// Copyright 2009 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 ( "bytes" "encoding/hex" "fmt" "internal/testenv" "math" "math/rand" "strconv" "strings" "testing" "testing/quick" ) func isNormalized(x *Int) bool { if len(x.abs) == 0 { return !x.neg } // len(x.abs) > 0 return x.abs[len(x.abs)-1] != 0 } type funZZ func(z, x, y *Int) *Int type argZZ struct { z, x, y *Int } var sumZZ = []argZZ{ {NewInt(0), NewInt(0), NewInt(0)}, {NewInt(1), NewInt(1), NewInt(0)}, {NewInt(1111111110), NewInt(123456789), NewInt(987654321)}, {NewInt(-1), NewInt(-1), NewInt(0)}, {NewInt(864197532), NewInt(-123456789), NewInt(987654321)}, {NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)}, } var prodZZ = []argZZ{ {NewInt(0), NewInt(0), NewInt(0)}, {NewInt(0), NewInt(1), NewInt(0)}, {NewInt(1), NewInt(1), NewInt(1)}, {NewInt(-991 * 991), NewInt(991), NewInt(-991)}, // TODO(gri) add larger products } func TestSignZ(t *testing.T) { var zero Int for _, a := range sumZZ { s := a.z.Sign() e := a.z.Cmp(&zero) if s != e { t.Errorf("got %d; want %d for z = %v", s, e, a.z) } } } func TestSetZ(t *testing.T) { for _, a := range sumZZ { var z Int z.Set(a.z) if !isNormalized(&z) { t.Errorf("%v is not normalized", z) } if (&z).Cmp(a.z) != 0 { t.Errorf("got z = %v; want %v", z, a.z) } } } func TestAbsZ(t *testing.T) { var zero Int for _, a := range sumZZ { var z Int z.Abs(a.z) var e Int e.Set(a.z) if e.Cmp(&zero) < 0 { e.Sub(&zero, &e) } if z.Cmp(&e) != 0 { t.Errorf("got z = %v; want %v", z, e) } } } func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) { var z Int f(&z, a.x, a.y) if !isNormalized(&z) { t.Errorf("%s%v is not normalized", msg, z) } if (&z).Cmp(a.z) != 0 { t.Errorf("%v %s %v\n\tgot z = %v; want %v", a.x, msg, a.y, &z, a.z) } } func TestSumZZ(t *testing.T) { AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) } SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) } for _, a := range sumZZ { arg := a testFunZZ(t, "AddZZ", AddZZ, arg) arg = argZZ{a.z, a.y, a.x} testFunZZ(t, "AddZZ symmetric", AddZZ, arg) arg = argZZ{a.x, a.z, a.y} testFunZZ(t, "SubZZ", SubZZ, arg) arg = argZZ{a.y, a.z, a.x} testFunZZ(t, "SubZZ symmetric", SubZZ, arg) } } func TestProdZZ(t *testing.T) { MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) } for _, a := range prodZZ { arg := a testFunZZ(t, "MulZZ", MulZZ, arg) arg = argZZ{a.z, a.y, a.x} testFunZZ(t, "MulZZ symmetric", MulZZ, arg) } } // mulBytes returns x*y via grade school multiplication. Both inputs // and the result are assumed to be in big-endian representation (to // match the semantics of Int.Bytes and Int.SetBytes). func mulBytes(x, y []byte) []byte { z := make([]byte, len(x)+len(y)) // multiply k0 := len(z) - 1 for j := len(y) - 1; j >= 0; j-- { d := int(y[j]) if d != 0 { k := k0 carry := 0 for i := len(x) - 1; i >= 0; i-- { t := int(z[k]) + int(x[i])*d + carry z[k], carry = byte(t), t>>8 k-- } z[k] = byte(carry) } k0-- } // normalize (remove leading 0's) i := 0 for i < len(z) && z[i] == 0 { i++ } return z[i:] } func checkMul(a, b []byte) bool { var x, y, z1 Int x.SetBytes(a) y.SetBytes(b) z1.Mul(&x, &y) var z2 Int z2.SetBytes(mulBytes(a, b)) return z1.Cmp(&z2) == 0 } func TestMul(t *testing.T) { if err := quick.Check(checkMul, nil); err != nil { t.Error(err) } } var mulRangesZ = []struct { a, b int64 prod string }{ // entirely positive ranges are covered by mulRangesN {-1, 1, "0"}, {-2, -1, "2"}, {-3, -2, "6"}, {-3, -1, "-6"}, {1, 3, "6"}, {-10, -10, "-10"}, {0, -1, "1"}, // empty range {-1, -100, "1"}, // empty range {-1, 1, "0"}, // range includes 0 {-1e9, 0, "0"}, // range includes 0 {-1e9, 1e9, "0"}, // range includes 0 {-10, -1, "3628800"}, // 10! {-20, -2, "-2432902008176640000"}, // -20! {-99, -1, "-933262154439441526816992388562667004907159682643816214685929" + "638952175999932299156089414639761565182862536979208272237582" + "511852109168640000000000000000000000", // -99! }, // overflow situations {math.MaxInt64 - 0, math.MaxInt64, "9223372036854775807"}, {math.MaxInt64 - 1, math.MaxInt64, "85070591730234615838173535747377725442"}, {math.MaxInt64 - 2, math.MaxInt64, "784637716923335094969050127519550606919189611815754530810"}, {math.MaxInt64 - 3, math.MaxInt64, "7237005577332262206126809393809643289012107973151163787181513908099760521240"}, } func TestMulRangeZ(t *testing.T) { var tmp Int // test entirely positive ranges for i, r := range mulRangesN { // skip mulRangesN entries that overflow int64 if int64(r.a) < 0 || int64(r.b) < 0 { continue } prod := tmp.MulRange(int64(r.a), int64(r.b)).String() if prod != r.prod { t.Errorf("#%da: got %s; want %s", i, prod, r.prod) } } // test other ranges for i, r := range mulRangesZ { prod := tmp.MulRange(r.a, r.b).String() if prod != r.prod { t.Errorf("#%db: got %s; want %s", i, prod, r.prod) } } } func TestBinomial(t *testing.T) { var z Int for _, test := range []struct { n, k int64 want string }{ {0, 0, "1"}, {0, 1, "0"}, {1, 0, "1"}, {1, 1, "1"}, {1, 10, "0"}, {4, 0, "1"}, {4, 1, "4"}, {4, 2, "6"}, {4, 3, "4"}, {4, 4, "1"}, {10, 1, "10"}, {10, 9, "10"}, {10, 5, "252"}, {11, 5, "462"}, {11, 6, "462"}, {100, 10, "17310309456440"}, {100, 90, "17310309456440"}, {1000, 10, "263409560461970212832400"}, {1000, 990, "263409560461970212832400"}, } { if got := z.Binomial(test.n, test.k).String(); got != test.want { t.Errorf("Binomial(%d, %d) = %s; want %s", test.n, test.k, got, test.want) } } } func BenchmarkBinomial(b *testing.B) { var z Int for i := 0; i < b.N; i++ { z.Binomial(1000, 990) } } // Examples from the Go Language Spec, section "Arithmetic operators" var divisionSignsTests = []struct { x, y int64 q, r int64 // T-division d, m int64 // Euclidean division }{ {5, 3, 1, 2, 1, 2}, {-5, 3, -1, -2, -2, 1}, {5, -3, -1, 2, -1, 2}, {-5, -3, 1, -2, 2, 1}, {1, 2, 0, 1, 0, 1}, {8, 4, 2, 0, 2, 0}, } func TestDivisionSigns(t *testing.T) { for i, test := range divisionSignsTests { x := NewInt(test.x) y := NewInt(test.y) q := NewInt(test.q) r := NewInt(test.r) d := NewInt(test.d) m := NewInt(test.m) q1 := new(Int).Quo(x, y) r1 := new(Int).Rem(x, y) if !isNormalized(q1) { t.Errorf("#%d Quo: %v is not normalized", i, *q1) } if !isNormalized(r1) { t.Errorf("#%d Rem: %v is not normalized", i, *r1) } if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 { t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r) } q2, r2 := new(Int).QuoRem(x, y, new(Int)) if !isNormalized(q2) { t.Errorf("#%d Quo: %v is not normalized", i, *q2) } if !isNormalized(r2) { t.Errorf("#%d Rem: %v is not normalized", i, *r2) } if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 { t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r) } d1 := new(Int).Div(x, y) m1 := new(Int).Mod(x, y) if !isNormalized(d1) { t.Errorf("#%d Div: %v is not normalized", i, *d1) } if !isNormalized(m1) { t.Errorf("#%d Mod: %v is not normalized", i, *m1) } if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 { t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m) } d2, m2 := new(Int).DivMod(x, y, new(Int)) if !isNormalized(d2) { t.Errorf("#%d Div: %v is not normalized", i, *d2) } if !isNormalized(m2) { t.Errorf("#%d Mod: %v is not normalized", i, *m2) } if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 { t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m) } } } func norm(x nat) nat { i := len(x) for i > 0 && x[i-1] == 0 { i-- } return x[:i] } func TestBits(t *testing.T) { for _, test := range []nat{ nil, {0}, {1}, {0, 1, 2, 3, 4}, {4, 3, 2, 1, 0}, {4, 3, 2, 1, 0, 0, 0, 0}, } { var z Int z.neg = true got := z.SetBits(test) want := norm(test) if got.abs.cmp(want) != 0 { t.Errorf("SetBits(%v) = %v; want %v", test, got.abs, want) } if got.neg { t.Errorf("SetBits(%v): got negative result", test) } bits := nat(z.Bits()) if bits.cmp(want) != 0 { t.Errorf("%v.Bits() = %v; want %v", z.abs, bits, want) } } } func checkSetBytes(b []byte) bool { hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes()) hex2 := hex.EncodeToString(b) for len(hex1) < len(hex2) { hex1 = "0" + hex1 } for len(hex1) > len(hex2) { hex2 = "0" + hex2 } return hex1 == hex2 } func TestSetBytes(t *testing.T) { if err := quick.Check(checkSetBytes, nil); err != nil { t.Error(err) } } func checkBytes(b []byte) bool { // trim leading zero bytes since Bytes() won't return them // (was issue 12231) for len(b) > 0 && b[0] == 0 { b = b[1:] } b2 := new(Int).SetBytes(b).Bytes() return bytes.Equal(b, b2) } func TestBytes(t *testing.T) { if err := quick.Check(checkBytes, nil); err != nil { t.Error(err) } } func checkQuo(x, y []byte) bool { u := new(Int).SetBytes(x) v := new(Int).SetBytes(y) if len(v.abs) == 0 { return true } r := new(Int) q, r := new(Int).QuoRem(u, v, r) if r.Cmp(v) >= 0 { return false } uprime := new(Int).Set(q) uprime.Mul(uprime, v) uprime.Add(uprime, r) return uprime.Cmp(u) == 0 } var quoTests = []struct { x, y string q, r string }{ { "476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357", "9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996", "50911", "1", }, { "11510768301994997771168", "1328165573307167369775", "8", "885443715537658812968", }, } func TestQuo(t *testing.T) { if err := quick.Check(checkQuo, nil); err != nil { t.Error(err) } for i, test := range quoTests { x, _ := new(Int).SetString(test.x, 10) y, _ := new(Int).SetString(test.y, 10) expectedQ, _ := new(Int).SetString(test.q, 10) expectedR, _ := new(Int).SetString(test.r, 10) r := new(Int) q, r := new(Int).QuoRem(x, y, r) if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 { t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR) } } } func TestQuoStepD6(t *testing.T) { // See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises // a code path which only triggers 1 in 10^{-19} cases. u := &Int{false, nat{0, 0, 1 + 1<<(_W-1), _M ^ (1 << (_W - 1))}} v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}} r := new(Int) q, r := new(Int).QuoRem(u, v, r) const expectedQ64 = "18446744073709551613" const expectedR64 = "3138550867693340382088035895064302439801311770021610913807" const expectedQ32 = "4294967293" const expectedR32 = "39614081266355540837921718287" if q.String() != expectedQ64 && q.String() != expectedQ32 || r.String() != expectedR64 && r.String() != expectedR32 { t.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q, r, expectedQ64, expectedR64, expectedQ32, expectedR32) } } func BenchmarkQuoRem(b *testing.B) { x, _ := new(Int).SetString("153980389784927331788354528594524332344709972855165340650588877572729725338415474372475094155672066328274535240275856844648695200875763869073572078279316458648124537905600131008790701752441155668003033945258023841165089852359980273279085783159654751552359397986180318708491098942831252291841441726305535546071", 0) y, _ := new(Int).SetString("7746362281539803897849273317883545285945243323447099728551653406505888775727297253384154743724750941556720663282745352402758568446486952008757638690735720782793164586481245379056001310087907017524411556680030339452580238411650898523599802732790857831596547515523593979861803187084910989428312522918414417263055355460715745539358014631136245887418412633787074173796862711588221766398229333338511838891484974940633857861775630560092874987828057333663969469797013996401149696897591265769095952887917296740109742927689053276850469671231961384715398038978492733178835452859452433234470997285516534065058887757272972533841547437247509415567206632827453524027585684464869520087576386907357207827931645864812453790560013100879070175244115566800303394525802384116508985235998027327908578315965475155235939798618031870849109894283125229184144172630553554607112725169432413343763989564437170644270643461665184965150423819594083121075825", 0) q := new(Int) r := new(Int) b.ResetTimer() for i := 0; i < b.N; i++ { q.QuoRem(y, x, r) } } var bitLenTests = []struct { in string out int }{ {"-1", 1}, {"0", 0}, {"1", 1}, {"2", 2}, {"4", 3}, {"0xabc", 12}, {"0x8000", 16}, {"0x80000000", 32}, {"0x800000000000", 48}, {"0x8000000000000000", 64}, {"0x80000000000000000000", 