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.
21 numTestSamples = 10000
24 var rn, kn, wn, fn = GetNormalDistributionParameters()
25 var re, ke, we, fe = GetExponentialDistributionParameters()
27 type statsResults struct {
34 func max(a, b float64) float64 {
41 func nearEqual(a, b, closeEnough, maxError float64) bool {
42 absDiff := math.Abs(a - b)
43 if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
46 return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
49 var testSeeds = []int64{1, 1754801282, 1698661970, 1550503961}
51 // checkSimilarDistribution returns success if the mean and stddev of the
52 // two statsResults are similar.
53 func (this *statsResults) checkSimilarDistribution(expected *statsResults) error {
54 if !nearEqual(this.mean, expected.mean, expected.closeEnough, expected.maxError) {
55 s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", this.mean, expected.mean, expected.closeEnough, expected.maxError)
59 if !nearEqual(this.stddev, expected.stddev, expected.closeEnough, expected.maxError) {
60 s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", this.stddev, expected.stddev, expected.closeEnough, expected.maxError)
67 func getStatsResults(samples []float64) *statsResults {
68 res := new(statsResults)
69 var sum, squaresum float64
70 for _, s := range samples {
74 res.mean = sum / float64(len(samples))
75 res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
79 func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
81 actual := getStatsResults(samples)
82 err := actual.checkSimilarDistribution(expected)
88 func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
90 chunk := len(samples) / nslices
91 for i := 0; i < nslices; i++ {
95 high = len(samples) - 1
97 high = (i + 1) * chunk
99 checkSampleDistribution(t, samples[low:high], expected)
104 // Normal distribution tests
107 func generateNormalSamples(nsamples int, mean, stddev float64, seed int64) []float64 {
108 r := New(NewSource(seed))
109 samples := make([]float64, nsamples)
110 for i := range samples {
111 samples[i] = r.NormFloat64()*stddev + mean
116 func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed int64) {
117 //fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
119 samples := generateNormalSamples(nsamples, mean, stddev, seed)
120 errorScale := max(1.0, stddev) // Error scales with stddev
121 expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
123 // Make sure that the entire set matches the expected distribution.
124 checkSampleDistribution(t, samples, expected)
126 // Make sure that each half of the set matches the expected distribution.
127 checkSampleSliceDistributions(t, samples, 2, expected)
129 // Make sure that each 7th of the set matches the expected distribution.
130 checkSampleSliceDistributions(t, samples, 7, expected)
135 func TestStandardNormalValues(t *testing.T) {
136 for _, seed := range testSeeds {
137 testNormalDistribution(t, numTestSamples, 0, 1, seed)
141 func TestNonStandardNormalValues(t *testing.T) {
148 for sd := 0.5; sd < sdmax; sd *= 2 {
149 for m := 0.5; m < mmax; m *= 2 {
150 for _, seed := range testSeeds {
151 testNormalDistribution(t, numTestSamples, m, sd, seed)
161 // Exponential distribution tests
164 func generateExponentialSamples(nsamples int, rate float64, seed int64) []float64 {
165 r := New(NewSource(seed))
166 samples := make([]float64, nsamples)
167 for i := range samples {
168 samples[i] = r.ExpFloat64() / rate
173 func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed int64) {
174 //fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed);
179 samples := generateExponentialSamples(nsamples, rate, seed)
180 errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
181 expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
183 // Make sure that the entire set matches the expected distribution.
184 checkSampleDistribution(t, samples, expected)
186 // Make sure that each half of the set matches the expected distribution.
187 checkSampleSliceDistributions(t, samples, 2, expected)
189 // Make sure that each 7th of the set matches the expected distribution.
