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big: fix ProbablyPrime bug, comments
(changes adopted from alc, agl) R=agl1, agl CC=golang-dev https://golang.org/cl/181137
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@ -356,7 +356,7 @@ func GcdInt(d, x, y, a, b *Int) {
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// ProbablyPrime performs n Miller-Rabin tests to check whether z is prime.
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// If it returns true, z is prime with probability 1 - 1/4^n.
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// If it returns false, z is not prime.
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func ProbablyPrime(z *Int, reps int) bool { return !z.neg && probablyPrime(z.abs, reps) }
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func ProbablyPrime(z *Int, n int) bool { return !z.neg && probablyPrime(z.abs, n) }
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// Rsh sets z = x >> s and returns z.
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@ -474,8 +474,15 @@ var primes = []string{
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"5",
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"7",
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"11",
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"13756265695458089029",
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"13496181268022124907",
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"10953742525620032441",
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"17908251027575790097",
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"98920366548084643601728869055592650835572950932266967461790948584315647051443",
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"94560208308847015747498523884063394671606671904944666360068158221458669711639",
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// http://primes.utm.edu/lists/small/small3.html
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"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
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"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
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@ -596,6 +596,9 @@ func powersOfTwoDecompose(n []Word) (q []Word, k Word) {
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// possible. n is the bit length of limit.
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func randomN(z []Word, rand *rand.Rand, limit []Word, n int) []Word {
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bitLengthOfMSW := uint(n % _W)
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if bitLengthOfMSW == 0 {
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bitLengthOfMSW = _W
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}
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mask := Word((1 << bitLengthOfMSW) - 1)
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z = makeN(z, len(limit), false)
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@ -616,7 +619,7 @@ func randomN(z []Word, rand *rand.Rand, limit []Word, n int) []Word {
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}
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}
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return z
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return normN(z)
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}
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@ -702,8 +705,8 @@ const (
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var bigOne = []Word{1}
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var bigTwo = []Word{2}
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// ProbablyPrime performs n Miller-Rabin tests to check whether n is prime.
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// If it returns true, n is prime with probability 1 - 1/4^n.
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// ProbablyPrime performs reps Miller-Rabin tests to check whether n is prime.
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// If it returns true, n is prime with probability 1 - 1/4^reps.
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// If it returns false, n is not prime.
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func probablyPrime(n []Word, reps int) bool {
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if len(n) == 0 {
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