Source file src/math/big/nat_test.go

Documentation: math/big

     1  // Copyright 2009 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package big
     6  
     7  import (
     8  	"fmt"
     9  	"runtime"
    10  	"strings"
    11  	"testing"
    12  )
    13  
    14  var cmpTests = []struct {
    15  	x, y nat
    16  	r    int
    17  }{
    18  	{nil, nil, 0},
    19  	{nil, nat(nil), 0},
    20  	{nat(nil), nil, 0},
    21  	{nat(nil), nat(nil), 0},
    22  	{nat{0}, nat{0}, 0},
    23  	{nat{0}, nat{1}, -1},
    24  	{nat{1}, nat{0}, 1},
    25  	{nat{1}, nat{1}, 0},
    26  	{nat{0, _M}, nat{1}, 1},
    27  	{nat{1}, nat{0, _M}, -1},
    28  	{nat{1, _M}, nat{0, _M}, 1},
    29  	{nat{0, _M}, nat{1, _M}, -1},
    30  	{nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
    31  	{nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
    32  }
    33  
    34  func TestCmp(t *testing.T) {
    35  	for i, a := range cmpTests {
    36  		r := a.x.cmp(a.y)
    37  		if r != a.r {
    38  			t.Errorf("#%d got r = %v; want %v", i, r, a.r)
    39  		}
    40  	}
    41  }
    42  
    43  type funNN func(z, x, y nat) nat
    44  type argNN struct {
    45  	z, x, y nat
    46  }
    47  
    48  var sumNN = []argNN{
    49  	{},
    50  	{nat{1}, nil, nat{1}},
    51  	{nat{1111111110}, nat{123456789}, nat{987654321}},
    52  	{nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
    53  	{nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
    54  	{nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
    55  }
    56  
    57  var prodNN = []argNN{
    58  	{},
    59  	{nil, nil, nil},
    60  	{nil, nat{991}, nil},
    61  	{nat{991}, nat{991}, nat{1}},
    62  	{nat{991 * 991}, nat{991}, nat{991}},
    63  	{nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
    64  	{nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
    65  	{nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
    66  	// 3^100 * 3^28 = 3^128
    67  	{
    68  		natFromString("11790184577738583171520872861412518665678211592275841109096961"),
    69  		natFromString("515377520732011331036461129765621272702107522001"),
    70  		natFromString("22876792454961"),
    71  	},
    72  	// z = 111....1 (70000 digits)
    73  	// x = 10^(99*700) + ... + 10^1400 + 10^700 + 1
    74  	// y = 111....1 (700 digits, larger than Karatsuba threshold on 32-bit and 64-bit)
    75  	{
    76  		natFromString(strings.Repeat("1", 70000)),
    77  		natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)),
    78  		natFromString(strings.Repeat("1", 700)),
    79  	},
    80  	// z = 111....1 (20000 digits)
    81  	// x = 10^10000 + 1
    82  	// y = 111....1 (10000 digits)
    83  	{
    84  		natFromString(strings.Repeat("1", 20000)),
    85  		natFromString("1" + strings.Repeat("0", 9999) + "1"),
    86  		natFromString(strings.Repeat("1", 10000)),
    87  	},
    88  }
    89  
    90  func natFromString(s string) nat {
    91  	x, _, _, err := nat(nil).scan(strings.NewReader(s), 0, false)
    92  	if err != nil {
    93  		panic(err)
    94  	}
    95  	return x
    96  }
    97  
    98  func TestSet(t *testing.T) {
    99  	for _, a := range sumNN {
   100  		z := nat(nil).set(a.z)
   101  		if z.cmp(a.z) != 0 {
   102  			t.Errorf("got z = %v; want %v", z, a.z)
   103  		}
   104  	}
   105  }
   106  
   107  func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
   108  	z := f(nil, a.x, a.y)
   109  	if z.cmp(a.z) != 0 {
   110  		t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
   111  	}
   112  }
   113  
   114  func TestFunNN(t *testing.T) {
   115  	for _, a := range sumNN {
   116  		arg := a
   117  		testFunNN(t, "add", nat.add, arg)
   118  
   119  		arg = argNN{a.z, a.y, a.x}
   120  		testFunNN(t, "add symmetric", nat.add, arg)
   121  
   122  		arg = argNN{a.x, a.z, a.y}
   123  		testFunNN(t, "sub", nat.sub, arg)
   124  
   125  		arg = argNN{a.y, a.z, a.x}
   126  		testFunNN(t, "sub symmetric", nat.sub, arg)
   127  	}
   128  
   129  	for _, a := range prodNN {
   130  		arg := a
   131  		testFunNN(t, "mul", nat.mul, arg)
   132  
   133  		arg = argNN{a.z, a.y, a.x}
   134  		testFunNN(t, "mul symmetric", nat.mul, arg)
   135  	}
   136  }
   137  
   138  var mulRangesN = []struct {
   139  	a, b uint64
   140  	prod string
   141  }{
   142  	{0, 0, "0"},
   143  	{1, 1, "1"},
   144  	{1, 2, "2"},
   145  	{1, 3, "6"},
   146  	{10, 10, "10"},
   147  	{0, 100, "0"},
   148  	{0, 1e9, "0"},
   149  	{1, 0, "1"},                    // empty range
   150  	{100, 1, "1"},                  // empty range
   151  	{1, 10, "3628800"},             // 10!
