Source file src/math/rand/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  	"bytes"
     9  	"errors"
    10  	"fmt"
    11  	"internal/testenv"
    12  	"io"
    13  	"math"
    14  	. "math/rand"
    15  	"os"
    16  	"runtime"
    17  	"strings"
    18  	"sync"
    19  	"testing"
    20  	"testing/iotest"
    21  )
    22  
    23  const (
    24  	numTestSamples = 10000
    25  )
    26  
    27  var rn, kn, wn, fn = GetNormalDistributionParameters()
    28  var re, ke, we, fe = GetExponentialDistributionParameters()
    29  
    30  type statsResults struct {
    31  	mean        float64
    32  	stddev      float64
    33  	closeEnough float64
    34  	maxError    float64
    35  }
    36  
    37  func nearEqual(a, b, closeEnough, maxError float64) bool {
    38  	absDiff := math.Abs(a - b)
    39  	if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
    40  		return true
    41  	}
    42  	return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
    43  }
    44  
    45  var testSeeds = []int64{1, 1754801282, 1698661970, 1550503961}
    46  
    47  // checkSimilarDistribution returns success if the mean and stddev of the
    48  // two statsResults are similar.
    49  func (sr *statsResults) checkSimilarDistribution(expected *statsResults) error {
    50  	if !nearEqual(sr.mean, expected.mean, expected.closeEnough, expected.maxError) {
    51  		s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", sr.mean, expected.mean, expected.closeEnough, expected.maxError)
    52  		fmt.Println(s)
    53  		return errors.New(s)
    54  	}
    55  	if !nearEqual(sr.stddev, expected.stddev, expected.closeEnough, expected.maxError) {
    56  		s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", sr.stddev, expected.stddev, expected.closeEnough, expected.maxError)
    57  		fmt.Println(s)
    58  		return errors.New(s)
    59  	}
    60  	return nil
    61  }
    62  
    63  func getStatsResults(samples []float64) *statsResults {
    64  	res := new(statsResults)
    65  	var sum, squaresum float64
    66  	for _, s := range samples {
    67  		sum += s
    68  		squaresum += s * s
    69  	}
    70  	res.mean = sum / float64(len(samples))
    71  	res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
    72  	return res
    73  }
    74  
    75  func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
    76  	t.Helper()
    77  	actual := getStatsResults(samples)
    78  	err := actual.checkSimilarDistribution(expected)
    79  	if err != nil {
    80  		t.Error(err)
    81  	}
    82  }
    83  
    84  func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
    85  	t.Helper()
    86  	chunk := len(samples) / nslices
    87  	for i := 0; i < nslices; i++ {
    88  		low := i * chunk
    89  		var high int
    90  		if i == nslices-1 {
    91  			high = len(samples) - 1
    92  		} else {
    93  			high = (i + 1) * chunk
    94  		}
    95  		checkSampleDistribution(t, samples[low:high], expected)
    96  	}
    97  }
    98  
    99  //
   100  // Normal distribution tests
   101  //
   102  
   103  func generateNormalSamples(nsamples int, mean, stddev float64, seed int64) []float64 {
   104  	r := New(NewSource(seed))
   105  	samples := make([]float64, nsamples)
   106  	for i := range samples {
   107  		samples[i] = r.NormFloat64()*stddev + mean
   108  	}
   109  	return samples
   110  }
   111  
   112  func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed int64) {
   113  	//fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
   114  
   115  	samples := generateNormalSamples(nsamples, mean, stddev, seed)
   116  	errorScale := max(1.0, stddev) // Error scales with stddev
   117  	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
   118  
   119  	// Make sure that the entire set matches the expected distribution.
   120  	checkSampleDistribution(t, samples, expected)
   121  
   122  	// Make sure that each half of the set matches the expected distribution.
   123  	checkSampleSliceDistributions(t, samples, 2, expected)
   124  
   125  	// Make sure that each 7th of the set matches the expected distribution.
