[Pkg-privacy-commits] [obfs4proxy] 80/151: Use Vose's Alias Method to sample the weighted distribution.
Ximin Luo
infinity0 at moszumanska.debian.org
Sat Aug 22 12:59:41 UTC 2015
This is an automated email from the git hooks/post-receive script.
infinity0 pushed a commit to branch master
in repository obfs4proxy.
commit 5abad1571c7d0869e29d55ca01df83fef8cd4606
Author: Yawning Angel <yawning at schwanenlied.me>
Date: Thu Jun 19 06:29:12 2014 +0000
Use Vose's Alias Method to sample the weighted distribution.
The weight generation code also was cleaned up (and now can support
generating distributions that look like what ScrambleSuit does as
a compile time change).
Per: http://www.keithschwarz.com/darts-dice-coins/
---
csrand/csrand.go | 6 +-
weighted_dist.go | 180 ++++++++++++++++-----
.../proxy_extras.go => weighted_dist_test.go | 59 +++++--
3 files changed, 188 insertions(+), 57 deletions(-)
diff --git a/csrand/csrand.go b/csrand/csrand.go
index a3299aa..b059ed0 100644
--- a/csrand/csrand.go
+++ b/csrand/csrand.go
@@ -68,9 +68,9 @@ func (r csRandSource) Seed(seed int64) {
// No-op.
}
-// Int63n returns, as a int64, a pseudo random number in [0, n).
-func Int63n(n int64) int64 {
- return CsRand.Int63n(n)
+// Intn returns, as a int, a pseudo random number in [0, n).
+func Intn(n int) int {
+ return CsRand.Intn(n)
}
// Float64 returns, as a float64, a pesudo random number in [0.0,1.0).
diff --git a/weighted_dist.go b/weighted_dist.go
index 02fb26d..7c47cb8 100644
--- a/weighted_dist.go
+++ b/weighted_dist.go
@@ -28,6 +28,7 @@
package obfs4
import (
+ "container/list"
"fmt"
"math/rand"
@@ -36,27 +37,25 @@ import (
)
const (
- minBuckets = 1
- maxBuckets = 100
+ minValues = 1
+ maxValues = 100
)
// wDist is a weighted distribution.
type wDist struct {
- minValue int
- maxValue int
- values []int
- buckets []int64
- totalWeight int64
+ minValue int
+ maxValue int
+ values []int
+ weights []float64
- rng *rand.Rand
+ alias []int
+ prob []float64
}
// newWDist creates a weighted distribution of values ranging from min to max
// based on a HashDrbg initialized with seed.
func newWDist(seed *drbg.Seed, min, max int) (w *wDist) {
- w = new(wDist)
- w.minValue = min
- w.maxValue = max
+ w = &wDist{minValue: min, maxValue: max}
if max <= min {
panic(fmt.Sprintf("wDist.Reset(): min >= max (%d, %d)", min, max))
@@ -67,46 +66,147 @@ func newWDist(seed *drbg.Seed, min, max int) (w *wDist) {
return
}
-// sample generates a random value according to the distribution.
-func (w *wDist) sample() int {
- retIdx := 0
- var totalWeight int64
- weight := csrand.Int63n(w.totalWeight)
- for i, bucketWeight := range w.buckets {
- totalWeight += bucketWeight
- if weight <= totalWeight {
- retIdx = i
- break
+// genValues creates a slice containing a random number of random values
+// that when scaled by adding minValue will fall into [min, max].
+func (w *wDist) genValues(rng *rand.Rand) {
+ nValues := (w.maxValue + 1) - w.minValue
+ values := rng.Perm(nValues)
+ if nValues < minValues {
+ nValues = minValues
+ }
+ if nValues > maxValues {
+ nValues = maxValues
+ }
+ nValues = rng.Intn(nValues) + 1
+ w.values = values[:nValues]
+}
+
+// genBiasedWeights generates a non-uniform weight list, similar to the
+// ScrambleSuit prob_dist module.
+func (w *wDist) genBiasedWeights(rng *rand.Rand) {
+ w.weights = make([]float64, len(w.values))
+
+ culmProb := 0.0
+ for i := range w.values {
+ p := (1.0 - culmProb) * rng.Float64()
+ w.weights[i] = p
+ culmProb += p
+ }
+}
+
+// genUniformWeights generates a uniform weight list.
+func (w *wDist) genUniformWeights(rng *rand.Rand) {
+ w.weights = make([]float64, len(w.values))
+ for i := range w.weights {
+ w.weights[i] = rng.Float64()
+ }
+}
+
+// genTables calculates the alias and prob tables used for Vose's Alias method.
+// Algorithm taken from http://www.keithschwarz.com/darts-dice-coins/
+func (w *wDist) genTables() {
+ n := len(w.weights)
+ var sum float64
+ for _, weight := range w.weights {
+ sum += weight
+ }
+
+ // Create arrays $Alias$ and $Prob$, each of size $n$.
+ alias := make([]int, n)
+ prob := make([]float64, n)
+
+ // Create two worklists, $Small$ and $Large$.
+ small := list.New()
+ large := list.New()
+
+ scaled := make([]float64, n)
+ for i, weight := range w.weights {
+ // Multiply each probability by $n$.
+ p_i := weight * float64(n) / sum
+ scaled[i] = p_i
+
+ // For each scaled probability $p_i$:
+ if scaled[i] < 1.0 {
+ // If $p_i < 1$, add $i$ to $Small$.
+ small.PushBack(i)
+ } else {
+ // Otherwise ($p_i \ge 1$), add $i$ to $Large$.
