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"
	"strings"
	"testing"
	"unicode"
)

var primes = []string{
	"2",
	"3",
	"5",
	"7",
	"11",

	"13756265695458089029",
	"13496181268022124907",
	"10953742525620032441",
	"17908251027575790097",

	// https://golang.org/issue/638
	"18699199384836356663",

	"98920366548084643601728869055592650835572950932266967461790948584315647051443",
	"94560208308847015747498523884063394671606671904944666360068158221458669711639",

	// https://primes.utm.edu/lists/small/small3.html
	"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
	"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
	"5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
	"203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",

	// ECC primes: https://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",

	// Arnault, "Rabin-Miller Primality Test: Composite Numbers Which Pass It",
	// Mathematics of Computation, 64(209) (January 1995), pp. 335-361.
	"1195068768795265792518361315725116351898245581", // strong pseudoprime to prime bases 2 through 29
	// strong pseudoprime to all prime bases up to 200
	`
     80383745745363949125707961434194210813883768828755814583748891752229
      74273765333652186502336163960045457915042023603208766569966760987284
       0439654082329287387918508691668573282677617710293896977394701670823
        0428687109997439976544144845341155872450633409279022275296229414984
         2306881685404326457534018329786111298960644845216191652872597534901`,

	// Extra-strong Lucas pseudoprimes. https://oeis.org/A217719
	"989",
	"3239",
	"5777",
	"10877",
	"27971",
	"29681",
	"30739",
	"31631",
	"39059",
	"72389",
	"73919",
	"75077",
	"100127",
	"113573",
	"125249",
	"137549",
	"137801",
	"153931",
	"155819",
	"161027",
	"162133",
	"189419",
	"218321",
	"231703",
	"249331",
	"370229",
	"429479",
	"430127",
	"459191",
	"473891",
	"480689",
	"600059",
	"621781",
	"632249",
	"635627",

	"3673744903",
	"3281593591",
	"2385076987",
	"2738053141",
	"2009621503",
	"1502682721",
	"255866131",
	"117987841",
	"587861",

	"6368689",
	"8725753",
	"80579735209",
	"105919633",
}

func cutSpace(r rune) rune {
	if unicode.IsSpace(r) {
		return -1
	}
	return r
}

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) || nreps != 1 && !p.ProbablyPrime(1) || !p.ProbablyPrime(0) {
			t.Errorf("#%d prime found to be non-prime (%s)", i, s)
		}
	}

	for i, s := range composites {
		s = strings.Map(cutSpace, s)
		c, _ := new(Int).SetString(s, 10)
		if c.ProbablyPrime(nreps) || nreps != 1 && c.ProbablyPrime(1) || c.ProbablyPrime(0) {
			t.Errorf("#%d composite found to be prime (%s)", i, s)
		}
	}

	// 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 _, n := range []int{0, 1, 5, 10, 20} {
		b.Run(fmt.Sprintf("n=%d", n), func(b *testing.B) {
			for i := 0; i < b.N; i++ {
				p.ProbablyPrime(n)
			}
		})
	}

	b.Run("Lucas", func(b *testing.B) {
		for i := 0; i < b.N; i++ {
			p.abs.probablyPrimeLucas()
		}
	})
	b.Run("MillerRabinBase2", func(b *testing.B) {
		for i := 0; i < b.N; i++ {
			p.abs.probablyPrimeMillerRabin(1, true)
		}
	})
}

func TestMillerRabinPseudoprimes(t *testing.T) {
	testPseudoprimes(t, "probablyPrimeMillerRabin",
		func(n nat) bool { return n.probablyPrimeMillerRabin(1, true) && !n.probablyPrimeLucas() },
		// https://oeis.org/A001262
		[]int{2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799, 49141, 52633, 65281, 74665, 80581, 85489, 88357, 90751})
}

func TestLucasPseudoprimes(t *testing.T) {
	testPseudoprimes(t, "probablyPrimeLucas",
		func(n nat) bool { return n.probablyPrimeLucas() && !n.probablyPrimeMillerRabin(1, true) },
		// https://oeis.org/A217719
		[]int{989, 3239, 5777, 10877, 27971, 29681, 30739, 31631, 39059, 72389, 73919, 75077})
}

func testPseudoprimes(t *testing.T, name string, cond func(nat) bool, want []int) {
	n := nat{1}
	for i := 3; i < 100000; i += 2 {
		if testing.Short() {
			if len(want) == 0 {
				break
			}
			if i < want[0]-2 {
				i = want[0] - 2
			}
		}
		n[0] = Word(i)
		pseudo := cond(n)
		if pseudo && (len(want) == 0 || i != want[0]) {
			t.Errorf("%s(%v, base=2) = true, want false", name, i)
		} else if !pseudo && len(want) >= 1 && i == want[0] {
			t.Errorf("%s(%v, base=2) = false, want true", name, i)
		}
		if len(want) > 0 && i == want[0] {
			want = want[1:]
		}
	}
	if len(want) > 0 {
		t.Fatalf("forgot to test %v", want)
	}
}