   126  	checkSampleSliceDistributions(t, samples, 7, expected)
   127  }
   128  
   129  // Actual tests
   130  
   131  func TestStandardNormalValues(t *testing.T) {
   132  	for _, seed := range testSeeds {
   133  		testNormalDistribution(t, numTestSamples, 0, 1, seed)
   134  	}
   135  }
   136  
   137  func TestNonStandardNormalValues(t *testing.T) {
   138  	sdmax := 1000.0
   139  	mmax := 1000.0
   140  	if testing.Short() {
   141  		sdmax = 5
   142  		mmax = 5
   143  	}
   144  	for sd := 0.5; sd < sdmax; sd *= 2 {
   145  		for m := 0.5; m < mmax; m *= 2 {
   146  			for _, seed := range testSeeds {
   147  				testNormalDistribution(t, numTestSamples, m, sd, seed)
   148  				if testing.Short() {
   149  					break
   150  				}
   151  			}
   152  		}
   153  	}
   154  }
   155  
   156  //
   157  // Exponential distribution tests
   158  //
   159  
   160  func generateExponentialSamples(nsamples int, rate float64, seed int64) []float64 {
   161  	r := New(NewSource(seed))
   162  	samples := make([]float64, nsamples)
   163  	for i := range samples {
   164  		samples[i] = r.ExpFloat64() / rate
   165  	}
   166  	return samples
   167  }
   168  
   169  func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed int64) {
   170  	//fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed);
   171  
   172  	mean := 1 / rate
   173  	stddev := mean
   174  
   175  	samples := generateExponentialSamples(nsamples, rate, seed)
   176  	errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
   177  	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
   178  
   179  	// Make sure that the entire set matches the expected distribution.
   180  	checkSampleDistribution(t, samples, expected)
   181  
   182  	// Make sure that each half of the set matches the expected distribution.
   183  	checkSampleSliceDistributions(t, samples, 2, expected)
   184  
   185  	// Make sure that each 7th of the set matches the expected distribution.
   186  	checkSampleSliceDistributions(t, samples, 7, expected)
   187  }
   188  
   189  // Actual tests
   190  
   191  func TestStandardExponentialValues(t *testing.T) {
   192  	for _, seed := range testSeeds {
   193  		testExponentialDistribution(t, numTestSamples, 1, seed)
   194  	}
   195  }
   196  
   197  func TestNonStandardExponentialValues(t *testing.T) {
   198  	for rate := 0.05; rate < 10; rate *= 2 {
   199  		for _, seed := range testSeeds {
   200  			testExponentialDistribution(t, numTestSamples, rate, seed)
   201  			if testing.Short() {
   202  				break
   203  			}
   204  		}
   205  	}
   206  }
   207  
   208  //
   209  // Table generation tests
   210  //
   211  
   212  func initNorm() (testKn []uint32, testWn, testFn []float32) {
   213  	const m1 = 1 << 31
   214  	var (
   215  		dn float64 = rn
   216  		tn         = dn
   217  		vn float64 = 9.91256303526217e-3
   218  	)
   219  
   220  	testKn = make([]uint32, 128)
   221  	testWn = make([]float32, 128)
   222  	testFn = make([]float32, 128)
   223  
   224  	q := vn / math.Exp(-0.5*dn*dn)
   225  	testKn[0] = uint32((dn / q) * m1)
   226  	testKn[1] = 0
   227  	testWn[0] = float32(q / m1)
   228  	testWn[127] = float32(dn / m1)
   229  	testFn[0] = 1.0
   230  	testFn[127] = float32(math.Exp(-0.5 * dn * dn))
   231  	for i := 126; i >= 1; i-- {
   232  		dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
   233  		testKn[i+1] = uint32((dn / tn) * m1)
   234  		tn = dn
   235  		testFn[i] = float32(math.Exp(-0.5 * dn * dn))
   236  		testWn[i] = float32(dn / m1)
   237  	}
   238  	return
   239  }
   240  
   241  func initExp() (testKe []uint32, testWe, testFe []float32) {
   242  	const m2 = 1 << 32
   243  	var (
   244  		de float64 = re
   245  		te         = de
   246  		ve float64 = 3.9496598225815571993e-3
   247  	)
   248  
   249  	testKe = make([]uint32, 256)
   250  	testWe = make([]float32, 256)
   251  	testFe = make([]float32, 256)
   252  
   253  	q := ve / math.Exp(-de)
   254  	testKe[0] = uint32((de / q) * m2)
   255  	testKe[1] = 0
   256  	testWe[0] = float32(q / m2)
   257  	testWe[255] = float32(de / m2)
   258  	testFe[0] = 1.0
   259  	testFe[255] = float32(math.Exp(-de))
   260  	for i := 254; i >= 1; i-- {
   261  		de = -math.Log(ve/de + math.Exp(-de))
   262  		testKe[i+1] = uint32((de / te) * m2)
   263  		te = de
   264  		testFe[i] = float32(math.Exp(-de))
   265  		testWe[i] = float32(de / m2)
   266  	}
   267  	return
   268  }
   269  
   270  // compareUint32Slices returns the first index where the two slices
   271  // disagree, or <0 if the lengths are the same and all elements
   272  // are identical.
