685 lines
17 KiB
Go
685 lines
17 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package rand_test
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import (
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"bytes"
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"errors"
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"fmt"
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"internal/testenv"
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"io"
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"math"
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. "math/rand"
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"os"
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"runtime"
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"testing"
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"testing/iotest"
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)
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const (
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numTestSamples = 10000
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)
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var rn, kn, wn, fn = GetNormalDistributionParameters()
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var re, ke, we, fe = GetExponentialDistributionParameters()
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type statsResults struct {
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mean float64
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stddev float64
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closeEnough float64
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maxError float64
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}
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func max(a, b float64) float64 {
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if a > b {
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return a
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}
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return b
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}
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func nearEqual(a, b, closeEnough, maxError float64) bool {
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absDiff := math.Abs(a - b)
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if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
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return true
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}
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return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
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}
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var testSeeds = []int64{1, 1754801282, 1698661970, 1550503961}
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// checkSimilarDistribution returns success if the mean and stddev of the
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// two statsResults are similar.
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func (this *statsResults) checkSimilarDistribution(expected *statsResults) error {
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if !nearEqual(this.mean, expected.mean, expected.closeEnough, expected.maxError) {
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s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", this.mean, expected.mean, expected.closeEnough, expected.maxError)
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fmt.Println(s)
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return errors.New(s)
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}
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if !nearEqual(this.stddev, expected.stddev, expected.closeEnough, expected.maxError) {
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s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", this.stddev, expected.stddev, expected.closeEnough, expected.maxError)
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fmt.Println(s)
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return errors.New(s)
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}
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return nil
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}
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func getStatsResults(samples []float64) *statsResults {
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res := new(statsResults)
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var sum, squaresum float64
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for _, s := range samples {
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sum += s
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squaresum += s * s
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}
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res.mean = sum / float64(len(samples))
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res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
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return res
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}
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func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
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t.Helper()
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actual := getStatsResults(samples)
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err := actual.checkSimilarDistribution(expected)
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if err != nil {
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t.Errorf(err.Error())
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}
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}
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func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
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t.Helper()
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chunk := len(samples) / nslices
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for i := 0; i < nslices; i++ {
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low := i * chunk
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var high int
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if i == nslices-1 {
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high = len(samples) - 1
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} else {
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high = (i + 1) * chunk
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}
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checkSampleDistribution(t, samples[low:high], expected)
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}
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}
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//
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// Normal distribution tests
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//
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func generateNormalSamples(nsamples int, mean, stddev float64, seed int64) []float64 {
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r := New(NewSource(seed))
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samples := make([]float64, nsamples)
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for i := range samples {
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samples[i] = r.NormFloat64()*stddev + mean
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}
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return samples
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}
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func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed int64) {
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//fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
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samples := generateNormalSamples(nsamples, mean, stddev, seed)
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errorScale := max(1.0, stddev) // Error scales with stddev
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expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
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// Make sure that the entire set matches the expected distribution.
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checkSampleDistribution(t, samples, expected)
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// Make sure that each half of the set matches the expected distribution.
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checkSampleSliceDistributions(t, samples, 2, expected)
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// Make sure that each 7th of the set matches the expected distribution.
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checkSampleSliceDistributions(t, samples, 7, expected)
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}
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// Actual tests
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func TestStandardNormalValues(t *testing.T) {
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for _, seed := range testSeeds {
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testNormalDistribution(t, numTestSamples, 0, 1, seed)
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}
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}
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func TestNonStandardNormalValues(t *testing.T) {
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sdmax := 1000.0
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mmax := 1000.0
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if testing.Short() {
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sdmax = 5
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mmax = 5
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}
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for sd := 0.5; sd < sdmax; sd *= 2 {
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for m := 0.5; m < mmax; m *= 2 {
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for _, seed := range testSeeds {
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testNormalDistribution(t, numTestSamples, m, sd, seed)
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if testing.Short() {
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break
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}
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}
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}
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}
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}
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//
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// Exponential distribution tests
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//
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func generateExponentialSamples(nsamples int, rate float64, seed int64) []float64 {
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r := New(NewSource(seed))
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samples := make([]float64, nsamples)
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for i := range samples {
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samples[i] = r.ExpFloat64() / rate
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}
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return samples
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}
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func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed int64) {
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//fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed);
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mean := 1 / rate
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stddev := mean
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samples := generateExponentialSamples(nsamples, rate, seed)
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errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
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expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
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// Make sure that the entire set matches the expected distribution.
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checkSampleDistribution(t, samples, expected)
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// Make sure that each half of the set matches the expected distribution.
