internal/library/duplicate_match.go

@@ -0,0 +1,357 @@
+package library
+
+import (
+	"math"
+	"math/bits"
+	"sort"
+)
+
+// Duplicate matching (M400 #3909).
+//
+// Pure functions over fingerprints: no database, no files. This is the part that
+// decides whether two tracks in the operator's library are proposed as one
+// recording, so every rule in it has to be falsifiable in a unit test.
+//
+// Two tiers, answering different questions:
+//
+//	exact     equal audio_stream_sha256 — the same encoded audio bytes. No score,
+//	          no threshold, no false positives (the #3885 pair).
+//	acoustic  chromaprint fingerprints that agree closely once aligned — the
+//	          same recording at another bitrate or in another codec.
+//
+// The acoustic comparison follows the approach of AcoustID's pg_acoustid
+// (acoustid_compare.c): vote on the relative offset between two fingerprints
+// using items that agree in their high bits, then measure disagreement at the
+// winning offset. Reimplemented from that description; no code was copied.
+// The alignment window and match-bit width below are taken from it.
+
+// maxAlignOffsetItems bounds how far apart two fingerprints may be shifted and
+// still be compared: ±120 items, about 15 seconds at chromaprint's ~8 items per
+// second. Covers a leading silence trimmed differently or a short intro; the
+// same bound pg_acoustid uses (ACOUSTID_MAX_ALIGN_OFFSET).
+const maxAlignOffsetItems = 120
+
+// alignMatchBits is how many high bits two items must share to vote for an
+// offset. Matching whole 32-bit items would miss the same recording at another
+// bitrate, whose low bits are noisier; 14 is pg_acoustid's MATCH_BITS.
+const alignMatchBits = 14
+
+// minOverlapItems is the least overlap worth a verdict: about 10 seconds. A few
+// items agreeing perfectly is not evidence that two recordings are one.
+const minOverlapItems = 80
+
+// minDistinctFraction rejects low-information fingerprints before they can
+// match. Near-silence, a sustained tone or a click track produces the same few
+// items over and over, and two such tracks agree closely without being the
+// same recording. Real music is overwhelmingly distinct item to item, so this
+// floor only catches the pathological case. A judgment value, not a measured
+// one — revisit if the sweep reports real tracks refused for it.
+const minDistinctFraction = 0.3
+
+// defaultAcousticMaxBitErrorRate is the most disagreement two aligned
+// fingerprints may show and still be proposed as one recording. Unrelated audio
+// sits near 0.5; the same recording re-encoded lands well under 0.1.
+//
+// Deliberately conservative. The operator's stated worry is the opposite of a
+// missed duplicate: "the same song can appear in different albums, usually it's
+// a different recording", and an instrumental shares its vocal version's
+// harmony, which chroma features capture. A false merge is the failure that
+// matters, and the report is reviewed anyway. This is an unmeasured default:
+// calibrate it against real pairs once the backfill (#3908) has populated the
+// library, then expose it in Settings (#3913).
+const defaultAcousticMaxBitErrorRate = 0.15
+
+// durationToleranceMs is how far apart two tracks' durations may be and still be
+// compared. Encoders pad and trim a little; different edits differ by more.
+const durationToleranceMs = 3000
+
+// maxAcousticGroupSize caps an acoustic group. A cluster bigger than this is far
+// more likely a shared jingle, a skit or a low-information pattern than eight
+// copies of one recording, and proposing it would bury the real duplicates.
+// Exact-tier groups are not capped: identical bytes are identical however many.
+const maxAcousticGroupSize = 8
+
+// acousticScore is the result of comparing two fingerprints.
+type acousticScore struct {
+	// Offset is how many items b is shifted against a: b[i+Offset] aligns with
+	// a[i].
+	Offset int
+	// Overlap is how many aligned items were compared.
+	Overlap int
+	// BitErrorRate is the fraction of differing bits over the overlap, 0..1.
+	BitErrorRate float64
+}
+
+// compareChromaprint aligns two raw fingerprints and measures how much they
+// disagree. ok is false when no verdict is possible: no offset gathered any
+// votes, the overlap at the best offset is too short, or either side carries
+// too little information to mean anything.
