[release-branch.go1.12] math/big: fix the bug in assembly implementation of shlVU on arm64

For the case where the addresses of parameter z and x of the function
shlVU overlap and the address of z is greater than x, x (input value)
can be polluted during the calculation when the high words of x are
overlapped with the low words of z (output value).

Updates #31084
Fixes #32940

Change-Id: I9bb0266a1d7856b8faa9a9b1975d6f57dece0479
Reviewed-on: https://go-review.googlesource.com/c/go/+/169780
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Cherry Zhang <cherryyz@google.com>
(cherry picked from commit 503e6ccd)
Reviewed-on: https://go-review.googlesource.com/c/go/+/185041
Run-TryBot: Dmitri Shuralyov <dmitshur@golang.org>

src/math/big/arith_arm64.s

@@ -194,83 +194,97 @@ len0:
 	MOVD	R2, c+56(FP)
 	RET
 
-
 // func shlVU(z, x []Word, s uint) (c Word)
+// This implementation handles the shift operation from the high word to the low word,
+// which may be an error for the case where the low word of x overlaps with the high
+// word of z. When calling this function directly, you need to pay attention to this
+// situation.
 TEXT ·shlVU(SB),NOSPLIT,$0
-	MOVD	z+0(FP), R0
-	MOVD	z_len+8(FP), R1
+	LDP	z+0(FP), (R0, R1)	// R0 = z.ptr, R1 = len(z)
 	MOVD	x+24(FP), R2
 	MOVD	s+48(FP), R3
-	MOVD	$0, R8		// in order not to affect the first element, R8 is initialized to zero
-	MOVD	$64, R4
-	SUB	R3, R4
+	ADD	R1<<3, R0	// R0 = &z[n]
+	ADD	R1<<3, R2	// R2 = &x[n]
 	CBZ	R1, len0
 	CBZ	R3, copy	// if the number of shift is 0, just copy x to z
-
-	TBZ	$0, R1, two
-	MOVD.P	8(R2), R6
-	LSR	R4, R6, R8
-	LSL	R3, R6
-	MOVD.P	R6, 8(R0)
+	MOVD	$64, R4
+	SUB	R3, R4
+	// handling the most significant element x[n-1]
+	MOVD.W	-8(R2), R6
+	LSR	R4, R6, R5	// return value
+	LSL	R3, R6, R8	// x[i] << s
+	SUB	$1, R1
+one:	TBZ	$0, R1, two
+	MOVD.W	-8(R2), R6
+	LSR	R4, R6, R7
+	ORR	R8, R7
+	LSL	R3, R6, R8
 	SUB	$1, R1
+	MOVD.W	R7, -8(R0)
 two:
 	TBZ	$1, R1, loop
-	LDP.P	16(R2), (R6, R7)
-	LSR	R4, R6, R9
-	LSL	R3, R6
-	ORR	R8, R6
-	LSR	R4, R7, R8
+	LDP.W	-16(R2), (R6, R7)
+	LSR	R4, R7, R10
+	ORR	R8, R10
 	LSL	R3, R7
-	ORR	R9, R7
-	STP.P	(R6, R7), 16(R0)
+	LSR	R4, R6, R9
+	ORR	R7, R9
+	LSL	R3, R6, R8
 	SUB	$2, R1
+	STP.W	(R9, R10), -16(R0)
 loop:
 	CBZ	R1, done
-	LDP.P	32(R2), (R10, R11)
-	LDP	-16(R2), (R12, R13)
-	LSR	R4, R10, R20
-	LSL	R3, R10
-	ORR	R8, R10		// z[i] = (x[i] << s) | (x[i-1] >> (64 - s))
-	LSR	R4, R11, R21
-	LSL	R3, R11
-	ORR	R20, R11
+	LDP.W	-32(R2), (R10, R11)
+	LDP	16(R2), (R12, R13)
+	LSR	R4, R13, R23
+	ORR	R8, R23		// z[i] = (x[i] << s) | (x[i-1] >> (64 - s))
+	LSL	R3, R13
 	LSR	R4, R12, R22
+	ORR	R13, R22
 	LSL	R3, R12
-	ORR	R21, R12
-	LSR	R4, R13, R8
-	LSL	R3, R13
-	ORR	R22, R13
-	STP.P	(R10, R11), 32(R0)
-	STP	(R12, R13), -16(R0)
+	LSR	R4, R11, R21
+	ORR	R12, R21
+	LSL	R3, R11
+	LSR	R4, R10, R20
+	ORR	R11, R20
+	LSL	R3, R10, R8
+	STP.W	(R20, R21), -32(R0)
+	STP	(R22, R23), 16(R0)
 	SUB	$4, R1
 	B	loop
 done:
-	MOVD	R8, c+56(FP)	// the part moved out from the last element
+	MOVD.W	R8, -8(R0)	// the first element x[0]
+	MOVD	R5, c+56(FP)	// the part moved out from x[n-1]
 	RET
 copy:
+	CMP	R0, R2
+	BEQ	len0
 	TBZ	$0, R1, ctwo
-	MOVD.P	8(R2), R3
-	MOVD.P	R3, 8(R0)
+	MOVD.W	-8(R2), R4
+	MOVD.W	R4, -8(R0)
 	SUB	$1, R1
 ctwo:
 	TBZ	$1, R1, cloop
-	LDP.P	16(R2), (R4, R5)
-	STP.P	(R4, R5), 16(R0)
+	LDP.W	-16(R2), (R4, R5)
+	STP.W	(R4, R5), -16(R0)
 	SUB	$2, R1
 cloop:
 	CBZ	R1, len0
-	LDP.P	32(R2), (R4, R5)
-	LDP	-16(R2), (R6, R7)
-	STP.P	(R4, R5), 32(R0)
-	STP	(R6, R7), -16(R0)
+	LDP.W	-32(R2), (R4, R5)
+	LDP	16(R2), (R6, R7)
+	STP.W	(R4, R5), -32(R0)
+	STP	(R6, R7), 16(R0)
 	SUB	$4, R1
 	B	cloop
 len0:
 	MOVD	$0, c+56(FP)
 	RET
 
