perf(query): Update CompressedBin IntersectionAlgo (#9000)

Updated algo to intersect. Getting upto 175% improvment overall
```
goos: linux
goarch: amd64
pkg: github.com/dgraph-io/dgraph/algo
cpu: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz
                                                                                          │     in1      │                 main_in                 │
                                                                                          │    sec/op    │    sec/op      vs base                  │
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.01:size=100:overlap=0.01:-8       91.21n ± ∞ ¹   387.70n ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.1:size=100:overlap=0.01:-8        336.0n ± ∞ ¹   1733.0n ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=1:size=100:overlap=0.01:-8          1.093µ ± ∞ ¹    3.481µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=10:size=100:overlap=0.01:-8         4.719µ ± ∞ ¹    8.600µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=100:size=100:overlap=0.01:-8        19.76µ ± ∞ ¹    44.32µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.01:size=1000:overlap=0.01:-8      481.7n ± ∞ ¹    784.2n ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.1:size=1000:overlap=0.01:-8       1.502µ ± ∞ ¹    3.667µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=1:size=1000:overlap=0.01:-8         5.454µ ± ∞ ¹   36.977µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=10:size=1000:overlap=0.01:-8        33.14µ ± ∞ ¹    70.73µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=100:size=1000:overlap=0.01:-8       179.8µ ± ∞ ¹    485.1µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.01:size=10000:overlap=0.01:-8     3.214µ ± ∞ ¹    4.459µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.1:size=10000:overlap=0.01:-8      12.00µ ± ∞ ¹    32.78µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=1:size=10000:overlap=0.01:-8        76.90µ ± ∞ ¹   356.05µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=10:size=10000:overlap=0.01:-8       371.6µ ± ∞ ¹    923.1µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=100:size=10000:overlap=0.01:-8      1.894m ± ∞ ¹    5.141m ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.01:size=100000:overlap=0.01:-8    48.13µ ± ∞ ¹    60.59µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.1:size=100000:overlap=0.01:-8     146.7µ ± ∞ ¹    611.9µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=1:size=100000:overlap=0.01:-8       943.7µ ± ∞ ¹   3359.6µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=10:size=100000:overlap=0.01:-8      3.926m ± ∞ ¹    8.849m ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=100:size=100000:overlap=0.01:-8     20.78m ± ∞ ¹
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.01:size=1000000:overlap=0.01:-8   862.4µ ± ∞ ¹   1142.5µ ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=0.1:size=1000000:overlap=0.01:-8    1.599m ± ∞ ¹    7.878m ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=1:size=1000000:overlap=0.01:-8      9.791m ± ∞ ¹   33.871m ± ∞ ¹         ~ (p=1.000 n=1) ²
ListIntersectCompressBin/compressed:IntersectWith:ratio=10:size=1000000:overlap=0.01:-8     44.40m ± ∞ ¹
geomean                                                                                     66.19µ          104.6µ        +175.93%               ³
                    

```

Author: Harshil Goel

algo/uidlist.go

@@ -24,7 +24,8 @@ import (
 	"github.com/dgraph-io/dgraph/protos/pb"
 )
 
-const jump = 32 // Jump size in InsersectWithJump.
+const jump = 32          // Jump size in InsersectWithJump.
+const linVsBinRatio = 10 // When is linear search better than binary
 
 // ApplyFilter applies a filter to our UIDList.
 func ApplyFilter(u *pb.List, f func(uint64, int) bool) {
@@ -60,7 +61,7 @@ func IntersectCompressedWith(pack *pb.UidPack, afterUID uint64, v, o *pb.List) {
 
 	// Select appropriate function based on heuristics.
 	ratio := float64(m) / float64(n)
-	if ratio < 500 {
+	if ratio < linVsBinRatio {
 		IntersectCompressedWithLinJump(&dec, v.Uids, &dst)
 	} else {
 		IntersectCompressedWithBin(&dec, v.Uids, &dst)
@@ -94,7 +95,7 @@ func IntersectCompressedWithLinJump(dec *codec.Decoder, v []uint64, o *[]uint64)
 // https://link.springer.com/chapter/10.1007/978-3-642-12476-1_3
 // Call seek on dec before calling this function
 func IntersectCompressedWithBin(dec *codec.Decoder, q []uint64, o *[]uint64) {
-	ld := dec.ApproxLen()
+	ld := codec.ExactLen(dec.Pack)
 	lq := len(q)
 
 	if lq == 0 {
@@ -105,46 +106,44 @@ func IntersectCompressedWithBin(dec *codec.Decoder, q []uint64, o *[]uint64) {
 	}
 
