libgo: update to Go1.16beta1 release

This does not yet include support for the //go:embed directive added
in this release.

	* Makefile.am (check-runtime): Don't create check-runtime-dir.
	(mostlyclean-local): Don't remove check-runtime-dir.
	(check-go-tool, check-vet): Copy in go.mod and modules.txt.
	(check-cgo-test, check-carchive-test): Add go.mod file.
	* Makefile.in: Regenerate.

Reviewed-on: https://go-review.googlesource.com/c/gofrontend/+/280172

9 files changed, 307 insertions, 34 deletions

diff --git a/libgo/go/math/big/arith.go b/libgo/go/math/big/arith.go
index b0885f261fe..750ce8aa398 100644
--- a/libgo/go/math/big/arith.go
+++ b/libgo/go/math/big/arith.go
@@ -60,12 +60,6 @@ func nlz(x Word) uint {
 	return uint(bits.LeadingZeros(uint(x)))
 }
 
-// q = (u1<<_W + u0 - r)/v
-func divWW_g(u1, u0, v Word) (q, r Word) {
-	qq, rr := bits.Div(uint(u1), uint(u0), uint(v))
-	return Word(qq), Word(rr)
-}
-
 // The resulting carry c is either 0 or 1.
 func addVV_g(z, x, y []Word) (c Word) {
 	// The comment near the top of this file discusses this for loop condition.
@@ -207,10 +201,87 @@ func addMulVVW_g(z, x []Word, y Word) (c Word) {
 	return
 }
 
-func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
+// q = ( x1 << _W + x0 - r)/y. m = floor(( _B^2 - 1 ) / d - _B). Requiring x1<y.
+// An approximate reciprocal with a reference to "Improved Division by Invariant Integers
+// (IEEE Transactions on Computers, 11 Jun. 2010)"
+func divWW(x1, x0, y, m Word) (q, r Word) {
+	s := nlz(y)
+	if s != 0 {
+		x1 = x1<<s | x0>>(_W-s)
+		x0 <<= s
+		y <<= s
+	}
+	d := uint(y)
+	// We know that
+	//   m = ⎣(B^2-1)/d⎦-B
+	//   ⎣(B^2-1)/d⎦ = m+B
+	//   (B^2-1)/d = m+B+delta1    0 <= delta1 <= (d-1)/d
+	//   B^2/d = m+B+delta2        0 <= delta2 <= 1
+	// The quotient we're trying to compute is
+	//   quotient = ⎣(x1*B+x0)/d⎦
+	//            = ⎣(x1*B*(B^2/d)+x0*(B^2/d))/B^2⎦
+	//            = ⎣(x1*B*(m+B+delta2)+x0*(m+B+delta2))/B^2⎦
+	//            = ⎣(x1*m+x1*B+x0)/B + x0*m/B^2 + delta2*(x1*B+x0)/B^2⎦
+	// The latter two terms of this three-term sum are between 0 and 1.
+	// So we can compute just the first term, and we will be low by at most 2.
+	t1, t0 := bits.Mul(uint(m), uint(x1))
+	_, c := bits.Add(t0, uint(x0), 0)
+	t1, _ = bits.Add(t1, uint(x1), c)
+	// The quotient is either t1, t1+1, or t1+2.
+	// We'll try t1 and adjust if needed.
+	qq := t1
+	// compute remainder r=x-d*q.
+	dq1, dq0 := bits.Mul(d, qq)
+	r0, b := bits.Sub(uint(x0), dq0, 0)
+	r1, _ := bits.Sub(uint(x1), dq1, b)
+	// The remainder we just computed is bounded above by B+d:
+	// r = x1*B + x0 - d*q.
+	//   = x1*B + x0 - d*⎣(x1*m+x1*B+x0)/B⎦
+	//   = x1*B + x0 - d*((x1*m+x1*B+x0)/B-alpha)                                   0 <= alpha < 1
+	//   = x1*B + x0 - x1*d/B*m                         - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦             - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦             - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*((B^2-1)/d-B-beta)        - x1*d - x0*d/B + d*alpha   0 <= beta < 1
+	//   = x1*B + x0 - x1*B + x1/B + x1*d + x1*d/B*beta - x1*d - x0*d/B + d*alpha
+	//   =        x0        + x1/B        + x1*d/B*beta        - x0*d/B + d*alpha
+	//   = x0*(1-d/B) + x1*(1+d*beta)/B + d*alpha
+	//   <  B*(1-d/B) +  d*B/B          + d          because x0<B (and 1-d/B>0), x1<d, 1+d*beta<=B, alpha<1
+	//   =  B - d     +  d              + d
+	//   = B+d
+	// So r1 can only be 0 or 1. If r1 is 1, then we know q was too small.
+	// Add 1 to q and subtract d from r. That guarantees that r is <B, so
+	// we no longer need to keep track of r1.
+	if r1 != 0 {
+		qq++
+		r0 -= d
+	}
+	// If the remainder is still too large, increment q one more time.
+	if r0 >= d {
+		qq++
+		r0 -= d
+	}
+	return Word(qq), Word(r0 >> s)
+}
+
+func divWVW(z []Word, xn Word, x []Word, y Word) (r Word) {
 	r = xn
+	if len(x) == 1 {
+		qq, rr := bits.Div(uint(r), uint(x[0]), uint(y))
+		z[0] = Word(qq)
+		return Word(rr)
+	}
+	rec := reciprocalWord(y)
 	for i := len(z) - 1; i >= 0; i-- {
-		z[i], r = divWW_g(r, x[i], y)
+		z[i], r = divWW(r, x[i], y, rec)
 	}
-	return
+	return r
+}
+
+// reciprocalWord return the reciprocal of the divisor. rec = floor(( _B^2 - 1 ) / u - _B). u = d1 << nlz(d1).
+func reciprocalWord(d1 Word) Word {
+	u := uint(d1 << nlz(d1))
+	x1 := ^u
+	x0 := uint(_M)
+	rec, _ := bits.Div(x1, x0, u) // (_B^2-1)/U-_B = (_B*(_M-C)+_M)/U
+	return Word(rec)
 }
diff --git a/libgo/go/math/big/arith_decl.go b/libgo/go/math/big/arith_decl.go
index 61df0df9f24..a14fda3087a 100644
--- a/libgo/go/math/big/arith_decl.go
+++ b/libgo/go/math/big/arith_decl.go
@@ -9,7 +9,6 @@ package big
 
