added go-fuzz testing for roaring ops vs naive implementation

roaring/fuzzer.go

@@ -16,6 +16,15 @@
 
 package roaring
 
+import (
+	"encoding/binary"
+	"fmt"
+	"io/ioutil"
+	"reflect"
+)
+
+// FuzzBitmapUnmarshalBinary fuzz tests the unmarshaling of binary
+// to both Pilosa and official roaring formats.
 func FuzzBitmapUnmarshalBinary(data []byte) int {
 	b := NewBitmap()
 	err := b.UnmarshalBinary(data)
@@ -24,3 +33,291 @@ func FuzzBitmapUnmarshalBinary(data []byte) int {
 	}
 	return 1
 }
+
+// FuzzRoaringOps fuzz tests different operations on roaring bitmaps,
+// comparing the results to a naive implementation of the operations
+// on uint64 slices.
+func FuzzRoaringOps(data []byte) int {
+	// number of uint64s not to include
+	const reserved = 4
+	// flipping is too inefficient for large values of end - start
+	// and will cause go-fuzz to hang if not controlled.
+	const maxFlips = 1000000
+
+	arr := bytesToUint64s(data)
+	if len(arr) <= reserved {
+		return 0
+	}
+
+	// start > end is possible. This will test correctness in unexpected conditions.
+	start, end, split, rand := arr[0], arr[1], int(arr[2]), arr[3]
+
+	// don't include start, end, split, rand in the slices
+	if split < reserved {
+		split = reserved
+	}
+	// ensure slice in bounds
+	if split > len(arr) {
+		split = len(arr)
+	}
+	// using removeSliceDuplicates guarantees that the slice inputs of the
+	// following functions do not have duplicates and are sorted, just as
+	// the Roaring Bitmap implementations are.
+	s1 := removeSliceDuplicates(arr[reserved:split])
+	s2 := removeSliceDuplicates(arr[split:])
+	if len(s1) == 0 {
+		s1 = nil
+	}
+	if len(s2) == 0 {
+		s2 = nil
+	}
+	bm1 := NewBitmap(arr[reserved:split]...)
+	bm2 := NewBitmap(arr[split:]...)
+
+	expected := s1
+	actual := bm1.Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("first slice:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expected = s2
+	actual = bm2.Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("second slice:\n expected: %v\n got: %v", expected, actual))
+	}
+	// Pure functions
+
+	expected = []uint64{maxInSlice(s1), maxInSlice(s2)}
+	actual = []uint64{bm1.Max(), bm2.Max()}
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("max values:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expected = intersectSlice(s1, s2)
+	actual = bm1.Intersect(bm2).Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("intersection:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expected = unionSlice(s1, s2)
+	actual = bm1.Union(bm2).Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("union:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expected = differenceSlice(s1, s2)
+	actual = bm1.Difference(bm2).Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("difference:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expected = xorSlice(s1, s2)
+	actual = bm1.Xor(bm2).Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("XOR:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	if (len(s1) > 0) != bm1.Any() {
+		panic(fmt.Sprintf("any:\n %v has %v values but got %v which has %v values", s1, len(s1), bm1.Slice(), bm1.Any()))
+	}
+	if (len(s2) > 0) != bm2.Any() {
+		panic(fmt.Sprintf("any:\n %v has %v values but got %v which has %v values", s2, len(s2), bm2.Slice(), bm2.Any()))
+	}
+
+	expected = []uint64{uint64(len(s1)), uint64(len(s2))}
+	actual = []uint64{bm1.Count(), bm2.Count()}
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("count:\n expected: %v\n got: %v", expected, actual))
+	}
+
+	expect := countRangeSlice(s1, start, end)
+	got := bm1.CountRange(start, end)
