sumdb/tlog: make NewTiles only generate strictly necessary tiles

Currently, NewTiles returns tiles for every partial tree size from
oldTreeSize to newTreeSize. However, if a log is only publishing
checkpoints at oldTreeSize and newTreeSize, the trees of sizes
oldTreeSize+1 to newTreeSize-1 are unverifiable, so those tiles are
unnecessary. Also, NewTiles currently returns tiles that already exists
as part of oldTreeSize, which are not new.

This has a significant performance and cost difference when uploading
tiles individually to e.g. object storage.

Change-Id: I92a5d76bc54e7022991e51997e793356ab5e7d5c
Reviewed-on: https://go-review.googlesource.com/c/mod/+/570295
Auto-Submit: Filippo Valsorda <filippo@golang.org>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Russ Cox <rsc@golang.org>
Reviewed-by: Cherry Mui <cherryyz@google.com>

sumdb/tlog/tile.go

@@ -115,16 +115,14 @@ func NewTiles(h int, oldTreeSize, newTreeSize int64) []Tile {
 	for level := uint(0); newTreeSize>>(H*level) > 0; level++ {
 		oldN := oldTreeSize >> (H * level)
 		newN := newTreeSize >> (H * level)
+		if oldN == newN {
+			continue
+		}
 		for n := oldN >> H; n < newN>>H; n++ {
 			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: 1 << H})
 		}
 		n := newN >> H
-		maxW := int(newN - n<<H)
-		minW := 1
-		if oldN > n<<H {
-			minW = int(oldN - n<<H)
-		}
-		for w := minW; w <= maxW; w++ {
+		if w := int(newN - n<<H); w > 0 {
 			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: w})
 		}
 	}

sumdb/tlog/tile_test.go

@@ -5,6 +5,7 @@
 package tlog
 
 import (
+	"fmt"
 	"testing"
 )
 
@@ -22,3 +23,28 @@ func FuzzParseTilePath(f *testing.F) {
 		ParseTilePath(path)
 	})
 }
+
+func TestNewTilesForSize(t *testing.T) {
+	for _, tt := range []struct {
+		old, new int64
+		want     int
+	}{
+		{1, 1, 0},
+		{100, 101, 1},
+		{1023, 1025, 3},
+		{1024, 1030, 1},
+		{1030, 2000, 1},
+		{1030, 10000, 10},
+		{49516517, 49516586, 3},
+	} {
+		t.Run(fmt.Sprintf("%d-%d", tt.old, tt.new), func(t *testing.T) {
+			tiles := NewTiles(10, tt.old, tt.new)
+			if got := len(tiles); got != tt.want {
+				t.Errorf("got %d, want %d", got, tt.want)
+				for _, tile := range tiles {
+					t.Logf("%+v", tile)
+				}
+			}
+		})
+	}
+}