math/big: move ProbablyPrime into its own source file

A later CL will be adding more code here.
It will help to keep it separate from the other code.

Change-Id: I971ba53de819cd10991b51fdec665984939a5f9b
Reviewed-on: https://go-review.googlesource.com/30709Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/math/big/int.go

@@ -550,19 +550,6 @@ func (z *Int) binaryGCD(a, b *Int) *Int {
 	return z.Lsh(u, k)
 }
 
-// ProbablyPrime performs n Miller-Rabin tests to check whether x is prime.
-// If x is prime, it returns true.
-// If x is not prime, it returns false with probability at least 1 - ¼ⁿ.
-//
-// It is not suitable for judging primes that an adversary may have crafted
-// to fool this test.
-func (x *Int) ProbablyPrime(n int) bool {
-	if n <= 0 {
-		panic("non-positive n for ProbablyPrime")
-	}
-	return !x.neg && x.abs.probablyPrime(n)
-}
-
 // Rand sets z to a pseudo-random number in [0, n) and returns z.
 func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
 	z.neg = false

src/math/big/int_test.go

@@ -760,96 +760,6 @@ func TestGcd(t *testing.T) {
 	}
 }
 
-var primes = []string{
-	"2",
-	"3",
-	"5",
-	"7",
-	"11",
-
-	"13756265695458089029",
-	"13496181268022124907",
-	"10953742525620032441",
-	"17908251027575790097",
-
-	// https://golang.org/issue/638
-	"18699199384836356663",
-
-	"98920366548084643601728869055592650835572950932266967461790948584315647051443",
-	"94560208308847015747498523884063394671606671904944666360068158221458669711639",
-
-	// http://primes.utm.edu/lists/small/small3.html
-	"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
-	"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
-	"5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
-	"203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
-
-	// ECC primes: http://tools.ietf.org/html/draft-ladd-safecurves-02
-	"3618502788666131106986593281521497120414687020801267626233049500247285301239",                                                                                  // Curve1174: 2^251-9
-	"57896044618658097711785492504343953926634992332820282019728792003956564819949",                                                                                 // Curve25519: 2^255-19
-	"9850501549098619803069760025035903451269934817616361666987073351061430442874302652853566563721228910201656997576599",                                           // E-382: 2^382-105
-	"42307582002575910332922579714097346549017899709713998034217522897561970639123926132812109468141778230245837569601494931472367",                                 // Curve41417: 2^414-17
-	"6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", // E-521: 2^521-1
-}
-
-var composites = []string{
-	"0",
-	"1",
-	"21284175091214687912771199898307297748211672914763848041968395774954376176754",
-	"6084766654921918907427900243509372380954290099172559290432744450051395395951",
-	"84594350493221918389213352992032324280367711247940675652888030554255915464401",
-	"82793403787388584738507275144194252681",
-}
-
-func TestProbablyPrime(t *testing.T) {
-	nreps := 20
-	if testing.Short() {
-		nreps = 1
-	}
-	for i, s := range primes {
-		p, _ := new(Int).SetString(s, 10)
-		if !p.ProbablyPrime(nreps) {
-			t.Errorf("#%d prime found to be non-prime (%s)", i, s)
-		}
-	}
-
-	for i, s := range composites {
-		c, _ := new(Int).SetString(s, 10)
-		if c.ProbablyPrime(nreps) {
-			t.Errorf("#%d composite found to be prime (%s)", i, s)
-		}
-		if testing.Short() {
-			break
-		}
-	}
-
-	// check that ProbablyPrime panics if n <= 0
-	c := NewInt(11) // a prime
-	for _, n := range []int{-1, 0, 1} {
-		func() {
-			defer func() {
-				if n <= 0 && recover() == nil {
-					t.Fatalf("expected panic from ProbablyPrime(%d)", n)
-				}
-			}()
-			if !c.ProbablyPrime(n) {
-				t.Fatalf("%v should be a prime", c)
-			}
-		}()
-	}
-}
-
-func BenchmarkProbablyPrime(b *testing.B) {
-	p, _ := new(Int).SetString("203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123", 10)
-	for _, rep := range []int{1, 5, 10, 20} {
-		b.Run(fmt.Sprintf("Rep=%d", rep), func(b *testing.B) {
-			for i := 0; i < b.N; i++ {
-				p.ProbablyPrime(rep)
-			}
-		})
-	}
-}
-
 type intShiftTest struct {
 	in    string
 	shift uint

src/math/big/nat.go

@@ -1179,96 +1179,6 @@ func (z nat) expNNMontgomery(x, y, m nat) nat {
 	return zz.norm()
 }
 
