runtime: make ARM integer div-by-zero traceback-friendly

The implementation of division in the 5 toolchain is a bit too magical.
Hide the magic from the traceback routines.

Also add a test for the results of the software divide routine.

Fixes #5805.

R=golang-dev, minux.ma
CC=golang-dev
https://golang.org/cl/13239052

src/pkg/runtime/vlop_arm.s

@@ -104,16 +104,13 @@ r = 1 // input n, output r
 s = 2 // three temporary variables
 M = 3
 a = 11
-// Please be careful when changing this, it is pretty fragile:
-// 1, don't use unconditional branch as the linker is free to reorder the blocks;
-// 2. if a == 11, beware that the linker will use R11 if you use certain instructions.
+// Be careful: R(a) == R11 will be used by the linker for synthesized instructions.
 TEXT udiv<>(SB),NOSPLIT,$-4
 	CLZ 	R(q), R(s) // find normalizing shift
 	MOVW.S	R(q)<<R(s), R(a)
-	ADD 	R(a)>>25, PC, R(a) // most significant 7 bits of divisor
-	MOVBU.NE	(4*36-64)(R(a)), R(a) // 36 == number of inst. between fast_udiv_tab and begin
+	MOVW	$fast_udiv_tab<>-64(SB), R(M)
+	MOVBU.NE	R(a)>>25(R(M)), R(a) // index by most significant 7 bits of divisor
 
-begin:
 	SUB.S	$7, R(s)
 	RSB 	$0, R(q), R(M) // M = -q
 	MOVW.PL	R(a)<<R(s), R(q)
@@ -141,9 +138,7 @@ begin:
 	ADD.CC	$1, R(q)
 	ADD.PL	R(M)<<1, R(r)
 	ADD.PL	$2, R(q)
-
-	// return, can't use RET here or fast_udiv_tab will be dropped during linking
-	MOVW	R14, R15
+	RET
 
 udiv_by_large_d:
 	// at this point we know d>=2^(31-6)=2^25
@@ -160,20 +155,34 @@ udiv_by_large_d:
 	CMN 	R(r), R(M)
 	ADD.CS	R(M), R(r)
 	ADD.CS	$1, R(q)
-
-	// return, can't use RET here or fast_udiv_tab will be dropped during linking
-	MOVW	R14, R15
+	RET
 
 udiv_by_0_or_1:
 	// carry set if d==1, carry clear if d==0
-	MOVW.CS	R(r), R(q)
-	MOVW.CS	$0, R(r)
-	BL.CC 	runtime·panicdivide(SB) // no way back
+	BCC udiv_by_0
+	MOVW	R(r), R(q)
+	MOVW	$0, R(r)
+	RET
 
-	// return, can't use RET here or fast_udiv_tab will be dropped during linking
-	MOVW	R14, R15
+udiv_by_0:
+	// The ARM toolchain expects it can emit references to DIV and MOD
+	// instructions. The linker rewrites each pseudo-instruction into
+	// a sequence that pushes two values onto the stack and then calls
+	// _divu, _modu, _div, or _mod (below), all of which have a 16-byte
+	// frame plus the saved LR. The traceback routine knows the expanded
+	// stack frame size at the pseudo-instruction call site, but it
+	// doesn't know that the frame has a non-standard layout. In particular,
+	// it expects to find a saved LR in the bottom word of the frame.
+	// Unwind the stack back to the pseudo-instruction call site, copy the
+	// saved LR where the traceback routine will look for it, and make it
+	// appear that panicdivide was called from that PC.
+	MOVW	0(R13), LR
+	ADD	$20, R13
+	MOVW	8(R13), R1 // actual saved LR
+	MOVW	R1, 0(R13) // expected here for traceback
+	B 	runtime·panicdivide(SB)
 