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checkSampleSliceDistributions(t, samples, 2, expected)
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// Make sure that each 7th of the set matches the expected distribution.
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checkSampleSliceDistributions(t, samples, 7, expected)
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}
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// Actual tests
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func TestStandardExponentialValues(t *testing.T) {
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for _, seed := range testSeeds {
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testExponentialDistribution(t, numTestSamples, 1, seed)
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}
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}
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func TestNonStandardExponentialValues(t *testing.T) {
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for rate := 0.05; rate < 10; rate *= 2 {
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for _, seed := range testSeeds {
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testExponentialDistribution(t, numTestSamples, rate, seed)
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if testing.Short() {
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break
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}
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}
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}
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}
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//
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// Table generation tests
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//
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func initNorm() (testKn []uint32, testWn, testFn []float32) {
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const m1 = 1 << 31
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var (
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dn float64 = rn
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tn = dn
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vn float64 = 9.91256303526217e-3
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)
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testKn = make([]uint32, 128)
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testWn = make([]float32, 128)
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testFn = make([]float32, 128)
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q := vn / math.Exp(-0.5*dn*dn)
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testKn[0] = uint32((dn / q) * m1)
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testKn[1] = 0
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testWn[0] = float32(q / m1)
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testWn[127] = float32(dn / m1)
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testFn[0] = 1.0
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testFn[127] = float32(math.Exp(-0.5 * dn * dn))
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for i := 126; i >= 1; i-- {
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dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
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testKn[i+1] = uint32((dn / tn) * m1)
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tn = dn
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testFn[i] = float32(math.Exp(-0.5 * dn * dn))
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testWn[i] = float32(dn / m1)
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}
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return
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}
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func initExp() (testKe []uint32, testWe, testFe []float32) {
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const m2 = 1 << 32
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var (
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de float64 = re
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te = de
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ve float64 = 3.9496598225815571993e-3
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)
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testKe = make([]uint32, 256)
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testWe = make([]float32, 256)
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testFe = make([]float32, 256)
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q := ve / math.Exp(-de)
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testKe[0] = uint32((de / q) * m2)
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testKe[1] = 0
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testWe[0] = float32(q / m2)
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testWe[255] = float32(de / m2)
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testFe[0] = 1.0
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testFe[255] = float32(math.Exp(-de))
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for i := 254; i >= 1; i-- {
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de = -math.Log(ve/de + math.Exp(-de))
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testKe[i+1] = uint32((de / te) * m2)
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te = de
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testFe[i] = float32(math.Exp(-de))
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testWe[i] = float32(de / m2)
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}
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return
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}
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// compareUint32Slices returns the first index where the two slices
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// disagree, or <0 if the lengths are the same and all elements
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// are identical.
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func compareUint32Slices(s1, s2 []uint32) int {
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if len(s1) != len(s2) {
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if len(s1) > len(s2) {
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return len(s2) + 1
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}
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return len(s1) + 1
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}
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for i := range s1 {
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if s1[i] != s2[i] {
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return i
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}
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}
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return -1
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}
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// compareFloat32Slices returns the first index where the two slices
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// disagree, or <0 if the lengths are the same and all elements
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// are identical.
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func compareFloat32Slices(s1, s2 []float32) int {
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if len(s1) != len(s2) {
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if len(s1) > len(s2) {
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return len(s2) + 1
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}
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return len(s1) + 1
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}
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for i := range s1 {
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if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
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return i
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}
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}
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return -1
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}
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func TestNormTables(t *testing.T) {
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testKn, testWn, testFn := initNorm()
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if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
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t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
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}
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if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
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t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
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}
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if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
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t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
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}
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}
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func TestExpTables(t *testing.T) {
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testKe, testWe, testFe := initExp()
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if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
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t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
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}
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if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
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t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
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}
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if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
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t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
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}
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}
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func hasSlowFloatingPoint() bool {
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switch runtime.GOARCH {
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case "arm":
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return os.Getenv("GOARM") == "5"
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case "mips", "mipsle", "mips64", "mips64le":
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// Be conservative and assume that all mips boards
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// have emulated floating point.
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// TODO: detect what it actually has.
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return true
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}
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return false
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}
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func TestFloat32(t *testing.T) {
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// For issue 6721, the problem came after 7533753 calls, so check 10e6.
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num := int(10e6)
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// But do the full amount only on builders (not locally).