 // implemented in arith_$GOARCH.s
 func mulWW(x, y Word) (z1, z0 Word)
-func divWW(x1, x0, y Word) (q, r Word)
 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)
@@ -18,4 +17,3 @@ 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)
diff --git a/libgo/go/math/big/arith_decl_pure.go b/libgo/go/math/big/arith_decl_pure.go
index ee8f92211e8..ac789850389 100644
--- a/libgo/go/math/big/arith_decl_pure.go
+++ b/libgo/go/math/big/arith_decl_pure.go
@@ -10,10 +10,6 @@ func mulWW(x, y Word) (z1, z0 Word) {
 	return mulWW_g(x, y)
 }
 
-func divWW(x1, x0, y Word) (q, r Word) {
-	return divWW_g(x1, x0, y)
-}
-
 func addVV(z, x, y []Word) (c Word) {
 	return addVV_g(z, x, y)
 }
@@ -55,7 +51,3 @@ func mulAddVWW(z, x []Word, y, r Word) (c Word) {
 func addMulVVW(z, x []Word, y Word) (c Word) {
 	return addMulVVW_g(z, x, y)
 }
-
-func divWVW(z []Word, xn Word, x []Word, y Word) (r Word) {
-	return divWVW_g(z, xn, x, y)
-}
diff --git a/libgo/go/math/big/arith_test.go b/libgo/go/math/big/arith_test.go
index 05136f1895f..2aca0effde2 100644
--- a/libgo/go/math/big/arith_test.go
+++ b/libgo/go/math/big/arith_test.go
@@ -7,6 +7,7 @@ package big
 import (
 	"fmt"
 	"internal/testenv"
+	"math/bits"
 	"math/rand"
 	"strings"
 	"testing"
@@ -179,6 +180,23 @@ func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
 	}
 }
 
