rand_test.go

     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 rand_test
     6  
     7  import (
     8  	"errors"
     9  	"fmt"
    10  	"internal/testenv"
    11  	"math"
    12  	. "math/rand/v2"
    13  	"os"
    14  	"runtime"
    15  	"sync"
    16  	"sync/atomic"
    17  	"testing"
    18  )
    19  
    20  const (
    21  	numTestSamples = 10000
    22  )
    23  
    24  var rn, kn, wn, fn = GetNormalDistributionParameters()
    25  var re, ke, we, fe = GetExponentialDistributionParameters()
    26  
    27  type statsResults struct {
    28  	mean        float64
    29  	stddev      float64
    30  	closeEnough float64
    31  	maxError    float64
    32  }
    33  
    34  func nearEqual(a, b, closeEnough, maxError float64) bool {
    35  	absDiff := math.Abs(a - b)
    36  	if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
    37  		return true
    38  	}
    39  	return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
    40  }
    41  
    42  var testSeeds = []uint64{1, 1754801282, 1698661970, 1550503961}
    43  
    44  // checkSimilarDistribution returns success if the mean and stddev of the
    45  // two statsResults are similar.
    46  func (sr *statsResults) checkSimilarDistribution(expected *statsResults) error {
    47  	if !nearEqual(sr.mean, expected.mean, expected.closeEnough, expected.maxError) {
    48  		s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", sr.mean, expected.mean, expected.closeEnough, expected.maxError)
    49  		fmt.Println(s)
    50  		return errors.New(s)
    51  	}
    52  	if !nearEqual(sr.stddev, expected.stddev, expected.closeEnough, expected.maxError) {
    53  		s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", sr.stddev, expected.stddev, expected.closeEnough, expected.maxError)
    54  		fmt.Println(s)
    55  		return errors.New(s)
    56  	}
    57  	return nil
    58  }
    59  
    60  func getStatsResults(samples []float64) *statsResults {
    61  	res := new(statsResults)
    62  	var sum, squaresum float64
    63  	for _, s := range samples {
    64  		sum += s
    65  		squaresum += s * s
    66  	}
    67  	res.mean = sum / float64(len(samples))
    68  	res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
    69  	return res
    70  }
    71  
    72  func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
    73  	t.Helper()
    74  	actual := getStatsResults(samples)
    75  	err := actual.checkSimilarDistribution(expected)
    76  	if err != nil {
    77  		t.Error(err)
    78  	}
    79  }
    80  
    81  func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
    82  	t.Helper()
    83  	chunk := len(samples) / nslices
    84  	for i := 0; i < nslices; i++ {
    85  		low := i * chunk
    86  		var high int
    87  		if i == nslices-1 {
    88  			high = len(samples) - 1
    89  		} else {
    90  			high = (i + 1) * chunk
    91  		}
    92  		checkSampleDistribution(t, samples[low:high], expected)
    93  	}
    94  }
    95  
    96  //
    97  // Normal distribution tests
    98  //
    99  
   100  func generateNormalSamples(nsamples int, mean, stddev float64, seed uint64) []float64 {
   101  	r := New(NewPCG(seed, seed))
   102  	samples := make([]float64, nsamples)
   103  	for i := range samples {
   104  		samples[i] = r.NormFloat64()*stddev + mean
   105  	}
   106  	return samples
   107  }
   108  
   109  func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed uint64) {
   110  	//fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
   111  
   112  	samples := generateNormalSamples(nsamples, mean, stddev, seed)
   113  	errorScale := max(1.0, stddev) // Error scales with stddev
   114  	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
   115  
   116  	// Make sure that the entire set matches the expected distribution.
   117  	checkSampleDistribution(t, samples, expected)
   118  
   119  	// Make sure that each half of the set matches the expected distribution.
   120  	checkSampleSliceDistributions(t, samples, 2, expected)
   121  
   122  	// Make sure that each 7th of the set matches the expected distribution.
