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package compress
import "math"
// Estimate returns a normalized compressibility estimate of block b.
// Values close to zero are likely uncompressible.
// Values above 0.1 are likely to be compressible.
// Values above 0.5 are very compressible.
// Very small lengths will return 0.
func Estimate(b []byte) float64 {
if len(b) < 16 {
return 0
}
// Correctly predicted order 1
hits := 0
lastMatch := false
var o1 [256]byte
var hist [256]int
c1 := byte(0)
for _, c := range b {
if c == o1[c1] {
// We only count a hit if there was two correct predictions in a row.
if lastMatch {
hits++
}
lastMatch = true
} else {
lastMatch = false
}
o1[c1] = c
c1 = c
hist[c]++
}
// Use x^0.6 to give better spread
prediction := math.Pow(float64(hits)/float64(len(b)), 0.6)
// Calculate histogram distribution
variance := float64(0)
avg := float64(len(b)) / 256
for _, v := range hist {
Δ := float64(v) - avg
variance += Δ * Δ
}
stddev := math.Sqrt(float64(variance)) / float64(len(b))
exp := math.Sqrt(1 / float64(len(b)))
// Subtract expected stddev
stddev -= exp
if stddev < 0 {
stddev = 0
}
stddev *= 1 + exp
// Use x^0.4 to give better spread
entropy := math.Pow(stddev, 0.4)
// 50/50 weight between prediction and histogram distribution
return math.Pow((prediction+entropy)/2, 0.9)
}
// ShannonEntropyBits returns the number of bits minimum required to represent
// an entropy encoding of the input bytes.
// https://en.wiktionary.org/wiki/Shannon_entropy
func ShannonEntropyBits(b []byte) int {
if len(b) == 0 {
return 0
}
var hist [256]int
for _, c := range b {
hist[c]++
}
shannon := float64(0)
invTotal := 1.0 / float64(len(b))
for _, v := range hist[:] {
if v > 0 {
n := float64(v)
shannon += math.Ceil(-math.Log2(n*invTotal) * n)
}
}
return int(math.Ceil(shannon))
}
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