math/big: fix Int.Exp

Fixes #7814.

LGTM=agl, adonovan
R=agl, adonovan
CC=golang-codereviews
https://golang.org/cl/90080043

diff --git a/src/pkg/math/big/int.go b/src/pkg/math/big/int.go
index 4591590d409817e6bf8b05af1be5674b6cd06c1a..269949d616070b5e45f5238a612e9e9b620b8db7 100644 (file)
--- a/src/pkg/math/big/int.go
+++ b/src/pkg/math/big/int.go
@@ -576,21 +576,22 @@ func (x *Int) BitLen() int {
 }
 
 // Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z.
-// If y <= 0, the result is 1; if m == nil or m == 0, z = x**y.
+// If y <= 0, the result is 1 mod |m|; if m == nil or m == 0, z = x**y.
 // See Knuth, volume 2, section 4.6.3.
 func (z *Int) Exp(x, y, m *Int) *Int {
-       if y.neg || len(y.abs) == 0 {
-               return z.SetInt64(1)
+       var yWords nat
+       if !y.neg {
+               yWords = y.abs
        }
-       // y > 0
+       // y >= 0
 
        var mWords nat
        if m != nil {
                mWords = m.abs // m.abs may be nil for m == 0
        }
 
-       z.abs = z.abs.expNN(x.abs, y.abs, mWords)
-       z.neg = len(z.abs) > 0 && x.neg && y.abs[0]&1 == 1 // 0 has no sign
+       z.abs = z.abs.expNN(x.abs, yWords, mWords)
+       z.neg = len(z.abs) > 0 && x.neg && len(yWords) > 0 && yWords[0]&1 == 1 // 0 has no sign
        return z
 }
 

diff --git a/src/pkg/math/big/int_test.go b/src/pkg/math/big/int_test.go
index 3dd9c5b712b72d200d71e5e60846f37cb67a0f12..299dc72fb1a2e4cdeca0448454df853ec8c01aa3 100644 (file)
--- a/src/pkg/math/big/int_test.go
+++ b/src/pkg/math/big/int_test.go
@@ -768,6 +768,19 @@ var expTests = []struct {
        x, y, m string
        out     string
 }{
+       // y <= 0
+       {"0", "0", "", "1"},
+       {"1", "0", "", "1"},
+       {"-10", "0", "", "1"},
+       {"1234", "-1", "", "1"},
+
+       // m == 1
+       {"0", "0", "1", "0"},
+       {"1", "0", "1", "0"},
+       {"-10", "0", "1", "0"},
+       {"1234", "-1", "1", "0"},
+
+       // misc
        {"5", "-7", "", "1"},
        {"-5", "-7", "", "1"},
        {"5", "0", "", "1"},

diff --git a/src/pkg/math/big/nat.go b/src/pkg/math/big/nat.go
index 6874900d0bdecf0d7a69c8a3a78e573bf0012b61..16a87f5c537480efaeab5ecfe2a36ba26e9af2b4 100644 (file)
--- a/src/pkg/math/big/nat.go
+++ b/src/pkg/math/big/nat.go
@@ -1233,10 +1233,15 @@ func (z nat) expNN(x, y, m nat) nat {
                z = nil
        }
 
+       // x**y mod 1 == 0
+       if len(m) == 1 && m[0] == 1 {
+               return z.setWord(0)
+       }
+       // m == 0 || m > 1
+
+       // x**0 == 1
        if len(y) == 0 {
-               z = z.make(1)
-               z[0] = 1
-               return z
+               return z.setWord(1)
        }
        // y > 0
 

diff --git a/src/pkg/math/big/nat_test.go b/src/pkg/math/big/nat_test.go
index f7105b09989a6efd1c4fd54f7df05d3b409317cb..a2ae53385c91512a7ace41dcb511e48d6ac43b5b 100644 (file)
--- a/src/pkg/math/big/nat_test.go
+++ b/src/pkg/math/big/nat_test.go
@@ -714,6 +714,12 @@ var expNNTests = []struct {
        x, y, m string
        out     string
 }{
+       {"0", "0", "0", "1"},
+       {"0", "0", "1", "0"},
+       {"1", "1", "1", "0"},
+       {"2", "1", "1", "0"},
+       {"2", "2", "1", "0"},
+       {"10", "100000000000", "1", "0"},
        {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
        {"0x8000000000000000", "2", "6719", "4944"},
        {"0x8000000000000000", "3", "6719", "5447"},
@@ -741,7 +747,7 @@ func TestExpNN(t *testing.T) {
 
                z := nat(nil).expNN(x, y, m)
                if z.cmp(out) != 0 {
-                       t.Errorf("#%d got %v want %v", i, z, out)
+                       t.Errorf("#%d got %s want %s", i, z.decimalString(), out.decimalString())
                }
        }
 }