80}, {"-0x4000000000000000000000", 87}, } func TestBitLen(t *testing.T) { for i, test := range bitLenTests { x, ok := new(Int).SetString(test.in, 0) if !ok { t.Errorf("#%d test input invalid: %s", i, test.in) continue } if n := x.BitLen(); n != test.out { t.Errorf("#%d got %d want %d", i, n, test.out) } } } var expTests = []struct { x, y, m string out string }{ // y <= 0 {"0", "0", "", "1"}, {"1", "0", "", "1"}, {"-10", "0", "", "1"}, {"1234", "-1", "", "1"}, {"1234", "-1", "0", "1"}, {"17", "-100", "1234", "865"}, {"2", "-100", "1234", ""}, // m == 1 {"0", "0", "1", "0"}, {"1", "0", "1", "0"}, {"-10", "0", "1", "0"}, {"1234", "-1", "1", "0"}, // misc {"5", "1", "3", "2"}, {"5", "-7", "", "1"}, {"-5", "-7", "", "1"}, {"5", "0", "", "1"}, {"-5", "0", "", "1"}, {"5", "1", "", "5"}, {"-5", "1", "", "-5"}, {"-5", "1", "7", "2"}, {"-2", "3", "2", "0"}, {"5", "2", "", "25"}, {"1", "65537", "2", "1"}, {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"}, {"0x8000000000000000", "2", "6719", "4944"}, {"0x8000000000000000", "3", "6719", "5447"}, {"0x8000000000000000", "1000", "6719", "1603"}, {"0x8000000000000000", "1000000", "6719", "3199"}, {"0x8000000000000000", "-1000000", "6719", "3663"}, // 3663 = ModInverse(3199, 6719) Issue #25865 {"0xffffffffffffffffffffffffffffffff", "0x12345678123456781234567812345678123456789", "0x01112222333344445555666677778889", "0x36168FA1DB3AAE6C8CE647E137F97A"}, { "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347", "298472983472983471903246121093472394872319615612417471234712061", "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464", "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291", }, // test case for issue 8822 { "11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865", "0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", "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}, { "-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xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", "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}, // test cases for issue 13907 {"0xffffffff00000001", "0xffffffff00000001", "0xffffffff00000001", "0"}, {"0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0"}, {"0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0"}, {"0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0"}, { "2", "0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", "0xAC6BDB41324A9A9BF166DE5E1389582FAF72B6651987EE07FC3192943DB56050A37329CBB4A099ED8193E0757767A13DD52312AB4B03310DCD7F48A9DA04FD50E8083969EDB767B0CF6095179A163AB3661A05FBD5FAAAE82918A9962F0B93B855F97993EC975EEAA80D740ADBF4FF747359D041D5C33EA71D281E446B14773BCA97B43A23FB801676BD207A436C6481F1D2B9078717461A5B9D32E688F87748544523B524B0D57D5EA77A2775D2ECFA032CFBDBF52FB3786160279004E57AE6AF874E7303CE53299CCC041C7BC308D82A5698F3A8D0C38271AE35F8E9DBFBB694B5C803D89F7AE435DE236D525F54759B65E372FCD68EF20FA7111F9E4AFF73", // odd "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}, { "2", "0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", "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even "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}, } func TestExp(t *testing.T) { for i, test := range expTests { x, ok1 := new(Int).SetString(test.x, 0) y, ok2 := new(Int).SetString(test.y, 0) var ok3, ok4 bool var out, m *Int if len(test.out) == 0 { out, ok3 = nil, true } else { out, ok3 = new(Int).SetString(test.out, 0) } if len(test.m) == 0 { m, ok4 = nil, true } else { m, ok4 = new(Int).SetString(test.m, 0) } if !ok1 || !ok2 || !ok3 || !ok4 { t.Errorf("#%d: error in input", i) continue } z1 := new(Int).Exp(x, y, m) if z1 != nil && !isNormalized(z1) { t.Errorf("#%d: %v is not normalized", i, *z1) } if !(z1 == nil && out == nil || z1.Cmp(out) == 0) { t.Errorf("#%d: got %x want %x", i, z1, out) } if m == nil { // The result should be the same as for m == 0; // specifically, there should be no div-zero panic. m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0 z2 := new(Int).Exp(x, y, m) if z2.Cmp(z1) != 0 { t.Errorf("#%d: got %x want %x", i, z2, z1) } } } } func BenchmarkExp(b *testing.B) { x, _ := new(Int).SetString("11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865", 0) y, _ := new(Int).SetString("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n, _ := new(Int).SetString("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out := new(Int) for i := 0; i < b.N; i++ { out.Exp(x, y, n) } } func BenchmarkExpMont(b *testing.B) { x, _ := new(Int).SetString("297778224889315382157302278696111964193", 0) y, _ := new(Int).SetString("2548977943381019743024248146923164919440527843026415174732254534318292492375775985739511369575861449426580651447974311336267954477239437734832604782764979371984246675241012538135715981292390886872929238062252506842498360562303324154310849745753254532852868768268023732398278338025070694508489163836616810661033068070127919590264734220833816416141878688318329193389865030063416339367925710474801991305827284114894677717927892032165200876093838921477120036402410731159852999623461591709308405270748511350289172153076023215", 0) var mods = []struct { name string val string }{ {"Odd", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF"}, {"Even1", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FE"}, {"Even2", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FC"}, {"Even3", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281F8"}, {"Even4", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281F0"}, {"Even8", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B21828100"}, {"Even32", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B00000000"}, {"Even64", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FF0000000000000000"}, {"Even96", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828283000000000000000000000000"}, {"Even128", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF00000000000000000000000000000000"}, {"Even255", "0x82828282828200FFFF28FF2B218281FF8000000000000000000000000000000000000000000000000000000000000000"}, {"SmallEven1", "0x7E"}, {"SmallEven2", "0x7C"}, {"SmallEven3", "0x78"}, {"SmallEven4", "0x70"}, } for _, mod := range mods { n, _ := new(Int).SetString(mod.val, 0) out := new(Int) b.Run(mod.name, func(b *testing.B) { b.ReportAllocs() for i := 0; i < b.N; i++ { out.Exp(x, y, n) } }) } } func BenchmarkExp2(b *testing.B) { x, _ := new(Int).SetString("2", 0) y, _ := new(Int).SetString("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n, _ := new(Int).SetString("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out := new(Int) for i := 0; i < b.N; i++ { out.Exp(x, y, n) } } func checkGcd(aBytes, bBytes []byte) bool { x := new(Int) y := new(Int) a := new(Int).SetBytes(aBytes) b := new(Int).SetBytes(bBytes) d := new(Int).GCD(x, y, a, b) x.Mul(x, a) y.Mul(y, b) x.Add(x, y) return x.Cmp(d) == 0 } // euclidExtGCD is a reference implementation of Euclid's // extended GCD algorithm for testing against optimized algorithms. // Requirements: a, b > 0 func euclidExtGCD(a, b *Int) (g, x, y *Int) { A := new(Int).Set(a) B := new(Int).Set(b) // A = Ua*a + Va*b // B = Ub*a + Vb*b Ua := new(Int).SetInt64(1) Va := new(Int) Ub := new(Int) Vb := new(Int).SetInt64(1) q := new(Int) temp := new(Int) r := new(Int) for len(B.abs) > 0 { q, r = q.QuoRem(A, B, r) A, B, r = B, r, A // Ua, Ub = Ub, Ua-q*Ub temp.Set(Ub) Ub.Mul(Ub, q) Ub.Sub(Ua, Ub) Ua.Set(temp) // Va, Vb = Vb, Va-q*Vb temp.Set(Vb) Vb.Mul(Vb, q) Vb.Sub(Va, Vb) Va.Set(temp) } return A, Ua, Va } func checkLehmerGcd(aBytes, bBytes []byte) bool { a := new(Int).SetBytes(aBytes) b := new(Int).SetBytes(bBytes) if a.Sign() <= 0 || b.Sign() <= 0 { return true // can only test positive arguments } d := new(Int).lehmerGCD(nil, nil, a, b) d0, _, _ := euclidExtGCD(a, b) return d.Cmp(d0) == 0 } func checkLehmerExtGcd(aBytes, bBytes []byte) bool { a := new(Int).SetBytes(aBytes) b := new(Int).SetBytes(bBytes) x := new(Int) y := new(Int) if a.Sign() <= 0 || b.Sign() <= 0 { return true // can only test positive arguments } d := new(Int).lehmerGCD(x, y, a, b) d0, x0, y0 := euclidExtGCD(a, b) return d.Cmp(d0) == 0 && x.Cmp(x0) == 0 && y.Cmp(y0) == 0 } var gcdTests = []struct { d, x, y, a, b string }{ // a <= 0 || b <= 0 {"0", "0", "0", "0", "0"}, {"7", "0", "1", "0", "7"}, {"7", "0", "-1", "0", "-7"}, {"11", "1", "0", "11", "0"}, {"7", "-1", "-2", "-77", "35"}, {"935", "-3", "8", "64515", "24310"}, {"935", "-3", "-8", "64515", "-24310"}, {"935", "3", "-8", "-64515", "-24310"}, {"1", "-9", "47", "120", "23"}, {"7", "1", "-2", "77", "35"}, {"935", "-3", "8", "64515", "24310"}, {"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"}, {"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"}, } func testGcd(t *testing.T, d, x, y, a, b *Int) { var X *Int if x != nil { X = new(Int) } var Y *Int if y != nil { Y = new(Int) } D := new(Int).GCD(X, Y, a, b) if D.Cmp(d) != 0 { t.Errorf("GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, D, d) } if x != nil && X.Cmp(x) != 0 { t.Errorf("GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, X, x) } if y != nil && Y.Cmp(y) != 0 { t.Errorf("GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, Y, y) } // check results in presence of aliasing (issue #11284) a2 := new(Int).Set(a) b2 := new(Int).Set(b) a2.GCD(X, Y, a2, b2) // result is same as 1st argument if a2.Cmp(d) != 0 { t.Errorf("aliased z = a GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, a2, d) } if x != nil && X.Cmp(x) != 0 { t.Errorf("aliased z = a GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, X, x) } if y != nil && Y.Cmp(y) != 0 { t.Errorf("aliased z = a GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, Y, y) } a2 = new(Int).Set(a) b2 = new(Int).Set(b) b2.GCD(X, Y, a2, b2) // result is same as 2nd argument if b2.Cmp(d) != 0 { t.Errorf("aliased z = b GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, b2, d) } if x != nil && X.Cmp(x) != 0 { t.Errorf("aliased z = b GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, X, x) } if y != nil && Y.Cmp(y) != 0 { t.Errorf("aliased z = b GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, Y, y) } a2 = new(Int).Set(a) b2 = new(Int).Set(b) D = new(Int).GCD(a2, b2, a2, b2) // x = a, y = b if D.Cmp(d) != 0 { t.Errorf("aliased x = a, y = b GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, D, d) } if x != nil && a2.Cmp(x) != 0 { t.Errorf("aliased x = a, y = b GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, a2, x) } if y != nil && b2.Cmp(y) != 0 { t.Errorf("aliased x = a, y = b GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, b2, y) } a2 = new(Int).Set(a) b2 = new(Int).Set(b) D = new(Int).GCD(b2, a2, a2, b2) // x = b, y = a if D.Cmp(d) != 0 { t.Errorf("aliased x = b, y = a GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, D, d) } if x != nil && b2.Cmp(x) != 0 { t.Errorf("aliased x = b, y = a GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, b2, x) } if y != nil && a2.Cmp(y) != 0 { t.Errorf("aliased x = b, y = a GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, a2, y) } } func TestGcd(t *testing.T) { for _, test := range gcdTests { d, _ := new(Int).SetString(test.d, 0) x, _ := new(Int).SetString(test.x, 0) y, _ := new(Int).SetString(test.y, 0) a, _ := new(Int).SetString(test.a, 0) b, _ := new(Int).SetString(test.b, 0) testGcd(t, d, nil, nil, a, b) testGcd(t, d, x, nil, a, b) testGcd(t, d, nil, y, a, b) testGcd(t, d, x, y, a, b) } if err := quick.Check(checkGcd, nil); err != nil { t.Error(err) } if err := quick.Check(checkLehmerGcd, nil); err != nil { t.Error(err) } if err := quick.Check(checkLehmerExtGcd, nil); err != nil { t.Error(err) } } type intShiftTest struct { in string shift uint out string } var rshTests = []intShiftTest{ {"0", 0, "0"}, {"-0", 0, "0"}, {"0", 1, "0"}, {"0", 2, "0"}, {"1", 0, "1"}, {"1", 1, "0"}, {"1", 2, "0"}, {"2", 0, "2"}, {"2", 1, "1"}, {"-1", 0, "-1"}, {"-1", 1, "-1"}, {"-1", 10, "-1"}, {"-100", 2, "-25"}, {"-100", 3, "-13"}, {"-100", 