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-rw-r--r--common/probdist/weighted_dist.go245
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diff --git a/common/probdist/weighted_dist.go b/common/probdist/weighted_dist.go
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-/*
- * Copyright (c) 2014, Yawning Angel <yawning at torproject dot org>
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions are met:
- *
- * * Redistributions of source code must retain the above copyright notice,
- * this list of conditions and the following disclaimer.
- *
- * * Redistributions in binary form must reproduce the above copyright notice,
- * this list of conditions and the following disclaimer in the documentation
- * and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
- * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
- * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
- * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
- * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
- * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
- * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
- * POSSIBILITY OF SUCH DAMAGE.
- */
-
-// Package probdist implements a weighted probability distribution suitable for
-// protocol parameterization. To allow for easy reproduction of a given
-// distribution, the drbg package is used as the random number source.
-package probdist
-
-import (
- "bytes"
- "container/list"
- "fmt"
- "math/rand"
- "sync"
-
- "github.com/OperatorFoundation/obfs4/common/csrand"
- "github.com/OperatorFoundation/obfs4/common/drbg"
-)
-
-const (
- minValues = 1
- maxValues = 100
-)
-
-// WeightedDist is a weighted distribution.
-type WeightedDist struct {
- sync.Mutex
-
- minValue int
- maxValue int
- biased bool
- values []int
- weights []float64
-
- alias []int
- prob []float64
-}
-
-// New creates a weighted distribution of values ranging from min to max
-// based on a HashDrbg initialized with seed. Optionally, bias the weight
-// generation to match the ScrambleSuit non-uniform distribution from
-// obfsproxy.
-func New(seed *drbg.Seed, min, max int, biased bool) (w *WeightedDist) {
- w = &WeightedDist{minValue: min, maxValue: max, biased: biased}
-
- if max <= min {
- panic(fmt.Sprintf("wDist.Reset(): min >= max (%d, %d)", min, max))
- }
-
- w.Reset(seed)
-
- return
-}
-
-// genValues creates a slice containing a random number of random values
-// that when scaled by adding minValue will fall into [min, max].
-func (w *WeightedDist) 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 *WeightedDist) genBiasedWeights(rng *rand.Rand) {
- w.weights = make([]float64, len(w.values))
-
- culmProb := 0.0
- for i := range w.weights {
- p := (1.0 - culmProb) * rng.Float64()
- w.weights[i] = p
- culmProb += p
- }
-}
-
-// genUniformWeights generates a uniform weight list.
-func (w *WeightedDist) 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 *WeightedDist) 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)
- }
- }
-
- // 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 *WeightedDist) Reset(seed *drbg.Seed) {
- // Initialize the deterministic random number generator.
- drbg, _ := drbg.NewHashDrbg(seed)
- rng := rand.New(drbg)
-
- w.Lock()
- defer w.Unlock()
-
- w.genValues(rng)
- if w.biased {
- w.genBiasedWeights(rng)
- } else {
- w.genUniformWeights(rng)
- }
- w.genTables()
-}
-
-// Sample generates a random value according to the distribution.
-func (w *WeightedDist) Sample() int {
- var idx int
-
- w.Lock()
- defer w.Unlock()
-
- // 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]
- }
-
- return w.minValue + w.values[idx]
-}
-
-// String returns a dump of the distribution table.
-func (w *WeightedDist) String() string {
- var buf bytes.Buffer
-
- buf.WriteString("[ ")
- for i, v := range w.values {
- p := w.weights[i]
- if p > 0.01 { // Squelch tiny probabilities.
- buf.WriteString(fmt.Sprintf("%d: %f ", v, p))
- }
- }
- buf.WriteString("]")
- return buf.String()
-}