+	if expect != got {
+		panic(fmt.Sprintf("count range:\n count from %v to %v in slice %v and bitmap %v:\n expected %v got %v",
+			start, end, s1, bm1.Slice(), expect, got))
+	}
+	expect = countRangeSlice(s2, start, end)
+	got = bm2.CountRange(start, end)
+	if expect != got {
+		panic(fmt.Sprintf("count range:\n count from %v to %v in slice %v and bitmap %v:\n expected %v got %v",
+			start, end, s2, bm2.Slice(), expect, got))
+	}
+
+	expected = rangeSlice(s1, start, end)
+	actual = bm1.SliceRange(start, end)
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("slice range:\n from %v to %v in slice %v and bitmap %v:\n expected %v\n got %v",
+			start, end, s1, bm1.Slice(), expected, actual))
+	}
+	expected = rangeSlice(s2, start, end)
+	actual = bm2.SliceRange(start, end)
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("slice range:\n from %v to %v in slice %v and bitmap %v:\n expected %v\n got %v",
+			start, end, s2, bm2.Slice(), expected, actual))
+	}
+
+	expect = uint64(len(intersectSlice(s1, s2)))
+	got = bm1.IntersectionCount(bm2)
+	if expect != got {
+		panic(fmt.Sprintf("intersection count:\n expected %v got %v", expect, got))
+	}
+
+	_, found := containedInSlice(s1, rand)
+	if found != bm1.Contains(rand) {
+		panic(fmt.Sprintf("contains:\n %v contains %v: %v\n %v contains %v: %v", s1, rand, found,
+			bm1.Slice(), rand, bm1.Contains(rand)))
+	}
+	_, found = containedInSlice(s2, rand)
+	if found != bm2.Contains(rand) {
+		panic(fmt.Sprintf("contains:\n %v contains %v: %v\n %v contains %v: %v", s2, rand, found,
+			bm2.Slice(), rand, bm2.Contains(rand)))
+	}
+
+	if end-start < maxFlips {
+		expected = flipSlice(s1, start, end)
+		actual = bm1.Flip(start, end).Slice()
+		if !reflect.DeepEqual(expected, actual) {
+			panic(fmt.Sprintf("flip:\n from %v to %v in slice %v and bitmap %v\n expected %v\n got %v",
+				start, end, s1, bm1.Slice(), expected, actual))
+		}
+		expected = flipSlice(s2, start, end)
+		actual = bm2.Flip(start, end).Slice()
+		if !reflect.DeepEqual(expected, actual) {
+			panic(fmt.Sprintf("flip:\n from %v to %v in slice %v and bitmap %v\n expected %v\n got %v",
+				start, end, s2, bm2.Slice(), expected, actual))
+		}
+	}
+
+	expected = make([]uint64, 0)
+	actual = make([]uint64, 0)
+	forEachInSlice(s1, func(v uint64) { expected = append(expected, v) })
+	bm1.ForEach(func(v uint64) { actual = append(actual, v) })
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("for each:\n expected %v\n got %v", expected, actual))
+	}
+	expected = make([]uint64, 0)
+	actual = make([]uint64, 0)
+	forEachInSlice(s2, func(v uint64) { expected = append(expected, v) })
+	bm2.ForEach(func(v uint64) { actual = append(actual, v) })
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("for each:\n expected %v\n got %v", expected, actual))
+	}
+
+	expected = make([]uint64, 0)
+	actual = make([]uint64, 0)
+	forEachInRangeSlice(s1, start, end, func(v uint64) { expected = append(expected, v) })
+	bm1.ForEachRange(start, end, func(v uint64) { actual = append(actual, v) })
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("for each in range:\n expected %v\n got %v", expected, actual))
+	}
+	expected = make([]uint64, 0)
+	actual = make([]uint64, 0)
+	forEachInRangeSlice(s2, start, end, func(v uint64) { expected = append(expected, v) })
+	bm2.ForEachRange(start, end, func(v uint64) { actual = append(actual, v) })
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("for each in range:\n expected %v\n got %v", expected, actual))
+	}
+
+	// Impure functions
+	// The following tests operations that mutate bitmaps.