100, "-1"}, {"4294967296", 0, "4294967296"}, {"4294967296", 1, "2147483648"}, {"4294967296", 2, "1073741824"}, {"18446744073709551616", 0, "18446744073709551616"}, {"18446744073709551616", 1, "9223372036854775808"}, {"18446744073709551616", 2, "4611686018427387904"}, {"18446744073709551616", 64, "1"}, {"340282366920938463463374607431768211456", 64, "18446744073709551616"}, {"340282366920938463463374607431768211456", 128, "1"}, } func TestRsh(t *testing.T) { for i, test := range rshTests { in, _ := new(Int).SetString(test.in, 10) expected, _ := new(Int).SetString(test.out, 10) out := new(Int).Rsh(in, test.shift) if !isNormalized(out) { t.Errorf("#%d: %v is not normalized", i, *out) } if out.Cmp(expected) != 0 { t.Errorf("#%d: got %s want %s", i, out, expected) } } } func TestRshSelf(t *testing.T) { for i, test := range rshTests { z, _ := new(Int).SetString(test.in, 10) expected, _ := new(Int).SetString(test.out, 10) z.Rsh(z, test.shift) if !isNormalized(z) { t.Errorf("#%d: %v is not normalized", i, *z) } if z.Cmp(expected) != 0 { t.Errorf("#%d: got %s want %s", i, z, expected) } } } var lshTests = []intShiftTest{ {"0", 0, "0"}, {"0", 1, "0"}, {"0", 2, "0"}, {"1", 0, "1"}, {"1", 1, "2"}, {"1", 2, "4"}, {"2", 0, "2"}, {"2", 1, "4"}, {"2", 2, "8"}, {"-87", 1, "-174"}, {"4294967296", 0, "4294967296"}, {"4294967296", 1, "8589934592"}, {"4294967296", 2, "17179869184"}, {"18446744073709551616", 0, "18446744073709551616"}, {"9223372036854775808", 1, "18446744073709551616"}, {"4611686018427387904", 2, "18446744073709551616"}, {"1", 64, "18446744073709551616"}, {"18446744073709551616", 64, "340282366920938463463374607431768211456"}, {"1", 128, "340282366920938463463374607431768211456"}, } func TestLsh(t *testing.T) { for i, test := range lshTests { in, _ := new(Int).SetString(test.in, 10) expected, _ := new(Int).SetString(test.out, 10) out := new(Int).Lsh(in, test.shift) if !isNormalized(out) { t.Errorf("#%d: %v is not normalized", i, *out) } if out.Cmp(expected) != 0 { t.Errorf("#%d: got %s want %s", i, out, expected) } } } func TestLshSelf(t *testing.T) { for i, test := range lshTests { z, _ := new(Int).SetString(test.in, 10) expected, _ := new(Int).SetString(test.out, 10) z.Lsh(z, test.shift) if !isNormalized(z) { t.Errorf("#%d: %v is not normalized", i, *z) } if z.Cmp(expected) != 0 { t.Errorf("#%d: got %s want %s", i, z, expected) } } } func TestLshRsh(t *testing.T) { for i, test := range rshTests { in, _ := new(Int).SetString(test.in, 10) out := new(Int).Lsh(in, test.shift) out = out.Rsh(out, test.shift) if !isNormalized(out) { t.Errorf("#%d: %v is not normalized", i, *out) } if in.Cmp(out) != 0 { t.Errorf("#%d: got %s want %s", i, out, in) } } for i, test := range lshTests { in, _ := new(Int).SetString(test.in, 10) out := new(Int).Lsh(in, test.shift) out.Rsh(out, test.shift) if !isNormalized(out) { t.Errorf("#%d: %v is not normalized", i, *out) } if in.Cmp(out) != 0 { t.Errorf("#%d: got %s want %s", i, out, in) } } } // Entries must be sorted by value in ascending order. var cmpAbsTests = []string{ "0", "1", "2", "10", "10000000", "2783678367462374683678456387645876387564783686583485", "2783678367462374683678456387645876387564783686583486", "32957394867987420967976567076075976570670947609750670956097509670576075067076027578341538", } func TestCmpAbs(t *testing.T) { values := make([]*Int, len(cmpAbsTests)) var prev *Int for i, s := range cmpAbsTests { x, ok := new(Int).SetString(s, 0) if !ok { t.Fatalf("SetString(%s, 0) failed", s) } if prev != nil && prev.Cmp(x) >= 0 { t.Fatal("cmpAbsTests entries not sorted in ascending order") } values[i] = x prev = x } for i, x := range values { for j, y := range values { // try all combinations of signs for x, y for k := 0; k < 4; k++ { var a, b Int a.Set(x) b.Set(y) if k&1 != 0 { a.Neg(&a) } if k&2 != 0 { b.Neg(&b) } got := a.CmpAbs(&b) want := 0 switch { case i > j: want = 1 case i < j: want = -1 } if got != want { t.Errorf("absCmp |%s|, |%s|: got %d; want %d", &a, &b, got, want) } } } } } func TestIntCmpSelf(t *testing.T) { for _, s := range cmpAbsTests { x, ok := new(Int).SetString(s, 0) if !ok { t.Fatalf("SetString(%s, 0) failed", s) } got := x.Cmp(x) want := 0 if got != want { t.Errorf("x = %s: x.Cmp(x): got %d; want %d", x, got, want) } } } var int64Tests = []string{ // int64 "0", "1", "-1", "4294967295", "-4294967295", "4294967296", "-4294967296", "9223372036854775807", "-9223372036854775807", "-9223372036854775808", // not int64 "0x8000000000000000", "-0x8000000000000001", "38579843757496759476987459679745", "-38579843757496759476987459679745", } func TestInt64(t *testing.T) { for _, s := range int64Tests { var x Int _, ok := x.SetString(s, 0) if !ok { t.Errorf("SetString(%s, 0) failed", s) continue } want, err := strconv.ParseInt(s, 0, 64) if err != nil { if err.(*strconv.NumError).Err == strconv.ErrRange { if x.IsInt64() { t.Errorf("IsInt64(%s) succeeded unexpectedly", s) } } else { t.Errorf("ParseInt(%s) failed", s) } continue } if !x.IsInt64() { t.Errorf("IsInt64(%s) failed unexpectedly", s) } got := x.Int64() if got != want { t.Errorf("Int64(%s) = %d; want %d", s, got, want) } } } var uint64Tests = []string{ // uint64 "0", "1", "4294967295", "4294967296", "8589934591", "8589934592", "9223372036854775807", "9223372036854775808", "0x08000000000000000", // not uint64 "0x10000000000000000", "-0x08000000000000000", "-1", } func TestUint64(t *testing.T) { for _, s := range uint64Tests { var x Int _, ok := x.SetString(s, 0) if !ok { t.Errorf("SetString(%s, 0) failed", s) continue } want, err := strconv.ParseUint(s, 0, 64) if err != nil { // check for sign explicitly (ErrRange doesn't cover signed input) if s[0] == '-' || err.