   273  func compareUint32Slices(s1, s2 []uint32) int {
   274  	if len(s1) != len(s2) {
   275  		if len(s1) > len(s2) {
   276  			return len(s2) + 1
   277  		}
   278  		return len(s1) + 1
   279  	}
   280  	for i := range s1 {
   281  		if s1[i] != s2[i] {
   282  			return i
   283  		}
   284  	}
   285  	return -1
   286  }
   287  
   288  // compareFloat32Slices returns the first index where the two slices
   289  // disagree, or <0 if the lengths are the same and all elements
   290  // are identical.
   291  func compareFloat32Slices(s1, s2 []float32) int {
   292  	if len(s1) != len(s2) {
   293  		if len(s1) > len(s2) {
   294  			return len(s2) + 1
   295  		}
   296  		return len(s1) + 1
   297  	}
   298  	for i := range s1 {
   299  		if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
   300  			return i
   301  		}
   302  	}
   303  	return -1
   304  }
   305  
   306  func TestNormTables(t *testing.T) {
   307  	testKn, testWn, testFn := initNorm()
   308  	if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
   309  		t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
   310  	}
   311  	if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
   312  		t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
   313  	}
   314  	if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
   315  		t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
   316  	}
   317  }
   318  
   319  func TestExpTables(t *testing.T) {
   320  	testKe, testWe, testFe := initExp()
   321  	if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
   322  		t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
   323  	}
   324  	if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
   325  		t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
   326  	}
   327  	if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
   328  		t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
   329  	}
   330  }
   331  
   332  func hasSlowFloatingPoint() bool {
   333  	switch runtime.GOARCH {
   334  	case "arm":
   335  		return os.Getenv("GOARM") == "5" || strings.HasSuffix(os.Getenv("GOARM"), ",softfloat")
   336  	case "mips", "mipsle", "mips64", "mips64le":
   337  		// Be conservative and assume that all mips boards
   338  		// have emulated floating point.
   339  		// TODO: detect what it actually has.
   340  		return true
   341  	}
   342  	return false
   343  }
   344  
   345  func TestFloat32(t *testing.T) {
   346  	// For issue 6721, the problem came after 7533753 calls, so check 10e6.
   347  	num := int(10e6)
   348  	// But do the full amount only on builders (not locally).
   349  	// But ARM5 floating point emulation is slow (Issue 10749), so
   350  	// do less for that builder:
   351  	if testing.Short() && (testenv.Builder() == "" || hasSlowFloatingPoint()) {
   352  		num /= 100 // 1.72 seconds instead of 172 seconds
   353  	}
   354  
   355  	r := New(NewSource(1))
   356  	for ct := 0; ct < num; ct++ {
   357  		f := r.Float32()
   358  		if f >= 1 {
   359  			t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
   360  		}
   361  	}
   362  }
   363  
   364  func testReadUniformity(t *testing.T, n int, seed int64) {
   365  	r := New(NewSource(seed))
   366  	buf := make([]byte, n)
   367  	nRead, err := r.Read(buf)
   368  	if err != nil {
   369  		t.Errorf("Read err %v", err)
   370  	}
   371  	if nRead != n {
   372  		t.Errorf("Read returned unexpected n; %d != %d", nRead, n)
   373  	}
   374  
   375  	// Expect a uniform distribution of byte values, which lie in [0, 255].
   376  	var (
   377  		mean       = 255.0 / 2
   378  		stddev     = 256.0 / math.Sqrt(12.0)
   379  		errorScale = stddev / math.Sqrt(float64(n))
   380  	)
   381  
   382  	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
   383  
   384  	// Cast bytes as floats to use the common distribution-validity checks.