+ large.PushBack(i)
}
}
- return w.minValue + w.values[retIdx]
+ // While $Small$ and $Large$ are not empty: ($Large$ might be emptied first)
+ for small.Len() > 0 && large.Len() > 0 {
+ // Remove the first element from $Small$; call it $l$.
+ l := small.Remove(small.Front()).(int)
+ // Remove the first element from $Large$; call it $g$.
+ g := large.Remove(large.Front()).(int)
+
+ // Set $Prob[l] = p_l$.
+ prob[l] = scaled[l]
+ // Set $Alias[l] = g$.
+ alias[l] = g
+
+ // Set $p_g := (p_g + p_l) - 1$. (This is a more numerically stable option.)
+ scaled[g] = (scaled[g] + scaled[l]) - 1.0
+
+ if scaled[g] < 1.0 {
+ // If $p_g < 1$, add $g$ to $Small$.
+ small.PushBack(g)
+ } else {
+ // Otherwise ($p_g \ge 1$), add $g$ to $Large$.
+ large.PushBack(g)
+ }
+ }
+
+ // While $Large$ is not empty:
+ for large.Len() > 0 {
+ // Remove the first element from $Large$; call it $g$.
+ g := large.Remove(large.Front()).(int)
+ // Set $Prob[g] = 1$.
+ prob[g] = 1.0
+ }
+
+ // While $Small$ is not empty: This is only possible due to numerical instability.
+ for small.Len() > 0 {
+ // Remove the first element from $Small$; call it $l$.
+ l := small.Remove(small.Front()).(int)
+ // Set $Prob[l] = 1$.
+ prob[l] = 1.0
+ }
+
+ w.prob = prob
+ w.alias = alias
}
// reset generates a new distribution with the same min/max based on a new seed.
func (w *wDist) reset(seed *drbg.Seed) {
// Initialize the deterministic random number generator.
drbg := drbg.NewHashDrbg(seed)
- w.rng = rand.New(drbg)
+ rng := rand.New(drbg)
- nBuckets := (w.maxValue + 1) - w.minValue
- w.values = w.rng.Perm(nBuckets)
- if nBuckets < minBuckets {
- nBuckets = minBuckets
- }
- if nBuckets > maxBuckets {
- nBuckets = maxBuckets
- }
- nBuckets = w.rng.Intn(nBuckets) + 1
-
- w.totalWeight = 0
- w.buckets = make([]int64, nBuckets)
- for i, _ := range w.buckets {
- prob := w.rng.Int63n(1000)
- w.buckets[i] = prob
- w.totalWeight += prob
+ w.genValues(rng)
+ //w.genBiasedWeights(rng)
+ w.genUniformWeights(rng)
+ w.genTables()
+}
+
+// sample generates a random value according to the distribution.
+func (w *wDist) sample() int {
+ var idx int
+
+ // Generate a fair die roll from an $n$-sided die; call the side $i$.
+ i := csrand.Intn(len(w.values))
+ // Flip a biased coin that comes up heads with probability $Prob[i]$.
+ if csrand.Float64() <= w.prob[i] {
+ // If the coin comes up "heads," return $i$.
+ idx = i
+ } else {
+ // Otherwise, return $Alias[i]$.
+ idx = w.alias[i]
}
- w.buckets[len(w.buckets)-1] = w.totalWeight
+
+ return w.minValue + w.values[idx]
}
/* vim :set ts=4 sw=4 sts=4 noet : */
diff --git a/obfs4proxy/proxy_extras.go b/weighted_dist_test.go
similarity index 60%
copy from obfs4proxy/proxy_extras.go
copy to weighted_dist_test.go
index 27b638b..14fecec 100644
--- a/obfs4proxy/proxy_extras.go
+++ b/weighted_dist_test.go
@@ -25,27 +25,58 @@
* POSSIBILITY OF SUCH DAMAGE.
*/
-package main
+package obfs4
import (
- "net/url"
+ "fmt"
+ "testing"
- "code.google.com/p/go.net/proxy"
-
- "github.com/yawning/obfs4"
+ "github.com/yawning/obfs4/drbg"
)
-// getProxyDialer is a trival wrapper around the go.net/proxy package to avoid
-// having it as a dependency for anything else.
-func getProxyDialer(uri *url.URL) (obfs4.DialFn, error) {
- if uri == nil {
- return proxy.Direct.Dial, nil
- }
+const debug = false
- dialer, err := proxy.FromURL(uri, proxy.Direct)
+func TestWeightedDist(t *testing.T) {
+ seed, err := drbg.NewSeed()
if err != nil {
- return nil, err
+ t.Fatal("failed to generate a DRBG seed:", err)
+ }
+
+ const nrTrials = 1000000
+
+ hist := make([]int, 1000)
+
+ w := newWDist(seed, 0, 999)
+ if debug {
+ // Dump a string representation of the probability table.
+ fmt.Println("Table:")
+ var sum float64
+ for _, weight := range w.weights {
+ sum += weight
+ }
+ for i, weight := range w.weights {
+ p := weight / sum
+ if p > 0.000001 { // Filter out tiny values.
+ fmt.Printf(" [%d]: %f\n", w.minValue+w.values[i], p)
+ }
+ }
+ fmt.Println()
+ }
+
+ for i := 0; i < nrTrials; i++ {
+ value := w.sample()
+ hist[value]++
}
- return dialer.Dial, nil
+ if debug {
+ fmt.Println("Generated:")
+ for value, count := range hist {
+ if count != 0 {
+ p := float64(count) / float64(nrTrials)
+ fmt.Printf(" [%d]: %f (%d)\n", value, p, count)
+ }
+ }
+ }
}
+
+/* vim :set ts=4 sw=4 sts=4 noet : */
--
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