   123  	checkSampleSliceDistributions(t, samples, 7, expected)
   124  }
   125  
   126  // Actual tests
   127  
   128  func TestStandardNormalValues(t *testing.T) {
   129  	for _, seed := range testSeeds {
   130  		testNormalDistribution(t, numTestSamples, 0, 1, seed)
   131  	}
   132  }
   133  
   134  func TestNonStandardNormalValues(t *testing.T) {
   135  	sdmax := 1000.0
   136  	mmax := 1000.0
   137  	if testing.Short() {
   138  		sdmax = 5
   139  		mmax = 5
   140  	}
   141  	for sd := 0.5; sd < sdmax; sd *= 2 {
   142  		for m := 0.5; m < mmax; m *= 2 {
   143  			for _, seed := range testSeeds {
   144  				testNormalDistribution(t, numTestSamples, m, sd, seed)
   145  				if testing.Short() {
   146  					break
   147  				}
   148  			}
   149  		}
   150  	}
   151  }
   152  
   153  //
   154  // Exponential distribution tests
   155  //
   156  
   157  func generateExponentialSamples(nsamples int, rate float64, seed uint64) []float64 {
   158  	r := New(NewPCG(seed, seed))
   159  	samples := make([]float64, nsamples)
   160  	for i := range samples {
   161  		samples[i] = r.ExpFloat64() / rate
   162  	}
   163  	return samples
   164  }
   165  
   166  func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed uint64) {
   167  	//fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed);
   168  
   169  	mean := 1 / rate
   170  	stddev := mean
   171  
   172  	samples := generateExponentialSamples(nsamples, rate, seed)
   173  	errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
   174  	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
   175  
   176  	// Make sure that the entire set matches the expected distribution.
   177  	checkSampleDistribution(t, samples, expected)
   178  
   179  	// Make sure that each half of the set matches the expected distribution.
   180  	checkSampleSliceDistributions(t, samples, 2, expected)
   181  
   182  	// Make sure that each 7th of the set matches the expected distribution.
   183  	checkSampleSliceDistributions(t, samples, 7, expected)
   184  }
   185  
   186  // Actual tests
   187  
   188  func TestStandardExponentialValues(t *testing.T) {
   189  	for _, seed := range testSeeds {
   190  		testExponentialDistribution(t, numTestSamples, 1, seed)
   191  	}
   192  }
   193  
   194  func TestNonStandardExponentialValues(t *testing.T) {
   195  	for rate := 0.05; rate < 10; rate *= 2 {
   196  		for _, seed := range testSeeds {
   197  			testExponentialDistribution(t, numTestSamples, rate, seed)
   198  			if testing.Short() {
   199  				break
   200  			}
   201  		}
   202  	}
   203  }
   204  
   205  //
   206  // Table generation tests
   207  //
   208  
   209  func initNorm() (testKn []uint32, testWn, testFn []float32) {
   210  	const m1 = 1 << 31
   211  	var (
   212  		dn float64 = rn
   213  		tn         = dn
   214  		vn float64 = 9.91256303526217e-3
   215  	)
   216  
   217  	testKn = make([]uint32, 128)
   218  	testWn = make([]float32, 128)
   219  	testFn = make([]float32, 128)
   220  
   221  	q := vn / math.Exp(-0.5*dn*dn)
   222  	testKn[0] = uint32((dn / q) * m1)
   223  	testKn[1] = 0
   224  	testWn[0] = float32(q / m1)
   225  	testWn[127] = float32(dn / m1)
   226  	testFn[0] = 1.0
   227  	testFn[127] = float32(math.Exp(-0.5 * dn * dn))
   228  	for i := 126; i >= 1; i-- {
   229  		dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
   230  		testKn[i+1] = uint32((dn / tn) * m1)
   231  		tn = dn
   232  		testFn[i] = float32(math.Exp(-0.5 * dn * dn))
   233  		testWn[i] = float32(dn / m1)
   234  	}
   235  	return
   236  }
   237  
   238  func initExp() (testKe []uint32, testWe, testFe []float32) {
   239  	const m2 = 1 << 32
   240  	var (
   241  		de float64 = re
   242  		te         = de
   243  		ve float64 = 3.9496598225815571993e-3
   244  	)
   245  
   246  	testKe = make([]uint32, 256)
   247  	testWe = make([]float32, 256)
   248  	testFe = make([]float32, 256)
   249  
   250  	q := ve / math.Exp(-de)
   251  	testKe[0] = uint32((de / q) * m2)
   252  	testKe[1] = 0
   253  	testWe[0] = float32(q / m2)
   254  	testWe[255] = float32(de / m2)
   255  	testFe[0] = 1.0
   256  	testFe[255] = float32(math.Exp(-de))
   257  	for i := 254; i >= 1; i-- {
   258  		de = -math.Log(ve/de + math.Exp(-de))
   259  		testKe[i+1] = uint32((de / te) * m2)
   260  		te = de
   261  		testFe[i] = float32(math.Exp(-de))
   262  		testWe[i] = float32(de / m2)
   263  	}
   264  	return
   265  }
   266  
   267  // compareUint32Slices returns the first index where the two slices
   268  // disagree, or <0 if the lengths are the same and all elements
   269  // are identical.