   152  	{1, 20, "2432902008176640000"}, // 20!
   153  	{1, 100,
   154  		"933262154439441526816992388562667004907159682643816214685929" +
   155  			"638952175999932299156089414639761565182862536979208272237582" +
   156  			"51185210916864000000000000000000000000", // 100!
   157  	},
   158  }
   159  
   160  func TestMulRangeN(t *testing.T) {
   161  	for i, r := range mulRangesN {
   162  		prod := string(nat(nil).mulRange(r.a, r.b).utoa(10))
   163  		if prod != r.prod {
   164  			t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
   165  		}
   166  	}
   167  }
   168  
   169  // allocBytes returns the number of bytes allocated by invoking f.
   170  func allocBytes(f func()) uint64 {
   171  	var stats runtime.MemStats
   172  	runtime.ReadMemStats(&stats)
   173  	t := stats.TotalAlloc
   174  	f()
   175  	runtime.ReadMemStats(&stats)
   176  	return stats.TotalAlloc - t
   177  }
   178  
   179  // TestMulUnbalanced tests that multiplying numbers of different lengths
   180  // does not cause deep recursion and in turn allocate too much memory.
   181  // Test case for issue 3807.
   182  func TestMulUnbalanced(t *testing.T) {
   183  	defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1))
   184  	x := rndNat(50000)
   185  	y := rndNat(40)
   186  	allocSize := allocBytes(func() {
   187  		nat(nil).mul(x, y)
   188  	})
   189  	inputSize := uint64(len(x)+len(y)) * _S
   190  	if ratio := allocSize / uint64(inputSize); ratio > 10 {
   191  		t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio)
   192  	}
   193  }
   194  
   195  // rndNat returns a random nat value >= 0 of (usually) n words in length.
   196  // In extremely unlikely cases it may be smaller than n words if the top-
   197  // most words are 0.
   198  func rndNat(n int) nat {
   199  	return nat(rndV(n)).norm()
   200  }
   201  
   202  // rndNat1 is like rndNat but the result is guaranteed to be > 0.
