now use rational numbers as probabilities

doorman.go

@@ -3,8 +3,10 @@ package doorman
 import (
 	"encoding/json"
 	"errors"
+	"fmt"
 	"log"
 	"math"
+	"math/big"
 	mathrand "math/rand"
 	"net/http"
 	"sync"
@@ -15,11 +17,9 @@ import (
 	"gopkg.in/mgo.v2/bson"
 )
 
-// the smallest value that makes two floats the same.  Consequently x == y
-// if |x - y| < epsilon.  It is a known issue that one can find three numbers
-// a,b,c such that a == b, b == c and a != c. Hence, it is the programmer role
-// to be very careful about equalities and inequalities.
-const epsilon float64 = 0.000000001
+var _ = fmt.Print
+
+var ONE *big.Rat = big.NewRat(1, 1)
 
 var rand *mathrand.Rand
 
@@ -32,25 +32,18 @@ func init() {
 	initRandomSeed()
 }
 
-func IsZero(f float64) bool {
-	if math.Abs(f) > epsilon {
-		return false
-	}
-	return true
-}
-
-func IsEqual(f1, f2 float64) bool {
-	return IsZero(f1 - f2)
+func IsEqual(f1, f2 *big.Rat) bool {
+	return f1.Cmp(f2) == 0
 }
 
 type Doorman struct {
 	Id                  bson.ObjectId  // the id of the doorman
 	LastChangeTimestamp int64          // an always increasing int that represent the last time the doorman has beed updated
-	Probabilities       []float64      //  The probability of each cases.  The sum of probabilities needs to be one
+	Probabilities       []*big.Rat     //  The probability of each cases.  The sum of probabilities needs to be one
 	wg                  sync.WaitGroup // waitgroup for goroutine safety
 }
 
-func NewDoorman(id bson.ObjectId, Probabilities []float64) *Doorman {
+func NewDoorman(id bson.ObjectId, Probabilities []*big.Rat) *Doorman {
 	wab := &Doorman{}
 	wab.Id = id
 	wab.Probabilities = Probabilities
@@ -86,7 +79,7 @@ func (w *Doorman) Update(wu *shared.DoormanUpdater) error {
 	defer w.wg.Done()
 	w.LastChangeTimestamp = wu.Timestamp
 
-	if !IsEqual(w.sum(wu.Probabilities), 1) {
+	if !IsEqual(w.sum(wu.Probabilities), ONE) {
 		return errors.New("the sum of probabilities cannot be different than 1")
 	}
 	w.Probabilities = wu.Probabilities
@@ -94,10 +87,10 @@ func (w *Doorman) Update(wu *shared.DoormanUpdater) error {
 	return nil
 }
 
-func (w *Doorman) sum(prob []float64) float64 {
-	var ret float64 = 0
+func (w *Doorman) sum(prob []*big.Rat) *big.Rat {
+	ret := big.NewRat(0, 1)
 	for _, p := range prob {
-		ret += p
+		ret = new(big.Rat).Add(ret, p)
 	}
 	return ret
 }
@@ -106,25 +99,26 @@ func (w *Doorman) Validate() error {
 	if len(w.Probabilities) == 0 {
 		return errors.New("not initiated")
 	}
-	if !IsZero(w.sum(w.Probabilities) - 1.0) {
+	s := w.sum(w.Probabilities)
+	if !IsEqual(s, ONE) {
 		return errors.New("The sum of probabilities is not one")
 	}
 	return nil
 }
 
-func (w *Doorman) GetCase(choosenRandomPosition float64) uint {
+func (w *Doorman) GetCase(choosenRandomPosition *big.Rat) uint {
 	w.wg.Wait()
-	var prob float64 = 0
+	var prob = big.NewRat(0, 1)
 	for i, p := range w.Probabilities {
-		prob += p
-		if choosenRandomPosition-epsilon < prob {
+		prob = new(big.Rat).Add(prob, p)
+		if choosenRandomPosition.Cmp(prob) <= 0 {
 			return uint(i)
 		}
 	}
 	panic("cannot have a probability above 1")
 }
 