+func compareChromaprint(a, b []int32) (acousticScore, bool) {
+	if len(a) < minOverlapItems || len(b) < minOverlapItems {
+		return acousticScore{}, false
+	}
+	if !informative(a) || !informative(b) {
+		return acousticScore{}, false
+	}
+
+	offset, ok := bestOffset(a, b)
+	if !ok {
+		return acousticScore{}, false
+	}
+
+	// a[i] aligns with b[i+offset]; walk the indices valid on both sides.
+	start := max(0, -offset)
+	end := min(len(a), len(b)-offset)
+	overlap := end - start
+	if overlap < minOverlapItems {
+		return acousticScore{}, false
+	}
+	errBits := 0
+	for i := start; i < end; i++ {
+		errBits += bits.OnesCount32(uint32(a[i]) ^ uint32(b[i+offset]))
+	}
+	return acousticScore{
+		Offset:       offset,
+		Overlap:      overlap,
+		BitErrorRate: float64(errBits) / float64(32*overlap),
+	}, true
+}
+
+// bestOffset returns the relative shift most items agree on.
+func bestOffset(a, b []int32) (int, bool) {
+	// Index a's items by their high bits. Each bucket keeps only a few
+	// positions: a value repeating many times is uninformative, and letting it
+	// vote once per repeat would make every pairing O(n²).
+	const keepPerBucket = 4
+	positions := make(map[uint32][]int, len(a))
+	for i, v := range a {
+		key := uint32(v) >> (32 - alignMatchBits)
+		if p := positions[key]; len(p) < keepPerBucket {
+			positions[key] = append(p, i)
+		}
+	}
+
+	votes := make([]int, 2*maxAlignOffsetItems+1)
+	for j, v := range b {
+		for _, i := range positions[uint32(v)>>(32-alignMatchBits)] {
+			off := j - i
+			if off >= -maxAlignOffsetItems && off <= maxAlignOffsetItems {
+				votes[off+maxAlignOffsetItems]++
+			}
+		}
+	}
+
+	best, bestVotes := 0, 0
+	for k, n := range votes {
+		// Strictly greater keeps the smallest shift on a tie, which is the more
+		// likely truth and keeps the result deterministic.
+		if n > bestVotes || (n == bestVotes && n > 0 && abs(k-maxAlignOffsetItems) < abs(best)) {
+			best, bestVotes = k-maxAlignOffsetItems, n
+		}
+	}
+	return best, bestVotes > 0
+}
+
+// informative reports whether a fingerprint varies enough to be compared.
+func informative(fp []int32) bool {
+	seen := make(map[int32]struct{}, len(fp))
+	for _, v := range fp {
+		seen[v] = struct{}{}
+	}
+	return float64(len(seen)) >= minDistinctFraction*float64(len(fp))
+}
+
+// fingerprintCandidate is one track as the grouping sees it.
+type fingerprintCandidate struct {
+	ID           string
+	DurationMs   int32
+	StreamSHA256 []byte
+	Chromaprint  []int32
+}
+
+// duplicateTier names what a group's evidence is.
+type duplicateTier string
+
+const (
+	tierExact    duplicateTier = "exact"
+	tierAcoustic duplicateTier = "acoustic"
+)
+
+// duplicateGroup is a set of tracks proposed as one recording. Members are
+// sorted by ID.
+type duplicateGroup struct {
+	Tier    duplicateTier
+	Members []string
+	// WorstBitErrorRate is the largest disagreement between any two members of
+	// an acoustic group — the weakest evidence the group rests on. Zero for
+	// exact groups.
+	WorstBitErrorRate float64
+}
+
+// groupingResult is what one grouping pass found.
+type groupingResult struct {
+	Groups []duplicateGroup
+	// OversizeClusters counts acoustic clusters discarded for exceeding
+	// maxAcousticGroupSize. Reported rather than silent: a sudden rise means the
+	// cap or the information floor needs attention.