 	// Pick the shorter list and do binary search
-	if ld < lq {
+	if ld <= lq {
 		for {
 			blockUids := dec.Uids()
 			if len(blockUids) == 0 {
 				break
 			}
-			IntersectWithBin(blockUids, q, o)
-			lastUid := blockUids[len(blockUids)-1]
-			qidx := sort.Search(len(q), func(idx int) bool {
-				return q[idx] >= lastUid
-			})
-			if qidx >= len(q) {
+			_, off := IntersectWithJump(blockUids, q, o)
+			q = q[off:]
+			if len(q) == 0 {
 				return
 			}
-			q = q[qidx:]
 			dec.Next()
 		}
 		return
 	}
 
-	var uids []uint64
-	for _, u := range q {
+	uids := dec.Uids()
+	qidx := 0
+	for {
+		if qidx >= len(q) {
+			return
+		}
+		u := q[qidx]
 		if len(uids) == 0 || u > uids[len(uids)-1] {
-			uids = dec.Seek(u, codec.SeekStart)
+			if lq*linVsBinRatio < ld {
+				uids = dec.LinearSeek(u)
+			} else {
+				uids = dec.SeekToBlock(u, codec.SeekCurrent)
+			}
 			if len(uids) == 0 {
 				return
 			}
 		}
-		uidIdx := sort.Search(len(uids), func(idx int) bool {
-			return uids[idx] >= u
-		})
-		if uidIdx >= len(uids) {
-			// We know that u < max(uids). If we didn't find it here, it's not here.
-			continue
-		}
-		if uids[uidIdx] == u {
-			*o = append(*o, u)
-			uidIdx++
+		_, off := IntersectWithJump(uids, q[qidx:], o)
+		if off == 0 {
+			off = 1 // if v[k] isn't in u, move forward
 		}
-		uids = uids[uidIdx:]
+		qidx += off
 	}
 }
 
@@ -233,7 +232,8 @@ func IntersectWithJump(u, v []uint64, o *[]uint64) (int, int) {
 // IntersectWithBin is based on the paper
 // "Fast Intersection Algorithms for Sorted Sequences"
 // https://link.springer.com/chapter/10.1007/978-3-642-12476-1_3
-func IntersectWithBin(d, q []uint64, o *[]uint64) {
+// Returns where to move the second array(q) to. O means not found
+func IntersectWithBin(d, q []uint64, o *[]uint64) int {
 	ld := len(d)
 	lq := len(q)
 
@@ -242,7 +242,7 @@ func IntersectWithBin(d, q []uint64, o *[]uint64) {
 		d, q = q, d
 	}
 	if ld == 0 || lq == 0 || d[ld-1] < q[0] || q[lq-1] < d[0] {
-		return
+		return 0
 	}
 
 	val := d[0]
@@ -256,6 +256,7 @@ func IntersectWithBin(d, q []uint64, o *[]uint64) {
 	})
 
 	binIntersect(d, q[minq:maxq], o)
+	return maxq
 }
 
 // binIntersect is the recursive function used.

algo/uidlist_test.go

@@ -373,7 +373,7 @@ func BenchmarkListIntersectCompressBin(b *testing.B) {
 		for _, r := range rs {
 			sz1 := sz
 			sz2 := int(float64(sz) * r)
-			if sz2 > 1000000 || sz2 == 0 {
+			if sz2 > 10000000 || sz2 == 0 {
 				break
 			}
 
@@ -389,8 +389,18 @@ func BenchmarkListIntersectCompressBin(b *testing.B) {
 			sort.Slice(v1, func(i, j int) bool { return v1[i] < v1[j] })
 
 			dst2 := &pb.List{}
+			dst1 := &pb.List{}
 			compressedUids := codec.Encode(v1, 256)
 
+			b.Run(fmt.Sprintf("linJump:IntersectWith:ratio=%v:size=%d:overlap=%.2f:", r, sz, overlap),
+				func(b *testing.B) {
+					for k := 0; k < b.N; k++ {
+						dec := codec.Decoder{Pack: compressedUids}
+						dec.Seek(0, codec.SeekStart)
+						IntersectCompressedWithLinJump(&dec, u1, &dst1.Uids)
+					}
+				})
+
 			b.Run(fmt.Sprintf("compressed:IntersectWith:ratio=%v:size=%d:overlap=%.2f:", r, sz, overlap),
 				func(b *testing.B) {
 					for k := 0; k < b.N; k++ {
@@ -399,7 +409,6 @@ func BenchmarkListIntersectCompressBin(b *testing.B) {
 						IntersectCompressedWithBin(&dec, u1, &dst2.Uids)
 					}
 				})
-			fmt.Println()
 
 			codec.FreePack(compressedUids)
 		}
@@ -493,6 +502,43 @@ func sortUint64(nums []uint64) {
 	sort.Slice(nums, func(i, j int) bool { return nums[i] < nums[j] })
 }
 