   203  func rndNat1(n int) nat {
   204  	x := nat(rndV(n)).norm()
   205  	if len(x) == 0 {
   206  		x.setWord(1)
   207  	}
   208  	return x
   209  }
   210  
   211  func BenchmarkMul(b *testing.B) {
   212  	mulx := rndNat(1e4)
   213  	muly := rndNat(1e4)
   214  	b.ResetTimer()
   215  	for i := 0; i < b.N; i++ {
   216  		var z nat
   217  		z.mul(mulx, muly)
   218  	}
   219  }
   220  
   221  func benchmarkNatMul(b *testing.B, nwords int) {
   222  	x := rndNat(nwords)
   223  	y := rndNat(nwords)
   224  	var z nat
   225  	b.ResetTimer()
   226  	for i := 0; i < b.N; i++ {
   227  		z.mul(x, y)
   228  	}
   229  }
   230  
   231  var mulBenchSizes = []int{10, 100, 1000, 10000, 100000}
   232  
   233  func BenchmarkNatMul(b *testing.B) {
   234  	for _, n := range mulBenchSizes {
   235  		if isRaceBuilder && n > 1e3 {
   236  			continue
   237  		}
   238  		b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
   239  			benchmarkNatMul(b, n)
   240  		})
   241  	}
   242  }
   243  
   244  func TestNLZ(t *testing.T) {
   245  	var x Word = _B >> 1
   246  	for i := 0; i <= _W; i++ {
   247  		if int(nlz(x)) != i {
   248  			t.Errorf("failed at %x: got %d want %d", x, nlz(x), i)
   249  		}
   250  		x >>= 1
   251  	}
   252  }
   253  
   254  type shiftTest struct {
   255  	in    nat
   256  	shift uint
   257  	out   nat
   258  }
   259  
   260  var leftShiftTests = []shiftTest{
   261  	{nil, 0, nil},
   262  	{nil, 1, nil},
   263  	{natOne, 0, natOne},
   264  	{natOne, 1, natTwo},
   265  	{nat{1 << (_W - 1)}, 1, nat{0}},
   266  	{nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
   267  }
   268  
   269  func TestShiftLeft(t *testing.T) {
   270  	for i, test := range leftShiftTests {
   271  		var z nat
   272  		z = z.shl(test.in, test.shift)
   273  		for j, d := range test.out {
   274  			if j >= len(z) || z[j] != d {
   275  				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
   276  				break
   277  			}
   278  		}
   279  	}
   280  }
   281  
   282  var rightShiftTests = []shiftTest{
   283  	{nil, 0, nil},
   284  	{nil, 1, nil},
   285  	{natOne, 0, natOne},
   286  	{natOne, 1, nil},
   287  	{natTwo, 1, natOne},
   288  	{nat{0, 1}, 1, nat{1 << (_W - 1)}},
   289  	{nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
   290  }
   291  
   292  func TestShiftRight(t *testing.T) {
   293  	for i, test := range rightShiftTests {
   294  		var z nat
   295  		z = z.shr(test.in, test.shift)
   296  		for j, d := range test.out {
   297  			if j >= len(z) || z[j] != d {
   298  				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
   299  				break
   300  			}
   301  		}
   302  	}
   303  }
   304  
   305  func BenchmarkZeroShifts(b *testing.B) {
   306  	x := rndNat(800)
   307  
   308  	b.Run("Shl", func(b *testing.B) {
   309  		for i := 0; i < b.N; i++ {
   310  			var z nat
   311  			z.shl(x, 0)
   312  		}
   313  	})
   314  	b.Run("ShlSame", func(b *testing.B) {
   315  		for i := 0; i < b.N; i++ {
   316  			x.shl(x, 0)
   317  		}
   318  	})
   319  
   320  	b.Run("Shr", func(b *testing.B) {
   321  		for i := 0; i < b.N; i++ {
   322  			var z nat
   323  			z.shr(x, 0)
   324  		}
   325  	})
   326  	b.Run("ShrSame", func(b *testing.B) {
   327  		for i := 0; i < b.N; i++ {
   328  			x.shr(x, 0)
   329  		}
   330  	})
   331  }
   332  
   333  type modWTest struct {
   334  	in       string
   335  	dividend string
   336  	out      string
   337  }
   338  
   339  var modWTests32 = []modWTest{
   340  	{"23492635982634928349238759823742", "252341", "220170"},
   341  }
   342  
   343  var modWTests64 = []modWTest{