+
+	nbm1, nbm2 := bm1.Clone(), bm2.Clone()
+	expected = shiftSlice(s1, 1)
+	tempBM, _ := nbm1.Shift(1)
+	actual = tempBM.Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("shift:\n in slice %v and bitmap %v \n expected %v\n got %v",
+			s1, bm1.Slice(), expected, actual))
+	}
+	expected = shiftSlice(s2, 1)
+	tempBM, _ = nbm2.Shift(1)
+	actual = tempBM.Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("shift:\n in slice %v and bitmap %v \n expected %v\n got %v",
+			s2, bm2.Slice(), expected, actual))
+	}
+
+	// reuse start and end as random values
+	rand2 := start
+	rand3 := end
+
+	nbm1 = bm1.Clone()
+	expected, echanged := addNToSlice(s1, rand)
+	achanged := nbm1.DirectAddN(rand)
+	actual = nbm1.Slice()
+	if echanged != achanged || !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("directAddN:\n adding %v in slice %v and bitmap %v \n expected %v and %v changed \n got %v and %v changed",
+			rand, s1, bm1.Slice(), expected, echanged, actual, achanged))
+	}
+	nbm2 = bm2.Clone()
+	expected, echanged = addNToSlice(s2, rand2, rand3)
+	achanged = nbm2.DirectAddN(rand2, rand3)
+	actual = nbm2.Slice()
+	if echanged != achanged || !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("directAddN:\n adding %v and %v in slice %v and bitmap %v \n expected %v and %v changed \n got %v and %v changed",
+			rand2, rand3, s2, bm2.Slice(), expected, echanged, actual, achanged))
+	}
+
+	nbm1 = bm1.Clone()
+	expected, echanged = removeNFromSlice(s1, rand2, rand3)
+	achanged = nbm1.DirectRemoveN(rand2, rand3)
+	actual = nbm1.Slice()
+	if echanged != achanged || !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("directRemoveN\n removing %v and %v in slice %v and bitmap %v \n expected %v and %v changed \n got %v and %v changed",
+			rand2, rand3, s1, bm1.Slice(), expected, echanged, actual, achanged))
+	}
+	nbm2 = bm2.Clone()
+	expected, echanged = removeNFromSlice(s2, rand)
+	achanged = nbm2.DirectRemoveN(rand)
+	actual = nbm2.Slice()
+	if echanged != achanged || !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("directRemoveN:\n removing %v in slice %v and bitmap %v \n expected %v and %v changed \n got %v and %v changed",
+			rand, s2, bm2.Slice(), expected, echanged, actual, achanged))
+	}
+
+	nbm1, nbm2 = bm1.Clone(), bm2.Clone()
+	expected = unionSlice(s1, s2)
+	nbm1.UnionInPlace(nbm2)
+	actual = nbm1.Slice()
+	if !reflect.DeepEqual(expected, actual) {
+		panic(fmt.Sprintf("union in place:\n expected %v\n got %v", expected, actual))
+	}
+
+	return 1
+}
+
+func bytesToUint64s(data []byte) []uint64 {
+	const uint64Size = 8
+	size := len(data) / uint64Size
+
+	slice := make([]uint64, 0)
+	for i := 0; i < size; i++ {
+		offset := i * uint64Size
+		num := binary.LittleEndian.Uint64(data[offset : offset+uint64Size])
+		slice = append(slice, num)
+	}
+	return slice
+}
+
+// copy and paste the following to a main file to run.
+// path should be the absolute path to the corpus.
+// make sure filename is not already in the corpus.
+func addSliceToCorpus(slice []uint64, filename, path string) {
+	data := uint64sToBytes(slice)
+	err := ioutil.WriteFile(path+"/"+filename, data, 0777)
+	if err != nil {
+		fmt.Printf("could not write to file: %v\n", err)
+	}
+}
+
+func uint64sToBytes(slice []uint64) []byte {
+	const uint64Size = 8
+	size := len(slice) * uint64Size
+
+	data := make([]byte, size)
+	for i := 0; i < len(slice); i++ {
+		offset := i * uint64Size
+		binary.LittleEndian.PutUint64(data[offset:offset+uint64Size], slice[i])
+	}
+	return data
+}

roaring/naive.go

@@ -0,0 +1,321 @@
+// Copyright 2017 Pilosa Corp.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package roaring
+
+import (
+	"math"
+	"sort"
+)
+
+// The following functions reimplement Roaring Bitmap methods, but done naively on
+// uint64 slices. Most of these functions are inefficient, which is acceptable because
+// this is purely for testing consistency with Roaring internal operations. Thus, the
+// functions should be easily guaranteed to produce the correct results.