   270  func compareUint32Slices(s1, s2 []uint32) int {
   271  	if len(s1) != len(s2) {
   272  		if len(s1) > len(s2) {
   273  			return len(s2) + 1
   274  		}
   275  		return len(s1) + 1
   276  	}
   277  	for i := range s1 {
   278  		if s1[i] != s2[i] {
   279  			return i
   280  		}
   281  	}
   282  	return -1
   283  }
   284  
   285  // compareFloat32Slices returns the first index where the two slices
   286  // disagree, or <0 if the lengths are the same and all elements
   287  // are identical.
   288  func compareFloat32Slices(s1, s2 []float32) int {
   289  	if len(s1) != len(s2) {
   290  		if len(s1) > len(s2) {
   291  			return len(s2) + 1
   292  		}
   293  		return len(s1) + 1
   294  	}
   295  	for i := range s1 {
   296  		if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
   297  			return i
   298  		}
   299  	}
   300  	return -1
   301  }
   302  
   303  func TestNormTables(t *testing.T) {
   304  	testKn, testWn, testFn := initNorm()
   305  	if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
   306  		t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
   307  	}
   308  	if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
   309  		t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
   310  	}
   311  	if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
   312  		t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
   313  	}
   314  }
   315  
   316  func TestExpTables(t *testing.T) {
   317  	testKe, testWe, testFe := initExp()
   318  	if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
   319  		t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
   320  	}
   321  	if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
   322  		t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
   323  	}
   324  	if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
   325  		t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
   326  	}
   327  }
   328  
   329  func hasSlowFloatingPoint() bool {
   330  	switch runtime.GOARCH {
   331  	case "arm":
   332  		return os.Getenv("GOARM") == "5"
   333  	case "mips", "mipsle", "mips64", "mips64le":
   334  		// Be conservative and assume that all mips boards
   335  		// have emulated floating point.
   336  		// TODO: detect what it actually has.
   337  		return true
   338  	}
   339  	return false
   340  }
   341  
   342  func TestFloat32(t *testing.T) {
   343  	// For issue 6721, the problem came after 7533753 calls, so check 10e6.
   344  	num := int(10e6)
   345  	// But do the full amount only on builders (not locally).
   346  	// But ARM5 floating point emulation is slow (Issue 10749), so
   347  	// do less for that builder:
   348  	if testing.Short() && (testenv.Builder() == "" || hasSlowFloatingPoint()) {
   349  		num /= 100 // 1.72 seconds instead of 172 seconds
   350  	}
   351  
   352  	r := testRand()
   353  	for ct := 0; ct < num; ct++ {
   354  		f := r.Float32()
   355  		if f >= 1 {
   356  			t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
   357  		}
   358  	}
   359  }
   360  
   361  func TestShuffleSmall(t *testing.T) {
   362  	// Check that Shuffle allows n=0 and n=1, but that swap is never called for them.
   363  	r := testRand()
   364  	for n := 0; n <= 1; n++ {
   365  		r.Shuffle(n, func(i, j int) { t.Fatalf("swap called, n=%d i=%d j=%d", n, i, j) })
   366  	}
   367  }
   368  
   369  // encodePerm converts from a permuted slice of length n, such as Perm generates, to an int in [0, n!).
   370  // See https://en.wikipedia.org/wiki/Lehmer_code.
   371  // encodePerm modifies the input slice.
   372  func encodePerm(s []int) int {
   373  	// Convert to Lehmer code.
   374  	for i, x := range s {
   375  		r := s[i+1:]
   376  		for j, y := range r {
   377  			if y > x {
   378  				r[j]--
   379  			}
   380  		}
   381  	}
   382  	// Convert to int in [0, n!).
   383  	m := 0
   384  	fact := 1
   385  	for i := len(s) - 1; i >= 0; i-- {
   386  		m += s[i] * fact
   387  		fact *= len(s) - i
   388  	}
   389  	return m
   390  }
   391  
   392  // TestUniformFactorial tests several ways of generating a uniform value in [0, n!).