   344  	{"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
   345  }
   346  
   347  func runModWTests(t *testing.T, tests []modWTest) {
   348  	for i, test := range tests {
   349  		in, _ := new(Int).SetString(test.in, 10)
   350  		d, _ := new(Int).SetString(test.dividend, 10)
   351  		out, _ := new(Int).SetString(test.out, 10)
   352  
   353  		r := in.abs.modW(d.abs[0])
   354  		if r != out.abs[0] {
   355  			t.Errorf("#%d failed: got %d want %s", i, r, out)
   356  		}
   357  	}
   358  }
   359  
   360  func TestModW(t *testing.T) {
   361  	if _W >= 32 {
   362  		runModWTests(t, modWTests32)
   363  	}
   364  	if _W >= 64 {
   365  		runModWTests(t, modWTests64)
   366  	}
   367  }
   368  
   369  var montgomeryTests = []struct {
   370  	x, y, m      string
   371  	k0           uint64
   372  	out32, out64 string
   373  }{
   374  	{
   375  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
   376  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
   377  		"0xfffffffffffffffffffffffffffffffffffffffffffffffff",
   378  		1,
   379  		"0x1000000000000000000000000000000000000000000",
   380  		"0x10000000000000000000000000000000000",
   381  	},
   382  	{
   383  		"0x000000000ffffff5",
   384  		"0x000000000ffffff0",
   385  		"0x0000000010000001",
   386  		0xff0000000fffffff,
   387  		"0x000000000bfffff4",
   388  		"0x0000000003400001",
   389  	},
   390  	{
   391  		"0x0000000080000000",
   392  		"0x00000000ffffffff",
   393  		"0x1000000000000001",
   394  		0xfffffffffffffff,
   395  		"0x0800000008000001",
   396  		"0x0800000008000001",
   397  	},
   398  	{
   399  		"0x0000000080000000",
   400  		"0x0000000080000000",
   401  		"0xffffffff00000001",
   402  		0xfffffffeffffffff,
   403  		"0xbfffffff40000001",
   404  		"0xbfffffff40000001",
   405  	},
   406  	{
   407  		"0x0000000080000000",
   408  		"0x0000000080000000",
   409  		"0x00ffffff00000001",
   410  		0xfffffeffffffff,
   411  		"0xbfffff40000001",
   412  		"0xbfffff40000001",
   413  	},
   414  	{
   415  		"0x0000000080000000",
   416  		"0x0000000080000000",
   417  		"0x0000ffff00000001",
   418  		0xfffeffffffff,
   419  		"0xbfff40000001",
   420  		"0xbfff40000001",
   421  	},
   422  	{
   423  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
   424  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
   425  		"0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
   426  		0xdecc8f1249812adf,
   427  		"0x04eb0e11d72329dc0915f86784820fc403275bf2f6620a20e0dd344c5cd0875e50deb5",
   428  		"0x0d7144739a7d8e11d72329dc0915f86784820fc403275bf2f61ed96f35dd34dbb3d6a0",
   429  	},
   430  	{
   431  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444",
   432  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc",
   433  		"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
   434  		0xdecc8f1249812adf,
   435  		"0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715",
   436  		"0x92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6",
   437  	},
   438  }
   439  
   440  func TestMontgomery(t *testing.T) {
   441  	one := NewInt(1)
   442  	_B := new(Int).Lsh(one, _W)
   443  	for i, test := range montgomeryTests {
   444  		x := natFromString(test.x)
   445  		y := natFromString(test.y)
   446  		m := natFromString(test.m)
   447  		for len(x) < len(m) {
   448  			x = append(x, 0)
   449  		}
   450  		for len(y) < len(m) {
   451  			y = append(y, 0)
   452  		}
   453  
   454  		if x.cmp(m) > 0 {
   455  			_, r := nat(nil).div(nil, x, m)
   456  			t.Errorf("#%d: x > m (0x%s > 0x%s; use 0x%s)", i, x.utoa(16), m.utoa(16), r.utoa(16))
   457  		}
   458  		if y.cmp(m) > 0 {