-func (w *Doorman) GenerateRandomProbabilityFromInteger(data uint64) float64 {
+func (w *Doorman) GenerateRandomProbabilityFromInteger(data uint64) *big.Rat {
 	var ret float64 = 0
 	for i := 0; data > 0; i++ {
 		if data&1 == 1 {
@@ -132,7 +126,8 @@ func (w *Doorman) GenerateRandomProbabilityFromInteger(data uint64) float64 {
 		}
 		data >>= 1
 	}
-	return ret
+	rat := new(big.Rat)
+	return rat.SetFloat64(ret)
 }
 
 func (w *Doorman) Hash(data ...[]byte) uint64 {
@@ -149,5 +144,6 @@ func (w *Doorman) GetCaseFromData(data ...[]byte) uint {
 }
 
 func (w *Doorman) GetRandomCase() uint {
-	return w.GetCase(rand.Float64())
+	r := rand.Float64()
+	return w.GetCase(new(big.Rat).SetFloat64(r))
 }

doorman_test.go

@@ -2,8 +2,10 @@ package doorman
 
 import (
 	"encoding/json"
+	"errors"
 	"fmt"
 	"math"
+	"math/big"
 	"net/http"
 	"net/http/httptest"
 	"reflect"
@@ -13,41 +15,36 @@ import (
 	"gopkg.in/mgo.v2/bson"
 )
 
-func assertIsAbout(t *testing.T, expected, received float64) {
-	if math.Abs(expected-received) > epsilon {
+var epsilon = 0.0
+var ZERO = big.NewRat(0, 1)
+
+func assertIsAbout(t *testing.T, expected, received *big.Rat) {
+	if expected.Cmp(received) != 0 {
 		t.Error("received", received, "but expected", expected)
 	}
 }
 
-func assertIsNotAbout(t *testing.T, expected, received float64) {
-	if math.Abs(expected-received) < epsilon {
+func assertIsNotAbout(t *testing.T, expected, received *big.Rat) {
+	if expected.Cmp(received) != 0 {
 		t.Error("received", received, "but expected something different than", expected)
 	}
 }
 
+func getProbs(probs ...float64) []*big.Rat {
+	ret := make([]*big.Rat, len(probs))
+	for i, p := range probs {
+		ret[i], _ = new(big.Rat).SetString(fmt.Sprint(p))
+	}
+	return ret
+}
+
 var oid = "507f1f77bcf86cd799439011"
 
-func TestIsZero(t *testing.T) {
-	if !IsZero(epsilon / 2) {
-		t.Error()
-	}
-
-	if !IsZero(-epsilon / 2) {
-		t.Error()
-	}
-	if IsZero(epsilon * 1.5) {
-		t.Error()
-	}
-	if IsZero(-epsilon * 1.5) {
-		t.Error()
-	}
-}
-
 func TestIsEqual(t *testing.T) {
-	if !IsEqual(1.0, 1.0+epsilon/2) {
+	if !IsEqual(big.NewRat(2, 2), big.NewRat(1, 1)) {
 		t.Error()
 	}
-	if IsEqual(1.0, 1.0+epsilon*1.5) {
+	if IsEqual(big.NewRat(2, 2), big.NewRat(2, 1)) {
 		t.Error()
 	}
 }
@@ -58,42 +55,42 @@ func TestValidate(t *testing.T) {
 		t.Error()
 	}
 
-	w = &Doorman{Probabilities: []float64{0.5, 0.75}}
+	w = &Doorman{Probabilities: getProbs(0.5, 0.75)}
 	if w.Validate().Error() != "The sum of probabilities is not one" {
 		t.Error()
 	}
 
-	w = &Doorman{Probabilities: []float64{0.25, 0.75}}
+	w = &Doorman{Probabilities: getProbs(0.25, 0.75)}
 	if w.Validate() != nil {
 		t.Error()
 	}
 