   393  func TestUniformFactorial(t *testing.T) {
   394  	r := New(NewPCG(1, 2))
   395  	top := 6
   396  	if testing.Short() {
   397  		top = 3
   398  	}
   399  	for n := 3; n <= top; n++ {
   400  		t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
   401  			// Calculate n!.
   402  			nfact := 1
   403  			for i := 2; i <= n; i++ {
   404  				nfact *= i
   405  			}
   406  
   407  			// Test a few different ways to generate a uniform distribution.
   408  			p := make([]int, n) // re-usable slice for Shuffle generator
   409  			tests := [...]struct {
   410  				name string
   411  				fn   func() int
   412  			}{
   413  				{name: "Int32N", fn: func() int { return int(r.Int32N(int32(nfact))) }},
   414  				{name: "Perm", fn: func() int { return encodePerm(r.Perm(n)) }},
   415  				{name: "Shuffle", fn: func() int {
   416  					// Generate permutation using Shuffle.
   417  					for i := range p {
   418  						p[i] = i
   419  					}
   420  					r.Shuffle(n, func(i, j int) { p[i], p[j] = p[j], p[i] })
   421  					return encodePerm(p)
   422  				}},
   423  			}
   424  
   425  			for _, test := range tests {
   426  				t.Run(test.name, func(t *testing.T) {
   427  					// Gather chi-squared values and check that they follow
   428  					// the expected normal distribution given n!-1 degrees of freedom.
   429  					// See https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test and
   430  					// https://www.johndcook.com/Beautiful_Testing_ch10.pdf.
   431  					nsamples := 10 * nfact
   432  					if nsamples < 1000 {
   433  						nsamples = 1000
   434  					}
   435  					samples := make([]float64, nsamples)
   436  					for i := range samples {
   437  						// Generate some uniformly distributed values and count their occurrences.
   438  						const iters = 1000
   439  						counts := make([]int, nfact)
   440  						for i := 0; i < iters; i++ {
   441  							counts[test.fn()]++
   442  						}
   443  						// Calculate chi-squared and add to samples.
   444  						want := iters / float64(nfact)
   445  						var χ2 float64
   446  						for _, have := range counts {
   447  							err := float64(have) - want
   448  							χ2 += err * err
   449  						}
   450  						χ2 /= want
   451  						samples[i] = χ2
   452  					}
   453  
   454  					// Check that our samples approximate the appropriate normal distribution.
   455  					dof := float64(nfact - 1)
   456  					expected := &statsResults{mean: dof, stddev: math.Sqrt(2 * dof)}
   457  					errorScale := max(1.0, expected.stddev)
   458  					expected.closeEnough = 0.10 * errorScale
   459  					expected.maxError = 0.08 // TODO: What is the right value here? See issue 21211.
   460  					checkSampleDistribution(t, samples, expected)
   461  				})
   462  			}
   463  		})
   464  	}
   465  }
   466  
   467  // Benchmarks
   468  
   469  var Sink uint64
   470  
   471  func testRand() *Rand {
   472  	return New(NewPCG(1, 2))
   473  }
   474  
   475  func BenchmarkSourceUint64(b *testing.B) {
   476  	s := NewPCG(1, 2)
   477  	var t uint64
   478  	for n := b.N; n > 0; n-- {
   479  		t += s.Uint64()
   480  	}
   481  	Sink = uint64(t)
   482  }
   483  
   484  func BenchmarkGlobalInt64(b *testing.B) {
   485  	var t int64
   486  	for n := b.N; n > 0; n-- {
   487  		t += Int64()
   488  	}
   489  	Sink = uint64(t)
   490  }
   491  
   492  func BenchmarkGlobalInt64Parallel(b *testing.B) {
   493  	b.RunParallel(func(pb *testing.PB) {
   494  		var t int64
   495  		for pb.Next() {