+func testFunVWext(t *testing.T, msg string, f funVW, f_g funVW, a argVW) {
+	// using the result of addVW_g/subVW_g as golden
+	z_g := make(nat, len(a.z))
+	c_g := f_g(z_g, a.x, a.y)
+	c := f(a.z, a.x, a.y)
+
+	for i, zi := range a.z {
+		if zi != z_g[i] {
+			t.Errorf("%s\n\tgot z[%d] = %#x; want %#x", msg, i, zi, z_g[i])
+			break
+		}
+	}
+	if c != c_g {
+		t.Errorf("%s\n\tgot c = %#x; want %#x", msg, c, c_g)
+	}
+}
+
 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))
@@ -213,6 +231,49 @@ func TestFunVW(t *testing.T) {
 	}
 }
 
+// Construct a vector comprising the same word, usually '0' or 'maximum uint'
+func makeWordVec(e Word, n int) []Word {
+	v := make([]Word, n)
+	for i := range v {
+		v[i] = e
+	}
+	return v
+}
+
+// Extended testing to addVW and subVW using various kinds of input data.
+// We utilize the results of addVW_g and subVW_g as golden reference to check
+// correctness.
+func TestFunVWExt(t *testing.T) {
+	// 32 is the current threshold that triggers an optimized version of
+	// calculation for large-sized vector, ensure we have sizes around it tested.
+	var vwSizes = []int{0, 1, 3, 4, 5, 8, 9, 23, 31, 32, 33, 34, 35, 36, 50, 120}
+	for _, n := range vwSizes {
+		// vector of random numbers, using the result of addVW_g/subVW_g as golden
+		x := rndV(n)
+		y := rndW()
+		z := make(nat, n)
+		arg := argVW{z, x, y, 0}
+		testFunVWext(t, "addVW, random inputs", addVW, addVW_g, arg)
+		testFunVWext(t, "subVW, random inputs", subVW, subVW_g, arg)
+
+		// vector of random numbers, but make 'x' and 'z' share storage
+		arg = argVW{x, x, y, 0}
+		testFunVWext(t, "addVW, random inputs, sharing storage", addVW, addVW_g, arg)
+		testFunVWext(t, "subVW, random inputs, sharing storage", subVW, subVW_g, arg)
+
+		// vector of maximum uint, to force carry flag set in each 'add'
+		y = ^Word(0)
+		x = makeWordVec(y, n)
+		arg = argVW{z, x, y, 0}
+		testFunVWext(t, "addVW, vector of max uint", addVW, addVW_g, arg)
+
+		// vector of '0', to force carry flag set in each 'sub'
+		x = makeWordVec(0, n)
+		arg = argVW{z, x, 1, 0}
+		testFunVWext(t, "subVW, vector of zero", subVW, subVW_g, arg)
+	}
+}
+
 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.
@@ -224,13 +285,36 @@ type argVU struct {
 	m  string // message.
 }
 
+var argshlVUIn = []Word{1, 2, 4, 8, 16, 32, 64, 0, 0, 0}
+var argshlVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshlVUr1 = []Word{2, 4, 8, 16, 32, 64, 128}
+var argshlVUrWm1 = []Word{1 << (_W - 1), 0, 1, 2, 4, 8, 16}
+
 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"},
-}
+	// additional test cases with shift values of 0, 1 and (_W-1)
+	{argshlVUIn, 7, 0, 0, 0, argshlVUr0, 0, "complete overlap of shlVU and shift of 0"},
+	{argshlVUIn, 7, 0, 0, 1, argshlVUr1, 0, "complete overlap of shlVU and shift of 1"},
+	{argshlVUIn, 7, 0, 0, _W - 1, argshlVUrWm1, 32, "complete overlap of shlVU and shift of _W - 1"},
+	{argshlVUIn, 7, 0, 1, 0, argshlVUr0, 0, "partial overlap by 6 Words of shlVU and shift of 0"},
+	{argshlVUIn, 7, 0, 1, 1, argshlVUr1, 0, "partial overlap by 6 Words of shlVU and shift of 1"},
+	{argshlVUIn, 7, 0, 1, _W - 1, argshlVUrWm1, 32, "partial overlap by 6 Words of shlVU and shift of _W - 1"},
+	{argshlVUIn, 7, 0, 2, 0, argshlVUr0, 0, "partial overlap by 5 Words of shlVU and shift of 0"},
+	{argshlVUIn, 7, 0, 2, 1, argshlVUr1, 0, "partial overlap by 5 Words of shlVU and shift of 1"},
+	{argshlVUIn, 7, 0, 2, _W - 1, argshlVUrWm1, 32, "partial overlap by 5 Words of shlVU abd shift of _W - 1"},
+	{argshlVUIn, 7, 0, 3, 0, argshlVUr0, 0, "partial overlap by 4 Words of shlVU and shift of 0"},
+	{argshlVUIn, 7, 0, 3, 1, argshlVUr1, 0, "partial overlap by 4 Words of shlVU and shift of 1"},
+	{argshlVUIn, 7, 0, 3, _W - 1, argshlVUrWm1, 32, "partial overlap by 4 Words of shlVU and shift of _W - 1"},
+}
+
+var argshrVUIn = []Word{0, 0, 0, 1, 2, 4, 8, 16, 32, 64}
+var argshrVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshrVUr1 = []Word{0, 1, 2, 4, 8, 16, 32}
+var argshrVUrWm1 = []Word{4, 8, 16, 32, 64, 128, 0}
 