+
+func sortSlice(slice []uint64) {
+	sort.Slice(slice, func(i, j int) bool { return slice[i] < slice[j] })
+}
+
+// removeSliceDuplicates removes duplicate values
+// in the slice and sorts the output.
+func removeSliceDuplicates(slice []uint64) []uint64 {
+	// just throw slice into a map and
+	// get the values out again
+	hash := make(map[uint64]bool)
+	for _, val := range slice {
+		hash[val] = true
+	}
+	unique := make([]uint64, 0)
+	for key := range hash {
+		unique = append(unique, key)
+	}
+
+	if len(unique) == 0 {
+		return nil
+	}
+	sortSlice(unique)
+	return unique
+}
+
+// intersect intersects two []uint64s, removing any duplicates
+// and sorting the final output.
+func intersectSlice(s1, s2 []uint64) []uint64 {
+	// throw both slices in maps
+	hash1 := make(map[uint64]bool)
+	for _, val := range s1 {
+		hash1[val] = true
+	}
+	hash2 := make(map[uint64]bool)
+	for _, val := range s2 {
+		hash2[val] = true
+	}
+
+	intersection := make([]uint64, 0)
+
+	// look for keys from hash1 also in hash2
+	for key := range hash1 {
+		if _, found := hash2[key]; found {
+			intersection = append(intersection, key)
+		}
+	}
+
+	if len(intersection) == 0 {
+		return nil
+	}
+	sortSlice(intersection)
+	return intersection
+}
+
+// union unions two []uint64s and sorts the output.
+func unionSlice(s1, s2 []uint64) []uint64 {
+	// just dump both slices in a map
+	// and get the values out again
+	hash := make(map[uint64]bool)
+	for _, val := range s1 {
+		hash[val] = true
+	}
+	for _, val := range s2 {
+		hash[val] = true
+	}
+	union := make([]uint64, 0)
+
+	for key := range hash {
+		union = append(union, key)
+	}
+
+	if len(union) == 0 {
+		return nil
+	}
+	sortSlice(union)
+	return union
+}
+
+// maxSlice returns the max in the slice.
+func maxInSlice(slice []uint64) uint64 {
+	if len(slice) == 0 {
+		return 0
+	}
+
+	max := uint64(0)
+	for _, val := range slice {
+		if val > max {
+			max = val
+		}
+	}
+	return max
+}
+
+// differenceSlice returns a slice containing the values
+// present in the first slice but not in the second.
+func differenceSlice(s1, s2 []uint64) []uint64 {
+	// throw s2 in a map, check if each value
+	// in s1 is also in that map
+	hash := make(map[uint64]bool)
+	for _, val := range s2 {
+		hash[val] = true
+	}
+	diff := make([]uint64, 0)
+	for _, val := range s1 {
+		if _, found := hash[val]; !found {
+			diff = append(diff, val)
+		}
+	}
+	// make sure duplicates in s1 are not added
+	diff = removeSliceDuplicates(diff)
+	return diff
+}
+
+// xorSlice returns an array containing the values
+// present in exactly one of the two slices.
+func xorSlice(s1, s2 []uint64) []uint64 {
+	// throw both slices in maps
+	hash1 := make(map[uint64]bool)
+	for _, val := range s1 {
+		hash1[val] = true
+	}
+	hash2 := make(map[uint64]bool)
+	for _, val := range s2 {
+		hash2[val] = true
+	}
+
+	xor := make([]uint64, 0)
+	// add all values in hash1 not in hash2
+	for key := range hash1 {
+		if _, found := hash2[key]; !found {
+			xor = append(xor, key)
+		}
+	}
+	// add all values in hash2 not in hash1
+	for key := range hash2 {
+		if _, found := hash1[key]; !found {
+			xor = append(xor, key)
+		}
+	}
+
+	if len(xor) == 0 {
+		return nil
+	}
+	sortSlice(xor)
+	return xor
+}
+
+// shiftSlice adds n to each element and sorts the slice, but ignores any values that
+// will cause an overflow. This does not modify the original slice, unlike the Roaring implementation.