   385  	samples := make([]float64, n)
   386  	for i, val := range buf {
   387  		samples[i] = float64(val)
   388  	}
   389  	// Make sure that the entire set matches the expected distribution.
   390  	checkSampleDistribution(t, samples, expected)
   391  }
   392  
   393  func TestReadUniformity(t *testing.T) {
   394  	testBufferSizes := []int{
   395  		2, 4, 7, 64, 1024, 1 << 16, 1 << 20,
   396  	}
   397  	for _, seed := range testSeeds {
   398  		for _, n := range testBufferSizes {
   399  			testReadUniformity(t, n, seed)
   400  		}
   401  	}
   402  }
   403  
   404  func TestReadEmpty(t *testing.T) {
   405  	r := New(NewSource(1))
   406  	buf := make([]byte, 0)
   407  	n, err := r.Read(buf)
   408  	if err != nil {
   409  		t.Errorf("Read err into empty buffer; %v", err)
   410  	}
   411  	if n != 0 {
   412  		t.Errorf("Read into empty buffer returned unexpected n of %d", n)
   413  	}
   414  }
   415  
   416  func TestReadByOneByte(t *testing.T) {
   417  	r := New(NewSource(1))
   418  	b1 := make([]byte, 100)
   419  	_, err := io.ReadFull(iotest.OneByteReader(r), b1)
   420  	if err != nil {
   421  		t.Errorf("read by one byte: %v", err)
   422  	}
   423  	r = New(NewSource(1))
   424  	b2 := make([]byte, 100)
   425  	_, err = r.Read(b2)
   426  	if err != nil {
   427  		t.Errorf("read: %v", err)
   428  	}
   429  	if !bytes.Equal(b1, b2) {
   430  		t.Errorf("read by one byte vs single read:\n%x\n%x", b1, b2)
   431  	}
   432  }
   433  
   434  func TestReadSeedReset(t *testing.T) {
   435  	r := New(NewSource(42))
   436  	b1 := make([]byte, 128)
   437  	_, err := r.Read(b1)
   438  	if err != nil {
   439  		t.Errorf("read: %v", err)
   440  	}
   441  	r.Seed(42)
   442  	b2 := make([]byte, 128)
   443  	_, err = r.Read(b2)
   444  	if err != nil {
   445  		t.Errorf("read: %v", err)
   446  	}
   447  	if !bytes.Equal(b1, b2) {
   448  		t.Errorf("mismatch after re-seed:\n%x\n%x", b1, b2)
   449  	}
   450  }
   451  
   452  func TestShuffleSmall(t *testing.T) {
   453  	// Check that Shuffle allows n=0 and n=1, but that swap is never called for them.
   454  	r := New(NewSource(1))
   455  	for n := 0; n <= 1; n++ {
   456  		r.Shuffle(n, func(i, j int) { t.Fatalf("swap called, n=%d i=%d j=%d", n, i, j) })
   457  	}
   458  }
   459  
   460  // encodePerm converts from a permuted slice of length n, such as Perm generates, to an int in [0, n!).
   461  // See https://en.wikipedia.org/wiki/Lehmer_code.
   462  // encodePerm modifies the input slice.
   463  func encodePerm(s []int) int {
   464  	// Convert to Lehmer code.
   465  	for i, x := range s {
   466  		r := s[i+1:]
   467  		for j, y := range r {
   468  			if y > x {
   469  				r[j]--
   470  			}
   471  		}
   472  	}
   473  	// Convert to int in [0, n!).
   474  	m := 0
   475  	fact := 1
   476  	for i := len(s) - 1; i >= 0; i-- {
   477  		m += s[i] * fact
   478  		fact *= len(s) - i
   479  	}
   480  	return m
   481  }
   482  
   483  // TestUniformFactorial tests several ways of generating a uniform value in [0, n!).
   484  func TestUniformFactorial(t *testing.T) {
   485  	r := New(NewSource(testSeeds[0]))
   486  	top := 6
   487  	if testing.Short() {
   488  		top = 3
   489  	}
   490  	for n := 3; n <= top; n++ {
   491  		t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
   492  			// Calculate n!.
   493  			nfact := 1
   494  			for i := 2; i <= n; i++ {
   495  				nfact *= i
   496  			}
   497  
   498  			// Test a few different ways to generate a uniform distribution.
