gcs.go

// Copyright (c) 2016-2017 The btcsuite developers
// Copyright (c) 2016-2017 The Lightning Network Developers
// Use of this source code is governed by an ISC
// license that can be found in the LICENSE file.

package gcs

import (
	"bytes"
	"fmt"
	"io"
	"sort"

	"github.com/aead/siphash"
	"github.com/btcsuite/btcd/wire"
	"github.com/kkdai/bstream"
)

// Inspired by https://github.com/rasky/gcs

var (
	// ErrNTooBig signifies that the filter can't handle N items.
	ErrNTooBig = fmt.Errorf("N is too big to fit in uint32")

	// ErrPTooBig signifies that the filter can't handle `1/2**P`
	// collision probability.
	ErrPTooBig = fmt.Errorf("P is too big to fit in uint32")
)

const (
	// KeySize is the size of the byte array required for key material for
	// the SipHash keyed hash function.
	KeySize = 16

	// varIntProtoVer is the protocol version to use for serializing N as a
	// VarInt.
	varIntProtoVer uint32 = 0
)

// fastReduction calculates a mapping that's more ore less equivalent to: x mod
// N. However, instead of using a mod operation, which using a non-power of two
// will lead to slowness on many processors due to unnecessary division, we
// instead use a "multiply-and-shift" trick which eliminates all divisions,
// described in:
// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
//
//  * v * N  >> log_2(N)
//
// In our case, using 64-bit integers, log_2 is 64. As most processors don't
// support 128-bit arithmetic natively, we'll be super portable and unfold the
// operation into several operations with 64-bit arithmetic. As inputs, we the
// number to reduce, and our modulus N divided into its high 32-bits and lower
// 32-bits.
func fastReduction(v, nHi, nLo uint64) uint64 {
	// First, we'll spit the item we need to reduce into its higher and
	// lower bits.
	vhi := v >> 32
	vlo := uint64(uint32(v))

	// Then, we distribute multiplication over each part.
	vnphi := vhi * nHi
	vnpmid := vhi * nLo
	npvmid := nHi * vlo
	vnplo := vlo * nLo

	// We calculate the carry bit.
	carry := (uint64(uint32(vnpmid)) + uint64(uint32(npvmid)) +
		(vnplo >> 32)) >> 32

	// Last, we add the high bits, the middle bits, and the carry.
	v = vnphi + (vnpmid >> 32) + (npvmid >> 32) + carry

	return v
}

// Filter describes an immutable filter that can be built from a set of data
// elements, serialized, deserialized, and queried in a thread-safe manner. The
// serialized form is compressed as a Golomb Coded Set (GCS), but does not
// include N or P to allow the user to encode the metadata separately if
// necessary. The hash function used is SipHash, a keyed function; the key used
// in building the filter is required in order to match filter values and is
// not included in the serialized form.
type Filter struct {
	n         uint32
	p         uint8
	modulusNP uint64

	filterData []byte
}

// BuildGCSFilter builds a new GCS filter with the collision probability of
// `1/(2**P)`, key `key`, and including every `[]byte` in `data` as a member of
// the set.
func BuildGCSFilter(P uint8, M uint64, key [KeySize]byte, data [][]byte) (*Filter, error) {
	// Some initial parameter checks: make sure we have data from which to
	// build the filter, and make sure our parameters will fit the hash
	// function we're using.
	if uint64(len(data)) >= (1 << 32) {
		return nil, ErrNTooBig
	}
	if P > 32 {
		return nil, ErrPTooBig
	}

	// Create the filter object and insert metadata.
	f := Filter{
		n: uint32(len(data)),
		p: P,
	}

	// First we'll compute the value of m, which is the modulus we use
	// within our finite field. We want to compute: mScalar * 2^P. We use
	// math.Round in order to round the value up, rather than down.
	f.modulusNP = uint64(f.n) * M

	// Shortcut if the filter is empty.
	if f.n == 0 {
		return &f, nil
	}

	// Build the filter.
	values := make([]uint64, 0, len(data))
	b := bstream.NewBStreamWriter(0)