-fast_udiv_tab:
+TEXT fast_udiv_tab<>(SB),NOSPLIT,$-4
 	// var tab [64]byte
 	// tab[0] = 255; for i := 1; i <= 63; i++ { tab[i] = (1<<14)/(64+i) }
 	// laid out here as little-endian uint32s

test/divmod.go

+// run
+
+// Copyright 2013 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.
+
+// Test division of variables. Generate many test cases,
+// compute correct answer using shift and subtract,
+// and then compare against results from divison and
+// modulus operators.
+//
+// Primarily useful for testing software div/mod.
+
+package main
+
+const long = false
+
+func main() {
+	if long {
+		// About 3e9 test cases (calls to checkdiv3).
+		// Too long for everyday testing.
+		gen2(3, 64, 2, 64, checkdiv1)
+		println(ntest)
+	} else {
+		// About 4e6 test cases (calls to checkdiv3).
+		// Runs for 8 seconds on ARM chromebook, much faster elsewhere.
+		gen2(2, 64, 1, 64, checkdiv1)
+	}
+}
+
+// generate all uint64 values x where x has at most n bits set in the low w
+// and call f(x) for each.
+func gen1(n, w int, f func(uint64)) {
+	gen(0, 0, n, w-1, f)
+}
+
+func gen(val uint64, nbits, maxbits, pos int, f func(uint64)) {
+	if pos < 0 {
+		f(val)
+		return
+	}
+	gen(val, nbits, maxbits, pos-1, f)
+	if nbits < maxbits {
+		gen(val|1<<uint(pos), nbits+1, maxbits, pos-1, f)
+	}
+}
+
+// generate all uint64 values x, y where x has at most n1 bits set in the low w1
+// and y has at most n2 bits set in the low w2 and call f(x, y) for each.
+func gen2(n1, w1, n2, w2 int, f func(uint64, uint64)) {
+	gen1(n1, w1, func(x uint64) {
+		gen1(n2, w2, func(y uint64) {
+			f(x, y)
+		})
+	})
+}
+
+// x and y are uint64s with at most 2 bits set.
+// Check those values and values above and below,
+// along with bitwise inversions of the same (done in checkdiv2).
+func checkdiv1(x, y uint64) {
+	checkdiv2(x, y)
+	// If the low bit is set in x or y, adding or subtracting 1
+	// produces a number that checkdiv1 is going to be called
+	// with anyway, so don't duplicate effort.
+	if x&1 == 0 {
+		checkdiv2(x+1, y)
+		checkdiv2(x-1, y)
+	}
+	if y&1 == 0 {
+		checkdiv2(x, y-1)
+		checkdiv2(x, y+1)
+		if x&1 == 0 {
+			checkdiv2(x+1, y-1)
+			checkdiv2(x-1, y-1)
+			checkdiv2(x-1, y+1)
+			checkdiv2(x+1, y+1)
+		}
+	}
+}
+
+func checkdiv2(x, y uint64) {
+	checkdiv3(x, y)
+	checkdiv3(^x, y)
+	checkdiv3(x, ^y)
+	checkdiv3(^x, ^y)
+}
+
+var ntest int64 = 0
+
+func checkdiv3(x, y uint64) {
+	ntest++
+	if ntest&(ntest-1) == 0 && long {
+		println(ntest, "...")
+	}
+	checkuint64(x, y)
+	if (uint64(uint32(x)) == x || uint64(uint32(^x)) == ^x) && (uint64(uint32(y)) == y || uint64(uint32(^y)) == ^y) {
+		checkuint32(uint32(x), uint32(y))
+	}
+	if (uint64(uint16(x)) == x || uint64(uint16(^x)) == ^x) && (uint64(uint16(y)) == y || uint64(uint16(^y)) == ^y) {
+		checkuint16(uint16(x), uint16(y))
+	}
+	if (uint64(uint8(x)) == x || uint64(uint8(^x)) == ^x) && (uint64(uint8(y)) == y || uint64(uint8(^y)) == ^y) {
+		checkuint8(uint8(x), uint8(y))
+	}
+	
+	
+	sx := int64(x)
+	sy := int64(y)
+	checkint64(sx, sy)
+	if (int64(int32(sx)) == sx || int64(int32(^sx)) == ^sx) && (int64(int32(sy)) == sy || int64(int32(^sy)) == ^sy) {
+		checkint32(int32(sx), int32(sy))
+	}
+	if (int64(int16(sx)) == sx || int64(int16(^sx)) == ^sx) && (int64(int16(sy)) == sy || int64(int16(^sy)) == ^sy) {
+		checkint16(int16(sx), int16(sy))
+	}