-// probablyPrime performs n Miller-Rabin tests to check whether x is prime.
-// If x is prime, it returns true.
-// If x is not prime, it returns false with probability at least 1 - ¼ⁿ.
-//
-// It is not suitable for judging primes that an adversary may have crafted
-// to fool this test.
-func (n nat) probablyPrime(reps int) bool {
-	if len(n) == 0 {
-		return false
-	}
-
-	if len(n) == 1 {
-		if n[0] < 2 {
-			return false
-		}
-
-		if n[0]%2 == 0 {
-			return n[0] == 2
-		}
-
-		// We have to exclude these cases because we reject all
-		// multiples of these numbers below.
-		switch n[0] {
-		case 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53:
-			return true
-		}
-	}
-
-	if n[0]&1 == 0 {
-		return false // n is even
-	}
-
-	const primesProduct32 = 0xC0CFD797         // Π {p ∈ primes, 2 < p <= 29}
-	const primesProduct64 = 0xE221F97C30E94E1D // Π {p ∈ primes, 2 < p <= 53}
-
-	var r Word
-	switch _W {
-	case 32:
-		r = n.modW(primesProduct32)
-	case 64:
-		r = n.modW(primesProduct64 & _M)
-	default:
-		panic("Unknown word size")
-	}
-
-	if r%3 == 0 || r%5 == 0 || r%7 == 0 || r%11 == 0 ||
-		r%13 == 0 || r%17 == 0 || r%19 == 0 || r%23 == 0 || r%29 == 0 {
-		return false
-	}
-
-	if _W == 64 && (r%31 == 0 || r%37 == 0 || r%41 == 0 ||
-		r%43 == 0 || r%47 == 0 || r%53 == 0) {
-		return false
-	}
-
-	nm1 := nat(nil).sub(n, natOne)
-	// determine q, k such that nm1 = q << k
-	k := nm1.trailingZeroBits()
-	q := nat(nil).shr(nm1, k)
-
-	nm3 := nat(nil).sub(nm1, natTwo)
-	rand := rand.New(rand.NewSource(int64(n[0])))
-
-	var x, y, quotient nat
-	nm3Len := nm3.bitLen()
-
-NextRandom:
-	for i := 0; i < reps; i++ {
-		x = x.random(rand, nm3, nm3Len)
-		x = x.add(x, natTwo)
-		y = y.expNN(x, q, n)
-		if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
-			continue
-		}
-		for j := uint(1); j < k; j++ {
-			y = y.mul(y, y)
-			quotient, y = quotient.div(y, y, n)
-			if y.cmp(nm1) == 0 {
-				continue NextRandom
-			}
-			if y.cmp(natOne) == 0 {
-				return false
-			}
-		}
-		return false
-	}
-
-	return true
-}
-
 // bytes writes the value of z into buf using big-endian encoding.
 // len(buf) must be >= len(z)*_S. The value of z is encoded in the
 // slice buf[i:]. The number i of unused bytes at the beginning of

src/math/big/prime.go

+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package big
+
+import "math/rand"
+
+// ProbablyPrime performs n Miller-Rabin tests to check whether x is prime.
+// If x is prime, it returns true.
+// If x is not prime, it returns false with probability at least 1 - ¼ⁿ.
+//
+// It is not suitable for judging primes that an adversary may have crafted
+// to fool this test.
+func (x *Int) ProbablyPrime(n int) bool {
+	if n <= 0 {
+		panic("non-positive n for ProbablyPrime")
+	}
+	return !x.neg && x.abs.probablyPrime(n)
+}
+
+// probablyPrime performs n Miller-Rabin tests to check whether x is prime.
+// If x is prime, it returns true.
+// If x is not prime, it returns false with probability at least 1 - ¼ⁿ.
+//
+// It is not suitable for judging primes that an adversary may have crafted
+// to fool this test.
+func (n nat) probablyPrime(reps int) bool {
+	if len(n) == 0 {
+		return false
+	}
+
+	if len(n) == 1 {
+		if n[0] < 2 {
+			return false
+		}
+
+		if n[0]%2 == 0 {
+			return n[0] == 2
+		}
+
+		// We have to exclude these cases because we reject all
+		// multiples of these numbers below.
+		switch n[0] {
+		case 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53:
+			return true
+		}
+	}
+
+	if n[0]&1 == 0 {
+		return false // n is even
+	}
+
+	const primesProduct32 = 0xC0CFD797         // Π {p ∈ primes, 2 < p <= 29}
+	const primesProduct64 = 0xE221F97C30E94E1D // Π {p ∈ primes, 2 < p <= 53}
+
+	var r Word
+	switch _W {
+	case 32:
+		r = n.modW(primesProduct32)
+	case 64:
+		r = n.modW(primesProduct64 & _M)
+	default:
+		panic("Unknown word size")
+	}
+
+	if r%3 == 0 || r%5 == 0 || r%7 == 0 || r%11 == 0 ||
+		r%13 == 0 || r%17 == 0 || r%19 == 0 || r%23 == 0 || r%29 == 0 {
+		return false
+	}
+
+	if _W == 64 && (r%31 == 0 || r%37 == 0 || r%41 == 0 ||
+		r%43 == 0 || r%47 == 0 || r%53 == 0) {
+		return false
+	}
+
+	nm1 := nat(nil).sub(n, natOne)
+	// determine q, k such that nm1 = q << k
+	k := nm1.trailingZeroBits()
+	q := nat(nil).shr(nm1, k)
+
+	nm3 := nat(nil).sub(nm1, natTwo)
+	rand := rand.New(rand.NewSource(int64(n[0])))
+
+	var x, y, quotient nat
+	nm3Len := nm3.bitLen()
+
+NextRandom:
+	for i := 0; i < reps; i++ {
+		x = x.random(rand, nm3, nm3Len)
+		x = x.add(x, natTwo)
+		y = y.expNN(x, q, n)
+		if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
+			continue
+		}
+		for j := uint(1); j < k; j++ {
+			y = y.mul(y, y)
+			quotient, y = quotient.div(y, y, n)
+			if y.cmp(nm1) == 0 {
+				continue NextRandom
+			}
+			if y.cmp(natOne) == 0 {
+				return false
+			}
+		}
+		return false
+	}
+
+	return true
+}