	// Insert the hash (fast-ranged over a space of N*P) of each data
	// element into a slice and sort the slice. This can be greatly
	// optimized with native 128-bit multiplication, but we're going to be
	// fully portable for now.
	//
	// First, we cache the high and low bits of modulusNP for the
	// multiplication of 2 64-bit integers into a 128-bit integer.
	nphi := f.modulusNP >> 32
	nplo := uint64(uint32(f.modulusNP))
	for _, d := range data {
		// For each datum, we assign the initial hash to a uint64.
		v := siphash.Sum64(d, &key)

		v = fastReduction(v, nphi, nplo)
		values = append(values, v)
	}
	sort.Slice(values, func(i, j int) bool { return values[i] < values[j] })

	// Write the sorted list of values into the filter bitstream,
	// compressing it using Golomb coding.
	var value, lastValue, remainder uint64
	for _, v := range values {
		// Calculate the difference between this value and the last,
		// modulo P.
		remainder = (v - lastValue) & ((uint64(1) << f.p) - 1)

		// Calculate the difference between this value and the last,
		// divided by P.
		value = (v - lastValue - remainder) >> f.p
		lastValue = v

		// Write the P multiple into the bitstream in unary; the
		// average should be around 1 (2 bits - 0b10).
		for value > 0 {
			b.WriteBit(true)
			value--
		}
		b.WriteBit(false)

		// Write the remainder as a big-endian integer with enough bits
		// to represent the appropriate collision probability.
		b.WriteBits(remainder, int(f.p))
	}

	// Copy the bitstream into the filter object and return the object.
	f.filterData = b.Bytes()

	return &f, nil
}

// FromBytes deserializes a GCS filter from a known N, P, and serialized filter
// as returned by Bytes().
func FromBytes(N uint32, P uint8, M uint64, d []byte) (*Filter, error) {
	// Basic sanity check.
	if P > 32 {
		return nil, ErrPTooBig
	}

	// Create the filter object and insert metadata.
	f := &Filter{
		n: N,
		p: P,
	}

	// First we'll compute the value of m, which is the modulus we use
	// within our finite field. We want to compute: mScalar * 2^P. We use
	// math.Round in order to round the value up, rather than down.
	f.modulusNP = uint64(f.n) * M

	// Copy the filter.
	f.filterData = make([]byte, len(d))
	copy(f.filterData, d)

	return f, nil
}

// FromNBytes deserializes a GCS filter from a known P, and serialized N and
// filter as returned by NBytes().
func FromNBytes(P uint8, M uint64, d []byte) (*Filter, error) {
	buffer := bytes.NewBuffer(d)
	N, err := wire.ReadVarInt(buffer, varIntProtoVer)
	if err != nil {
		return nil, err
	}
	if N >= (1 << 32) {
		return nil, ErrNTooBig
	}
	return FromBytes(uint32(N), P, M, buffer.Bytes())
}

// Bytes returns the serialized format of the GCS filter, which does not
// include N or P (returned by separate methods) or the key used by SipHash.
func (f *Filter) Bytes() ([]byte, error) {
	filterData := make([]byte, len(f.filterData))
	copy(filterData, f.filterData)
	return filterData, nil
}

// NBytes returns the serialized format of the GCS filter with N, which does
// not include P (returned by a separate method) or the key used by SipHash.
func (f *Filter) NBytes() ([]byte, error) {
	var buffer bytes.Buffer
	buffer.Grow(wire.VarIntSerializeSize(uint64(f.n)) + len(f.filterData))

	err := wire.WriteVarInt(&buffer, varIntProtoVer, uint64(f.n))
	if err != nil {
		return nil, err
	}

	_, err = buffer.Write(f.filterData)
	if err != nil {
		return nil, err
	}

	return buffer.Bytes(), nil
}

// PBytes returns the serialized format of the GCS filter with P, which does
// not include N (returned by a separate method) or the key used by SipHash.
func (f *Filter) PBytes() ([]byte, error) {
	filterData := make([]byte, len(f.filterData)+1)
	filterData[0] = f.p
	copy(filterData[1:], f.filterData)
	return filterData, nil
}