 var argshrVU = []argVU{
 	// test cases for shrVU
@@ -238,23 +322,36 @@ var argshrVU = []argVU{
 	{[]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"},
+	// additional test cases with shift values of 0, 1 and (_W-1)
+	{argshrVUIn, 7, 3, 3, 0, argshrVUr0, 0, "complete overlap of shrVU and shift of 0"},
+	{argshrVUIn, 7, 3, 3, 1, argshrVUr1, 1 << (_W - 1), "complete overlap of shrVU and shift of 1"},
+	{argshrVUIn, 7, 3, 3, _W - 1, argshrVUrWm1, 2, "complete overlap of shrVU and shift of _W - 1"},
+	{argshrVUIn, 7, 3, 2, 0, argshrVUr0, 0, "partial overlap by 6 Words of shrVU and shift of 0"},
+	{argshrVUIn, 7, 3, 2, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 6 Words of shrVU and shift of 1"},
+	{argshrVUIn, 7, 3, 2, _W - 1, argshrVUrWm1, 2, "partial overlap by 6 Words of shrVU and shift of _W - 1"},
+	{argshrVUIn, 7, 3, 1, 0, argshrVUr0, 0, "partial overlap by 5 Words of shrVU and shift of 0"},
+	{argshrVUIn, 7, 3, 1, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 5 Words of shrVU and shift of 1"},
+	{argshrVUIn, 7, 3, 1, _W - 1, argshrVUrWm1, 2, "partial overlap by 5 Words of shrVU and shift of _W - 1"},
+	{argshrVUIn, 7, 3, 0, 0, argshrVUr0, 0, "partial overlap by 4 Words of shrVU and shift of 0"},
+	{argshrVUIn, 7, 3, 0, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 4 Words of shrVU and shift of 1"},
+	{argshrVUIn, 7, 3, 0, _W - 1, argshrVUrWm1, 2, "partial overlap by 4 Words of shrVU and shift of _W - 1"},
 }
 
 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.
+	// work on copy of a.d to preserve the original data.
 	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]
+	z := b[a.zp : a.zp+a.l]
+	x := b[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])
+			t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot z[%d] = %#x; want %#x", a.d, 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)
+		t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot c = %#x; want %#x", a.d, a.m, a.zp, a.zp+a.l, a.xp, a.xp+a.l, a.s, c, a.c)
 	}
 }
 
@@ -274,11 +371,24 @@ 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))
+	p = p.shl(p, 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)
+		t.Errorf("shl(%v, %v)\n\tgot  %s\n\twant %s", p, n, got, want)
+	}
+}
+
+const issue42838Value = "159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625"
+
+func TestIssue42838(t *testing.T) {
+	const s = 192
+	z, _, _, _ := nat(nil).scan(strings.NewReader(issue42838Value), 0, false)
+	z = z.shl(z, s)
+	got := string(z.utoa(10))
+	want := "1" + strings.Repeat("0", s)
+	if got != want {
+		t.Errorf("shl(%v, %v)\n\tgot  %s\n\twant %s", z, s, got, want)
 	}
 }
 