190 checkSampleSliceDistributions(t, samples, 7, expected)
195 func TestStandardExponentialValues(t *testing.T) {
196 for _, seed := range testSeeds {
197 testExponentialDistribution(t, numTestSamples, 1, seed)
201 func TestNonStandardExponentialValues(t *testing.T) {
202 for rate := 0.05; rate < 10; rate *= 2 {
203 for _, seed := range testSeeds {
204 testExponentialDistribution(t, numTestSamples, rate, seed)
213 // Table generation tests
216 func initNorm() (testKn []uint32, testWn, testFn []float32) {
221 vn float64 = 9.91256303526217e-3
224 testKn = make([]uint32, 128)
225 testWn = make([]float32, 128)
226 testFn = make([]float32, 128)
228 q := vn / math.Exp(-0.5*dn*dn)
229 testKn[0] = uint32((dn / q) * m1)
231 testWn[0] = float32(q / m1)
232 testWn[127] = float32(dn / m1)
234 testFn[127] = float32(math.Exp(-0.5 * dn * dn))
235 for i := 126; i >= 1; i-- {
236 dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
237 testKn[i+1] = uint32((dn / tn) * m1)
239 testFn[i] = float32(math.Exp(-0.5 * dn * dn))
240 testWn[i] = float32(dn / m1)
245 func initExp() (testKe []uint32, testWe, testFe []float32) {
250 ve float64 = 3.9496598225815571993e-3
253 testKe = make([]uint32, 256)
254 testWe = make([]float32, 256)
255 testFe = make([]float32, 256)
257 q := ve / math.Exp(-de)
258 testKe[0] = uint32((de / q) * m2)
260 testWe[0] = float32(q / m2)
261 testWe[255] = float32(de / m2)
263 testFe[255] = float32(math.Exp(-de))
264 for i := 254; i >= 1; i-- {
265 de = -math.Log(ve/de + math.Exp(-de))
266 testKe[i+1] = uint32((de / te) * m2)
268 testFe[i] = float32(math.Exp(-de))
269 testWe[i] = float32(de / m2)
274 // compareUint32Slices returns the first index where the two slices
275 // disagree, or <0 if the lengths are the same and all elements
277 func compareUint32Slices(s1, s2 []uint32) int {
278 if len(s1) != len(s2) {
279 if len(s1) > len(s2) {
292 // compareFloat32Slices returns the first index where the two slices
293 // disagree, or <0 if the lengths are the same and all elements
295 func compareFloat32Slices(s1, s2 []float32) int {
296 if len(s1) != len(s2) {
297 if len(s1) > len(s2) {
303 if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
310 func TestNormTables(t *testing.T) {
311 testKn, testWn, testFn := initNorm()
312 if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
313 t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
315 if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
316 t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
318 if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
319 t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
323 func TestExpTables(t *testing.T) {
324 testKe, testWe, testFe := initExp()
325 if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
326 t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
328 if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
329 t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
331 if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
332 t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
336 func hasSlowFloatingPoint() bool {
337 switch runtime.GOARCH {
339 return os.Getenv("GOARM") == "5"
340 case "mips", "mipsle", "mips64", "mips64le":
341 // Be conservative and assume that all mips boards
342 // have emulated floating point.
343 // TODO: detect what it actually has.
349 func TestFloat32(t *testing.T) {
350 // For issue 6721, the problem came after 7533753 calls, so check 10e6.
352 // But do the full amount only on builders (not locally).
353 // But ARM5 floating point emulation is slow (Issue 10749), so
354 // do less for that builder:
355 if testing.Short() && (testenv.Builder() == "" || hasSlowFloatingPoint()) {
356 num /= 100 // 1.72 seconds instead of 172 seconds
360 for ct := 0; ct < num; ct++ {
363 t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
368 func TestShuffleSmall(t *testing.T) {
369 // Check that Shuffle allows n=0 and n=1, but that swap is never called for them.
371 for n := 0; n <= 1; n++ {
372 r.Shuffle(n, func(i, j int) { t.Fatalf("swap called, n=%d i=%d j=%d", n, i, j) })
376 // encodePerm converts from a permuted slice of length n, such as Perm generates, to an int in [0, n!).
377 // See https://en.wikipedia.org/wiki/Lehmer_code.
378 // encodePerm modifies the input slice.
379 func encodePerm(s []int) int {
380 // Convert to Lehmer code.
381 for i, x := range s {
383 for j, y := range r {
389 // Convert to int in [0, n!).
392 for i := len(s) - 1; i >= 0; i-- {
399 // TestUniformFactorial tests several ways of generating a uniform value in [0, n!).
400 func TestUniformFactorial(t *testing.T) {
401 r := New(NewSource(testSeeds[0]))
406 for n := 3; n <= top; n++ {
407 t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
410 for i := 2; i <= n; i++ {
414 // Test a few different ways to generate a uniform distribution.
415 p := make([]int, n) // re-usable slice for Shuffle generator
416 tests := [...]struct {
420 {name: "Int32N", fn: func() int { return int(r.Int32N(int32(nfact))) }},
421 {name: "int31n", fn: func() int { return int(Int32NForTest(r, int32(nfact))) }},
422 {name: "Perm", fn: func() int { return encodePerm(r.Perm(n)) }},
423 {name: "Shuffle", fn: func() int {
424 // Generate permutation using Shuffle.
428 r.Shuffle(n, func(i, j int) { p[i], p[j] = p[j], p[i] })
433 for _, test := range tests {
434 t.Run(test.name, func(t *testing.T) {
435 // Gather chi-squared values and check that they follow
436 // the expected normal distribution given n!-1 degrees of freedom.
437 // See https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test and
438 // https://www.johndcook.com/Beautiful_Testing_ch10.pdf.
439 nsamples := 10 * nfact
443 samples := make([]float64, nsamples)
444 for i := range samples {
445 // Generate some uniformly distributed values and count their occurrences.
447 counts := make([]int, nfact)
448 for i := 0; i < iters; i++ {
451 // Calculate chi-squared and add to samples.
452 want := iters / float64(nfact)
454 for _, have := range counts {
455 err := float64(have) - want
462 // Check that our samples approximate the appropriate normal distribution.
