1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
|
package quantile
import (
"math"
"math/rand"
"sort"
"testing"
)
var (
Targets = map[float64]float64{
0.01: 0.001,
0.10: 0.01,
0.50: 0.05,
0.90: 0.01,
0.99: 0.001,
}
TargetsSmallEpsilon = map[float64]float64{
0.01: 0.0001,
0.10: 0.001,
0.50: 0.005,
0.90: 0.001,
0.99: 0.0001,
}
LowQuantiles = []float64{0.01, 0.1, 0.5}
HighQuantiles = []float64{0.99, 0.9, 0.5}
)
const RelativeEpsilon = 0.01
func verifyPercsWithAbsoluteEpsilon(t *testing.T, a []float64, s *Stream) {
sort.Float64s(a)
for quantile, epsilon := range Targets {
n := float64(len(a))
k := int(quantile * n)
if k < 1 {
k = 1
}
lower := int((quantile - epsilon) * n)
if lower < 1 {
lower = 1
}
upper := int(math.Ceil((quantile + epsilon) * n))
if upper > len(a) {
upper = len(a)
}
w, min, max := a[k-1], a[lower-1], a[upper-1]
if g := s.Query(quantile); g < min || g > max {
t.Errorf("q=%f: want %v [%f,%f], got %v", quantile, w, min, max, g)
}
}
}
func verifyLowPercsWithRelativeEpsilon(t *testing.T, a []float64, s *Stream) {
sort.Float64s(a)
for _, qu := range LowQuantiles {
n := float64(len(a))
k := int(qu * n)
lowerRank := int((1 - RelativeEpsilon) * qu * n)
upperRank := int(math.Ceil((1 + RelativeEpsilon) * qu * n))
w, min, max := a[k-1], a[lowerRank-1], a[upperRank-1]
if g := s.Query(qu); g < min || g > max {
t.Errorf("q=%f: want %v [%f,%f], got %v", qu, w, min, max, g)
}
}
}
func verifyHighPercsWithRelativeEpsilon(t *testing.T, a []float64, s *Stream) {
sort.Float64s(a)
for _, qu := range HighQuantiles {
n := float64(len(a))
k := int(qu * n)
lowerRank := int((1 - (1+RelativeEpsilon)*(1-qu)) * n)
upperRank := int(math.Ceil((1 - (1-RelativeEpsilon)*(1-qu)) * n))
w, min, max := a[k-1], a[lowerRank-1], a[upperRank-1]
if g := s.Query(qu); g < min || g > max {
t.Errorf("q=%f: want %v [%f,%f], got %v", qu, w, min, max, g)
}
}
}
func populateStream(s *Stream) []float64 {
a := make([]float64, 0, 1e5+100)
for i := 0; i < cap(a); i++ {
v := rand.NormFloat64()
// Add 5% asymmetric outliers.
if i%20 == 0 {
v = v*v + 1
}
s.Insert(v)
a = append(a, v)
}
return a
}
func TestTargetedQuery(t *testing.T) {
rand.Seed(42)
s := NewTargeted(Targets)
a := populateStream(s)
verifyPercsWithAbsoluteEpsilon(t, a, s)
}
func TestTargetedQuerySmallSampleSize(t *testing.T) {
rand.Seed(42)
s := NewTargeted(TargetsSmallEpsilon)
a := []float64{1, 2, 3, 4, 5}
for _, v := range a {
s.Insert(v)
}
verifyPercsWithAbsoluteEpsilon(t, a, s)
// If not yet flushed, results should be precise:
if !s.flushed() {
for φ, want := range map[float64]float64{
0.01: 1,
0.10: 1,
0.50: 3,
0.90: 5,
0.99: 5,
} {
if got := s.Query(φ); got != want {
t.Errorf("want %f for φ=%f, got %f", want, φ, got)
}
}
}
}
func TestLowBiasedQuery(t *testing.T) {
rand.Seed(42)
s := NewLowBiased(RelativeEpsilon)
a := populateStream(s)
verifyLowPercsWithRelativeEpsilon(t, a, s)
}
func TestHighBiasedQuery(t *testing.T) {
rand.Seed(42)
s := NewHighBiased(RelativeEpsilon)
a := populateStream(s)
verifyHighPercsWithRelativeEpsilon(t, a, s)
}
// BrokenTestTargetedMerge is broken, see Merge doc comment.
func BrokenTestTargetedMerge(t *testing.T) {
rand.Seed(42)
s1 := NewTargeted(Targets)
s2 := NewTargeted(Targets)
a := populateStream(s1)
a = append(a, populateStream(s2)...)
s1.Merge(s2.Samples())
verifyPercsWithAbsoluteEpsilon(t, a, s1)
}
// BrokenTestLowBiasedMerge is broken, see Merge doc comment.
func BrokenTestLowBiasedMerge(t *testing.T) {
rand.Seed(42)
s1 := NewLowBiased(RelativeEpsilon)
s2 := NewLowBiased(RelativeEpsilon)
a := populateStream(s1)
a = append(a, populateStream(s2)...)
s1.Merge(s2.Samples())
verifyLowPercsWithRelativeEpsilon(t, a, s2)
}
// BrokenTestHighBiasedMerge is broken, see Merge doc comment.
func BrokenTestHighBiasedMerge(t *testing.T) {
rand.Seed(42)
s1 := NewHighBiased(RelativeEpsilon)
s2 := NewHighBiased(RelativeEpsilon)
a := populateStream(s1)
a = append(a, populateStream(s2)...)
s1.Merge(s2.Samples())
verifyHighPercsWithRelativeEpsilon(t, a, s2)
}
func TestUncompressed(t *testing.T) {
q := NewTargeted(Targets)
for i := 100; i > 0; i-- {
q.Insert(float64(i))
}
if g := q.Count(); g != 100 {
t.Errorf("want count 100, got %d", g)
}
// Before compression, Query should have 100% accuracy.
for quantile := range Targets {
w := quantile * 100
if g := q.Query(quantile); g != w {
t.Errorf("want %f, got %f", w, g)
}
}
}
func TestUncompressedSamples(t *testing.T) {
q := NewTargeted(map[float64]float64{0.99: 0.001})
for i := 1; i <= 100; i++ {
q.Insert(float64(i))
}
if g := q.Samples().Len(); g != 100 {
t.Errorf("want count 100, got %d", g)
}
}
func TestUncompressedOne(t *testing.T) {
q := NewTargeted(map[float64]float64{0.99: 0.01})
q.Insert(3.14)
if g := q.Query(0.90); g != 3.14 {
t.Error("want PI, got", g)
}
}
func TestDefaults(t *testing.T) {
if g := NewTargeted(map[float64]float64{0.99: 0.001}).Query(0.99); g != 0 {
t.Errorf("want 0, got %f", g)
}
}
|
