// 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 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)
}
}
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