(*strconv.NumError).Err == strconv.ErrRange { if x.IsUint64() { t.Errorf("IsUint64(%s) succeeded unexpectedly", s) } } else { t.Errorf("ParseUint(%s) failed", s) } continue } if !x.IsUint64() { t.Errorf("IsUint64(%s) failed unexpectedly", s) } got := x.Uint64() if got != want { t.Errorf("Uint64(%s) = %d; want %d", s, got, want) } } } var bitwiseTests = []struct { x, y string and, or, xor, andNot string }{ {"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"}, {"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"}, {"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"}, {"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"}, {"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"}, {"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"}, {"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"}, {"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"}, {"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"}, {"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"}, {"0xff", "-0x0a", "0xf6", "-0x01", "-0xf7", "0x09"}, {"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"}, {"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"}, {"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"}, { "0x1000009dc6e3d9822cba04129bcbe3401", "0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", "0x1000001186210100001000009048c2001", "0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd", "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc", "0x8c40c2d8822caa04120b8321400", }, { "0x1000009dc6e3d9822cba04129bcbe3401", "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", "0x8c40c2d8822caa04120b8321401", "-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd", "-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe", "0x1000001186210100001000009048c2000", }, { "-0x1000009dc6e3d9822cba04129bcbe3401", "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", "-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd", "-0x1000001186210100001000009048c2001", "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc", "0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc", }, } type bitFun func(z, x, y *Int) *Int func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) { expected := new(Int) expected.SetString(exp, 0) out := f(new(Int), x, y) if out.Cmp(expected) != 0 { t.Errorf("%s: got %s want %s", msg, out, expected) } } func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) { self := new(Int) self.Set(x) expected := new(Int) expected.SetString(exp, 0) self = f(self, self, y) if self.Cmp(expected) != 0 { t.Errorf("%s: got %s want %s", msg, self, expected) } } func altBit(x *Int, i int) uint { z := new(Int).Rsh(x, uint(i)) z = z.And(z, NewInt(1)) if z.Cmp(new(Int)) != 0 { return 1 } return 0 } func altSetBit(z *Int, x *Int, i int, b uint) *Int { one := NewInt(1) m := one.Lsh(one, uint(i)) switch b { case 1: return z.Or(x, m) case 0: return z.AndNot(x, m) } panic("set bit is not 0 or 1") } func testBitset(t *testing.T, x *Int) { n := x.BitLen() z := new(Int).Set(x) z1 := new(Int).Set(x) for i := 0; i < n+10; i++ { old := z.Bit(i) old1 := altBit(z1, i) if old != old1 { t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1) } z := new(Int).SetBit(z, i, 1) z1 := altSetBit(new(Int), z1, i, 1) if z.Bit(i) == 0 { t.Errorf("bitset: bit %d of %s got 0 want 1", i, x) } if z.Cmp(z1) != 0 { t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1) } z.SetBit(z, i, 0) altSetBit(z1, z1, i, 0) if z.Bit(i) != 0 { t.Errorf("bitset: bit %d of %s got 1 want 0", i, x) } if z.Cmp(z1) != 0 { t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1) } altSetBit(z1, z1, i, old) z.SetBit(z, i, old) if z.Cmp(z1) != 0 { t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1) } } if z.Cmp(x) != 0 { t.Errorf("bitset: got %s want %s", z, x) } } var bitsetTests = []struct { x string i int b uint }{ {"0", 0, 0}, {"0", 200, 0}, {"1", 0, 1}, {"1", 1, 0}, {"-1", 0, 1}, {"-1", 200, 1}, {"0x2000000000000000000000000000", 108, 0}, {"0x2000000000000000000000000000", 109, 1}, {"0x2000000000000000000000000000", 110, 0}, {"-0x2000000000000000000000000001", 108, 1}, {"-0x2000000000000000000000000001", 109, 0}, {"-0x2000000000000000000000000001", 110, 1}, } func TestBitSet(t *testing.T) { for _, test := range bitwiseTests { x := new(Int) x.SetString(test.x, 0) testBitset(t, x) x = new(Int) x.SetString(test.y, 0) testBitset(t, x) } for i, test := range bitsetTests { x := new(Int) x.SetString(test.x, 0) b := x.Bit(test.i) if b != test.b { t.Errorf("#%d got %v want %v", i, b, test.b) } } z := NewInt(1) z.SetBit(NewInt(0), 2, 1) if z.Cmp(NewInt(4)) != 0 { t.Errorf("destination leaked into result; got %s want 4", z) } } var tzbTests = []struct { in string out uint }{ {"0", 0}, {"1", 0}, {"-1", 0}, {"4", 2}, {"-8", 3}, {"0x4000000000000000000", 74}, {"-0x8000000000000000000", 75}, } func TestTrailingZeroBits(t *testing.T) { for i, test := range tzbTests { in, _ := new(Int).SetString(test.in, 0) want := test.out got := in.TrailingZeroBits() if got != want { t.Errorf("#%d: got %v want %v", i, got, want) } } } func BenchmarkBitset(b *testing.B) { z := new(Int) z.SetBit(z, 512, 1) b.ResetTimer() for i := b.N - 1; i >= 0; i-- { z.SetBit(z, i&512, 1) } } func BenchmarkBitsetNeg(b *testing.B) { z := NewInt(-1) z.SetBit(z, 512, 0) b.ResetTimer() for i := b.N - 1; i >= 0; i-- { z.SetBit(z, i&512, 0) } } func BenchmarkBitsetOrig(b *testing.B) { z := new(Int) altSetBit(z, z, 512, 1) b.ResetTimer() for i := b.N - 1; i >= 0; i-- { altSetBit(z, z, i&512, 1) } } func BenchmarkBitsetNegOrig(b *testing.B) { z := NewInt(-1) altSetBit(z, z, 512, 0) b.ResetTimer() for i := b.N - 1; i >= 0; i-- { altSetBit(z, z, i&512, 0) } } // tri generates the trinomial 2**(n*2) - 2**n - 1, which is always 3 mod 4 and // 7 mod 8, so that 2 is always a quadratic residue. func tri(n uint) *Int { x := NewInt(1) x.Lsh(x, n) x2 := new(Int).Lsh(x, n) x2.Sub(x2, x) x2.Sub(x2, intOne) return x2 } func BenchmarkModSqrt225_Tonelli(b *testing.B) { p := tri(225) x := NewInt(2) for i := 0; i < b.N; i++ { x.SetUint64(2) x.modSqrtTonelliShanks(x, p) } } func BenchmarkModSqrt225_3Mod4(b *testing.B) { p := tri(225) x := new(Int).SetUint64(2) for i := 0; i < b.N; i++ { x.SetUint64(2) x.modSqrt3Mod4Prime(x, p) } } func