Adding upstream version 1.16.10.upstream/1.16.10upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 681 insertions, 0 deletions

diff --git a/src/math/rand/rand_test.go b/src/math/rand/rand_test.go
new file mode 100644
index 0000000..e037aae
--- /dev/null
+++ b/src/math/rand/rand_test.go
@@ -0,0 +1,681 @@
+// 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 rand
+
+import (
+	"bytes"
+	"errors"
+	"fmt"
+	"internal/testenv"
+	"io"
+	"math"
+	"os"
+	"runtime"
+	"testing"
+	"testing/iotest"
+)
+
+const (
+	numTestSamples = 10000
+)
+
+type statsResults struct {
+	mean        float64
+	stddev      float64
+	closeEnough float64
+	maxError    float64
+}
+
+func max(a, b float64) float64 {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func nearEqual(a, b, closeEnough, maxError float64) bool {
+	absDiff := math.Abs(a - b)
+	if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
+		return true
+	}
+	return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
+}
+
+var testSeeds = []int64{1, 1754801282, 1698661970, 1550503961}
+
+// checkSimilarDistribution returns success if the mean and stddev of the
+// two statsResults are similar.
+func (this *statsResults) checkSimilarDistribution(expected *statsResults) error {
+	if !nearEqual(this.mean, expected.mean, expected.closeEnough, expected.maxError) {
+		s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", this.mean, expected.mean, expected.closeEnough, expected.maxError)
+		fmt.Println(s)
+		return errors.New(s)
+	}
+	if !nearEqual(this.stddev, expected.stddev, expected.closeEnough, expected.maxError) {
+		s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", this.stddev, expected.stddev, expected.closeEnough, expected.maxError)
+		fmt.Println(s)
+		return errors.New(s)
+	}
+	return nil
+}
+
+func getStatsResults(samples []float64) *statsResults {
+	res := new(statsResults)
+	var sum, squaresum float64
+	for _, s := range samples {
+		sum += s
+		squaresum += s * s
+	}
+	res.mean = sum / float64(len(samples))
+	res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
+	return res
+}
+
+func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
+	t.Helper()
+	actual := getStatsResults(samples)
+	err := actual.checkSimilarDistribution(expected)
+	if err != nil {
+		t.Errorf(err.Error())
+	}
+}
+
+func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
+	t.Helper()
+	chunk := len(samples) / nslices
+	for i := 0; i < nslices; i++ {
+		low := i * chunk
+		var high int
+		if i == nslices-1 {
+			high = len(samples) - 1
+		} else {
+			high = (i + 1) * chunk
+		}
+		checkSampleDistribution(t, samples[low:high], expected)
+	}
+}
+
+//
+// Normal distribution tests
+//
+
+func generateNormalSamples(nsamples int, mean, stddev float64, seed int64) []float64 {
+	r := New(NewSource(seed))
+	samples := make([]float64, nsamples)
+	for i := range samples {
+		samples[i] = r.NormFloat64()*stddev + mean
+	}
+	return samples
+}
+
+func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed int64) {
+	//fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
+
+	samples := generateNormalSamples(nsamples, mean, stddev, seed)
+	errorScale := max(1.0, stddev) // Error scales with stddev
+	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
+
+	// Make sure that the entire set matches the expected distribution.
+	checkSampleDistribution(t, samples, expected)
+
+	// Make sure that each half of the set matches the expected distribution.
+	checkSampleSliceDistributions(t, samples, 2, expected)
+
+	// Make sure that each 7th of the set matches the expected distribution.