   499  			p := make([]int, n) // re-usable slice for Shuffle generator
   500  			tests := [...]struct {
   501  				name string
   502  				fn   func() int
   503  			}{
   504  				{name: "Int31n", fn: func() int { return int(r.Int31n(int32(nfact))) }},
   505  				{name: "int31n", fn: func() int { return int(Int31nForTest(r, int32(nfact))) }},
   506  				{name: "Perm", fn: func() int { return encodePerm(r.Perm(n)) }},
   507  				{name: "Shuffle", fn: func() int {
   508  					// Generate permutation using Shuffle.
   509  					for i := range p {
   510  						p[i] = i
   511  					}
   512  					r.Shuffle(n, func(i, j int) { p[i], p[j] = p[j], p[i] })
   513  					return encodePerm(p)
   514  				}},
   515  			}
   516  
   517  			for _, test := range tests {
   518  				t.Run(test.name, func(t *testing.T) {
   519  					// Gather chi-squared values and check that they follow
   520  					// the expected normal distribution given n!-1 degrees of freedom.
   521  					// See https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test and
   522  					// https://www.johndcook.com/Beautiful_Testing_ch10.pdf.
   523  					nsamples := 10 * nfact
   524  					if nsamples < 200 {
   525  						nsamples = 200
   526  					}
   527  					samples := make([]float64, nsamples)
   528  					for i := range samples {
   529  						// Generate some uniformly distributed values and count their occurrences.
   530  						const iters = 1000
   531  						counts := make([]int, nfact)
   532  						for i := 0; i < iters; i++ {
   533  							counts[test.fn()]++
   534  						}
   535  						// Calculate chi-squared and add to samples.
   536  						want := iters / float64(nfact)
   537  						var χ2 float64
   538  						for _, have := range counts {
   539  							err := float64(have) - want
   540  							χ2 += err * err
   541  						}
   542  						χ2 /= want
   543  						samples[i] = χ2
   544  					}
   545  
   546  					// Check that our samples approximate the appropriate normal distribution.
   547  					dof := float64(nfact - 1)
   548  					expected := &statsResults{mean: dof, stddev: math.Sqrt(2 * dof)}
   549  					errorScale := max(1.0, expected.stddev)
   550  					expected.closeEnough = 0.10 * errorScale
   551  					expected.maxError = 0.08 // TODO: What is the right value here? See issue 21211.
   552  					checkSampleDistribution(t, samples, expected)
   553  				})
   554  			}
   555  		})
   556  	}
   557  }
   558  
   559  func TestSeedNop(t *testing.T) {
   560  	// If the global Seed takes effect, then resetting it to a certain value
   561  	// should provide predictable output to functions using it.
   562  	t.Run("randseednop=0", func(t *testing.T) {
   563  		t.Setenv("GODEBUG", "randseednop=0")
   564  		Seed(1)
   565  		before := Int63()
   566  		Seed(1)
   567  		after := Int63()
   568  		if before != after {
   569  			t.Fatal("global Seed should take effect")
   570  		}
   571  	})
   572  	// If calls to the global Seed are no-op then functions using it should
   573  	// provide different output, even if it was reset to the same value.