BenchmarkModSqrt231_Tonelli(b *testing.B) { p := tri(231) p.Sub(p, intOne) p.Sub(p, intOne) // tri(231) - 2 is a prime == 5 mod 8 x := new(Int).SetUint64(7) for i := 0; i < b.N; i++ { x.SetUint64(7) x.modSqrtTonelliShanks(x, p) } } func BenchmarkModSqrt231_5Mod8(b *testing.B) { p := tri(231) p.Sub(p, intOne) p.Sub(p, intOne) // tri(231) - 2 is a prime == 5 mod 8 x := new(Int).SetUint64(7) for i := 0; i < b.N; i++ { x.SetUint64(7) x.modSqrt5Mod8Prime(x, p) } } func TestBitwise(t *testing.T) { x := new(Int) y := new(Int) for _, test := range bitwiseTests { x.SetString(test.x, 0) y.SetString(test.y, 0) testBitFun(t, "and", (*Int).And, x, y, test.and) testBitFunSelf(t, "and", (*Int).And, x, y, test.and) testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot) testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot) testBitFun(t, "or", (*Int).Or, x, y, test.or) testBitFunSelf(t, "or", (*Int).Or, x, y, test.or) testBitFun(t, "xor", (*Int).Xor, x, y, test.xor) testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor) } } var notTests = []struct { in string out string }{ {"0", "-1"}, {"1", "-2"}, {"7", "-8"}, {"0", "-1"}, {"-81910", "81909"}, { "298472983472983471903246121093472394872319615612417471234712061", "-298472983472983471903246121093472394872319615612417471234712062", }, } func TestNot(t *testing.T) { in := new(Int) out := new(Int) expected := new(Int) for i, test := range notTests { in.SetString(test.in, 10) expected.SetString(test.out, 10) out = out.Not(in) if out.Cmp(expected) != 0 { t.Errorf("#%d: got %s want %s", i, out, expected) } out = out.Not(out) if out.Cmp(in) != 0 { t.Errorf("#%d: got %s want %s", i, out, in) } } } var modInverseTests = []struct { element string modulus string }{ {"1234567", "458948883992"}, {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"}, {"-10", "13"}, // issue #16984 {"10", "-13"}, {"-17", "-13"}, } func TestModInverse(t *testing.T) { var element, modulus, gcd, inverse Int one := NewInt(1) for _, test := range modInverseTests { (&element).SetString(test.element, 10) (&modulus).SetString(test.modulus, 10) (&inverse).ModInverse(&element, &modulus) (&inverse).Mul(&inverse, &element) (&inverse).Mod(&inverse, &modulus) if (&inverse).Cmp(one) != 0 { t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse) } } // exhaustive test for small values for n := 2; n < 100; n++ { (&modulus).SetInt64(int64(n)) for x := 1; x < n; x++ { (&element).SetInt64(int64(x)) (&gcd).GCD(nil, nil, &element, &modulus) if (&gcd).Cmp(one) != 0 { continue } (&inverse).ModInverse(&element, &modulus) (&inverse).Mul(&inverse, &element) (&inverse).Mod(&inverse, &modulus) if (&inverse).Cmp(one) != 0 { t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse) } } } } func BenchmarkModInverse(b *testing.B) { p := new(Int).SetInt64(1) // Mersenne prime 2**1279 -1 p.abs = p.abs.shl(p.abs, 1279) p.Sub(p, intOne) x := new(Int).Sub(p, intOne) z := new(Int) for i := 0; i < b.N; i++ { z.ModInverse(x, p) } } // testModSqrt is a helper for TestModSqrt, // which checks that ModSqrt can compute a square-root of elt^2. func testModSqrt(t *testing.T, elt, mod, sq, sqrt *Int) bool { var sqChk, sqrtChk, sqrtsq Int sq.Mul(elt, elt) sq.Mod(sq, mod) z := sqrt.ModSqrt(sq, mod) if z != sqrt { t.Errorf("ModSqrt returned wrong value %s", z) } // test ModSqrt arguments outside the range [0,mod) sqChk.Add(sq, mod) z = sqrtChk.ModSqrt(&sqChk, mod) if z != &sqrtChk || z.Cmp(sqrt) != 0 { t.Errorf("ModSqrt returned inconsistent value %s", z) } sqChk.Sub(sq, mod) z = sqrtChk.ModSqrt(&sqChk, mod) if z != &sqrtChk || z.Cmp(sqrt) != 0 { t.Errorf("ModSqrt returned inconsistent value %s", z) } // test x aliasing z z = sqrtChk.ModSqrt(sqrtChk.Set(sq), mod) if z != &sqrtChk || z.Cmp(sqrt) != 0 { t.Errorf("ModSqrt returned inconsistent value %s", z) } // make sure we actually got a square root if sqrt.Cmp(elt) == 0 { return true // we found the "desired" square root } sqrtsq.Mul(sqrt, sqrt) // make sure we found the "other" one sqrtsq.Mod(&sqrtsq, mod) return sq.Cmp(&sqrtsq) == 0 } func TestModSqrt(t *testing.T) { var elt, mod, modx4, sq, sqrt Int r := rand.New(rand.NewSource(9)) for i, s := range primes[1:] { // skip 2, use only odd primes mod.SetString(s, 10) modx4.Lsh(&mod, 2) // test a few random elements per prime for x := 1; x < 5; x++ { elt.Rand(r, &modx4) elt.Sub(&elt, &mod) // test range [-mod, 3*mod) if !testModSqrt(t, &elt, &mod, &sq, &sqrt) { t.Errorf("#%d: failed (sqrt(e) = %s)", i, &sqrt) } } if testing.Short() && i > 2 { break } } if testing.Short() { return } // exhaustive test for small values for n := 3; n < 100; n++ { mod.SetInt64(int64(n)) if !mod.ProbablyPrime(10) { continue } isSquare := make([]bool, n) // test all the squares for x := 1; x < n; x++ { elt.SetInt64(int64(x)) if !testModSqrt(t, &elt, &mod, &sq, &sqrt) { t.Errorf("#%d: failed (sqrt(%d,%d) = %s)", x, &elt, &mod, &sqrt) } isSquare[sq.Uint64()] = true } // test all non-squares for x := 1; x < n; x++ { sq.SetInt64(int64(x)) z := sqrt.ModSqrt(&sq, &mod) if !isSquare[x] && z != nil { t.Errorf("#%d: failed (sqrt(%d,%d) = nil)", x, &sqrt, &mod) } } } } func TestJacobi(t *testing.T) { testCases := []struct { x, y int64 result int }{ {0, 1, 1}, {0, -1, 1}, {1, 1, 1}, {1, -1, 1}, {0, 5, 0}, {1, 5, 1}, {2, 5, -1}, {-2, 5, -1}, {2, -5, -1}, {-2, -5, 1}, {3, 5, -1}, {5, 5, 0}, {-5, 5, 0}, {6, 5, 1}, {6, -5, 1}, {-6, 5, 1}, {-6, -5, -1}, } var x, y Int for i, test := range testCases { x.SetInt64(test.x) y.SetInt64(test.y) expected := test.result actual := Jacobi(&x, &y) if actual != expected { t.Errorf("#%d: Jacobi(%d, %d) = %d, but expected %d", i, test.x, test.y, actual, expected) } } } func TestJacobiPanic(t *testing.T) { const failureMsg = "test failure" defer func() { msg := recover() if msg == nil || msg == failureMsg { panic(msg) } t.Log(msg) }() x := NewInt(1) y := NewInt(2) // Jacobi should panic when the second argument is even. Jacobi(x, y) panic(failureMsg) } func TestIssue2607(t *testing.T) { // This