+func shiftSlice(slice []uint64, n int) []uint64 {
+	shifted := make([]uint64, 0)
+	for _, val := range slice {
+		if uint64(n) <= math.MaxUint64-val {
+			shifted = append(shifted, val+uint64(n))
+		}
+	}
+
+	if len(shifted) == 0 {
+		return nil
+	}
+	sortSlice(shifted)
+	return shifted
+}
+
+// forEachSlice executes fn for each element in the slice.
+func forEachInSlice(slice []uint64, fn func(uint64)) {
+	for _, val := range slice {
+		fn(val)
+	}
+}
+
+// forEachRangeSlice executes fn for each element in slice that is in [start, end).
+func forEachInRangeSlice(slice []uint64, start, end uint64, fn func(uint64)) {
+	for _, val := range slice {
+		if start <= val && val < end {
+			fn(val)
+		}
+	}
+}
+
+// containedInSlice returns the index of the first instance of v and true
+// if v is in slice and returns -1 and false otherwise.
+func containedInSlice(slice []uint64, v uint64) (int, bool) {
+	for idx := range slice {
+		if v == slice[idx] {
+			return idx, true
+		}
+	}
+	return -1, false
+}
+
+// addNToSlice adds the contents of a to slice and returns the new slice and
+// number of values successfully added. This somewhat mimics *Bitmap.DirectAddN
+// and but does not modify slice in place, so it returns that new slice instead.
+func addNToSlice(slice []uint64, a ...uint64) ([]uint64, int) {
+	newSlice := make([]uint64, len(slice))
+	copy(newSlice, slice)
+	changed := 0
+
+	for _, val := range a {
+		if _, found := containedInSlice(newSlice, val); !found {
+			newSlice = append(newSlice, val)
+			changed++
+		}
+	}
+
+	if len(newSlice) == 0 {
+		return nil, changed
+	}
+	sortSlice(newSlice)
+	return newSlice, changed
+}
+
+// removeNFromSlice removes the contents of a from slice and returns the new slice and
+// number of values successfully removed. This somewhat mimics *Bitmap.DirectRemoveN
+// and but does not modify slice in place, so it returns that new slice instead.
+func removeNFromSlice(slice []uint64, a ...uint64) ([]uint64, int) {
+	newSlice := make([]uint64, len(slice))
+	copy(newSlice, slice)
+	changed := 0
+
+	for _, val := range a {
+		if i, found := containedInSlice(newSlice, val); found {
+			newSlice = append(newSlice[:i], newSlice[i+1:]...)
+			changed++
+		}
+	}
+
+	if len(newSlice) == 0 {
+		return nil, changed
+	}
+	sortSlice(newSlice)
+	return newSlice, changed
+}
+
+// countRangeSlice returns the number of values in slice that are in [start, end).
+func countRangeSlice(slice []uint64, start, end uint64) uint64 {
+	count := uint64(0)
+	for _, val := range slice {
+		if start <= val && val < end {
+			count++
+		}
+	}
+	return count
+}
+
+// rangeSlice returns a sorted slice of integers between [start, end).
+func rangeSlice(slice []uint64, start, end uint64) []uint64 {
+	newSlice := make([]uint64, 0)
+	for _, val := range slice {
+		if start <= val && val < end {
+			newSlice = append(newSlice, val)
+		}
+	}
+
+	if len(newSlice) == 0 {
+		return nil
+	}
+	sortSlice(newSlice)
+	return newSlice
+}
+
+// flipSplice returns a slice containing all numbers in [start, end]
+// that are not in the original slice, as well as the numbers in the
+// original slice not in [start, end].
