math/big: handle negative moduli in ModInverse

Currently, there is no check for a negative modulus in ModInverse.
Negative moduli are passed internally to GCD, which returns 0 for
negative arguments. Mod is symmetric with respect to negative moduli,
so the calculation can be done by just negating the modulus before
passing the arguments to GCD.

Fixes #24949

Change-Id: Ifd1e64c9b2343f0489c04ab65504e73a623378c7
Reviewed-on: https://go-review.googlesource.com/108115
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>

src/math/big/int.go

@@ -663,8 +663,12 @@ func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
 // inverse in the ring ℤ/nℤ.  In this case, z is unchanged and the return value
 // is nil.
 func (z *Int) ModInverse(g, n *Int) *Int {
+	// GCD expects parameters a and b to be > 0.
+	if n.neg {
+		var n2 Int
+		n = n2.Neg(n)
+	}
 	if g.neg {
-		// GCD expects parameters a and b to be > 0.
 		var g2 Int
 		g = g2.Mod(g, n)
 	}

src/math/big/int_test.go

@@ -1409,19 +1409,21 @@ var modInverseTests = []struct {
 	{"1234567", "458948883992"},
 	{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
 	{"-10", "13"}, // issue #16984
+	{"10", "-13"},
+	{"-17", "-13"},
 }
 
 func TestModInverse(t *testing.T) {
 	var element, modulus, gcd, inverse Int
 	one := NewInt(1)
-	for i, test := range modInverseTests {
+	for _, test := range modInverseTests {
 		(&element).SetString(test.element, 10)
 		(&modulus).SetString(test.modulus, 10)
 		(&inverse).ModInverse(&element, &modulus)
 		(&inverse).Mul(&inverse, &element)
 		(&inverse).Mod(&inverse, &modulus)
 		if (&inverse).Cmp(one) != 0 {
-			t.Errorf("#%d: failed (e·e^(-1)=%s)", i, &inverse)
+			t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
 		}
 	}
 	// exhaustive test for small values