+	OversizeClusters int
+}
+
+// groupDuplicates proposes duplicate groups among candidates.
+//
+// Exact groups come first: tracks sharing an audio stream hash. Each exact group
+// is then treated as a single unit for the acoustic pass, so its members are
+// never compared with each other again.
+//
+// Acoustic grouping is COMPLETE-LINKAGE: a unit joins a group only if it matches
+// every unit already in it, within the duration tolerance and the bit-error
+// limit. Single-linkage would let a chain of near-misses — A close to B, B close
+// to C — drag A and C, which are not close, into one proposed merge. Complete
+// linkage also means any member can be chosen as the survivor (#3911).
+//
+// When an acoustic group absorbs an exact group, the result is tier acoustic:
+// a group is only as certain as its weakest link.
+//
+// The output does not depend on input order.
+func groupDuplicates(cands []fingerprintCandidate, maxBitErrorRate float64) groupingResult {
+	var res groupingResult
+
+	// Exact tier.
+	byHash := map[string][]fingerprintCandidate{}
+	var noHash []fingerprintCandidate
+	for _, c := range cands {
+		if len(c.StreamSHA256) == 0 {
+			noHash = append(noHash, c)
+			continue
+		}
+		k := string(c.StreamSHA256)
+		byHash[k] = append(byHash[k], c)
+	}
+
+	// A unit is one exact group, or one track with no exact duplicate.
+	type unit struct {
+		members    []fingerprintCandidate
+		durationMs int32
+		print      []int32
+		exact      bool
+	}
+	var units []unit
+	for _, group := range byHash {
+		sortCandidates(group)
+		u := unit{members: group, durationMs: group[0].DurationMs, exact: len(group) > 1}
+		for _, m := range group {
+			if len(m.Chromaprint) > 0 {
+				u.print = m.Chromaprint
+				break
+			}
+		}
+		units = append(units, u)
+	}
+	for _, c := range noHash {
+		units = append(units, unit{members: []fingerprintCandidate{c}, durationMs: c.DurationMs, print: c.Chromaprint})
+	}
+
+	// Deterministic order: duration, then the first member's ID. Sorting by
+	// duration also lets the scan below stop as soon as durations are too far
+	// apart, which is the blocking #3910 relies on.
+	sort.Slice(units, func(i, j int) bool {
+		if units[i].durationMs != units[j].durationMs {
+			return units[i].durationMs < units[j].durationMs
+		}
+		return units[i].members[0].ID < units[j].members[0].ID
+	})
+
+	assigned := make([]bool, len(units))
+	for i := range units {
+		if assigned[i] || len(units[i].print) == 0 {
+			continue
+		}
+		group := []int{i}
+		worst := 0.0
+		for j := i + 1; j < len(units); j++ {
+			if units[j].durationMs-units[i].durationMs > durationToleranceMs {
+				break
+			}
+			if assigned[j] || len(units[j].print) == 0 {
+				continue
+			}
+			// Complete linkage: j must match every member so far.
+			joined, worstWithJ := true, worst
+			for _, g := range group {
+				if abs32(units[j].durationMs-units[g].durationMs) > durationToleranceMs {
+					joined = false
+					break
+				}
+				score, ok := compareChromaprint(units[g].print, units[j].print)
+				if !ok || score.BitErrorRate > maxBitErrorRate {
+					joined = false
+					break
+				}
+				worstWithJ = math.Max(worstWithJ, score.BitErrorRate)
+			}
+			if joined {
+				group = append(group, j)
+				worst = worstWithJ
+			}
+		}
+
+		if len(group) == 1 {
+			continue
+		}
+		// Count units, not tracks: an absorbed exact group is one piece of
+		// acoustic evidence however many identical files it holds.
+		if len(group) > maxAcousticGroupSize {
+			res.OversizeClusters++
+			for _, g := range group {
+				assigned[g] = true
+			}
+			continue
+		}
+		var members []string
+		for _, g := range group {
+			assigned[g] = true
+			for _, m := range units[g].members {
+				members = append(members, m.ID)
+			}
+		}
+		sort.Strings(members)
+		res.Groups = append(res.Groups, duplicateGroup{
+			Tier: tierAcoustic, Members: members, WorstBitErrorRate: worst,
+		})
+	}
+
+	// Exact groups that no acoustic group absorbed stand on their own.