-
 // func shrVU(z, x []Word, s uint) (c Word)
+// This implementation handles the shift operation from the low word to the high word,
+// which may be an error for the case where the high word of x overlaps with the low
+// word of z. When calling this function directly, you need to pay attention to this
+// situation.
 TEXT ·shrVU(SB),NOSPLIT,$0
 	MOVD	z+0(FP), R0
 	MOVD	z_len+8(FP), R1
@@ -330,6 +344,8 @@ done:
 	MOVD	R8, (R0)	// deal with the last element
 	RET
 copy:
+	CMP	R0, R2
+	BEQ	len0
 	TBZ	$0, R1, ctwo
 	MOVD.P	8(R2), R3
 	MOVD.P	R3, 8(R0)

src/math/big/arith_test.go

@@ -255,6 +255,75 @@ func TestFunVW(t *testing.T) {
 	}
 }
 
+type argVU struct {
+	d  []Word // d is a Word slice, the input parameters x and z come from this array.
+	l  uint   // l is the length of the input parameters x and z.
+	xp uint   // xp is the starting position of the input parameter x, x := d[xp:xp+l].
+	zp uint   // zp is the starting position of the input parameter z, z := d[zp:zp+l].
+	s  uint   // s is the shift number.
+	r  []Word // r is the expected output result z.
+	c  Word   // c is the expected return value.
+	m  string // message.
+}
+
+var argshlVU = []argVU{
+	// test cases for shlVU
+	{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0}, 7, 0, 0, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "complete overlap of shlVU"},
+	{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0}, 7, 0, 3, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by half of shlVU"},
+	{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0}, 7, 0, 6, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by 1 Word of shlVU"},
+	{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0, 0}, 7, 0, 7, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "no overlap of shlVU"},
+}
+
+var argshrVU = []argVU{
+	// test cases for shrVU
+	{[]Word{0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 1, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "complete overlap of shrVU"},
+	{[]Word{0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 4, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by half of shrVU"},
+	{[]Word{0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 7, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by 1 Word of shrVU"},
+	{[]Word{0, 0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 8, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "no overlap of shrVU"},
+}
+
+func testShiftFunc(t *testing.T, f func(z, x []Word, s uint) Word, a argVU) {
+	// save a.d for error message, or it will be overwritten.
+	b := make([]Word, len(a.d))
+	copy(b, a.d)
+	z := a.d[a.zp : a.zp+a.l]
+	x := a.d[a.xp : a.xp+a.l]
+	c := f(z, x, a.s)
+	for i, zi := range z {
+		if zi != a.r[i] {
+			t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot z[%d] = %#x; want %#x", b, a.m, a.zp, a.zp+a.l, a.xp, a.xp+a.l, a.s, i, zi, a.r[i])
+			break
+		}
+	}
+	if c != a.c {
+		t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot c = %#x; want %#x", b, a.m, a.zp, a.zp+a.l, a.xp, a.xp+a.l, a.s, c, a.c)
+	}
+}
+
+func TestShiftOverlap(t *testing.T) {
+	for _, a := range argshlVU {
+		arg := a
+		testShiftFunc(t, shlVU, arg)
+	}
+
+	for _, a := range argshrVU {
+		arg := a
+		testShiftFunc(t, shrVU, arg)
+	}
+}
+
+func TestIssue31084(t *testing.T) {
+	// compute 10^n via 5^n << n.
+	const n = 165
+	p := nat(nil).expNN(nat{5}, nat{n}, nil)
+	p = p.shl(p, uint(n))
+	got := string(p.utoa(10))
+	want := "1" + strings.Repeat("0", n)
+	if got != want {
+		t.Errorf("shl(%v, %v)\n\tgot %s; want %s\n", p, uint(n), got, want)
+	}
+}
+
 func BenchmarkAddVW(b *testing.B) {
 	for _, n := range benchSizes {
 		if isRaceBuilder && n > 1e3 {