code sequence used to hang. n := NewInt(10) n.Rand(rand.New(rand.NewSource(9)), n) } func TestSqrt(t *testing.T) { root := 0 r := new(Int) for i := 0; i < 10000; i++ { if (root+1)*(root+1) <= i { root++ } n := NewInt(int64(i)) r.SetInt64(-2) r.Sqrt(n) if r.Cmp(NewInt(int64(root))) != 0 { t.Errorf("Sqrt(%v) = %v, want %v", n, r, root) } } for i := 0; i < 1000; i += 10 { n, _ := new(Int).SetString("1"+strings.Repeat("0", i), 10) r := new(Int).Sqrt(n) root, _ := new(Int).SetString("1"+strings.Repeat("0", i/2), 10) if r.Cmp(root) != 0 { t.Errorf("Sqrt(1e%d) = %v, want 1e%d", i, r, i/2) } } // Test aliasing. r.SetInt64(100) r.Sqrt(r) if r.Int64() != 10 { t.Errorf("Sqrt(100) = %v, want 10 (aliased output)", r.Int64()) } } // We can't test this together with the other Exp tests above because // it requires a different receiver setup. func TestIssue22830(t *testing.T) { one := new(Int).SetInt64(1) base, _ := new(Int).SetString("84555555300000000000", 10) mod, _ := new(Int).SetString("66666670001111111111", 10) want, _ := new(Int).SetString("17888885298888888889", 10) var tests = []int64{ 0, 1, -1, } for _, n := range tests { m := NewInt(n) if got := m.Exp(base, one, mod); got.Cmp(want) != 0 { t.Errorf("(%v).Exp(%s, 1, %s) = %s, want %s", n, base, mod, got, want) } } } func BenchmarkSqrt(b *testing.B) { n, _ := new(Int).SetString("1"+strings.Repeat("0", 1001), 10) b.ResetTimer() t := new(Int) for i := 0; i < b.N; i++ { t.Sqrt(n) } } func benchmarkIntSqr(b *testing.B, nwords int) { x := new(Int) x.abs = rndNat(nwords) t := new(Int) b.ResetTimer() for i := 0; i < b.N; i++ { t.Mul(x, x) } } func BenchmarkIntSqr(b *testing.B) { for _, n := range sqrBenchSizes { if isRaceBuilder && n > 1e3 { continue } b.Run(fmt.Sprintf("%d", n), func(b *testing.B) { benchmarkIntSqr(b, n) }) } } func benchmarkDiv(b *testing.B, aSize, bSize int) { var r = rand.New(rand.NewSource(1234)) aa := randInt(r, uint(aSize)) bb := randInt(r, uint(bSize)) if aa.Cmp(bb) < 0 { aa, bb = bb, aa } x := new(Int) y := new(Int) b.ResetTimer() for i := 0; i < b.N; i++ { x.DivMod(aa, bb, y) } } func BenchmarkDiv(b *testing.B) { sizes := []int{ 10, 20, 50, 100, 200, 500, 1000, 1e4, 1e5, 1e6, 1e7, } for _, i := range sizes { j := 2 * i b.Run(fmt.Sprintf("%d/%d", j, i), func(b *testing.B) { benchmarkDiv(b, j, i) }) } } func TestFillBytes(t *testing.T) { checkResult := func(t *testing.T, buf []byte, want *Int) { t.Helper() got := new(Int).SetBytes(buf) if got.CmpAbs(want) != 0 { t.Errorf("got 0x%x, want 0x%x: %x", got, want, buf) } } panics := func(f func()) (panic bool) { defer func() { panic = recover() != nil }() f() return } for _, n := range []string{ "0", "1000", "0xffffffff", "-0xffffffff", "0xffffffffffffffff", "0x10000000000000000", "0xabababababababababababababababababababababababababa", "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", } { t.Run(n, func(t *testing.T) { t.Logf(n) x, ok := new(Int).SetString(n, 0) if !ok { panic("invalid test entry") } // Perfectly sized buffer. byteLen := (x.BitLen() + 7) / 8 buf := make([]byte, byteLen) checkResult(t, x.FillBytes(buf), x) // Way larger, checking all bytes get zeroed. buf = make([]byte, 100) for i := range buf { buf[i] = 0xff } checkResult(t, x.FillBytes(buf), x) // Too small. if byteLen > 0 { buf = make([]byte, byteLen-1) if !panics(func() { x.FillBytes(buf) }) { t.Errorf("expected panic for small buffer and value %x", x) } } }) } } func TestNewIntMinInt64(t *testing.T) { // Test for uint64 cast in NewInt. want := int64(math.MinInt64) if got := NewInt(want).Int64(); got != want { t.Fatalf("wanted %d, got %d", want, got) } } func TestNewIntAllocs(t *testing.T) { testenv.SkipIfOptimizationOff(t) for _, n := range []int64{0, 7, -7, 1 << 30, -1 << 30, 1 << 50, -1 << 50} { x := NewInt(3) got := testing.AllocsPerRun(100, func() { // NewInt should inline, and all its allocations // can happen on the stack. Passing the result of NewInt // to Add should not cause any of those allocations to escape. x.Add(x, NewInt(n)) }) if got != 0 { t.Errorf("x.Add(x, NewInt(%d)), wanted 0 allocations, got %f", n, got) } } } func TestFloat64(t *testing.T) { for _, test := range []struct { istr string f float64 acc Accuracy }{ {"-1000000000000000000000000000000000000000000000000000000", -1000000000000000078291540404596243842305360299886116864.000000, Below}, {"-9223372036854775809", math.MinInt64, Above}, {"-9223372036854775808", -9223372036854775808, Exact}, // -2^63 {"-9223372036854775807", -9223372036854775807, Below}, {"-18014398509481985", -18014398509481984.000000, Above}, {"-18014398509481984", -18014398509481984.000000, Exact}, // -2^54 {"-18014398509481983", -18014398509481984.000000, Below}, {"-9007199254740993", -9007199254740992.000000, Above}, {"-9007199254740992", -9007199254740992.000000, Exact}, // -2^53 {"-9007199254740991", -9007199254740991.000000, Exact}, {"-4503599627370497", -4503599627370497.000000, Exact}, {"-4503599627370496", -4503599627370496.000000, Exact}, // -2^52 {"-4503599627370495", -4503599627370495.000000, Exact}, {"-12345", -12345, Exact}, {"-1", -1, Exact}, {"0", 0, Exact}, {"1", 1, Exact}, {"12345", 12345, Exact}, {"0x1010000000000000", 0x1010000000000000, Exact}, // >2^53 but exact nonetheless {"9223372036854775807", 9223372036854775808, Above}, {"9223372036854775808", 9223372036854775808, Exact}, // +2^63 {"1000000000000000000000000000000000000000000000000000000", 1000000000000000078291540404596243842305360299886116864.000000, Above}, } { i, ok := new(Int).SetString(test.istr, 0) if !ok { t.Errorf("SetString(%s) failed", test.istr) continue } // Test against expectation. f, acc := i.Float64() if f != test.f || acc != test.acc { t.Errorf("%s: got %f (%s); want %f (%s)", test.istr, f, acc, test.f, test.acc) } // Cross-check the fast path against the big.Float implementation. f2, acc2 := new(Float).SetInt(i).Float64() if f != f2 || acc != acc2 { t.Errorf("%s: got %f (%s); Float.Float64 gives %f (%s)", test.istr, f, acc, f2, acc2) } } }