+	checkSampleSliceDistributions(t, samples, 7, expected)
+}
+
+// Actual tests
+
+func TestStandardNormalValues(t *testing.T) {
+	for _, seed := range testSeeds {
+		testNormalDistribution(t, numTestSamples, 0, 1, seed)
+	}
+}
+
+func TestNonStandardNormalValues(t *testing.T) {
+	sdmax := 1000.0
+	mmax := 1000.0
+	if testing.Short() {
+		sdmax = 5
+		mmax = 5
+	}
+	for sd := 0.5; sd < sdmax; sd *= 2 {
+		for m := 0.5; m < mmax; m *= 2 {
+			for _, seed := range testSeeds {
+				testNormalDistribution(t, numTestSamples, m, sd, seed)
+				if testing.Short() {
+					break
+				}
+			}
+		}
+	}
+}
+
+//
+// Exponential distribution tests
+//
+
+func generateExponentialSamples(nsamples int, rate float64, seed int64) []float64 {
+	r := New(NewSource(seed))
+	samples := make([]float64, nsamples)
+	for i := range samples {
+		samples[i] = r.ExpFloat64() / rate
+	}
+	return samples
+}
+
+func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed int64) {
+	//fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed);
+
+	mean := 1 / rate
+	stddev := mean
+
+	samples := generateExponentialSamples(nsamples, rate, seed)
+	errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
+	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
+
+	// Make sure that the entire set matches the expected distribution.
+	checkSampleDistribution(t, samples, expected)
+
+	// Make sure that each half of the set matches the expected distribution.
+	checkSampleSliceDistributions(t, samples, 2, expected)
+
+	// Make sure that each 7th of the set matches the expected distribution.
+	checkSampleSliceDistributions(t, samples, 7, expected)
+}
+
+// Actual tests
+
+func TestStandardExponentialValues(t *testing.T) {
+	for _, seed := range testSeeds {
+		testExponentialDistribution(t, numTestSamples, 1, seed)
+	}
+}
+
+func TestNonStandardExponentialValues(t *testing.T) {
+	for rate := 0.05; rate < 10; rate *= 2 {
+		for _, seed := range testSeeds {
+			testExponentialDistribution(t, numTestSamples, rate, seed)
+			if testing.Short() {
+				break
+			}
+		}
+	}
+}
+
+//
+// Table generation tests
+//
+
+func initNorm() (testKn []uint32, testWn, testFn []float32) {
+	const m1 = 1 << 31
+	var (
+		dn float64 = rn
+		tn         = dn
+		vn float64 = 9.91256303526217e-3
+	)
+
+	testKn = make([]uint32, 128)
+	testWn = make([]float32, 128)
+	testFn = make([]float32, 128)
+
+	q := vn / math.Exp(-0.5*dn*dn)
+	testKn[0] = uint32((dn / q) * m1)
+	testKn[1] = 0
+	testWn[0] = float32(q / m1)
+	testWn[127] = float32(dn / m1)
+	testFn[0] = 1.0
+	testFn[127] = float32(math.Exp(-0.5 * dn * dn))
+	for i := 126; i >= 1; i-- {
+		dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
+		testKn[i+1] = uint32((dn / tn) * m1)
+		tn = dn
+		testFn[i] = float32(math.Exp(-0.5 * dn * dn))
+		testWn[i] = float32(dn / m1)
+	}
+	return
+}
+
+func initExp() (testKe []uint32, testWe, testFe []float32) {
+	const m2 = 1 << 32
+	var (
+		de float64 = re
+		te         = de
+		ve float64 = 3.9496598225815571993e-3
+	)
+
+	testKe = make([]uint32, 256)
+	testWe = make([]float32, 256)
+	testFe = make([]float32, 256)
+
+	q := ve / math.Exp(-de)
+	testKe[0] = uint32((de / q) * m2)
+	testKe[1] = 0
+	testWe[0] = float32(q / m2)
+	testWe[255] = float32(de / m2)
+	testFe[0] = 1.0
+	testFe[255] = float32(math.Exp(-de))
+	for i := 254; i >= 1; i-- {
+		de = -math.Log(ve/de + math.Exp(-de))
+		testKe[i+1] = uint32((de / te) * m2)
+		te = de
+		testFe[i] = float32(math.Exp(-de))
+		testWe[i] = float32(de / m2)
+	}
+	return
+}
+
+// compareUint32Slices returns the first index where the two slices
+// disagree, or <0 if the lengths are the same and all elements
+// are identical.
