1 files changed, 398 insertions, 0 deletions
diff --git a/src/math/rand/rand_test.go b/src/math/rand/rand_test.go
new file mode 100644
index 000000000..ab0dc49b4
--- /dev/null
+++ b/src/math/rand/rand_test.go
@@ -0,0 +1,398 @@
+// 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 (
+	"errors"
+	"fmt"
+	"math"
+	"testing"
+)
+
+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, 0, 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) {
+	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) {
+	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])
+	}
+}
+
+// For issue 6721, the problem came after 7533753 calls, so check 10e6.
+func TestFloat32(t *testing.T) {
+	r := New(NewSource(1))
+	for ct := 0; ct < 10e6; ct++ {
+		f := r.Float32()
+		if f >= 1 {
+			t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
+		}
+	}
+}
+
+// Benchmarks
+
+func BenchmarkInt63Threadsafe(b *testing.B) {
+	for n := b.N; n > 0; n-- {
+		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)
+	}
+}