// NPBytes returns the serialized format of the GCS filter with N and P, which
// does not include the key used by SipHash.
func (f *Filter) NPBytes() ([]byte, error) {
	var buffer bytes.Buffer
	buffer.Grow(wire.VarIntSerializeSize(uint64(f.n)) + 1 + len(f.filterData))

	err := wire.WriteVarInt(&buffer, varIntProtoVer, uint64(f.n))
	if err != nil {
		return nil, err
	}

	err = buffer.WriteByte(f.p)
	if err != nil {
		return nil, err
	}

	_, err = buffer.Write(f.filterData)
	if err != nil {
		return nil, err
	}

	return buffer.Bytes(), nil
}

// P returns the filter's collision probability as a negative power of 2 (that
// is, a collision probability of `1/2**20` is represented as 20).
func (f *Filter) P() uint8 {
	return f.p
}

// N returns the size of the data set used to build the filter.
func (f *Filter) N() uint32 {
	return f.n
}

// Match checks whether a []byte value is likely (within collision probability)
// to be a member of the set represented by the filter.
func (f *Filter) Match(key [KeySize]byte, data []byte) (bool, error) {
	// Create a filter bitstream.
	filterData, err := f.Bytes()
	if err != nil {
		return false, err
	}

	b := bstream.NewBStreamReader(filterData)

	// We take the high and low bits of modulusNP for the multiplication
	// of 2 64-bit integers into a 128-bit integer.
	nphi := f.modulusNP >> 32
	nplo := uint64(uint32(f.modulusNP))

	// Then we hash our search term with the same parameters as the filter.
	term := siphash.Sum64(data, &key)
	term = fastReduction(term, nphi, nplo)

	// Go through the search filter and look for the desired value.
	var value uint64
	for i := uint32(0); i < f.N(); i++ {
		// Read the difference between previous and new value from
		// bitstream.
		delta, err := f.readFullUint64(b)
		if err != nil {
			if err == io.EOF {
				return false, nil
			}
			return false, err
		}

		// Add the delta to the previous value.
		value += delta
		switch {

		// The current value matches our query term, success.
		case value == term:
			return true, nil

		// The current value is greater than our query term, thus no
		// future decoded value can match because the values
		// monotonically increase.
		case value > term:
			return false, nil
		}
	}

	// All values were decoded and none produced a successful match. This
	// indicates that the items in the filter were all smaller than our
	// target.
	return false, nil
}

// MatchAny returns checks whether any []byte value is likely (within collision
// probability) to be a member of the set represented by the filter faster than
// calling Match() for each value individually.
func (f *Filter) MatchAny(key [KeySize]byte, data [][]byte) (bool, error) {
	// TODO(conner): add real heuristics to query optimization
	switch {

	case len(data) >= int(f.N()/2):
		return f.HashMatchAny(key, data)

	default:
		return f.ZipMatchAny(key, data)
	}
}

// ZipMatchAny returns checks whether any []byte value is likely (within
// collision probability) to be a member of the set represented by the filter
// faster than calling Match() for each value individually.
//
// NOTE: This method should outperform HashMatchAny when the number of query
// entries is smaller than the number of filter entries.
func (f *Filter) ZipMatchAny(key [KeySize]byte, data [][]byte) (bool, error) {
	// Basic anity check.
	if len(data) == 0 {
		return false, nil
	}

	// Create a filter bitstream.
	filterData, err := f.Bytes()
	if err != nil {
		return false, err
	}

	b := bstream.NewBStreamReader(filterData)

	// Create an uncompressed filter of the search values.
	values := make([]uint64, 0, len(data))

	// First, we cache the high and low bits of modulusNP for the
	// multiplication of 2 64-bit integers into a 128-bit integer.
	nphi := f.modulusNP >> 32
	nplo := uint64(uint32(f.modulusNP))
	for _, d := range data {
		// For each datum, we assign the initial hash to a uint64.
		v := siphash.Sum64(d, &key)