+func compareUint32Slices(s1, s2 []uint32) int {
+	if len(s1) != len(s2) {
+		if len(s1) > len(s2) {
+			return len(s2) + 1
+		}
+		return len(s1) + 1
+	}
+	for i := range s1 {
+		if s1[i] != s2[i] {
+			return i
+		}
+	}
+	return -1
+}
+
+// compareFloat32Slices returns the first index where the two slices
+// disagree, or <0 if the lengths are the same and all elements
+// are identical.
+func compareFloat32Slices(s1, s2 []float32) int {
+	if len(s1) != len(s2) {
+		if len(s1) > len(s2) {
+			return len(s2) + 1
+		}
+		return len(s1) + 1
+	}
+	for i := range s1 {
+		if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
+			return i
+		}
+	}
+	return -1
+}
+
+func TestNormTables(t *testing.T) {
+	testKn, testWn, testFn := initNorm()
+	if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
+		t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
+	}
+	if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
+		t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
+	}
+	if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
+		t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
+	}
+}
+
+func TestExpTables(t *testing.T) {
+	testKe, testWe, testFe := initExp()
+	if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
+		t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
+	}
+	if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
+		t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
+	}
+	if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
+		t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
+	}
+}
+
+func hasSlowFloatingPoint() bool {
+	switch runtime.GOARCH {
+	case "arm":
+		return os.Getenv("GOARM") == "5"
+	case "mips", "mipsle", "mips64", "mips64le":
+		// Be conservative and assume that all mips boards
+		// have emulated floating point.
+		// TODO: detect what it actually has.
+		return true
+	}
+	return false
+}
+
+func TestFloat32(t *testing.T) {
+	// For issue 6721, the problem came after 7533753 calls, so check 10e6.
+	num := int(10e6)
+	// But do the full amount only on builders (not locally).
+	// But ARM5 floating point emulation is slow (Issue 10749), so
+	// do less for that builder:
+	if testing.Short() && (testenv.Builder() == "" || hasSlowFloatingPoint()) {
+		num /= 100 // 1.72 seconds instead of 172 seconds
+	}
+
+	r := New(NewSource(1))
+	for ct := 0; ct < num; ct++ {
+		f := r.Float32()
+		if f >= 1 {
+			t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
+		}
+	}
+}
+
+func testReadUniformity(t *testing.T, n int, seed int64) {
+	r := New(NewSource(seed))
+	buf := make([]byte, n)
+	nRead, err := r.Read(buf)
+	if err != nil {
+		t.Errorf("Read err %v", err)
+	}
+	if nRead != n {
+		t.Errorf("Read returned unexpected n; %d != %d", nRead, n)
+	}
+
+	// Expect a uniform distribution of byte values, which lie in [0, 255].
+	var (
+		mean       = 255.0 / 2
+		stddev     = 256.0 / math.Sqrt(12.0)
+		errorScale = stddev / math.Sqrt(float64(n))
+	)
+
+	expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
+
+	// Cast bytes as floats to use the common distribution-validity checks.
+	samples := make([]float64, n)
+	for i, val := range buf {
+		samples[i] = float64(val)
+	}
+	// Make sure that the entire set matches the expected distribution.
