[release-branch.go1.9] math/big: protect against aliasing in nat.divLarge

In nat.divLarge (having signature (z nat).divLarge(u, uIn, v nat)),
we check whether z aliases uIn or v, but aliasing is currently not
checked for the u parameter.

Unfortunately, z and u aliasing each other can in some cases cause
errors in the computation.

The q return parameter (which will hold the result's quotient), is
unconditionally initialized as

    q = z.make(m + 1)

When cap(z) ≥ m+1, z.make() will reuse z's backing array, causing q
and z to share the same backing array. If then z aliases u, setting q
during the quotient computation will then corrupt u, which at that
point already holds computation state.

To fix this, we add an alias(z, u) check at the beginning of the
function, taking care of aliasing the same way we already do for uIn
and v.

Fixes #22830

Change-Id: I3ab81120d5af6db7772a062bb1dfc011de91f7ad
Reviewed-on: https://go-review.googlesource.com/78995
Run-TryBot: Alberto Donizetti <[email protected]>
Run-TryBot: Robert Griesemer <[email protected]>
TryBot-Result: Gobot Gobot <[email protected]>
Reviewed-by: Robert Griesemer <[email protected]>
Reviewed-on: https://go-review.googlesource.com/88322
Run-TryBot: Andrew Bonventre <[email protected]>

Author: ALTree

src/math/big/int_test.go

@@ -1536,6 +1536,26 @@ func TestSqrt(t *testing.T) {
 	}
 }
 
+// We can't test this together with the other Exp tests above because
+// it requires a different receiver setup.
+func TestIssue22830(t *testing.T) {
+	one := new(Int).SetInt64(1)
+	base, _ := new(Int).SetString("84555555300000000000", 10)
+	mod, _ := new(Int).SetString("66666670001111111111", 10)
+	want, _ := new(Int).SetString("17888885298888888889", 10)
+
+	var tests = []int64{
+		0, 1, -1,
+	}
+
+	for _, n := range tests {
+		m := NewInt(n)
+		if got := m.Exp(base, one, mod); got.Cmp(want) != 0 {
+			t.Errorf("(%v).Exp(%s, 1, %s) = %s, want %s", n, base, mod, got, want)
+		}
+	}
+}
+
 func BenchmarkSqrt(b *testing.B) {
 	n, _ := new(Int).SetString("1"+strings.Repeat("0", 1001), 10)
 	b.ResetTimer()

src/math/big/nat.go

@@ -566,8 +566,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	// 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
+	if alias(z, u) || alias(z, uIn) || alias(z, v) {
+		z = nil // z is an alias for u or uIn or v - cannot reuse
 	}
 	q = z.make(m + 1)