+	for i, u := range units {
+		if assigned[i] || !u.exact {
+			continue
+		}
+		members := make([]string, len(u.members))
+		for k, m := range u.members {
+			members[k] = m.ID
+		}
+		res.Groups = append(res.Groups, duplicateGroup{Tier: tierExact, Members: members})
+	}
+
+	sort.Slice(res.Groups, func(i, j int) bool {
+		return res.Groups[i].Members[0] < res.Groups[j].Members[0]
+	})
+	return res
+}
+
+func sortCandidates(cs []fingerprintCandidate) {
+	sort.Slice(cs, func(i, j int) bool { return cs[i].ID < cs[j].ID })
+}
+
+func abs(n int) int {
+	if n < 0 {
+		return -n
+	}
+	return n
+}
+
+func abs32(n int32) int32 {
+	if n < 0 {
+		return -n
+	}
+	return n
+}

internal/library/duplicate_match_test.go

@@ -0,0 +1,241 @@
+package library
+
+import (
+	"math"
+	"math/rand/v2"
+	"reflect"
+	"testing"
+)
+
+// printLen is a realistic fingerprint length: fpcalc's 120s at ~8 items/second.
+const printLen = 960
+
+// randomPrint is a deterministic stand-in for one recording's fingerprint.
+func randomPrint(seed uint64, n int) []int32 {
+	r := rand.New(rand.NewPCG(seed, seed^0x9e3779b97f4a7c15))
+	fp := make([]int32, n)
+	for i := range fp {
+		fp[i] = int32(r.Uint32())
+	}
+	return fp
+}
+
+// withBitNoise flips exactly round(fraction × all bits) distinct bits — the
+// same recording through a different encoder, at a known bit-error rate.
+func withBitNoise(fp []int32, fraction float64, seed uint64) []int32 {
+	out := append([]int32(nil), fp...)
+	r := rand.New(rand.NewPCG(seed, seed^0x243f6a8885a308d3))
+	total := 32 * len(fp)
+	for _, pos := range r.Perm(total)[:int(math.Round(fraction*float64(total)))] {
+		out[pos/32] ^= int32(uint32(1) << (pos % 32))
+	}
+	return out
+}
+
+func constantPrint(v int32, n int) []int32 {
+	fp := make([]int32, n)
+	for i := range fp {
+		fp[i] = v
+	}
+	return fp
+}
+
+func TestCompareChromaprint(t *testing.T) {
+	base := randomPrint(1, printLen)
+
+	t.Run("identical", func(t *testing.T) {
+		got, ok := compareChromaprint(base, base)
+		if !ok || got.BitErrorRate != 0 || got.Offset != 0 || got.Overlap != printLen {
+			t.Fatalf("got %+v ok=%v, want an exact alignment", got, ok)
+		}
+	})
+
+	t.Run("re-encoded: known bit noise is measured exactly", func(t *testing.T) {
+		got, ok := compareChromaprint(base, withBitNoise(base, 0.03, 2))
+		if !ok {
+			t.Fatal("a re-encode was not comparable")
+		}
+		if want := math.Round(0.03*32*printLen) / (32 * printLen); got.BitErrorRate != want {
+			t.Fatalf("BitErrorRate = %v, want %v", got.BitErrorRate, want)
+		}
+	})
+
+	// b starts 40 items later in the same audio: b[j] = a[j+40], so a[i] aligns
+	// with b[i-40].