   574  	t.Run("randseednop=1", func(t *testing.T) {
   575  		t.Setenv("GODEBUG", "randseednop=1")
   576  		Seed(1)
   577  		before := Int63()
   578  		Seed(1)
   579  		after := Int63()
   580  		if before == after {
   581  			t.Fatal("global Seed should be a no-op")
   582  		}
   583  	})
   584  	t.Run("GODEBUG unset", func(t *testing.T) {
   585  		Seed(1)
   586  		before := Int63()
   587  		Seed(1)
   588  		after := Int63()
   589  		if before == after {
   590  			t.Fatal("global Seed should default to being a no-op")
   591  		}
   592  	})
   593  }
   594  
   595  // Benchmarks
   596  
   597  func BenchmarkInt63Threadsafe(b *testing.B) {
   598  	for n := b.N; n > 0; n-- {
   599  		Int63()
   600  	}
   601  }
   602  
   603  func BenchmarkInt63ThreadsafeParallel(b *testing.B) {
   604  	b.RunParallel(func(pb *testing.PB) {
   605  		for pb.Next() {
   606  			Int63()
   607  		}
   608  	})
   609  }
   610  
   611  func BenchmarkInt63Unthreadsafe(b *testing.B) {
   612  	r := New(NewSource(1))
   613  	for n := b.N; n > 0; n-- {
   614  		r.Int63()
   615  	}
   616  }
   617  
   618  func BenchmarkIntn1000(b *testing.B) {
   619  	r := New(NewSource(1))
   620  	for n := b.N; n > 0; n-- {
   621  		r.Intn(1000)
   622  	}
   623  }
   624  
   625  func BenchmarkInt63n1000(b *testing.B) {
   626  	r := New(NewSource(1))
   627  	for n := b.N; n > 0; n-- {
   628  		r.Int63n(1000)
   629  	}
   630  }
   631  
   632  func BenchmarkInt31n1000(b *testing.B) {
   633  	r := New(NewSource(1))
   634  	for n := b.N; n > 0; n-- {
   635  		r.Int31n(1000)
   636  	}
   637  }
   638  
   639  func BenchmarkFloat32(b *testing.B) {
   640  	r := New(NewSource(1))
   641  	for n := b.N; n > 0; n-- {
   642  		r.Float32()
   643  	}
   644  }
   645  
   646  func BenchmarkFloat64(b *testing.B) {
   647  	r := New(NewSource(1))
   648  	for n := b.N; n > 0; n-- {
   649  		r.Float64()
   650  	}
   651  }
   652  
   653  func BenchmarkPerm3(b *testing.B) {
   654  	r := New(NewSource(1))
   655  	for n := b.N; n > 0; n-- {
   656  		r.Perm(3)
   657  	}
   658  }
   659  
   660  func BenchmarkPerm30(b *testing.B) {
   661  	r := New(NewSource(1))
   662  	for n := b.N; n > 0; n-- {
   663  		r.Perm(30)
   664  	}
   665  }
   666  
   667  func BenchmarkPerm30ViaShuffle(b *testing.B) {
   668  	r := New(NewSource(1))
   669  	for n := b.N; n > 0; n-- {
   670  		p := make([]int, 30)
   671  		for i := range p {
   672  			p[i] = i
   673  		}
   674  		r.Shuffle(30, func(i, j int) { p[i], p[j] = p[j], p[i] })
   675  	}
   676  }
   677  
   678  // BenchmarkShuffleOverhead uses a minimal swap function
   679  // to measure just the shuffling overhead.
   680  func BenchmarkShuffleOverhead(b *testing.B) {
   681  	r := New(NewSource(1))
   682  	for n := b.N; n > 0; n-- {
   683  		r.Shuffle(52, func(i, j int) {
   684  			if i < 0 || i >= 52 || j < 0 || j >= 52 {
   685  				b.Fatalf("bad swap(%d, %d)", i, j)
   686  			}
   687  		})
   688  	}
   689  }
   690  
   691  func BenchmarkRead3(b *testing.B) {
   692  	r := New(NewSource(1))
   693  	buf := make([]byte, 3)
   694  	b.ResetTimer()
   695  	for n := b.N; n > 0; n-- {
   696  		r.Read(buf)
   697  	}
   698  }
   699  
   700  func BenchmarkRead64(b *testing.B) {
   701  	r := New(NewSource(1))
   702  	buf := make([]byte, 64)
   703  	b.ResetTimer()
   704  	for n := b.N; n > 0; n-- {
   705  		r.Read(buf)
   706  	}
   707  }
   708  
   709  func BenchmarkRead1000(b *testing.B) {
   710  	r := New(NewSource(1))
   711  	buf := make([]byte, 1000)
   712  	b.ResetTimer()
   713  	for n := b.N; n > 0; n-- {
   714  		r.Read(buf)
   715  	}
   716  }
   717  
   718  func BenchmarkConcurrent(b *testing.B) {
   719  	const goroutines = 4
   720  	var wg sync.WaitGroup
   721  	wg.Add(goroutines)
   722  	for i := 0; i < goroutines; i++ {
   723  		go func() {
   724  			defer wg.Done()
   725  			for n := b.N; n > 0; n-- {
   726  				Int63()
   727  			}
   728  		}()
   729  	}
   730  	wg.Wait()
   731  }
   732  

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