+func flipSlice(slice []uint64, start, end uint64) []uint64 {
+	if start > end {
+		sortSlice(slice)
+		return slice
+	}
+
+	flipped := make([]uint64, 0)
+	// add values in slice outside [start, end]
+	hash := make(map[uint64]bool)
+	for _, val := range slice {
+		hash[val] = true
+	}
+	for val := range hash {
+		if val < start || val > end {
+			flipped = append(flipped, val)
+		}
+	}
+
+	for i := start; i <= end; i++ {
+		if _, found := containedInSlice(slice, i); !found {
+			flipped = append(flipped, i)
+		}
+	}
+
+	if len(flipped) == 0 {
+		return nil
+	}
+	sortSlice(flipped)
+	return flipped
+}

roaring/naive_test.go

@@ -0,0 +1,305 @@
+// Copyright 2017 Pilosa Corp.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package roaring
+
+import (
+	"reflect"
+	"testing"
+)
+
+func TestSortSlice(t *testing.T) {
+	a := []uint64{1, 3, 2, 8, 5, 21, 13}
+	sortSlice(a)
+	if !reflect.DeepEqual(a, []uint64{1, 2, 3, 5, 8, 13, 21}) {
+		t.Fatalf("unexpected sorting: %v", a)
+	}
+}
+
+func TestRemoveSliceDuplicates(t *testing.T) {
+	a := []uint64{2, 3, 2, 1, 2, 5, 8, 5, 13, 3, 2, 5, 144}
+	a = removeSliceDuplicates(a)
+
+	if !reflect.DeepEqual(a, []uint64{1, 2, 3, 5, 8, 13, 144}) {
+		t.Fatalf("unexpected values: %v", a)
+	}
+
+	a = append(a, 21, 8, 3, 3, 5, 5, 1, 34, 21, 21)
+	a = removeSliceDuplicates(a)
+
+	if !reflect.DeepEqual(a, []uint64{1, 2, 3, 5, 8, 13, 21, 34, 144}) {
+		t.Fatalf("unexpected values: %v", a)
+	}
+}
+
+func TestIntersectSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+	c := intersectSlice(a, b)
+
+	if !reflect.DeepEqual(c, []uint64{1, 5, 9}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(c, intersectSlice(b, a)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(c, intersectSlice(c, a)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestUnionSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+	c := unionSlice(a, b)
+
+	if !reflect.DeepEqual(c, []uint64{1, 2, 4, 5, 9, 12, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(c, unionSlice(b, a)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(c, unionSlice(c, a)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestMaxInSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	v := maxInSlice(a)
+	if uint64(24) != v {
+		t.Fatalf("expected %v, but got %v", uint64(24), v)
+	}
+
+	for i := uint64(1000); i <= uint64(100000); i++ {
+		a = append(a, i)
+		if v = maxInSlice(a); v != i {
+			t.Fatalf("expected %v, but got %v", i, v)
+		}
+	}
+}
+
+func TestDifferenceSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+
+	c := differenceSlice(a, b)
+	if !reflect.DeepEqual(c, []uint64{4, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = differenceSlice(b, a)
+	if !reflect.DeepEqual(c, []uint64{2, 12}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = differenceSlice(a, a)
+	if !reflect.DeepEqual(c, []uint64(nil)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestXorSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+	c := xorSlice(a, b)
+
+	if !reflect.DeepEqual(c, []uint64{2, 4, 12, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(c, xorSlice(b, a)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(xorSlice(c, a), []uint64{1, 2, 5, 9, 12}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if !reflect.DeepEqual(xorSlice(c, b), []uint64{1, 4, 5, 9, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestShiftSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+
+	c := shiftSlice(a, 12)
+	if !reflect.DeepEqual(c, []uint64{13, 16, 17, 21, 25, 36}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = shiftSlice(a, 0)
+	if !reflect.DeepEqual(c, []uint64{1, 4, 5, 9, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestForEachInSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	c := make([]uint64, 0)
+
+	forEachInSlice(a, func(v uint64) {
+		c = append(c, v+1)
+	})
+	if !reflect.DeepEqual(c, []uint64{2, 5, 10, 6, 25, 14}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestForEachInRangeSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	c := make([]uint64, 0)
+
+	forEachInRangeSlice(a, uint64(3), uint64(12), func(v uint64) {
+		c = append(c, v+1)
+	})
+	if !reflect.DeepEqual(c, []uint64{5, 10, 6}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestContainedInSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+
+	c := uint64(4)
+	idx, found := containedInSlice(a, c)
+	if !found {
+		t.Fatalf("%v should be in %v", c, a)
+	}
+	if a[idx] != c {
+		t.Fatalf("%v is not at position %v", c, idx)
+	}
+
+	c = uint64(12)
+	idx, found = containedInSlice(a, c)
+	if found {
+		t.Fatalf("%v should not be in %v", c, a)
+	}
+	if idx != -1 {
+		t.Fatalf("expected %v, got %v", -1, idx)
+	}
+}
+
+func TestAddNToSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+
+	c, changed := addNToSlice(a, b...)