+	t.Run("offset inside the window is recovered", func(t *testing.T) {
+		got, ok := compareChromaprint(base, base[40:])
+		if !ok || got.Offset != -40 || got.BitErrorRate != 0 || got.Overlap != printLen-40 {
+			t.Fatalf("got %+v ok=%v, want offset -40 with no error", got, ok)
+		}
+	})
+
+	t.Run("offset beyond the window never matches", func(t *testing.T) {
+		got, ok := compareChromaprint(base, base[200:])
+		if ok && got.BitErrorRate <= defaultAcousticMaxBitErrorRate {
+			t.Fatalf("a 200-item shift matched: %+v", got)
+		}
+	})
+
+	t.Run("unrelated recordings sit near 0.5", func(t *testing.T) {
+		got, ok := compareChromaprint(base, randomPrint(99, printLen))
+		if ok && got.BitErrorRate < 0.4 {
+			t.Fatalf("unrelated fingerprints scored %v", got.BitErrorRate)
+		}
+	})
+
+	t.Run("too short an overlap gives no verdict", func(t *testing.T) {
+		if got, ok := compareChromaprint(base, base[:minOverlapItems-1]); ok {
+			t.Fatalf("a %d-item fingerprint was compared: %+v", minOverlapItems-1, got)
+		}
+	})
+
+	// Two near-silent tracks agree perfectly without being one recording. The
+	// information floor is the only thing standing between them and a merge.
+	t.Run("low-information fingerprints give no verdict", func(t *testing.T) {
+		silence := constantPrint(0x1234, printLen)
+		if got, ok := compareChromaprint(silence, silence); ok {
+			t.Fatalf("silence compared as a match: %+v", got)
+		}
+	})
+
+	t.Run("the threshold separates close from not close", func(t *testing.T) {
+		near, _ := compareChromaprint(base, withBitNoise(base, 0.10, 3))
+		far, _ := compareChromaprint(base, withBitNoise(base, 0.20, 4))
+		if near.BitErrorRate > defaultAcousticMaxBitErrorRate {
+			t.Errorf("10%% noise (%v) is over the threshold", near.BitErrorRate)
+		}
+		if far.BitErrorRate <= defaultAcousticMaxBitErrorRate {
+			t.Errorf("20%% noise (%v) is under the threshold", far.BitErrorRate)
+		}
+	})
+}
+
+func TestGroupDuplicates_ExactTier(t *testing.T) {
+	hash := []byte("sha256-of-www-instrumental-bytes")
+	res := groupDuplicates([]fingerprintCandidate{
+		{ID: "www-01", DurationMs: 215000, StreamSHA256: hash},
+		{ID: "www-02", DurationMs: 215000, StreamSHA256: hash},
+		{ID: "lovesick", DurationMs: 198000, StreamSHA256: []byte("another")},
+	}, defaultAcousticMaxBitErrorRate)
+	want := []duplicateGroup{{Tier: tierExact, Members: []string{"www-01", "www-02"}}}
+	if !reflect.DeepEqual(res.Groups, want) {
+		t.Fatalf("groups = %+v, want %+v", res.Groups, want)
+	}
+}
+
+func TestGroupDuplicates_AcousticPair(t *testing.T) {
+	p := randomPrint(10, printLen)
+	res := groupDuplicates([]fingerprintCandidate{
+		{ID: "album", DurationMs: 240000, Chromaprint: p},
+		{ID: "compilation", DurationMs: 241000, Chromaprint: withBitNoise(p, 0.05, 11)},
+	}, defaultAcousticMaxBitErrorRate)
+	if len(res.Groups) != 1 || res.Groups[0].Tier != tierAcoustic ||
+		!reflect.DeepEqual(res.Groups[0].Members, []string{"album", "compilation"}) {
+		t.Fatalf("groups = %+v, want one acoustic pair", res.Groups)
+	}
+	if got := res.Groups[0].WorstBitErrorRate; math.Abs(got-0.05) > 0.001 {
+		t.Fatalf("WorstBitErrorRate = %v, want about 0.05", got)
+	}
+}
+
+// A is close to B and B is close to C, but A and C are not close. Under
+// single linkage all three would be proposed as one recording; complete linkage
+// must keep C out.