   496  			t += Int64()
   497  		}
   498  		atomic.AddUint64(&Sink, uint64(t))
   499  	})
   500  }
   501  
   502  func BenchmarkGlobalUint64(b *testing.B) {
   503  	var t uint64
   504  	for n := b.N; n > 0; n-- {
   505  		t += Uint64()
   506  	}
   507  	Sink = t
   508  }
   509  
   510  func BenchmarkGlobalUint64Parallel(b *testing.B) {
   511  	b.RunParallel(func(pb *testing.PB) {
   512  		var t uint64
   513  		for pb.Next() {
   514  			t += Uint64()
   515  		}
   516  		atomic.AddUint64(&Sink, t)
   517  	})
   518  }
   519  
   520  func BenchmarkInt64(b *testing.B) {
   521  	r := testRand()
   522  	var t int64
   523  	for n := b.N; n > 0; n-- {
   524  		t += r.Int64()
   525  	}
   526  	Sink = uint64(t)
   527  }
   528  
   529  var AlwaysFalse = false
   530  
   531  func keep[T int | uint | int32 | uint32 | int64 | uint64](x T) T {
   532  	if AlwaysFalse {
   533  		return -x
   534  	}
   535  	return x
   536  }
   537  
   538  func BenchmarkUint64(b *testing.B) {
   539  	r := testRand()
   540  	var t uint64
   541  	for n := b.N; n > 0; n-- {
   542  		t += r.Uint64()
   543  	}
   544  	Sink = t
   545  }
   546  
   547  func BenchmarkGlobalIntN1000(b *testing.B) {
   548  	var t int
   549  	arg := keep(1000)
   550  	for n := b.N; n > 0; n-- {
   551  		t += IntN(arg)
   552  	}
   553  	Sink = uint64(t)
   554  }
   555  
   556  func BenchmarkIntN1000(b *testing.B) {
   557  	r := testRand()
   558  	var t int
   559  	arg := keep(1000)
   560  	for n := b.N; n > 0; n-- {
   561  		t += r.IntN(arg)
   562  	}
   563  	Sink = uint64(t)
   564  }
   565  
   566  func BenchmarkInt64N1000(b *testing.B) {
   567  	r := testRand()
   568  	var t int64
   569  	arg := keep(int64(1000))
   570  	for n := b.N; n > 0; n-- {
   571  		t += r.Int64N(arg)
   572  	}
   573  	Sink = uint64(t)
   574  }
   575  
   576  func BenchmarkInt64N1e8(b *testing.B) {
   577  	r := testRand()
   578  	var t int64
   579  	arg := keep(int64(1e8))
   580  	for n := b.N; n > 0; n-- {
   581  		t += r.Int64N(arg)
   582  	}
   583  	Sink = uint64(t)
   584  }
   585  
   586  func BenchmarkInt64N1e9(b *testing.B) {
   587  	r := testRand()
   588  	var t int64
   589  	arg := keep(int64(1e9))
   590  	for n := b.N; n > 0; n-- {
   591  		t += r.Int64N(arg)
   592  	}
   593  	Sink = uint64(t)
   594  }
   595  
   596  func BenchmarkInt64N2e9(b *testing.B) {
   597  	r := testRand()
   598  	var t int64
   599  	arg := keep(int64(2e9))
   600  	for n := b.N; n > 0; n-- {
   601  		t += r.Int64N(arg)
   602  	}
   603  	Sink = uint64(t)
   604  }
   605  
   606  func BenchmarkInt64N1e18(b *testing.B) {
   607  	r := testRand()
   608  	var t int64
   609  	arg := keep(int64(1e18))
   610  	for n := b.N; n > 0; n-- {
   611  		t += r.Int64N(arg)
   612  	}
   613  	Sink = uint64(t)
   614  }
   615  
   616  func BenchmarkInt64N2e18(b *testing.B) {
   617  	r := testRand()
   618  	var t int64
   619  	arg := keep(int64(2e18))
   620  	for n := b.N; n > 0; n-- {
   621  		t += r.Int64N(arg)
   622  	}
   623  	Sink = uint64(t)
   624  }
   625  
   626  func BenchmarkInt64N4e18(b *testing.B) {
   627  	r := testRand()
   628  	var t int64
   629  	arg := keep(int64(4e18))
   630  	for n := b.N; n > 0; n-- {
   631  		t += r.Int64N(arg)
   632  	}
   633  	Sink = uint64(t)
   634  }
   635  
   636  func BenchmarkInt32N1000(b *testing.B) {
   637  	r := testRand()
   638  	var t int32
   639  	arg := keep(int32(1000))
   640  	for n := b.N; n > 0; n-- {