		// We'll then reduce the value down to the range of our
		// modulus.
		v = fastReduction(v, nphi, nplo)
		values = append(values, v)
	}
	sort.Slice(values, func(i, j int) bool { return values[i] < values[j] })

	querySize := len(values)

	// Zip down the filters, comparing values until we either run out of
	// values to compare in one of the filters or we reach a matching
	// value.
	var (
		value      uint64
		queryIndex int
	)
out:
	for i := uint32(0); i < f.N(); i++ {
		// Advance filter we're searching or return false if we're at
		// the end because nothing matched.
		delta, err := f.readFullUint64(b)
		if err != nil {
			if err == io.EOF {
				return false, nil
			}
			return false, err
		}
		value += delta

		for {
			switch {

			// All query items have been exhausted and we haven't
			// had a match, therefore there are no matches.
			case queryIndex == querySize:
				return false, nil

			// The current item in the query matches the decoded
			// value, success.
			case values[queryIndex] == value:
				return true, nil

			// The current item in the query is greater than the
			// current decoded value, continue to decode the next
			// delta and try again.
			case values[queryIndex] > value:
				continue out
			}

			queryIndex++
		}
	}

	// All items in the filter were decoded and none produced a successful
	// match.
	return false, nil
}

// HashMatchAny returns checks whether any []byte value is likely (within
// collision probability) to be a member of the set represented by the filter
// faster than calling Match() for each value individually.
//
// NOTE: This method should outperform MatchAny if the number of query entries
// approaches the number of filter entries, len(data) >= f.N().
func (f *Filter) HashMatchAny(key [KeySize]byte, data [][]byte) (bool, error) {
	// Basic sanity check.
	if len(data) == 0 {
		return false, nil
	}

	// Create a filter bitstream.
	filterData, err := f.Bytes()
	if err != nil {
		return false, err
	}

	b := bstream.NewBStreamReader(filterData)

	var (
		values    = make(map[uint32]struct{}, f.N())
		lastValue uint64
	)

	// First, decompress the filter and construct an index of the keys
	// contained within the filter. Index construction terminates after all
	// values have been read from the bitstream.
	for {
		// Read the next diff value from the filter, add it to the
		// last value, and set the new value in the index.
		value, err := f.readFullUint64(b)
		if err == nil {
			lastValue += value
			values[uint32(lastValue)] = struct{}{}
			continue
		} else if err == io.EOF {
			break
		}

		return false, err
	}

	// We cache the high and low bits of modulusNP for the multiplication of
	// 2 64-bit integers into a 128-bit integer.
	nphi := f.modulusNP >> 32
	nplo := uint64(uint32(f.modulusNP))

	// Finally, run through the provided data items, querying the index to
	// determine if the filter contains any elements of interest.
	for _, d := range data {
		// For each datum, we assign the initial hash to
		// a uint64.
		v := siphash.Sum64(d, &key)

		// We'll then reduce the value down to the range
		// of our modulus.
		v = fastReduction(v, nphi, nplo)

		if _, ok := values[uint32(v)]; !ok {
			continue
		}

		return true, nil
	}

	return false, nil
}

// readFullUint64 reads a value represented by the sum of a unary multiple of
// the filter's P modulus (`2**P`) and a big-endian P-bit remainder.
func (f *Filter) readFullUint64(b *bstream.BStream) (uint64, error) {
	var quotient uint64

	// Count the 1s until we reach a 0.
	c, err := b.ReadBit()
	if err != nil {
		return 0, err
	}
	for c {
		quotient++
		c, err = b.ReadBit()
		if err != nil {
			return 0, err
		}
	}

	// Read P bits.
	remainder, err := b.ReadBits(int(f.p))
	if err != nil {
		return 0, err
	}

	// Add the multiple and the remainder.
	v := (quotient << f.p) + remainder
	return v, nil
}