+	if (int64(int8(sx)) == sx || int64(int8(^sx)) == ^sx) && (int64(int8(sy)) == sy || int64(int8(^sy)) == ^sy) {
+		checkint8(int8(sx), int8(sy))
+	}
+}
+
+// Check result of x/y, x%y for various types.
+
+func checkuint(x, y uint) {
+	if y == 0 {
+		divzerouint(x, y)
+		modzerouint(x, y)
+		return
+	}
+	q, r := udiv(uint64(x), uint64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != uint(q) {
+		print("uint(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != uint(r) {
+		print("uint(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkuint64(x, y uint64) {
+	if y == 0 {
+		divzerouint64(x, y)
+		modzerouint64(x, y)
+		return
+	}
+	q, r := udiv(x, y)
+	q1 := x/y
+	r1 := x%y
+	if q1 != q {
+		print("uint64(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != r {
+		print("uint64(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkuint32(x, y uint32) {
+	if y == 0 {
+		divzerouint32(x, y)
+		modzerouint32(x, y)
+		return
+	}
+	q, r := udiv(uint64(x), uint64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != uint32(q) {
+		print("uint32(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != uint32(r) {
+		print("uint32(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkuint16(x, y uint16) {
+	if y == 0 {
+		divzerouint16(x, y)
+		modzerouint16(x, y)
+		return
+	}
+	q, r := udiv(uint64(x), uint64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != uint16(q) {
+		print("uint16(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != uint16(r) {
+		print("uint16(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkuint8(x, y uint8) {
+	if y == 0 {
+		divzerouint8(x, y)
+		modzerouint8(x, y)
+		return
+	}
+	q, r := udiv(uint64(x), uint64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != uint8(q) {
+		print("uint8(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != uint8(r) {
+		print("uint8(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkint(x, y int) {
+	if y == 0 {
+		divzeroint(x, y)
+		modzeroint(x, y)
+		return
+	}
+	q, r := idiv(int64(x), int64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != int(q) {
+		print("int(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != int(r) {
+		print("int(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkint64(x, y int64) {
+	if y == 0 {
+		divzeroint64(x, y)
+		modzeroint64(x, y)
+		return
+	}
+	q, r := idiv(x, y)
+	q1 := x/y
+	r1 := x%y
+	if q1 != q {
+		print("int64(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != r {
+		print("int64(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkint32(x, y int32) {
+	if y == 0 {
+		divzeroint32(x, y)
+		modzeroint32(x, y)
+		return
+	}
+	q, r := idiv(int64(x), int64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != int32(q) {
+		print("int32(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != int32(r) {
+		print("int32(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkint16(x, y int16) {
+	if y == 0 {
+		divzeroint16(x, y)
+		modzeroint16(x, y)
+		return
+	}
+	q, r := idiv(int64(x), int64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != int16(q) {
+		print("int16(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != int16(r) {
+		print("int16(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func checkint8(x, y int8) {
+	if y == 0 {
+		divzeroint8(x, y)
+		modzeroint8(x, y)
+		return
+	}
+	q, r := idiv(int64(x), int64(y))
+	q1 := x/y