src/math/big/prime_test.go

+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package big
+
+import (
+	"fmt"
+	"testing"
+)
+
+var primes = []string{
+	"2",
+	"3",
+	"5",
+	"7",
+	"11",
+
+	"13756265695458089029",
+	"13496181268022124907",
+	"10953742525620032441",
+	"17908251027575790097",
+
+	// https://golang.org/issue/638
+	"18699199384836356663",
+
+	"98920366548084643601728869055592650835572950932266967461790948584315647051443",
+	"94560208308847015747498523884063394671606671904944666360068158221458669711639",
+
+	// http://primes.utm.edu/lists/small/small3.html
+	"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
+	"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
+	"5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
+	"203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
+
+	// ECC primes: http://tools.ietf.org/html/draft-ladd-safecurves-02
+	"3618502788666131106986593281521497120414687020801267626233049500247285301239",                                                                                  // Curve1174: 2^251-9
+	"57896044618658097711785492504343953926634992332820282019728792003956564819949",                                                                                 // Curve25519: 2^255-19
+	"9850501549098619803069760025035903451269934817616361666987073351061430442874302652853566563721228910201656997576599",                                           // E-382: 2^382-105
+	"42307582002575910332922579714097346549017899709713998034217522897561970639123926132812109468141778230245837569601494931472367",                                 // Curve41417: 2^414-17
+	"6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", // E-521: 2^521-1
+}
+
+var composites = []string{
+	"0",
+	"1",
+	"21284175091214687912771199898307297748211672914763848041968395774954376176754",
+	"6084766654921918907427900243509372380954290099172559290432744450051395395951",
+	"84594350493221918389213352992032324280367711247940675652888030554255915464401",
+	"82793403787388584738507275144194252681",
+}
+
+func TestProbablyPrime(t *testing.T) {
+	nreps := 20
+	if testing.Short() {
+		nreps = 1
+	}
+	for i, s := range primes {
+		p, _ := new(Int).SetString(s, 10)
+		if !p.ProbablyPrime(nreps) {
+			t.Errorf("#%d prime found to be non-prime (%s)", i, s)
+		}
+	}
+
+	for i, s := range composites {
+		c, _ := new(Int).SetString(s, 10)
+		if c.ProbablyPrime(nreps) {
+			t.Errorf("#%d composite found to be prime (%s)", i, s)
+		}
+		if testing.Short() {
+			break
+		}
+	}
+
+	// check that ProbablyPrime panics if n <= 0
+	c := NewInt(11) // a prime
+	for _, n := range []int{-1, 0, 1} {
+		func() {
+			defer func() {
+				if n <= 0 && recover() == nil {
+					t.Fatalf("expected panic from ProbablyPrime(%d)", n)
+				}
+			}()
+			if !c.ProbablyPrime(n) {
+				t.Fatalf("%v should be a prime", c)
+			}
+		}()
+	}
+}
+
+func BenchmarkProbablyPrime(b *testing.B) {
+	p, _ := new(Int).SetString("203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123", 10)
+	for _, rep := range []int{1, 5, 10, 20} {
+		b.Run(fmt.Sprintf("Rep=%d", rep), func(b *testing.B) {
+			for i := 0; i < b.N; i++ {
+				p.ProbablyPrime(rep)
+			}
+		})
+	}
+}