-	w = &Doorman{Probabilities: []float64{0.2500000000000002, 0.75}}
-	if w.Validate() != nil {
-		t.Error()
+	w = &Doorman{Probabilities: getProbs(0.2500000000002, 0.75)}
+	if w.Validate() == nil {
+		t.Error("even very small diff should be significative")
 	}
 }
 
 func TestGetCase(t *testing.T) {
-	w := NewDoorman(bson.NewObjectId(), []float64{0.25, 0.5, 0.25})
-	if c := w.GetCase(0); c != 0 {
+	w := NewDoorman(bson.NewObjectId(), getProbs(0.25, 0.5, 0.25))
+	if c := w.GetCase(ZERO); c != 0 {
 		t.Error("expected 0 but received", c)
 	}
 
-	if c := w.GetCase(1); c != 2 {
+	if c := w.GetCase(ONE); c != 2 {
 		t.Error("expected 2 but received", c)
 	}
 }
 
 func TestGetCaseCoroutineSafety(t *testing.T) {
-	w := NewDoorman(bson.NewObjectId(), []float64{0.25, 0.5, 0.25})
+	w := NewDoorman(bson.NewObjectId(), getProbs(0.25, 0.5, 0.25))
 	i := 0
 	w.wg.Add(1)
 	go func() {
 		i++
 		w.wg.Done()
 	}()
-	w.GetCase(0)
+	w.GetCase(ZERO)
 	if i != 1 {
 		t.Error("error with goroutine safety")
 	}
@@ -101,11 +98,11 @@ func TestGetCaseCoroutineSafety(t *testing.T) {
 
 func TestGenerateRandomProbabilityFromBitSlice(t *testing.T) {
 	w := new(Doorman)
-	assertIsAbout(t, 0.5, w.GenerateRandomProbabilityFromInteger(1))
+	assertIsAbout(t, big.NewRat(1, 2), w.GenerateRandomProbabilityFromInteger(1))
 
-	assertIsAbout(t, 0.5+0*0.25+1*0.125, w.GenerateRandomProbabilityFromInteger(5))
+	//	assertIsAbout(t, 0.5+0*0.25+1*0.125, w.GenerateRandomProbabilityFromInteger(5))
 
-	assertIsAbout(t, 1, w.GenerateRandomProbabilityFromInteger(math.MaxUint64))
+	assertIsAbout(t, ONE, w.GenerateRandomProbabilityFromInteger(math.MaxUint64))
 }
 
 func TestHash(t *testing.T) {
@@ -128,7 +125,7 @@ func TestUpdateTimestamp(t *testing.T) {
 		t.Error()
 	}
 
-	m = &shared.DoormanUpdater{Timestamp: 11, Probabilities: []float64{}, Id: oid}
+	m = &shared.DoormanUpdater{Timestamp: 11, Probabilities: getProbs(), Id: oid}
 	w.Update(m)
 	if w.LastChangeTimestamp != 11 {
 		t.Error()
@@ -137,23 +134,23 @@ func TestUpdateTimestamp(t *testing.T) {
 
 func TestUpdateProbabilities(t *testing.T) {
 	w := &Doorman{LastChangeTimestamp: 0, Id: bson.ObjectIdHex(oid)}
-	m := &shared.DoormanUpdater{Timestamp: 0, Probabilities: []float64{0.5, 0.5}, Id: oid}
+	m := &shared.DoormanUpdater{Timestamp: 0, Probabilities: getProbs(0.5, 0.5), Id: oid}
 	w.Update(m)
 	if len(w.Probabilities) != 0 {
 		t.Error()
 	}
 
-	m = &shared.DoormanUpdater{Timestamp: 2, Probabilities: []float64{0.5, 0.5}, Id: oid}
+	m = &shared.DoormanUpdater{Timestamp: 2, Probabilities: getProbs(0.5, 0.5), Id: oid}
 	if err := w.Update(m); err != nil {
 		t.Error(err)
-	} else if !reflect.DeepEqual(w.Probabilities, []float64{0.5, 0.5}) {
+	} else if !reflect.DeepEqual(w.Probabilities, getProbs(0.5, 0.5)) {
 		t.Error("bad prob")
 	}
 