+	checkSampleDistribution(t, samples, expected)
+}
+
+func TestReadUniformity(t *testing.T) {
+	testBufferSizes := []int{
+		2, 4, 7, 64, 1024, 1 << 16, 1 << 20,
+	}
+	for _, seed := range testSeeds {
+		for _, n := range testBufferSizes {
+			testReadUniformity(t, n, seed)
+		}
+	}
+}
+
+func TestReadEmpty(t *testing.T) {
+	r := New(NewSource(1))
+	buf := make([]byte, 0)
+	n, err := r.Read(buf)
+	if err != nil {
+		t.Errorf("Read err into empty buffer; %v", err)
+	}
+	if n != 0 {
+		t.Errorf("Read into empty buffer returned unexpected n of %d", n)
+	}
+}
+
+func TestReadByOneByte(t *testing.T) {
+	r := New(NewSource(1))
+	b1 := make([]byte, 100)
+	_, err := io.ReadFull(iotest.OneByteReader(r), b1)
+	if err != nil {
+		t.Errorf("read by one byte: %v", err)
+	}
+	r = New(NewSource(1))
+	b2 := make([]byte, 100)
+	_, err = r.Read(b2)
+	if err != nil {
+		t.Errorf("read: %v", err)
+	}
+	if !bytes.Equal(b1, b2) {
+		t.Errorf("read by one byte vs single read:\n%x\n%x", b1, b2)
+	}
+}
+
+func TestReadSeedReset(t *testing.T) {
+	r := New(NewSource(42))
+	b1 := make([]byte, 128)
+	_, err := r.Read(b1)
+	if err != nil {
+		t.Errorf("read: %v", err)
+	}
+	r.Seed(42)
+	b2 := make([]byte, 128)
+	_, err = r.Read(b2)
+	if err != nil {
+		t.Errorf("read: %v", err)
+	}
+	if !bytes.Equal(b1, b2) {
+		t.Errorf("mismatch after re-seed:\n%x\n%x", b1, b2)
+	}
+}
+
+func TestShuffleSmall(t *testing.T) {
+	// Check that Shuffle allows n=0 and n=1, but that swap is never called for them.
+	r := New(NewSource(1))
+	for n := 0; n <= 1; n++ {
+		r.Shuffle(n, func(i, j int) { t.Fatalf("swap called, n=%d i=%d j=%d", n, i, j) })
+	}
+}
+
+// encodePerm converts from a permuted slice of length n, such as Perm generates, to an int in [0, n!).
+// See https://en.wikipedia.org/wiki/Lehmer_code.
+// encodePerm modifies the input slice.
+func encodePerm(s []int) int {
+	// Convert to Lehmer code.
+	for i, x := range s {
+		r := s[i+1:]
+		for j, y := range r {
+			if y > x {
+				r[j]--
+			}
+		}
+	}
+	// Convert to int in [0, n!).
+	m := 0
+	fact := 1
+	for i := len(s) - 1; i >= 0; i-- {
+		m += s[i] * fact
+		fact *= len(s) - i
+	}
+	return m
+}
+
+// TestUniformFactorial tests several ways of generating a uniform value in [0, n!).
+func TestUniformFactorial(t *testing.T) {
+	r := New(NewSource(testSeeds[0]))
+	top := 6
+	if testing.Short() {
+		top = 3
+	}
+	for n := 3; n <= top; n++ {
+		t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
+			// Calculate n!.
+			nfact := 1
+			for i := 2; i <= n; i++ {
+				nfact *= i
+			}
+
+			// Test a few different ways to generate a uniform distribution.
+			p := make([]int, n) // re-usable slice for Shuffle generator
+			tests := [...]struct {
+				name string
+				fn   func() int
+			}{
+				{name: "Int31n", fn: func() int { return int(r.Int31n(int32(nfact))) }},
+				{name: "int31n", fn: func() int { return int(r.int31n(int32(nfact))) }},
+				{name: "Perm", fn: func() int { return encodePerm(r.Perm(n)) }},
+				{name: "Shuffle", fn: func() int {
+					// Generate permutation using Shuffle.
+					for i := range p {
+						p[i] = i
+					}
+					r.Shuffle(n, func(i, j int) { p[i], p[j] = p[j], p[i] })
+					return encodePerm(p)
+				}},
+			}
+
+			for _, test := range tests {
+				t.Run(test.name, func(t *testing.T) {
+					// Gather chi-squared values and check that they follow
+					// the expected normal distribution given n!-1 degrees of freedom.
