, v, shift)
 		v = v1
 	}
-	u[len(uIn)] = shlVW(u[0:len(uIn)], uIn, shift)
+	u[len(uIn)] = shlVU(u[0:len(uIn)], uIn, shift)
 
 	// D2.
 	for j := m; j >= 0; j-- {
@@ -596,7 +596,7 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	}
 
 	q = q.norm()
-	shrVW(u, u, shift)
+	shrVU(u, u, shift)
 	r = u.norm()
 
 	return q, r
@@ -824,7 +824,7 @@ func (z nat) shl(x nat, s uint) nat {
 
 	n := m + int(s/_W)
 	z = z.make(n + 1)
-	z[n] = shlVW(z[n-m:n], x, Word(s%_W))
+	z[n] = shlVU(z[n-m:n], x, s%_W)
 	z[0 : n-m].clear()
 
 	return z.norm()
@@ -841,7 +841,7 @@ func (z nat) shr(x nat, s uint) nat {
 	// n > 0
 
 	z = z.make(n)
-	shrVW(z, x[m-n:], Word(s%_W))
+	shrVU(z, x[m-n:], s%_W)
 
 	return z.norm()
 }
@@ -972,25 +972,26 @@ func (x nat) modW(d Word) (r Word) {
 }
 
 
-// powersOfTwoDecompose finds q and k such that q * 1<<k = n and q is odd.
-func (n nat) powersOfTwoDecompose() (q nat, k Word) {
-	if len(n) == 0 {
-		return n, 0
+// powersOfTwoDecompose finds q and k with x = q * 1<<k and q is odd, or q and k are 0.
+func (x nat) powersOfTwoDecompose() (q nat, k int) {
+	if len(x) == 0 {
+		return x, 0
 	}
 
-	zeroWords := 0
-	for n[zeroWords] == 0 {
-		zeroWords++
+	// One of the words must be non-zero by definition,
+	// so this loop will terminate with i < len(x), and
+	// i is the number of 0 words.
+	i := 0
+	for x[i] == 0 {
+		i++
 	}
-	// One of the words must be non-zero by invariant, therefore
-	// zeroWords < len(n).
-	x := trailingZeroBits(n[zeroWords])
+	n := trailingZeroBits(x[i]) // x[i] != 0
 
-	q = q.make(len(n) - zeroWords)
-	shrVW(q, n[zeroWords:], Word(x))
-	q = q.norm()
+	q = make(nat, len(x)-i)
+	shrVU(q, x[i:], uint(n))
 
-	k = Word(_W*zeroWords + x)
+	q = q.norm()
+	k = i*_W + n
 	return
 }
 
@@ -1161,7 +1162,7 @@ NextRandom:
 		if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
 			continue
 		}
-		for j := Word(1); j < k; j++ {
+		for j := 1; j < k; j++ {
 			y = y.mul(y, y)
 			quotient, y = quotient.div(y, y, n)
 			if y.cmp(nm1) == 0 {