+	if !reflect.DeepEqual(c, []uint64{1, 2, 4, 5, 9, 12, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+	if changed != 2 {
+		t.Fatalf("changes expected %v, got %v", 2, changed)
+	}
+
+	c, changed = addNToSlice(b, a...)
+	if !reflect.DeepEqual(c, []uint64{1, 2, 4, 5, 9, 12, 13, 24}) {
+		t.Fatalf("%v and %v should be the same", c, a)
+	}
+	if changed != 3 {
+		t.Fatalf("changes expected %v, got %v", 3, changed)
+	}
+
+	c, changed = addNToSlice(a, a...)
+	if !reflect.DeepEqual(c, []uint64{1, 4, 5, 9, 13, 24}) {
+		t.Fatalf("%v and %v should be the same", c, a)
+	}
+	if changed != 0 {
+		t.Fatalf("changes expected %v, got %v", 0, changed)
+	}
+}
+
+func TestRemoveNFromSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+	b := []uint64{2, 1, 9, 5, 12}
+
+	c, changed := removeNFromSlice(a, b...)
+	if !reflect.DeepEqual(c, []uint64{4, 13, 24}) {
+		t.Fatalf("%v and %v should be the same", c, []uint64{4, 13, 24})
+	}
+	if changed != 3 {
+		t.Fatalf("%v changes expected, got %v", 3, changed)
+	}
+
+	c, changed = removeNFromSlice(b, a...)
+	if !reflect.DeepEqual(c, []uint64{2, 12}) {
+		t.Fatalf("%v and %v should be the same", c, []uint64{2, 12})
+	}
+	if changed != 3 {
+		t.Fatalf("%v changes expected, got %v", 3, changed)
+	}
+
+	c, changed = removeNFromSlice(a, a...)
+	if !reflect.DeepEqual(c, []uint64(nil)) {
+		t.Fatalf("%v and %v should be the same", c, a)
+	}
+	if changed != 6 {
+		t.Fatalf("%v changes expected, got %v", 0, changed)
+	}
+}
+
+func TestCountRangeSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+
+	c := countRangeSlice(a, uint64(3), uint64(12))
+	if c != 3 {
+		t.Fatalf("expected %v, got %v", 3, c)
+	}
+
+	c = countRangeSlice(a, uint64(0), uint64(25))
+	if c != 6 {
+		t.Fatalf("expected %v, got %v", 6, c)
+	}
+
+	c = countRangeSlice(a, uint64(12), uint64(4))
+	if c != 0 {
+		t.Fatalf("expected %v, got %v", 0, c)
+	}
+}
+
+func TestRangeSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+
+	c := rangeSlice(a, uint64(3), uint64(12))
+	if !reflect.DeepEqual(c, []uint64{4, 5, 9}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = rangeSlice(a, uint64(0), uint64(25))
+	if !reflect.DeepEqual(c, []uint64{1, 4, 5, 9, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = rangeSlice(a, uint64(5), uint64(5))
+	if !reflect.DeepEqual(c, []uint64(nil)) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}
+
+func TestFlipSlice(t *testing.T) {
+	a := []uint64{1, 4, 9, 5, 24, 13}
+
+	c := flipSlice(a, uint64(3), uint64(12))
+	if !reflect.DeepEqual(c, []uint64{1, 3, 6, 7, 8, 10, 11, 12, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = flipSlice(a, uint64(13), uint64(12))
+	if !reflect.DeepEqual(c, []uint64{1, 4, 5, 9, 13, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+
+	c = flipSlice(a, uint64(9), uint64(13))
+	if !reflect.DeepEqual(c, []uint64{1, 4, 5, 10, 11, 12, 24}) {
+		t.Fatalf("unexpected values: %v", c)
+	}
+}