big: fix mistakes with probablyPrime

probablyPrime would return false negatives in some cases.

This code has now been tested against GMP for several million iterations without issues.

Fixes #638.

R=rsc
CC=golang-dev
https://golang.org/cl/252041

diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go
index 7267adb287d6516a72d91de24d25199658c66f96..70dbe5900c95e7e19fec058fd5df9651565d7025 100644 (file)
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -480,6 +480,9 @@ var primes = []string{
        "10953742525620032441",
        "17908251027575790097",
 
+       // http://code.google.com/p/go/issues/detail?id=638
+       "18699199384836356663",
+
        "98920366548084643601728869055592650835572950932266967461790948584315647051443",
        "94560208308847015747498523884063394671606671904944666360068158221458669711639",
 
@@ -503,14 +506,14 @@ func TestProbablyPrime(t *testing.T) {
        for i, s := range primes {
                p, _ := new(Int).SetString(s, 10)
                if !ProbablyPrime(p, 20) {
-                       t.Errorf("#%d prime found to be non-prime", i)
+                       t.Errorf("#%d prime found to be non-prime (%s)", i, s)
                }
        }
 
        for i, s := range composites {
                c, _ := new(Int).SetString(s, 10)
                if ProbablyPrime(c, 20) {
-                       t.Errorf("#%d composite found to be prime", i)
+                       t.Errorf("#%d composite found to be prime (%s)", i, s)
                }
        }
 }

diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go
index da9f1d735cc61769b984963ed533495949706ef5..0f4d4c37e88fde38467895cba0ba5b1034a6084d 100644 (file)
--- a/src/pkg/big/nat.go
+++ b/src/pkg/big/nat.go
@@ -586,6 +586,7 @@ func powersOfTwoDecompose(n []Word) (q []Word, k Word) {
 
        q = makeN(nil, len(n)-zeroWords, false)
        shiftRight(q, n[zeroWords:], x)
+       q = normN(q)
 
        k = Word(_W*zeroWords + x)
        return
@@ -705,7 +706,7 @@ const (
 var bigOne = []Word{1}
 var bigTwo = []Word{2}
 
-// ProbablyPrime performs reps Miller-Rabin tests to check whether n is prime.
+// probablyPrime performs reps Miller-Rabin tests to check whether n is prime.
 // If it returns true, n is prime with probability 1 - 1/4^reps.
 // If it returns false, n is not prime.
 func probablyPrime(n []Word, reps int) bool {
@@ -714,6 +715,10 @@ func probablyPrime(n []Word, reps int) bool {
        }
 
        if len(n) == 1 {
+               if n[0] < 2 {
+                       return false
+               }
+
                if n[0]%2 == 0 {
                        return n[0] == 2
                }
@@ -761,7 +766,7 @@ func probablyPrime(n []Word, reps int) bool {
 NextRandom:
        for i := 0; i < reps; i++ {
                x = randomN(x, rand, nm3, nm3Len)
-               addNN(x, x, bigTwo)
+               x = addNN(x, x, bigTwo)
                y = expNNN(y, x, q, n)
                if cmpNN(y, bigOne) == 0 || cmpNN(y, nm1) == 0 {
                        continue