@@ -299,6 +409,24 @@ func BenchmarkAddVW(b *testing.B) {
 	}
 }
 
+// Benchmarking addVW using vector of maximum uint to force carry flag set
+func BenchmarkAddVWext(b *testing.B) {
+	for _, n := range benchSizes {
+		if isRaceBuilder && n > 1e3 {
+			continue
+		}
+		y := ^Word(0)
+		x := makeWordVec(y, n)
+		z := make([]Word, n)
+		b.Run(fmt.Sprint(n), func(b *testing.B) {
+			b.SetBytes(int64(n * _S))
+			for i := 0; i < b.N; i++ {
+				addVW(z, x, y)
+			}
+		})
+	}
+}
+
 func BenchmarkSubVW(b *testing.B) {
 	for _, n := range benchSizes {
 		if isRaceBuilder && n > 1e3 {
@@ -316,6 +444,24 @@ func BenchmarkSubVW(b *testing.B) {
 	}
 }
 
+// Benchmarking subVW using vector of zero to force carry flag set
+func BenchmarkSubVWext(b *testing.B) {
+	for _, n := range benchSizes {
+		if isRaceBuilder && n > 1e3 {
+			continue
+		}
+		x := makeWordVec(0, n)
+		y := Word(1)
+		z := make([]Word, n)
+		b.Run(fmt.Sprint(n), func(b *testing.B) {
+			b.SetBytes(int64(n * _S))
+			for i := 0; i < b.N; i++ {
+				subVW(z, x, y)
+			}
+		})
+	}
+}
+
 type funVWW func(z, x []Word, y, r Word) (c Word)
 type argVWW struct {
 	z, x nat
@@ -397,7 +543,6 @@ func TestFunVWW(t *testing.T) {
 
 		if a.y != 0 && a.r < a.y {
 			arg := argWVW{a.x, a.c, a.z, a.y, a.r}
-			testFunWVW(t, "divWVW_g", divWVW_g, arg)
 			testFunWVW(t, "divWVW", divWVW, arg)
 		}
 	}
@@ -440,6 +585,42 @@ func TestMulAddWWW(t *testing.T) {
 	}
 }
 
+var divWWTests = []struct {
+	x1, x0, y Word
+	q, r      Word
+}{
+	{_M >> 1, 0, _M, _M >> 1, _M >> 1},
+	{_M - (1 << (_W - 2)), _M, 3 << (_W - 2), _M, _M - (1 << (_W - 2))},
+}
+
+const testsNumber = 1 << 16
+
+func TestDivWW(t *testing.T) {
+	i := 0
+	for i, test := range divWWTests {
+		rec := reciprocalWord(test.y)
+		q, r := divWW(test.x1, test.x0, test.y, rec)
+		if q != test.q || r != test.r {
+			t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
+		}
+	}
+	//random tests
+	for ; i < testsNumber; i++ {
+		x1 := rndW()
+		x0 := rndW()
+		y := rndW()
+		if x1 >= y {
+			continue
+		}
+		rec := reciprocalWord(y)
+		qGot, rGot := divWW(x1, x0, y, rec)
+		qWant, rWant := bits.Div(uint(x1), uint(x0), uint(y))
+		if uint(qGot) != qWant || uint(rGot) != rWant {
+			t.Errorf("#%d got (%x, %x) want (%x, %x)", i, qGot, rGot, qWant, rWant)
+		}
+	}
+}
+
 func BenchmarkMulAddVWW(b *testing.B) {
 	for _, n := range benchSizes {
 		if isRaceBuilder && n > 1e3 {
@@ -474,3 +655,19 @@ func BenchmarkAddMulVVW(b *testing.B) {
 		})
 	}
 }
+func BenchmarkDivWVW(b *testing.B) {
+	for _, n := range benchSizes {
+		if isRaceBuilder && n > 1e3 {
+			continue
+		}
+		x := rndV(n)
+		y := rndW()
+		z := make([]Word, n)
+		b.Run(fmt.Sprint(n), func(b *testing.B) {
+			b.SetBytes(int64(n * _W))
+			for i := 0; i < b.N; i++ {
+				divWVW(z, 0, x, y)
+			}
+		})
+	}
+}
diff --git a/libgo/go/math/big/decimal.go b/libgo/go/math/big/decimal.go
index ae9ffb5db6a..716f03bfa43 100644
--- a/libgo/go/math/big/decimal.go
+++ b/libgo/go/math/big/decimal.go
@@ -166,18 +166,21 @@ func (x *decimal) String() string {
 	switch {
 	case x.exp <= 0:
 		// 0.00ddd
+		buf = make([]byte, 0, 2+(-x.exp)+len(x.mant))
 		buf = append(buf, "0."...)
 		buf = appendZeros(buf, -x.exp)
 		buf = append(buf, x.mant...)
 