   459  			_, r := nat(nil).div(nil, x, m)
   460  			t.Errorf("#%d: y > m (0x%s > 0x%s; use 0x%s)", i, y.utoa(16), m.utoa(16), r.utoa(16))
   461  		}
   462  
   463  		var out nat
   464  		if _W == 32 {
   465  			out = natFromString(test.out32)
   466  		} else {
   467  			out = natFromString(test.out64)
   468  		}
   469  
   470  		// t.Logf("#%d: len=%d\n", i, len(m))
   471  
   472  		// check output in table
   473  		xi := &Int{abs: x}
   474  		yi := &Int{abs: y}
   475  		mi := &Int{abs: m}
   476  		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)
   477  		if out.cmp(p.abs.norm()) != 0 {
   478  			t.Errorf("#%d: out in table=0x%s, computed=0x%s", i, out.utoa(16), p.abs.norm().utoa(16))
   479  		}
   480  
   481  		// check k0 in table
   482  		k := new(Int).Mod(&Int{abs: m}, _B)
   483  		k = new(Int).Sub(_B, k)
   484  		k = new(Int).Mod(k, _B)
   485  		k0 := Word(new(Int).ModInverse(k, _B).Uint64())
   486  		if k0 != Word(test.k0) {
   487  			t.Errorf("#%d: k0 in table=%#x, computed=%#x\n", i, test.k0, k0)
   488  		}
   489  
   490  		// check montgomery with correct k0 produces correct output
   491  		z := nat(nil).montgomery(x, y, m, k0, len(m))
   492  		z = z.norm()
   493  		if z.cmp(out) != 0 {
   494  			t.Errorf("#%d: got 0x%s want 0x%s", i, z.utoa(16), out.utoa(16))
   495  		}
   496  	}
   497  }
   498  
   499  var expNNTests = []struct {
   500  	x, y, m string
   501  	out     string
   502  }{
   503  	{"0", "0", "0", "1"},
   504  	{"0", "0", "1", "0"},
   505  	{"1", "1", "1", "0"},
   506  	{"2", "1", "1", "0"},
   507  	{"2", "2", "1", "0"},
   508  	{"10", "100000000000", "1", "0"},
   509  	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
   510  	{"0x8000000000000000", "2", "6719", "4944"},
   511  	{"0x8000000000000000", "3", "6719", "5447"},
   512  	{"0x8000000000000000", "1000", "6719", "1603"},
   513  	{"0x8000000000000000", "1000000", "6719", "3199"},
   514  	{
   515  		"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
   516  		"298472983472983471903246121093472394872319615612417471234712061",
   517  		"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
   518  		"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
   519  	},
   520  	{
   521  		"11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
   522  		"426343618817810911523",
   523  		"444747819283133684179",
   524  		"42",
   525  	},
   526  }
   527  
   528  func TestExpNN(t *testing.T) {
   529  	for i, test := range expNNTests {
   530  		x := natFromString(test.x)
   531  		y := natFromString(test.y)
   532  		out := natFromString(test.out)
   533  
   534  		var m nat
   535  		if len(test.m) > 0 {
   536  			m = natFromString(test.m)
   537  		}
   538  
   539  		z := nat(nil).expNN(x, y, m)
   540  		if z.cmp(out) != 0 {
   541  			t.Errorf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
   542  		}
   543  	}
   544  }
   545  
   546  func BenchmarkExp3Power(b *testing.B) {
   547  	const x = 3
   548  	for _, y := range []Word{
   549  		0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000,
   550  	} {
   551  		b.Run(fmt.Sprintf("%#x", y), func(b *testing.B) {
   552  			var z nat
   553  			for i := 0; i < b.N; i++ {
   554  				z.expWW(x, y)
   555  			}
   556  		})
   557  	}
   558  }
   559  
   560  func fibo(n int) nat {
   561  	switch n {
   562  	case 0:
   563  		return nil
   564  	case 1:
   565  		return nat{1}
   566  	}
   567  	f0 := fibo(0)
   568  	f1 := fibo(1)
   569  	var f2 nat
   570  	for i := 1; i < n; i++ {
   571  		f2 = f2.add(f0, f1)
   572  		f0, f1, f2 = f1, f2, f0
   573  	}
   574  	return f1
   575  }
   576  