+	r1 := x%y
+	if q1 != int8(q) {
+		print("int8(", x, "/", y, ") = ", q1, ", want ", q, "\n")
+	}
+	if r1 != int8(r) {
+		print("int8(", x, "%", y, ") = ", r1, ", want ", r, "\n")
+	}
+}
+
+func divzerouint(x, y uint) uint {
+	defer checkudivzero("uint", uint64(x))
+	return x / y
+}
+
+func divzerouint64(x, y uint64) uint64 {
+	defer checkudivzero("uint64", uint64(x))
+	return x / y
+}
+
+func divzerouint32(x, y uint32) uint32 {
+	defer checkudivzero("uint32", uint64(x))
+	return x / y
+}
+
+func divzerouint16(x, y uint16) uint16 {
+	defer checkudivzero("uint16", uint64(x))
+	return x / y
+}
+
+func divzerouint8(x, y uint8) uint8 {
+	defer checkudivzero("uint8", uint64(x))
+	return x / y
+}
+
+func checkudivzero(typ string, x uint64) {
+	if recover() == nil {
+		print(typ, "(", x, " / 0) did not panic")
+	}
+}
+
+func divzeroint(x, y int) int {
+	defer checkdivzero("int", int64(x))
+	return x / y
+}
+
+func divzeroint64(x, y int64) int64 {
+	defer checkdivzero("int64", int64(x))
+	return x / y
+}
+
+func divzeroint32(x, y int32) int32 {
+	defer checkdivzero("int32", int64(x))
+	return x / y
+}
+
+func divzeroint16(x, y int16) int16 {
+	defer checkdivzero("int16", int64(x))
+	return x / y
+}
+
+func divzeroint8(x, y int8) int8 {
+	defer checkdivzero("int8", int64(x))
+	return x / y
+}
+
+func checkdivzero(typ string, x int64) {
+	if recover() == nil {
+		print(typ, "(", x, " / 0) did not panic")
+	}
+}
+
+func modzerouint(x, y uint) uint {
+	defer checkumodzero("uint", uint64(x))
+	return x % y
+}
+
+func modzerouint64(x, y uint64) uint64 {
+	defer checkumodzero("uint64", uint64(x))
+	return x % y
+}
+
+func modzerouint32(x, y uint32) uint32 {
+	defer checkumodzero("uint32", uint64(x))
+	return x % y
+}
+
+func modzerouint16(x, y uint16) uint16 {
+	defer checkumodzero("uint16", uint64(x))
+	return x % y
+}
+
+func modzerouint8(x, y uint8) uint8 {
+	defer checkumodzero("uint8", uint64(x))
+	return x % y
+}
+
+func checkumodzero(typ string, x uint64) {
+	if recover() == nil {
+		print(typ, "(", x, " % 0) did not panic")
+	}
+}
+
+func modzeroint(x, y int) int {
+	defer checkmodzero("int", int64(x))
+	return x % y
+}
+
+func modzeroint64(x, y int64) int64 {
+	defer checkmodzero("int64", int64(x))
+	return x % y
+}
+
+func modzeroint32(x, y int32) int32 {
+	defer checkmodzero("int32", int64(x))
+	return x % y
+}
+
+func modzeroint16(x, y int16) int16 {
+	defer checkmodzero("int16", int64(x))
+	return x % y
+}
+
+func modzeroint8(x, y int8) int8 {
+	defer checkmodzero("int8", int64(x))
+	return x % y
+}
+
+func checkmodzero(typ string, x int64) {
+	if recover() == nil {
+		print(typ, "(", x, " % 0) did not panic")
+	}
+}
+
+// unsigned divide and mod using shift and subtract.
+func udiv(x, y uint64) (q, r uint64) {
+	sh := 0
+	for y+y > y && y+y <= x {
+		sh++
+		y <<= 1
+	}
+	for ; sh >= 0; sh-- {
+		q <<= 1
+		if x >= y {
+			x -= y
+			q |= 1
+		}
+		y >>= 1
+	}
+	return q, x	
+}
+
+// signed divide and mod: do unsigned and adjust signs.
+func idiv(x, y int64) (q, r int64) {
+	// special case for minint / -1 = minint
+	if x-1 > x && y == -1 {
+		return x, 0
+	}
+	ux := uint64(x)
+	uy := uint64(y)
+	if x < 0 {
+		ux = -ux
+	}
+	if y < 0 {
+		uy = -uy
+	}
+	uq, ur := udiv(ux, uy)
+	q = int64(uq)
+	r = int64(ur)
+	if x < 0 {
+		r = -r
+	}
+	if (x < 0) != (y < 0) {
+		q = -q
+	}
+	return q, r
+}