4 files changed, 42 insertions, 21 deletions
diff --git a/src/math/big/int.go b/src/math/big/int.go
index 3998652e9..d22e39e7c 100644
--- a/src/math/big/int.go
+++ b/src/math/big/int.go
@@ -752,15 +752,16 @@ func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
 	return z
 }
 
-// ModInverse sets z to the multiplicative inverse of g in the group ℤ/pℤ (where
-// p is a prime) and returns z.
-func (z *Int) ModInverse(g, p *Int) *Int {
+// ModInverse sets z to the multiplicative inverse of g in the ring ℤ/nℤ
+// and returns z. If g and n are not relatively prime, the result is undefined.
+func (z *Int) ModInverse(g, n *Int) *Int {
 	var d Int
-	d.GCD(z, nil, g, p)
-	// x and y are such that g*x + p*y = d. Since p is prime, d = 1. Taking
-	// that modulo p results in g*x = 1, therefore x is the inverse element.
+	d.GCD(z, nil, g, n)
+	// x and y are such that g*x + n*y = d. Since g and n are
+	// relatively prime, d = 1. Taking that modulo n results in
+	// g*x = 1, therefore x is the inverse element.
 	if z.neg {
-		z.Add(z, p)
+		z.Add(z, n)
 	}
 	return z
 }
@@ -1016,12 +1017,12 @@ func (z *Int) UnmarshalJSON(text []byte) error {
 	return nil
 }
 
-// MarshalText implements the encoding.TextMarshaler interface
+// MarshalText implements the encoding.TextMarshaler interface.
 func (z *Int) MarshalText() (text []byte, err error) {
 	return []byte(z.String()), nil
 }
 
-// UnmarshalText implements the encoding.TextUnmarshaler interface
+// UnmarshalText implements the encoding.TextUnmarshaler interface.
 func (z *Int) UnmarshalText(text []byte) error {
 	if _, ok := z.SetString(string(text), 0); !ok {
 		return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
diff --git a/src/math/big/int_test.go b/src/math/big/int_test.go
index ec05fbb1c..6070cf325 100644
--- a/src/math/big/int_test.go
+++ b/src/math/big/int_test.go
@@ -1448,24 +1448,40 @@ func TestNot(t *testing.T) {
 
 var modInverseTests = []struct {
 	element string
-	prime   string
+	modulus string
 }{
-	{"1", "7"},
-	{"1", "13"},
+	{"1234567", "458948883992"},
 	{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
 }
 
 func TestModInverse(t *testing.T) {
-	var element, prime Int
+	var element, modulus, gcd, inverse Int
 	one := NewInt(1)
 	for i, test := range modInverseTests {
 		(&element).SetString(test.element, 10)
-		(&prime).SetString(test.prime, 10)
-		inverse := new(Int).ModInverse(&element, &prime)
-		inverse.Mul(inverse, &element)
-		inverse.Mod(inverse, &prime)
-		if inverse.Cmp(one) != 0 {
-			t.Errorf("#%d: failed (e·e^(-1)=%s)", i, inverse)
+		(&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)
+		}
+	}
+	// exhaustive test for small values
+	for n := 2; n < 100; n++ {
+		(&modulus).SetInt64(int64(n))
+		for x := 1; x < n; x++ {
+			(&element).SetInt64(int64(x))
+			(&gcd).GCD(nil, nil, &element, &modulus)
+			if (&gcd).Cmp(one) != 0 {
+				continue
+			}
+			(&inverse).ModInverse(&element, &modulus)
+			(&inverse).Mul(&inverse, &element)
+			(&inverse).Mod(&inverse, &modulus)
+			if (&inverse).Cmp(one) != 0 {
+				t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
+			}
 		}
 	}
 }
diff --git a/src/math/big/rat.go b/src/math/big/rat.go
index e6ab0bb48..c5339fe44 100644
--- a/src/math/big/rat.go
+++ b/src/math/big/rat.go
@@ -552,6 +552,9 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
 		if z.b.abs, _, err = z.b.abs.scan(strings.NewReader(s), 10); err != nil {
 			return nil, false
 		}
+		if len(z.b.abs) == 0 {
+			return nil, false
+		}
 		return z.norm(), true
 	}
 
@@ -699,12 +702,12 @@ func (z *Rat) GobDecode(buf []byte) error {
 	return nil
 }
 
-// MarshalText implements the encoding.TextMarshaler interface
+// MarshalText implements the encoding.TextMarshaler interface.
 func (r *Rat) MarshalText() (text []byte, err error) {
 	return []byte(r.RatString()), nil
 }
 
-// UnmarshalText implements the encoding.TextUnmarshaler interface
+// UnmarshalText implements the encoding.TextUnmarshaler interface.
 func (r *Rat) UnmarshalText(text []byte) error {
 	if _, ok := r.SetString(string(text)); !ok {
 		return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Rat", text)
diff --git a/src/math/big/rat_test.go b/src/math/big/rat_test.go
index 598eac8cc..5dbbb3510 100644
--- a/src/math/big/rat_test.go
+++ b/src/math/big/rat_test.go
@@ -89,6 +89,7 @@ var setStringTests = []struct {
 	{"53/70893980658822810696", "53/70893980658822810696", true},
 	{"106/141787961317645621392", "53/70893980658822810696", true},
 	{"204211327800791583.81095", "4084226556015831676219/20000", true},
+	{in: "1/0", ok: false},
 }
 
 func TestRatSetString(t *testing.T) {