 	case /* 0 < */ x.exp < len(x.mant):
 		// dd.ddd
+		buf = make([]byte, 0, 1+len(x.mant))
 		buf = append(buf, x.mant[:x.exp]...)
 		buf = append(buf, '.')
 		buf = append(buf, x.mant[x.exp:]...)
 
 	default: // len(x.mant) <= x.exp
 		// ddd00
+		buf = make([]byte, 0, x.exp)
 		buf = append(buf, x.mant...)
 		buf = appendZeros(buf, x.exp-len(x.mant))
 	}
diff --git a/libgo/go/math/big/float.go b/libgo/go/math/big/float.go
index da964eef3e8..42050e2c39d 100644
--- a/libgo/go/math/big/float.go
+++ b/libgo/go/math/big/float.go
@@ -322,10 +322,11 @@ func (z *Float) SetMantExp(mant *Float, exp int) *Float {
 		mant.validate()
 	}
 	z.Copy(mant)
-	if z.form != finite {
-		return z
+
+	if z.form == finite {
+		// 0 < |mant| < +Inf
+		z.setExpAndRound(int64(z.exp)+int64(exp), 0)
 	}
-	z.setExpAndRound(int64(z.exp)+int64(exp), 0)
 	return z
 }
 
diff --git a/libgo/go/math/big/link_test.go b/libgo/go/math/big/link_test.go
index 2212bd444ff..42f9cefca07 100644
--- a/libgo/go/math/big/link_test.go
+++ b/libgo/go/math/big/link_test.go
@@ -7,7 +7,7 @@ package big
 import (
 	"bytes"
 	"internal/testenv"
-	"io/ioutil"
+	"os"
 	"os/exec"
 	"path/filepath"
 	"testing"
@@ -27,7 +27,7 @@ func TestLinkerGC(t *testing.T) {
 import _ "math/big"
 func main() {}
 `)
-	if err := ioutil.WriteFile(goFile, file, 0644); err != nil {
+	if err := os.WriteFile(goFile, file, 0644); err != nil {
 		t.Fatal(err)
 	}
 	cmd := exec.Command(goBin, "build", "-o", "x.exe", "x.go")
diff --git a/libgo/go/math/big/nat.go b/libgo/go/math/big/nat.go
index 8c43de69d33..068176e1c1a 100644
--- a/libgo/go/math/big/nat.go
+++ b/libgo/go/math/big/nat.go
@@ -751,6 +751,7 @@ func (q nat) divBasic(u, v nat) {
 
 	// D2.
 	vn1 := v[n-1]
+	rec := reciprocalWord(vn1)
 	for j := m; j >= 0; j-- {
 		// D3.
 		qhat := Word(_M)
@@ -760,7 +761,7 @@ func (q nat) divBasic(u, v nat) {
 		}
 		if ujn != vn1 {
 			var rhat Word
-			qhat, rhat = divWW(ujn, u[j+n-1], vn1)
+			qhat, rhat = divWW(ujn, u[j+n-1], vn1, rec)
 
 			// x1 | x2 = q̂v_{n-2}
 			vn2 := v[n-2]
diff --git a/libgo/go/math/big/nat_test.go b/libgo/go/math/big/nat_test.go
index 89e913fc16e..08508189321 100644
--- a/libgo/go/math/big/nat_test.go
+++ b/libgo/go/math/big/nat_test.go
@@ -804,3 +804,13 @@ func TestIssue37499(t *testing.T) {
 		t.Fatalf("incorrect quotient: %s", s)
 	}
 }
+
+// TestIssue42552 triggers an edge case of recursive division
+// where the first division loop is never entered, and correcting
+// the remainder takes exactly two iterations in the final loop.
+func TestIssue42552(t *testing.T) {
+	u := natFromString("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")
+	v := natFromString("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")
+	q := nat(nil).make(16)
+	q.div(q, u, v)
+}