463 dof := float64(nfact - 1)
464 expected := &statsResults{mean: dof, stddev: math.Sqrt(2 * dof)}
465 errorScale := max(1.0, expected.stddev)
466 expected.closeEnough = 0.10 * errorScale
467 expected.maxError = 0.08 // TODO: What is the right value here? See issue 21211.
468 checkSampleDistribution(t, samples, expected)
479 func testRand() *Rand {
480 return New(NewSource(1))
483 func BenchmarkSourceUint64(b *testing.B) {
484 s := NewSource(1).(Source64)
486 for n := b.N; n > 0; n-- {
492 func BenchmarkGlobalInt64(b *testing.B) {
494 for n := b.N; n > 0; n-- {
500 func BenchmarkGlobalInt63Parallel(b *testing.B) {
501 b.RunParallel(func(pb *testing.PB) {
506 atomic.AddUint64(&Sink, uint64(t))
510 func BenchmarkGlobalUint64(b *testing.B) {
512 for n := b.N; n > 0; n-- {
518 func BenchmarkGlobalUint64Parallel(b *testing.B) {
519 b.RunParallel(func(pb *testing.PB) {
524 atomic.AddUint64(&Sink, t)
528 func BenchmarkInt64(b *testing.B) {
531 for n := b.N; n > 0; n-- {
537 var AlwaysFalse = false
539 func keep[T int | uint | int32 | uint32 | int64 | uint64](x T) T {
546 func BenchmarkUint64(b *testing.B) {
549 for n := b.N; n > 0; n-- {
555 func BenchmarkGlobalIntN1000(b *testing.B) {
558 for n := b.N; n > 0; n-- {
564 func BenchmarkIntN1000(b *testing.B) {
568 for n := b.N; n > 0; n-- {
574 func BenchmarkInt64N1000(b *testing.B) {
577 arg := keep(int64(1000))
578 for n := b.N; n > 0; n-- {
584 func BenchmarkInt64N1e8(b *testing.B) {
587 arg := keep(int64(1e8))
588 for n := b.N; n > 0; n-- {
594 func BenchmarkInt64N1e9(b *testing.B) {
597 arg := keep(int64(1e9))
598 for n := b.N; n > 0; n-- {
604 func BenchmarkInt64N2e9(b *testing.B) {
607 arg := keep(int64(2e9))
608 for n := b.N; n > 0; n-- {
614 func BenchmarkInt64N1e18(b *testing.B) {
617 arg := keep(int64(1e18))
618 for n := b.N; n > 0; n-- {
624 func BenchmarkInt64N2e18(b *testing.B) {
627 arg := keep(int64(2e18))
628 for n := b.N; n > 0; n-- {
634 func BenchmarkInt64N4e18(b *testing.B) {
637 arg := keep(int64(4e18))
638 for n := b.N; n > 0; n-- {
644 func BenchmarkInt32N1000(b *testing.B) {
647 arg := keep(int32(1000))
648 for n := b.N; n > 0; n-- {
654 func BenchmarkInt32N1e8(b *testing.B) {
657 arg := keep(int32(1e8))
658 for n := b.N; n > 0; n-- {
664 func BenchmarkInt32N1e9(b *testing.B) {
667 arg := keep(int32(1e9))
668 for n := b.N; n > 0; n-- {
674 func BenchmarkInt32N2e9(b *testing.B) {
677 arg := keep(int32(2e9))
678 for n := b.N; n > 0; n-- {
684 func BenchmarkFloat32(b *testing.B) {
687 for n := b.N; n > 0; n-- {
693 func BenchmarkFloat64(b *testing.B) {
696 for n := b.N; n > 0; n-- {
702 func BenchmarkExpFloat64(b *testing.B) {
705 for n := b.N; n > 0; n-- {
711 func BenchmarkNormFloat64(b *testing.B) {
714 for n := b.N; n > 0; n-- {
720 func BenchmarkPerm3(b *testing.B) {
723 for n := b.N; n > 0; n-- {
730 func BenchmarkPerm30(b *testing.B) {
733 for n := b.N; n > 0; n-- {
739 func BenchmarkPerm30ViaShuffle(b *testing.B) {
742 for n := b.N; n > 0; n-- {
747 r.Shuffle(30, func(i, j int) { p[i], p[j] = p[j], p[i] })
753 // BenchmarkShuffleOverhead uses a minimal swap function
754 // to measure just the shuffling overhead.
755 func BenchmarkShuffleOverhead(b *testing.B) {
757 for n := b.N; n > 0; n-- {
758 r.Shuffle(30, func(i, j int) {
759 if i < 0 || i >= 30 || j < 0 || j >= 30 {
760 b.Fatalf("bad swap(%d, %d)", i, j)
766 func BenchmarkConcurrent(b *testing.B) {
768 var wg sync.WaitGroup
770 for i := 0; i < goroutines; i++ {
773 for n := b.N; n > 0; n-- {