+					// See https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test and
+					// https://www.johndcook.com/Beautiful_Testing_ch10.pdf.
+					nsamples := 10 * nfact
+					if nsamples < 200 {
+						nsamples = 200
+					}
+					samples := make([]float64, nsamples)
+					for i := range samples {
+						// Generate some uniformly distributed values and count their occurrences.
+						const iters = 1000
+						counts := make([]int, nfact)
+						for i := 0; i < iters; i++ {
+							counts[test.fn()]++
+						}
+						// Calculate chi-squared and add to samples.
+						want := iters / float64(nfact)
+						var χ2 float64
+						for _, have := range counts {
+							err := float64(have) - want
+							χ2 += err * err
+						}
+						χ2 /= want
+						samples[i] = χ2
+					}
+
+					// Check that our samples approximate the appropriate normal distribution.
+					dof := float64(nfact - 1)
+					expected := &statsResults{mean: dof, stddev: math.Sqrt(2 * dof)}
+					errorScale := max(1.0, expected.stddev)
+					expected.closeEnough = 0.10 * errorScale
+					expected.maxError = 0.08 // TODO: What is the right value here? See issue 21211.
+					checkSampleDistribution(t, samples, expected)
+				})
+			}
+		})
+	}
+}
+
+// Benchmarks
+
+func BenchmarkInt63Threadsafe(b *testing.B) {
+	for n := b.N; n > 0; n-- {
+		Int63()
+	}
+}
+
+func BenchmarkInt63ThreadsafeParallel(b *testing.B) {
+	b.RunParallel(func(pb *testing.PB) {
+		for pb.Next() {
+			Int63()
+		}
+	})
+}
+
+func BenchmarkInt63Unthreadsafe(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Int63()
+	}
+}
+
+func BenchmarkIntn1000(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Intn(1000)
+	}
+}
+
+func BenchmarkInt63n1000(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Int63n(1000)
+	}
+}
+
+func BenchmarkInt31n1000(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Int31n(1000)
+	}
+}
+
+func BenchmarkFloat32(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Float32()
+	}
+}
+
+func BenchmarkFloat64(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Float64()
+	}
+}
+
+func BenchmarkPerm3(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Perm(3)
+	}
+}
+
+func BenchmarkPerm30(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Perm(30)
+	}
+}
+
+func BenchmarkPerm30ViaShuffle(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		p := make([]int, 30)
+		for i := range p {
+			p[i] = i
+		}
+		r.Shuffle(30, func(i, j int) { p[i], p[j] = p[j], p[i] })
+	}
+}
+
+// BenchmarkShuffleOverhead uses a minimal swap function
+// to measure just the shuffling overhead.
+func BenchmarkShuffleOverhead(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Shuffle(52, func(i, j int) {
+			if i < 0 || i >= 52 || j < 0 || j >= 52 {
+				b.Fatalf("bad swap(%d, %d)", i, j)
+			}
+		})
+	}
+}
+
+func BenchmarkRead3(b *testing.B) {
+	r := New(NewSource(1))
+	buf := make([]byte, 3)
+	b.ResetTimer()
+	for n := b.N; n > 0; n-- {
+		r.Read(buf)
+	}
+}
+
+func BenchmarkRead64(b *testing.B) {
+	r := New(NewSource(1))
+	buf := make([]byte, 64)
+	b.ResetTimer()
+	for n := b.N; n > 0; n-- {
+		r.Read(buf)
+	}
+}
+
+func BenchmarkRead1000(b *testing.B) {
+	r := New(NewSource(1))
+	buf := make([]byte, 1000)
+	b.ResetTimer()
+	for n := b.N; n > 0; n-- {
+		r.Read(buf)
+	}
+}