   641  		t += r.Int32N(arg)
   642  	}
   643  	Sink = uint64(t)
   644  }
   645  
   646  func BenchmarkInt32N1e8(b *testing.B) {
   647  	r := testRand()
   648  	var t int32
   649  	arg := keep(int32(1e8))
   650  	for n := b.N; n > 0; n-- {
   651  		t += r.Int32N(arg)
   652  	}
   653  	Sink = uint64(t)
   654  }
   655  
   656  func BenchmarkInt32N1e9(b *testing.B) {
   657  	r := testRand()
   658  	var t int32
   659  	arg := keep(int32(1e9))
   660  	for n := b.N; n > 0; n-- {
   661  		t += r.Int32N(arg)
   662  	}
   663  	Sink = uint64(t)
   664  }
   665  
   666  func BenchmarkInt32N2e9(b *testing.B) {
   667  	r := testRand()
   668  	var t int32
   669  	arg := keep(int32(2e9))
   670  	for n := b.N; n > 0; n-- {
   671  		t += r.Int32N(arg)
   672  	}
   673  	Sink = uint64(t)
   674  }
   675  
   676  func BenchmarkFloat32(b *testing.B) {
   677  	r := testRand()
   678  	var t float32
   679  	for n := b.N; n > 0; n-- {
   680  		t += r.Float32()
   681  	}
   682  	Sink = uint64(t)
   683  }
   684  
   685  func BenchmarkFloat64(b *testing.B) {
   686  	r := testRand()
   687  	var t float64
   688  	for n := b.N; n > 0; n-- {
   689  		t += r.Float64()
   690  	}
   691  	Sink = uint64(t)
   692  }
   693  
   694  func BenchmarkExpFloat64(b *testing.B) {
   695  	r := testRand()
   696  	var t float64
   697  	for n := b.N; n > 0; n-- {
   698  		t += r.ExpFloat64()
   699  	}
   700  	Sink = uint64(t)
   701  }
   702  
   703  func BenchmarkNormFloat64(b *testing.B) {
   704  	r := testRand()
   705  	var t float64
   706  	for n := b.N; n > 0; n-- {
   707  		t += r.NormFloat64()
   708  	}
   709  	Sink = uint64(t)
   710  }
   711  
   712  func BenchmarkPerm3(b *testing.B) {
   713  	r := testRand()
   714  	var t int
   715  	for n := b.N; n > 0; n-- {
   716  		t += r.Perm(3)[0]
   717  	}
   718  	Sink = uint64(t)
   719  
   720  }
   721  
   722  func BenchmarkPerm30(b *testing.B) {
   723  	r := testRand()
   724  	var t int
   725  	for n := b.N; n > 0; n-- {
   726  		t += r.Perm(30)[0]
   727  	}
   728  	Sink = uint64(t)
   729  }
   730  
   731  func BenchmarkPerm30ViaShuffle(b *testing.B) {
   732  	r := testRand()
   733  	var t int
   734  	for n := b.N; n > 0; n-- {
   735  		p := make([]int, 30)
   736  		for i := range p {
   737  			p[i] = i
   738  		}
   739  		r.Shuffle(30, func(i, j int) { p[i], p[j] = p[j], p[i] })
   740  		t += p[0]
   741  	}
   742  	Sink = uint64(t)
   743  }
   744  
   745  // BenchmarkShuffleOverhead uses a minimal swap function
   746  // to measure just the shuffling overhead.
   747  func BenchmarkShuffleOverhead(b *testing.B) {
   748  	r := testRand()
   749  	for n := b.N; n > 0; n-- {
   750  		r.Shuffle(30, func(i, j int) {
   751  			if i < 0 || i >= 30 || j < 0 || j >= 30 {
   752  				b.Fatalf("bad swap(%d, %d)", i, j)
   753  			}
   754  		})
   755  	}
   756  }
   757  
   758  func BenchmarkConcurrent(b *testing.B) {
   759  	const goroutines = 4
   760  	var wg sync.WaitGroup
   761  	wg.Add(goroutines)
   762  	for i := 0; i < goroutines; i++ {
   763  		go func() {
   764  			defer wg.Done()
   765  			for n := b.N; n > 0; n-- {
   766  				Int64()
   767  			}
   768  		}()
   769  	}
   770  	wg.Wait()
   771  }
   772  
   773  func TestN(t *testing.T) {
   774  	for i := 0; i < 1000; i++ {
   775  		v := N(10)
   776  		if v < 0 || v >= 10 {
   777  			t.Fatalf("N(10) returned %d", v)
   778  		}
   779  	}
   780  }
   781
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