+func fillNumsDiff(N1, N2, N3 int) ([]uint64, []uint64, []uint64) {
+	rand.Seed(time.Now().UnixNano())
+
+	commonNums := make([]uint64, N1)
+	blockNums := make([]uint64, N1+N2)
+	otherNums := make([]uint64, N1+N3)
+	allC := make(map[uint64]bool)
+
+	for i := 0; i < N1; i++ {
+		val := rand.Uint64() % 1000
+		commonNums[i] = val
+		blockNums[i] = val
+		otherNums[i] = val
+		allC[val] = true
+	}
+
+	for i := N1; i < N1+N2; i++ {
+		val := rand.Uint64() % 1000
+		blockNums[i] = val
+		allC[val] = true
+	}
+
+	for i := N1; i < N1+N3; i++ {
+		val := rand.Uint64()
+		for ok := true; ok; _, ok = allC[val] {
+			val = rand.Uint64() % 1000
+		}
+		otherNums[i] = val
+	}
+
+	sortUint64(commonNums)
+	sortUint64(blockNums)
+	sortUint64(otherNums)
+
+	return commonNums, blockNums, otherNums
+}
+
 func fillNums(N1, N2 int) ([]uint64, []uint64, []uint64) {
 	rand.Seed(time.Now().UnixNano())
 
@@ -545,12 +591,12 @@ func TestIntersectCompressedWithLinJump(t *testing.T) {
 }
 
 func TestIntersectCompressedWithBin(t *testing.T) {
-	lengths := []int{0, 1, 3, 11, 100}
+	//lengths := []int{0, 1, 3, 11, 100, 500, 1000}
 
-	for _, N1 := range lengths {
-		for _, N2 := range lengths {
+	for _, N1 := range []int{11} {
+		for _, N2 := range []int{3} {
 			// Intersection of blockNums and otherNums is commonNums.
-			commonNums, blockNums, otherNums := fillNums(N1, N2)
+			commonNums, blockNums, otherNums := fillNumsDiff(N1/10, N1, N2)
 
 			enc := codec.Encoder{BlockSize: 10}
 			for _, num := range blockNums {
@@ -570,7 +616,7 @@ func TestIntersectCompressedWithBin(t *testing.T) {
 }
 
 func TestIntersectCompressedWithBinMissingSize(t *testing.T) {
-	lengths := []int{0, 1, 3, 11, 100}
+	lengths := []int{0, 1, 3, 11, 100, 500, 1000}
 
 	for _, N1 := range lengths {
 		for _, N2 := range lengths {

codec/codec.go

@@ -223,6 +223,64 @@ func (d *Decoder) ApproxLen() int {
 
 type searchFunc func(int) bool
 
+// SeekToBlock will find the block containing the uid, and unpack it. When we are going to
+// intersect the list later, this function is useful. As this function skips the search function
+// and returns the entire block, it is faster than Seek. Unlike seek, we don't truncate the uids
+// returned, which would be done by the intersect function anyways.
+func (d *Decoder) SeekToBlock(uid uint64, whence seekPos) []uint64 {
+	if d.Pack == nil {
+		return []uint64{}
+	}
+	prevBlockIdx := d.blockIdx
+	d.blockIdx = 0
+	if uid == 0 {
+		return d.UnpackBlock()
+	}
+
+	// If for some reason we are searching an older uid, we need to search the entire pack
+	if prevBlockIdx > 0 && uid < d.Pack.Blocks[prevBlockIdx].Base {
+		prevBlockIdx = 0
+	}
+
+	blocksFunc := func() searchFunc {
+		var f searchFunc
+		switch whence {
+		case SeekStart:
+			f = func(i int) bool { return d.Pack.Blocks[i+prevBlockIdx].Base >= uid }
+		case SeekCurrent:
+			f = func(i int) bool { return d.Pack.Blocks[i+prevBlockIdx].Base > uid }
+		}
+		return f
+	}
+
+	idx := sort.Search(len(d.Pack.Blocks[prevBlockIdx:]), blocksFunc()) + prevBlockIdx
+	// The first block.Base >= uid.
+	if idx == 0 {
+		return d.UnpackBlock()
+	}
+	// The uid is the first entry in the block.
+	if idx < len(d.Pack.Blocks) && d.Pack.Blocks[idx].Base == uid {
+		d.blockIdx = idx
+		return d.UnpackBlock()
+	}
+
+	// Either the idx = len(pack.Blocks) that means it wasn't found in any of the block's base. Or,
+	// we found the first block index whose base is greater than uid. In these cases, go to the
+	// previous block and search there.
+	d.blockIdx = idx - 1 // Move to the previous block. If blockIdx<0, unpack will deal with it.
+	if d.blockIdx != prevBlockIdx {
+		d.UnpackBlock() // And get all their uids.
+	}
+
+	if uid <= d.uids[len(d.uids)-1] {
+		return d.uids
+	}
+
+	// Could not find any uid in the block, which is >= uid. The next block might still have valid
+	// entries > uid.
+	return d.Next()
+}
+
 // Seek will search for uid in a packed block using the specified whence position.
 // The value of whence must be one of the predefined values SeekStart or SeekCurrent.
 // SeekStart searches uid and includes it as part of the results.