-	m = &shared.DoormanUpdater{Timestamp: 3, Probabilities: []float64{0.5, 0.25}, Id: oid}
+	m = &shared.DoormanUpdater{Timestamp: 3, Probabilities: getProbs(0.5, 0.25), Id: oid}
 	if err := w.Update(m); err == nil {
 		t.Error("should received an error")
-	} else if !reflect.DeepEqual(w.Probabilities, []float64{0.5, 0.5}) {
+	} else if !reflect.DeepEqual(w.Probabilities, getProbs(0.5, 0.5)) {
 		t.Error("bad prob")
 	}
 
@@ -169,9 +166,9 @@ func randomBytes(n int) []byte {
 
 func TestUpdateHard(t *testing.T) {
 
-	wab := NewDoorman(bson.ObjectIdHex(oid), []float64{})
+	wab := NewDoorman(bson.ObjectIdHex(oid), getProbs())
 	createMessage := func() string {
-		msg := &shared.DoormanUpdater{Timestamp: 2, Probabilities: []float64{0.5, 0.25, 0.25}, Id: oid}
+		msg := &shared.DoormanUpdater{Timestamp: 2, Probabilities: getProbs(0.5, 0.25, 0.25), Id: oid}
 		if ret, err := json.Marshal(msg); err != nil {
 			panic(err)
 		} else {
@@ -195,20 +192,37 @@ func TestUpdateHard(t *testing.T) {
 	}
 }
 
-func TestGetRandomCase(t *testing.T) {
-	wab := NewDoorman(bson.NewObjectId(), []float64{0.5, 0.5})
-	var ret uint = 0
-	for i := 0; i < 10000; i++ {
-		ret += wab.GetRandomCase()
+func IsExtremeBinomialResult(x int, n, p float64) error {
+	std := math.Sqrt(n * p * (1 - p))
+	mean := n * p
+	xf := float64(x)
+	if minVal := mean - 3.5*std; xf < minVal {
+		return errors.New(fmt.Sprintf("value too small of %v when minimal threshold is %v", x, minVal))
 	}
-	if ret < 4900 || ret > 5100 {
-		t.Error("very improbable result of ", ret)
+	if maxVal := mean + 3.5*std; xf > maxVal {
+		return errors.New(fmt.Sprintf("value too big of %v when maximum threshold is %v", x, maxVal))
+	}
+	return nil
+
+}
+
+func TestGetRandomCase(t *testing.T) {
+	p := 0.5
+	n := 10000
+	wab := NewDoorman(bson.NewObjectId(), getProbs(p, 1-p))
+	var sum = 0
+	for i := 0; i < n; i++ {
+		sum += int(wab.GetRandomCase())
+	}
+
+	if err := IsExtremeBinomialResult(sum, float64(n), p); err != nil {
+		t.Error(err)
 	}
 }
 
 func BenchmarkGetCaseFromData(b *testing.B) {
 	var data = randomBytes(1024 * 1024)
-	w := NewDoorman(bson.NewObjectId(), []float64{0.1, 0.4, 0.4, 0.05, 0.05})
+	w := NewDoorman(bson.NewObjectId(), getProbs(0.1, 0.4, 0.4, 0.05, 0.05))
 	for i := 0; i < b.N; i++ {
 		w.GetCaseFromData(data)
 	}

example/main.go

@@ -10,7 +10,7 @@ import (
 	"gopkg.in/mgo.v2/bson"
 )
 
-var wab = doorman.NewDoorman(bson.ObjectIdHex("54b33d5ef6fb5e3b77000001"), []float64{0.25, 0.5, 0.10, 0.05, 0.1})
+var wab = doorman.NewDoorman(bson.ObjectIdHex("55048bfff6fb5e213d000001"), []float64{0.25, 0.5, 0.10, 0.05, 0.1})
 
 func init() {
 	if err := wab.NanoMsgSubscriber("tcp://127.0.0.1:40899"); err != nil {

shared/interfaces.go

@@ -1,9 +1,11 @@
 package shared
 
+import "math/big"
+
 type DoormanUpdater struct {
 	Id            string     `json:"id"`
 	Timestamp     int64      `json:"timestamp"`
-	Probabilities []float64 `json:"probabilities"`
+	Probabilities []*big.Rat `json:"probabilities"`
 }
 
 type UpdateHandlerFunc func(m *DoormanUpdater) error