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// But ARM5 floating point emulation is slow (Issue 10749), so
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// do less for that builder:
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if testing.Short() && (testenv.Builder() == "" || hasSlowFloatingPoint()) {
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num /= 100 // 1.72 seconds instead of 172 seconds
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}
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r := New(NewSource(1))
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for ct := 0; ct < num; ct++ {
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f := r.Float32()
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if f >= 1 {
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t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
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}
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}
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}
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func testReadUniformity(t *testing.T, n int, seed int64) {
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r := New(NewSource(seed))
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buf := make([]byte, n)
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nRead, err := r.Read(buf)
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if err != nil {
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t.Errorf("Read err %v", err)
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}
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if nRead != n {
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t.Errorf("Read returned unexpected n; %d != %d", nRead, n)
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}
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// Expect a uniform distribution of byte values, which lie in [0, 255].
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var (
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mean = 255.0 / 2
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stddev = 256.0 / math.Sqrt(12.0)
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errorScale = stddev / math.Sqrt(float64(n))
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)
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expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
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// Cast bytes as floats to use the common distribution-validity checks.
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samples := make([]float64, n)
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for i, val := range buf {
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samples[i] = float64(val)
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}
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// Make sure that the entire set matches the expected distribution.
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checkSampleDistribution(t, samples, expected)
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}
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func TestReadUniformity(t *testing.T) {
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testBufferSizes := []int{
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2, 4, 7, 64, 1024, 1 << 16, 1 << 20,
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}
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for _, seed := range testSeeds {
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for _, n := range testBufferSizes {
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testReadUniformity(t, n, seed)
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}
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}
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}
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func TestReadEmpty(t *testing.T) {
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r := New(NewSource(1))
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buf := make([]byte, 0)
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n, err := r.Read(buf)
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if err != nil {
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t.Errorf("Read err into empty buffer; %v", err)
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}
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if n != 0 {
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t.Errorf("Read into empty buffer returned unexpected n of %d", n)
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}
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}
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func TestReadByOneByte(t *testing.T) {
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r := New(NewSource(1))
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b1 := make([]byte, 100)
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_, err := io.ReadFull(iotest.OneByteReader(r), b1)
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if err != nil {
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t.Errorf("read by one byte: %v", err)
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}
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r = New(NewSource(1))
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b2 := make([]byte, 100)
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_, err = r.Read(b2)
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if err != nil {
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t.Errorf("read: %v", err)
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}
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if !bytes.Equal(b1, b2) {
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t.Errorf("read by one byte vs single read:\n%x\n%x", b1, b2)
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}
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}
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func TestReadSeedReset(t *testing.T) {
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r := New(NewSource(42))
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b1 := make([]byte, 128)
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_, err := r.Read(b1)
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if err != nil {
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t.Errorf("read: %v", err)
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}
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r.Seed(42)
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b2 := make([]byte, 128)
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_, err = r.Read(b2)
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if err != nil {
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t.Errorf("read: %v", err)
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}
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if !bytes.Equal(b1, b2) {
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t.Errorf("mismatch after re-seed:\n%x\n%x", b1, b2)
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}
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}
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func TestShuffleSmall(t *testing.T) {
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// Check that Shuffle allows n=0 and n=1, but that swap is never called for them.
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r := New(NewSource(1))
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for n := 0; n <= 1; n++ {
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r.Shuffle(n, func(i, j int) { t.Fatalf("swap called, n=%d i=%d j=%d", n, i, j) })
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}
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}
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// encodePerm converts from a permuted slice of length n, such as Perm generates, to an int in [0, n!).
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// See https://en.wikipedia.org/wiki/Lehmer_code.
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// encodePerm modifies the input slice.
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func encodePerm(s []int) int {
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// Convert to Lehmer code.
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for i, x := range s {
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r := s[i+1:]
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for j, y := range r {
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if y > x {
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r[j]--
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}
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}
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}
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// Convert to int in [0, n!).
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m := 0
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fact := 1
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for i := len(s) - 1; i >= 0; i-- {
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m += s[i] * fact
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fact *= len(s) - i
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}
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return m
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}
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// TestUniformFactorial tests several ways of generating a uniform value in [0, n!).
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func TestUniformFactorial(t *testing.T) {
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r := New(NewSource(testSeeds[0]))
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top := 6
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if testing.Short() {
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top = 3
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}
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for n := 3; n <= top; n++ {
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t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
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// Calculate n!.
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nfact := 1
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for i := 2; i <= n; i++ {
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nfact *= i
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}
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// Test a few different ways to generate a uniform distribution.
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p := make([]int, n) // re-usable slice for Shuffle generator
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tests := [...]struct {
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name string
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fn func() int
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}{
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{name: "Int31n", fn: func() int { return int(r.Int31n(int32(nfact))) }},
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{name: "int31n", fn: func() int { return int(Int31nForTest(r, 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)
|
|
}
|
|
}
|