   577  var fiboNums = []string{
   578  	"0",
   579  	"55",
   580  	"6765",
   581  	"832040",
   582  	"102334155",
   583  	"12586269025",
   584  	"1548008755920",
   585  	"190392490709135",
   586  	"23416728348467685",
   587  	"2880067194370816120",
   588  	"354224848179261915075",
   589  }
   590  
   591  func TestFibo(t *testing.T) {
   592  	for i, want := range fiboNums {
   593  		n := i * 10
   594  		got := string(fibo(n).utoa(10))
   595  		if got != want {
   596  			t.Errorf("fibo(%d) failed: got %s want %s", n, got, want)
   597  		}
   598  	}
   599  }
   600  
   601  func BenchmarkFibo(b *testing.B) {
   602  	for i := 0; i < b.N; i++ {
   603  		fibo(1e0)
   604  		fibo(1e1)
   605  		fibo(1e2)
   606  		fibo(1e3)
   607  		fibo(1e4)
   608  		fibo(1e5)
   609  	}
   610  }
   611  
   612  var bitTests = []struct {
   613  	x    string
   614  	i    uint
   615  	want uint
   616  }{
   617  	{"0", 0, 0},
   618  	{"0", 1, 0},
   619  	{"0", 1000, 0},
   620  
   621  	{"0x1", 0, 1},
   622  	{"0x10", 0, 0},
   623  	{"0x10", 3, 0},
   624  	{"0x10", 4, 1},
   625  	{"0x10", 5, 0},
   626  
   627  	{"0x8000000000000000", 62, 0},
   628  	{"0x8000000000000000", 63, 1},
   629  	{"0x8000000000000000", 64, 0},
   630  
   631  	{"0x3" + strings.Repeat("0", 32), 127, 0},
   632  	{"0x3" + strings.Repeat("0", 32), 128, 1},
   633  	{"0x3" + strings.Repeat("0", 32), 129, 1},
   634  	{"0x3" + strings.Repeat("0", 32), 130, 0},
   635  }
   636  
   637  func TestBit(t *testing.T) {
   638  	for i, test := range bitTests {
   639  		x := natFromString(test.x)
   640  		if got := x.bit(test.i); got != test.want {
   641  			t.Errorf("#%d: %s.bit(%d) = %v; want %v", i, test.x, test.i, got, test.want)
   642  		}
   643  	}
   644  }
   645  
   646  var stickyTests = []struct {
   647  	x    string
   648  	i    uint
   649  	want uint
   650  }{
   651  	{"0", 0, 0},
   652  	{"0", 1, 0},
   653  	{"0", 1000, 0},
   654  
   655  	{"0x1", 0, 0},
   656  	{"0x1", 1, 1},
   657  
   658  	{"0x1350", 0, 0},
   659  	{"0x1350", 4, 0},
   660  	{"0x1350", 5, 1},
   661  
   662  	{"0x8000000000000000", 63, 0},
   663  	{"0x8000000000000000", 64, 1},
   664  
   665  	{"0x1" + strings.Repeat("0", 100), 400, 0},
   666  	{"0x1" + strings.Repeat("0", 100), 401, 1},
   667  }
   668  
   669  func TestSticky(t *testing.T) {
   670  	for i, test := range stickyTests {
   671  		x := natFromString(test.x)
   672  		if got := x.sticky(test.i); got != test.want {
   673  			t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i, got, test.want)
   674  		}
   675  		if test.want == 1 {
   676  			// all subsequent i's should also return 1
   677  			for d := uint(1); d <= 3; d++ {
   678  				if got := x.sticky(test.i + d); got != 1 {
   679  					t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i+d, got, 1)
   680  				}
   681  			}
   682  		}
   683  	}
   684  }
   685  
   686  func testSqr(t *testing.T, x nat) {
   687  	got := make(nat, 2*len(x))
   688  	want := make(nat, 2*len(x))
   689  	got = got.sqr(x)
   690  	want = want.mul(x, x)
   691  	if got.cmp(want) != 0 {
   692  		t.Errorf("basicSqr(%v), got %v, want %v", x, got, want)
   693  	}
   694  }
   695  
   696  func TestSqr(t *testing.T) {
   697  	for _, a := range prodNN {
   698  		if a.x != nil {
   699  			testSqr(t, a.x)
   700  		}
   701  		if a.y != nil {
   702  			testSqr(t, a.y)
   703  		}
   704  		if a.z != nil {
   705  			testSqr(t, a.z)
   706  		}
   707  	}
   708  }
   709  
   710  func benchmarkNatSqr(b *testing.B, nwords int) {
   711  	x := rndNat(nwords)
   712  	var z nat
   713  	b.ResetTimer()
