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Source file src/math/big/nat_test.go

Documentation: math/big

  // 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 (
  	"fmt"
  	"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 := string(nat(nil).mulRange(r.a, r.b).utoa(10))
  		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)
  	}
  }
  
  var montgomeryTests = []struct {
  	x, y, m      string
  	k0           uint64
  	out32, out64 string
  }{
  	{
  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
  		"0xfffffffffffffffffffffffffffffffffffffffffffffffff",
  		1,
  		"0x1000000000000000000000000000000000000000000",
  		"0x10000000000000000000000000000000000",
  	},
  	{
  		"0x000000000ffffff5",
  		"0x000000000ffffff0",
  		"0x0000000010000001",
  		0xff0000000fffffff,
  		"0x000000000bfffff4",
  		"0x0000000003400001",
  	},
  	{
  		"0x0000000080000000",
  		"0x00000000ffffffff",
  		"0x1000000000000001",
  		0xfffffffffffffff,
  		"0x0800000008000001",
  		"0x0800000008000001",
  	},
  	{
  		"0x0000000080000000",
  		"0x0000000080000000",
  		"0xffffffff00000001",
  		0xfffffffeffffffff,
  		"0xbfffffff40000001",
  		"0xbfffffff40000001",
  	},
  	{
  		"0x0000000080000000",
  		"0x0000000080000000",
  		"0x00ffffff00000001",
  		0xfffffeffffffff,
  		"0xbfffff40000001",
  		"0xbfffff40000001",
  	},
  	{
  		"0x0000000080000000",
  		"0x0000000080000000",
  		"0x0000ffff00000001",
  		0xfffeffffffff,
  		"0xbfff40000001",
  		"0xbfff40000001",
  	},
  	{
  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
  		"0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
  		0xdecc8f1249812adf,
  		"0x04eb0e11d72329dc0915f86784820fc403275bf2f6620a20e0dd344c5cd0875e50deb5",
  		"0x0d7144739a7d8e11d72329dc0915f86784820fc403275bf2f61ed96f35dd34dbb3d6a0",
  	},
  	{
  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444",
  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc",
  		"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
  		0xdecc8f1249812adf,
  		"0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715",
  		"0x92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6",
  	},
  }
  
  func TestMontgomery(t *testing.T) {
  	one := NewInt(1)
  	_B := new(Int).Lsh(one, _W)
  	for i, test := range montgomeryTests {
  		x := natFromString(test.x)
  		y := natFromString(test.y)
  		m := natFromString(test.m)
  		for len(x) < len(m) {
  			x = append(x, 0)
  		}
  		for len(y) < len(m) {
  			y = append(y, 0)
  		}
  
  		if x.cmp(m) > 0 {
  			_, r := nat(nil).div(nil, x, m)
  			t.Errorf("#%d: x > m (0x%s > 0x%s; use 0x%s)", i, x.utoa(16), m.utoa(16), r.utoa(16))
  		}
  		if y.cmp(m) > 0 {
  			_, r := nat(nil).div(nil, x, m)
  			t.Errorf("#%d: y > m (0x%s > 0x%s; use 0x%s)", i, y.utoa(16), m.utoa(16), r.utoa(16))
  		}
  
  		var out nat
  		if _W == 32 {
  			out = natFromString(test.out32)
  		} else {
  			out = natFromString(test.out64)
  		}
  
  		// t.Logf("#%d: len=%d\n", i, len(m))
  
  		// check output in table
  		xi := &Int{abs: x}
  		yi := &Int{abs: y}
  		mi := &Int{abs: m}
  		p := new(Int).Mod(new(Int).Mul(xi, new(Int).Mul(yi, new(Int).ModInverse(new(Int).Lsh(one, uint(len(m))*_W), mi))), mi)
  		if out.cmp(p.abs.norm()) != 0 {
  			t.Errorf("#%d: out in table=0x%s, computed=0x%s", i, out.utoa(16), p.abs.norm().utoa(16))
  		}
  
  		// check k0 in table
  		k := new(Int).Mod(&Int{abs: m}, _B)
  		k = new(Int).Sub(_B, k)
  		k = new(Int).Mod(k, _B)
  		k0 := Word(new(Int).ModInverse(k, _B).Uint64())
  		if k0 != Word(test.k0) {
  			t.Errorf("#%d: k0 in table=%#x, computed=%#x\n", i, test.k0, k0)
  		}
  
  		// check montgomery with correct k0 produces correct output
  		z := nat(nil).montgomery(x, y, m, k0, len(m))
  		z = z.norm()
  		if z.cmp(out) != 0 {
  			t.Errorf("#%d: got 0x%s want 0x%s", i, z.utoa(16), out.utoa(16))
  		}
  	}
  }
  
  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",
  	},
  	{
  		"11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
  		"426343618817810911523",
  		"444747819283133684179",
  		"42",
  	},
  }
  
  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.utoa(10), out.utoa(10))
  		}
  	}
  }
  
  func BenchmarkExp3Power(b *testing.B) {
  	const x = 3
  	for _, y := range []Word{
  		0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000,
  	} {
  		b.Run(fmt.Sprintf("%#x", y), func(b *testing.B) {
  			var z nat
  			for i := 0; i < b.N; i++ {
  				z.expWW(x, y)
  			}
  		})
  	}
  }
  
  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 := string(fibo(n).utoa(10))
  		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)
  				}
  			}
  		}
  	}
  }
  

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