// 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 ( "runtime" "strings" "testing" ) var cmpTests = []struct { x, y nat r int }{ {nil, nil, 0}, {nil, nat(nil), 0}, {nat(nil), nil, 0}, {nat(nil), nat(nil), 0}, {nat{0}, nat{0}, 0}, {nat{0}, nat{1}, -1}, {nat{1}, nat{0}, 1}, {nat{1}, nat{1}, 0}, {nat{0, _M}, nat{1}, 1}, {nat{1}, nat{0, _M}, -1}, {nat{1, _M}, nat{0, _M}, 1}, {nat{0, _M}, nat{1, _M}, -1}, {nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1}, {nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1}, } func TestCmp(t *testing.T) { for i, a := range cmpTests { r := a.x.cmp(a.y) if r != a.r { t.Errorf("#%d got r = %v; want %v", i, r, a.r) } } } type funNN func(z, x, y nat) nat type argNN struct { z, x, y nat } var sumNN = []argNN{ {}, {nat{1}, nil, nat{1}}, {nat{1111111110}, nat{123456789}, nat{987654321}}, {nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}}, {nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}}, {nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}}, } var prodNN = []argNN{ {}, {nil, nil, nil}, {nil, nat{991}, nil}, {nat{991}, nat{991}, nat{1}}, {nat{991 * 991}, nat{991}, nat{991}}, {nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}}, {nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}}, {nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}}, // 3^100 * 3^28 = 3^128 { natFromString("11790184577738583171520872861412518665678211592275841109096961"), natFromString("515377520732011331036461129765621272702107522001"), natFromString("22876792454961"), }, // z = 111....1 (70000 digits) // x = 10^(99*700) + ... + 10^1400 + 10^700 + 1 // y = 111....1 (700 digits, larger than Karatsuba threshold on 32-bit and 64-bit) { natFromString(strings.Repeat("1", 70000)), natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)), natFromString(strings.Repeat("1", 700)), }, // z = 111....1 (20000 digits) // x = 10^10000 + 1 // y = 111....1 (10000 digits) { natFromString(strings.Repeat("1", 20000)), natFromString("1" + strings.Repeat("0", 9999) + "1"), natFromString(strings.Repeat("1", 10000)), }, } func natFromString(s string) nat { x, _, _, err := nat(nil).scan(strings.NewReader(s), 0, false) if err != nil { panic(err) } return x } func TestSet(t *testing.T) { for _, a := range sumNN { z := nat(nil).set(a.z) if z.cmp(a.z) != 0 { t.Errorf("got z = %v; want %v", z, a.z) } } } func testFunNN(t *testing.T, msg string, f funNN, a argNN) { z := f(nil, a.x, a.y) if z.cmp(a.z) != 0 { t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z) } } func TestFunNN(t *testing.T) { for _, a := range sumNN { arg := a testFunNN(t, "add", nat.add, arg) arg = argNN{a.z, a.y, a.x} testFunNN(t, "add symmetric", nat.add, arg) arg = argNN{a.x, a.z, a.y} testFunNN(t, "sub", nat.sub, arg) arg = argNN{a.y, a.z, a.x} testFunNN(t, "sub symmetric", nat.sub, arg) } for _, a := range prodNN { arg := a testFunNN(t, "mul", nat.mul, arg) arg = argNN{a.z, a.y, a.x} testFunNN(t, "mul symmetric", nat.mul, arg) } } var mulRangesN = []struct { a, b uint64 prod string }{ {0, 0, "0"}, {1, 1, "1"}, {1, 2, "2"}, {1, 3, "6"}, {10, 10, "10"}, {0, 100, "0"}, {0, 1e9, "0"}, {1, 0, "1"}, // empty range {100, 1, "1"}, // empty range {1, 10, "3628800"}, // 10! {1, 20, "2432902008176640000"}, // 20! {1, 100, "933262154439441526816992388562667004907159682643816214685929" + "638952175999932299156089414639761565182862536979208272237582" + "51185210916864000000000000000000000000", // 100! }, } func TestMulRangeN(t *testing.T) { for i, r := range mulRangesN { prod := nat(nil).mulRange(r.a, r.b).decimalString() if prod != r.prod { t.Errorf("#%d: got %s; want %s", i, prod, r.prod) } } } // allocBytes returns the number of bytes allocated by invoking f. func allocBytes(f func()) uint64 { var stats runtime.MemStats runtime.ReadMemStats(&stats) t := stats.TotalAlloc f() runtime.ReadMemStats(&stats) return stats.TotalAlloc - t } // TestMulUnbalanced tests that multiplying numbers of different lengths // does not cause deep recursion and in turn allocate too much memory. // Test case for issue 3807. func TestMulUnbalanced(t *testing.T) { defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1)) x := rndNat(50000) y := rndNat(40) allocSize := allocBytes(func() { nat(nil).mul(x, y) }) inputSize := uint64(len(x)+len(y)) * _S if ratio := allocSize / uint64(inputSize); ratio > 10 { t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio) } } func rndNat(n int) nat { return nat(rndV(n)).norm() } func BenchmarkMul(b *testing.B) { mulx := rndNat(1e4) muly := rndNat(1e4) b.ResetTimer() for i := 0; i < b.N; i++ { var z nat z.mul(mulx, muly) } } func TestNLZ(t *testing.T) { var x Word = _B >> 1 for i := 0; i <= _W; i++ { if int(nlz(x)) != i { t.Errorf("failed at %x: got %d want %d", x, nlz(x), i) } x >>= 1 } } type shiftTest struct { in nat shift uint out nat } var leftShiftTests = []shiftTest{ {nil, 0, nil}, {nil, 1, nil}, {natOne, 0, natOne}, {natOne, 1, natTwo}, {nat{1 << (_W - 1)}, 1, nat{0}}, {nat{1 << (_W - 1), 0}, 1, nat{0, 1}}, } func TestShiftLeft(t *testing.T) { for i, test := range leftShiftTests { var z nat z = z.shl(test.in, test.shift) for j, d := range test.out { if j >= len(z) || z[j] != d { t.Errorf("#%d: got: %v want: %v", i, z, test.out) break } } } } var rightShiftTests = []shiftTest{ {nil, 0, nil}, {nil, 1, nil}, {natOne, 0, natOne}, {natOne, 1, nil}, {natTwo, 1, natOne}, {nat{0, 1}, 1, nat{1 << (_W - 1)}}, {nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}}, } func TestShiftRight(t *testing.T) { for i, test := range rightShiftTests { var z nat z = z.shr(test.in, test.shift) for j, d := range test.out { if j >= len(z) || z[j] != d { t.Errorf("#%d: got: %v want: %v", i, z, test.out) break } } } } type modWTest struct { in string dividend string out string } var modWTests32 = []modWTest{ {"23492635982634928349238759823742", "252341", "220170"}, } var modWTests64 = []modWTest{ {"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"}, } func runModWTests(t *testing.T, tests []modWTest) { for i, test := range tests { in, _ := new(Int).SetString(test.in, 10) d, _ := new(Int).SetString(test.dividend, 10) out, _ := new(Int).SetString(test.out, 10) r := in.abs.modW(d.abs[0]) if r != out.abs[0] { t.Errorf("#%d failed: got %d want %s", i, r, out) } } } func TestModW(t *testing.T) { if _W >= 32 { runModWTests(t, modWTests32) } if _W >= 64 { runModWTests(t, modWTests64) } } func TestTrailingZeroBits(t *testing.T) { // test 0 case explicitly if n := trailingZeroBits(0); n != 0 { t.Errorf("got trailingZeroBits(0) = %d; want 0", n) } x := Word(1) for i := uint(0); i < _W; i++ { n := trailingZeroBits(x) if n != i { t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W) } x <<= 1 } // test 0 case explicitly if n := nat(nil).trailingZeroBits(); n != 0 { t.Errorf("got nat(nil).trailingZeroBits() = %d; want 0", n) } y := nat(nil).set(natOne) for i := uint(0); i <= 3*_W; i++ { n := y.trailingZeroBits() if n != i { t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.hexString(), n, i) } y = y.shl(y, 1) } } var montgomeryTests = []struct { x, y, m string k0 uint64 out32, out64 string }{ { "0xffffffffffffffffffffffffffffffffffffffffffffffffe", "0xffffffffffffffffffffffffffffffffffffffffffffffffe", "0xfffffffffffffffffffffffffffffffffffffffffffffffff", 0x0000000000000000, "0xffffffffffffffffffffffffffffffffffffffffff", "0xffffffffffffffffffffffffffffffffff", }, { "0x0000000080000000", "0x00000000ffffffff", "0x0000000010000001", 0xff0000000fffffff, "0x0000000088000000", "0x0000000007800001", }, { "0xffffffffffffffffffffffffffffffff00000000000022222223333333333444444444", "0xffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc", "0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1", 0xdecc8f1249812adf, "0x22bb05b6d95eaaeca2bb7c05e51f807bce9064b5fbad177161695e4558f9474e91cd79", "0x14beb58d230f85b6d95eaaeca2bb7c05e51f807bce9064b5fb45669afa695f228e48cd", }, { "0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444", "0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc", "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1", 0xdecc8f1249812adf, "0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715", "0x92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6", }, } func TestMontgomery(t *testing.T) { for i, test := range montgomeryTests { x := natFromString(test.x) y := natFromString(test.y) m := natFromString(test.m) var out nat if _W == 32 { out = natFromString(test.out32) } else { out = natFromString(test.out64) } k0 := Word(test.k0 & _M) // mask k0 to ensure that it fits for 32-bit systems. z := nat(nil).montgomery(x, y, m, k0, len(m)) z = z.norm() if z.cmp(out) != 0 { t.Errorf("#%d got %s want %s", i, z.decimalString(), out.decimalString()) } } } var expNNTests = []struct { x, y, m string out string }{ {"0", "0", "0", "1"}, {"0", "0", "1", "0"}, {"1", "1", "1", "0"}, {"2", "1", "1", "0"}, {"2", "2", "1", "0"}, {"10", "100000000000", "1", "0"}, {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"}, {"0x8000000000000000", "2", "6719", "4944"}, {"0x8000000000000000", "3", "6719", "5447"}, {"0x8000000000000000", "1000", "6719", "1603"}, {"0x8000000000000000", "1000000", "6719", "3199"}, { "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347", "298472983472983471903246121093472394872319615612417471234712061", "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464", "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291", }, } func TestExpNN(t *testing.T) { for i, test := range expNNTests { x := natFromString(test.x) y := natFromString(test.y) out := natFromString(test.out) var m nat if len(test.m) > 0 { m = natFromString(test.m) } z := nat(nil).expNN(x, y, m) if z.cmp(out) != 0 { t.Errorf("#%d got %s want %s", i, z.decimalString(), out.decimalString()) } } } func ExpHelper(b *testing.B, x, y Word) { var z nat for i := 0; i < b.N; i++ { z.expWW(x, y) } } func BenchmarkExp3Power0x10(b *testing.B) { ExpHelper(b, 3, 0x10) } func BenchmarkExp3Power0x40(b *testing.B) { ExpHelper(b, 3, 0x40) } func BenchmarkExp3Power0x100(b *testing.B) { ExpHelper(b, 3, 0x100) } func BenchmarkExp3Power0x400(b *testing.B) { ExpHelper(b, 3, 0x400) } func BenchmarkExp3Power0x1000(b *testing.B) { ExpHelper(b, 3, 0x1000) } func BenchmarkExp3Power0x4000(b *testing.B) { ExpHelper(b, 3, 0x4000) } func BenchmarkExp3Power0x10000(b *testing.B) { ExpHelper(b, 3, 0x10000) } func BenchmarkExp3Power0x40000(b *testing.B) { ExpHelper(b, 3, 0x40000) } func BenchmarkExp3Power0x100000(b *testing.B) { ExpHelper(b, 3, 0x100000) } func BenchmarkExp3Power0x400000(b *testing.B) { ExpHelper(b, 3, 0x400000) } func fibo(n int) nat { switch n { case 0: return nil case 1: return nat{1} } f0 := fibo(0) f1 := fibo(1) var f2 nat for i := 1; i < n; i++ { f2 = f2.add(f0, f1) f0, f1, f2 = f1, f2, f0 } return f1 } var fiboNums = []string{ "0", "55", "6765", "832040", "102334155", "12586269025", "1548008755920", "190392490709135", "23416728348467685", "2880067194370816120", "354224848179261915075", } func TestFibo(t *testing.T) { for i, want := range fiboNums { n := i * 10 got := fibo(n).decimalString() if got != want { t.Errorf("fibo(%d) failed: got %s want %s", n, got, want) } } } func BenchmarkFibo(b *testing.B) { for i := 0; i < b.N; i++ { fibo(1e0) fibo(1e1) fibo(1e2) fibo(1e3) fibo(1e4) fibo(1e5) } } var bitTests = []struct { x string i uint want uint }{ {"0", 0, 0}, {"0", 1, 0}, {"0", 1000, 0}, {"0x1", 0, 1}, {"0x10", 0, 0}, {"0x10", 3, 0}, {"0x10", 4, 1}, {"0x10", 5, 0}, {"0x8000000000000000", 62, 0}, {"0x8000000000000000", 63, 1}, {"0x8000000000000000", 64, 0}, {"0x3" + strings.Repeat("0", 32), 127, 0}, {"0x3" + strings.Repeat("0", 32), 128, 1}, {"0x3" + strings.Repeat("0", 32), 129, 1}, {"0x3" + strings.Repeat("0", 32), 130, 0}, } func TestBit(t *testing.T) { for i, test := range bitTests { x := natFromString(test.x) if got := x.bit(test.i); got != test.want { t.Errorf("#%d: %s.bit(%d) = %v; want %v", i, test.x, test.i, got, test.want) } } } var stickyTests = []struct { x string i uint want uint }{ {"0", 0, 0}, {"0", 1, 0}, {"0", 1000, 0}, {"0x1", 0, 0}, {"0x1", 1, 1}, {"0x1350", 0, 0}, {"0x1350", 4, 0}, {"0x1350", 5, 1}, {"0x8000000000000000", 63, 0}, {"0x8000000000000000", 64, 1}, {"0x1" + strings.Repeat("0", 100), 400, 0}, {"0x1" + strings.Repeat("0", 100), 401, 1}, } func TestSticky(t *testing.T) { for i, test := range stickyTests { x := natFromString(test.x) if got := x.sticky(test.i); got != test.want { t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i, got, test.want) } if test.want == 1 { // all subsequent i's should also return 1 for d := uint(1); d <= 3; d++ { if got := x.sticky(test.i + d); got != 1 { t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i+d, got, 1) } } } } }