   714  	for i := 0; i < b.N; i++ {
   715  		z.sqr(x)
   716  	}
   717  }
   718  
   719  var sqrBenchSizes = []int{
   720  	1, 2, 3, 5, 8, 10, 20, 30, 50, 80,
   721  	100, 200, 300, 500, 800,
   722  	1000, 10000, 100000,
   723  }
   724  
   725  func BenchmarkNatSqr(b *testing.B) {
   726  	for _, n := range sqrBenchSizes {
   727  		if isRaceBuilder && n > 1e3 {
   728  			continue
   729  		}
   730  		b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
   731  			benchmarkNatSqr(b, n)
   732  		})
   733  	}
   734  }
   735  
   736  func BenchmarkNatSetBytes(b *testing.B) {
   737  	const maxLength = 128
   738  	lengths := []int{
   739  		// No remainder:
   740  		8, 24, maxLength,
   741  		// With remainder:
   742  		7, 23, maxLength - 1,
   743  	}
   744  	n := make(nat, maxLength/_W) // ensure n doesn't need to grow during the test
   745  	buf := make([]byte, maxLength)
   746  	for _, l := range lengths {
   747  		b.Run(fmt.Sprint(l), func(b *testing.B) {
   748  			for i := 0; i < b.N; i++ {
   749  				n.setBytes(buf[:l])
   750  			}
   751  		})
   752  	}
   753  }
   754  
   755  func TestNatDiv(t *testing.T) {
   756  	sizes := []int{
   757  		1, 2, 5, 8, 15, 25, 40, 65, 100,
   758  		200, 500, 800, 1500, 2500, 4000, 6500, 10000,
   759  	}
   760  	for _, i := range sizes {
   761  		for _, j := range sizes {
   762  			a := rndNat1(i)
   763  			b := rndNat1(j)
   764  			// the test requires b >= 2
   765  			if len(b) == 1 && b[0] == 1 {
   766  				b[0] = 2
   767  			}
   768  			// choose a remainder c < b
   769  			c := rndNat1(len(b))
   770  			if len(c) == len(b) && c[len(c)-1] >= b[len(b)-1] {
   771  				c[len(c)-1] = 0
   772  				c = c.norm()
   773  			}
   774  			// compute x = a*b+c
   775  			x := nat(nil).mul(a, b)
   776  			x = x.add(x, c)
   777  
   778  			var q, r nat
   779  			q, r = q.div(r, x, b)
   780  			if q.cmp(a) != 0 {
   781  				t.Fatalf("wrong quotient: got %s; want %s for %s/%s", q.utoa(10), a.utoa(10), x.utoa(10), b.utoa(10))
   782  			}
   783  			if r.cmp(c) != 0 {
   784  				t.Fatalf("wrong remainder: got %s; want %s for %s/%s", r.utoa(10), c.utoa(10), x.utoa(10), b.utoa(10))
   785  			}
   786  		}
   787  	}
   788  }
   789  
   790  // TestIssue37499 triggers the edge case of divBasic where
   791  // the inaccurate estimate of the first word's quotient
   792  // happens at the very beginning of the loop.
   793  func TestIssue37499(t *testing.T) {
   794  	// Choose u and v such that v is slightly larger than u >> N.
   795  	// This tricks divBasic into choosing 1 as the first word
   796  	// of the quotient. This works in both 32-bit and 64-bit settings.
   797  	u := natFromString("0x2b6c385a05be027f5c22005b63c42a1165b79ff510e1706b39f8489c1d28e57bb5ba4ef9fd9387a3e344402c0a453381")
   798  	v := natFromString("0x2b6c385a05be027f5c22005b63c42a1165b79ff510e1706c")
   799  
   800  	q := nat(nil).make(8)
   801  	q.divBasic(u, v)
   802  	q = q.norm()
   803  	if s := string(q.utoa(16)); s != "fffffffffffffffffffffffffffffffffffffffffffffffb" {
   804  		t.Fatalf("incorrect quotient: %s", s)
   805  	}
   806  }
   807  
   808  // TestIssue42552 triggers an edge case of recursive division
   809  // where the first division loop is never entered, and correcting
   810  // the remainder takes exactly two iterations in the final loop.
   811  func TestIssue42552(t *testing.T) {
   812  	u := natFromString("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")
   813  	v := natFromString("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")
   814  	q := nat(nil).make(16)
   815  	q.div(q, u, v)
   816  }
   817  

View as plain text