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LogLog and HyperLogLog estimators in Golang
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package main | |
import ( | |
// "encoding/binary" | |
"crypto/rand" | |
"fmt" | |
"hash" | |
"hash/fnv" | |
"io" | |
"io/ioutil" | |
"math" | |
"strings" | |
) | |
var ( | |
lsbp32bp = [...]uint32{0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, | |
4, 8, 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9} | |
lsbp64bp = [...]uint64{0, 1, 2, 7, 3, 13, 8, 19, 4, 25, 14, 28, 9, 34, 20, | |
40, 5, 17, 26, 38, 15, 46, 29, 48, 10, 31, 35, 54, 21, 50, 41, 57, 63, | |
6, 12, 18, 24, 27, 33, 39, 16, 37, 45, 47, 30, 53, 49, 56, 62, 11, 23, | |
32, 36, 44, 52, 55, 61, 22, 43, 51, 60, 42, 59, 58} | |
) | |
type estimator interface { | |
Write([]byte) (int, error) | |
Get() float64 | |
} | |
func rank(n uint64) uint64 { | |
if n == 0 { | |
return 64 | |
} | |
var p uint64 | |
for (n>>p)&1 == 0 { | |
p += 1 | |
} | |
return p | |
} | |
func lsbp32(v uint32) uint32 { | |
return lsbp32bp[((v&-v)*0x077cb531)>>27] | |
} | |
func lsbp64(v uint64) uint64 { | |
return lsbp64bp[((v&-v)*0x218a392cd3d5dbf)>>58] | |
} | |
type LLEstimator struct { | |
k, m uint64 | |
hash hash.Hash64 | |
buckets []uint64 | |
} | |
func NewLLEstimator(k uint64) (lle *LLEstimator) { | |
m := uint64(math.Pow(2, float64(k))) | |
buckets := make([]uint64, m) | |
h := fnv.New64a() | |
lle = &LLEstimator{k: k, m: m, hash: h, buckets: buckets} | |
return | |
} | |
func (e *LLEstimator) alpha() (alpha float64) { | |
switch e.m { | |
case 16: | |
alpha = 0.75207 | |
case 32: | |
alpha = 0.77308 | |
case 64: | |
alpha = 0.78356 | |
default: | |
alpha = 0.79402 | |
} | |
return | |
} | |
func (e *LLEstimator) Write(p []byte) (n int, err error) { | |
if n, err = e.hash.Write(p); err != nil { | |
return | |
} | |
hashSum := e.hash.Sum64() | |
e.hash.Reset() | |
j := hashSum & (e.m - 1) | |
r := rank(hashSum >> e.k) | |
if r > e.buckets[j] { | |
e.buckets[j] = r | |
} | |
return | |
} | |
func (e *LLEstimator) Get() float64 { | |
var bucketval float64 | |
for b := range e.buckets { | |
bucketval += float64(e.buckets[b]) | |
} | |
bucketval /= float64(e.m) | |
return e.alpha() * float64(e.m) * math.Pow(2, bucketval) | |
} | |
type HLLEstimator struct { | |
b uint64 | |
m float64 | |
hash hash.Hash64 | |
buckets []uint64 | |
} | |
func NewHLLEstimator(b uint64) *HLLEstimator { | |
m := math.Pow(2, float64(b)) | |
buckets := make([]uint64, uint(m)) | |
h := fnv.New64a() | |
return &HLLEstimator{b: b, m: m, buckets: buckets, hash: h} | |
} | |
func (e *HLLEstimator) alpha() (alpha float64) { | |
switch e.m { | |
case 16.0: | |
alpha = 0.673 | |
case 32.0: | |
alpha = 0.697 | |
case 64.0: | |
alpha = 0.709 | |
default: | |
alpha = 0.7213 / (1 + 1.079/e.m) | |
} | |
return | |
} | |
func (e *HLLEstimator) rho(v uint64) (r uint64) { | |
m := uint64(math.Pow(2, float64(e.b)-1)) | |
lsbp := lsbp64(v) + 1 | |
if m < lsbp { | |
r = m | |
} else { | |
r = lsbp | |
} | |
return | |
} | |
func (e *HLLEstimator) Write(p []byte) (n int, err error) { | |
if n, err = e.hash.Write(p); err != nil { | |
return | |
} | |
hashSum := e.hash.Sum64() | |
e.hash.Reset() | |
i := hashSum & ((1 << e.b) - 1) | |
r := e.rho(hashSum >> e.b) | |
if r > e.buckets[i] { | |
e.buckets[i] = r | |
} | |
return | |
} | |
func (e *HLLEstimator) Get() (dv float64) { | |
var bucketsum float64 | |
for i := range e.buckets { | |
bucketsum += math.Pow(2, -float64(e.buckets[i])) | |
} | |
est := e.alpha() * math.Pow(e.m, 2) / bucketsum | |
if est < 5.0/2*e.m { | |
var v int | |
for i := range e.buckets { | |
if e.buckets[i] == 0 { | |
v += 1 | |
} | |
} | |
if v == 0 { | |
dv = est | |
} else { | |
dv = e.m * math.Log(e.m/float64(v)) | |
} | |
} else if est <= (1.0 / 30 * math.Pow(2, 32)) { | |
dv = est | |
} else if est > (1.0 / 30 * math.Pow(2, 32)) { | |
dv = -math.Pow(2, 32) * math.Log(1.0-est/math.Pow(2, 32)) | |
} | |
return | |
} | |
func getRandomBytes() []byte { | |
c := 16 | |
b := make([]byte, c) | |
if _, err := io.ReadFull(rand.Reader, b); err != nil { | |
fmt.Println("error:", err) | |
return b | |
} | |
return b | |
} | |
func estimateDiscreteTimestamps(path string) (real int, est float64, err error) { | |
content, err := ioutil.ReadFile(path) | |
if err != nil { | |
return | |
} | |
lines := strings.Split(string(content), "\n") | |
uniques := map[string]bool{} | |
lle := NewHLLEstimator(6) | |
for i := range lines { | |
uniques[lines[i]] = true | |
io.WriteString(lle, lines[i]) | |
} | |
real = len(uniques) | |
est = lle.Get() | |
return | |
} | |
func main() { | |
// real, est, _ := estimateDiscreteTimestamps("timeseries.txt") | |
// fmt.Println("real:", real) | |
// fmt.Println("estimated:", est) | |
e := NewHLLEstimator(6) | |
uniques := map[string]bool{} | |
for i := 0; i < 1000000; i++ { | |
b := getRandomBytes() | |
uniques[string(b)] = true | |
e.Write(b) | |
} | |
est := e.Get() | |
fmt.Printf("estimated: %f (%f%% err)\n", est, math.Abs(100.0-(est/float64(len(uniques))*100))) | |
fmt.Println("real:", len(uniques)) | |
} |
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