big: fix ProbablyPrime bug, comments

(changes adopted from alc, agl)

R=agl1, agl
CC=golang-dev
https://golang.org/cl/181137

3 files changed, 14 insertions, 4 deletions

diff --git a/src/pkg/big/int.go b/src/pkg/big/int.go
index 5a0f7c0dfd..b48954ef8b 100644
--- a/src/pkg/big/int.go
+++ b/src/pkg/big/int.go
@@ -356,7 +356,7 @@ func GcdInt(d, x, y, a, b *Int) {
 // ProbablyPrime performs n Miller-Rabin tests to check whether z is prime.
 // If it returns true, z is prime with probability 1 - 1/4^n.
 // If it returns false, z is not prime.
-func ProbablyPrime(z *Int, reps int) bool { return !z.neg && probablyPrime(z.abs, reps) }
+func ProbablyPrime(z *Int, n int) bool { return !z.neg && probablyPrime(z.abs, n) }
 
 
 // Rsh sets z = x >> s and returns z.
diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go
index b2c33fcc45..c178bab770 100644
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -474,8 +474,15 @@ var primes = []string{
 	"5",
 	"7",
 	"11",
+
+	"13756265695458089029",
+	"13496181268022124907",
+	"10953742525620032441",
+	"17908251027575790097",
+
 	"98920366548084643601728869055592650835572950932266967461790948584315647051443",
 	"94560208308847015747498523884063394671606671904944666360068158221458669711639",
+
 	// http://primes.utm.edu/lists/small/small3.html
 	"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
 	"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go
index 877bc98112..da9f1d735c 100644
--- a/src/pkg/big/nat.go
+++ b/src/pkg/big/nat.go
@@ -596,6 +596,9 @@ func powersOfTwoDecompose(n []Word) (q []Word, k Word) {
 // possible. n is the bit length of limit.
 func randomN(z []Word, rand *rand.Rand, limit []Word, n int) []Word {
 	bitLengthOfMSW := uint(n % _W)
+	if bitLengthOfMSW == 0 {
+		bitLengthOfMSW = _W
+	}
 	mask := Word((1 << bitLengthOfMSW) - 1)
 	z = makeN(z, len(limit), false)
 
@@ -616,7 +619,7 @@ func randomN(z []Word, rand *rand.Rand, limit []Word, n int) []Word {
 		}
 	}
 
-	return z
+	return normN(z)
 }
 
 
@@ -702,8 +705,8 @@ const (
 var bigOne = []Word{1}
 var bigTwo = []Word{2}
 
-// ProbablyPrime performs n Miller-Rabin tests to check whether n is prime.
-// If it returns true, n is prime with probability 1 - 1/4^n.
+// 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 {
 	if len(n) == 0 {