+func TestGroupDuplicates_NoChaining(t *testing.T) {
+	a := randomPrint(20, printLen)
+	b := withBitNoise(a, 0.10, 21)
+	c := withBitNoise(b, 0.10, 22)
+	if s, _ := compareChromaprint(a, c); s.BitErrorRate <= defaultAcousticMaxBitErrorRate {
+		t.Fatalf("fixture broken: A and C are close (%v), so this cannot test chaining", s.BitErrorRate)
+	}
+	res := groupDuplicates([]fingerprintCandidate{
+		{ID: "a", DurationMs: 200000, Chromaprint: a},
+		{ID: "b", DurationMs: 200000, Chromaprint: b},
+		{ID: "c", DurationMs: 200000, Chromaprint: c},
+	}, defaultAcousticMaxBitErrorRate)
+	if len(res.Groups) != 1 || !reflect.DeepEqual(res.Groups[0].Members, []string{"a", "b"}) {
+		t.Fatalf("groups = %+v, want only {a, b}", res.Groups)
+	}
+}
+
+func TestGroupDuplicates_DurationTolerance(t *testing.T) {
+	p := randomPrint(30, printLen)
+	res := groupDuplicates([]fingerprintCandidate{
+		{ID: "edit", DurationMs: 200000, Chromaprint: p},
+		{ID: "extended", DurationMs: 200000 + durationToleranceMs + 1, Chromaprint: p},
+	}, defaultAcousticMaxBitErrorRate)
+	if len(res.Groups) != 0 {
+		t.Fatalf("tracks %dms apart were grouped: %+v", durationToleranceMs+1, res.Groups)
+	}
+}
+
+// Nine tracks that all match are far likelier a shared jingle than nine copies
+// of one recording. The cluster must be reported, not proposed.
+func TestGroupDuplicates_OversizeClusterIsDiscarded(t *testing.T) {
+	p := randomPrint(40, printLen)
+	var cands []fingerprintCandidate
+	for i := range maxAcousticGroupSize + 1 {
+		cands = append(cands, fingerprintCandidate{
+			ID: string(rune('a' + i)), DurationMs: 30000, Chromaprint: withBitNoise(p, 0.01, uint64(100+i)),
+		})
+	}
+	res := groupDuplicates(cands, defaultAcousticMaxBitErrorRate)
+	if len(res.Groups) != 0 || res.OversizeClusters != 1 {
+		t.Fatalf("groups = %+v, oversize = %d; want none proposed and 1 oversize", res.Groups, res.OversizeClusters)
+	}
+}
+
+// Two byte-identical copies plus a re-encode of the same recording are one
+// group, and it is only as certain as its weakest link.
+func TestGroupDuplicates_ExactGroupAbsorbedIntoAcoustic(t *testing.T) {
+	p := randomPrint(50, printLen)
+	hash := []byte("same-bytes")
+	res := groupDuplicates([]fingerprintCandidate{
+		{ID: "x1", DurationMs: 180000, StreamSHA256: hash, Chromaprint: p},
+		{ID: "x2", DurationMs: 180000, StreamSHA256: hash, Chromaprint: p},
+		{ID: "y", DurationMs: 180000, StreamSHA256: []byte("other-bytes"), Chromaprint: withBitNoise(p, 0.03, 51)},
+	}, defaultAcousticMaxBitErrorRate)
+	want := []string{"x1", "x2", "y"}
+	if len(res.Groups) != 1 || res.Groups[0].Tier != tierAcoustic || !reflect.DeepEqual(res.Groups[0].Members, want) {
+		t.Fatalf("groups = %+v, want one acoustic group %v", res.Groups, want)
+	}
+}
+
+func TestGroupDuplicates_UnrelatedTracksNeverGroup(t *testing.T) {
+	var cands []fingerprintCandidate
+	for i := range 6 {
+		cands = append(cands, fingerprintCandidate{
+			ID: string(rune('a' + i)), DurationMs: 210000, Chromaprint: randomPrint(uint64(60+i), printLen),
+		})
+	}
+	if res := groupDuplicates(cands, defaultAcousticMaxBitErrorRate); len(res.Groups) != 0 {
+		t.Fatalf("unrelated recordings were grouped: %+v", res.Groups)
+	}
+}
+
+func TestGroupDuplicates_OrderIndependent(t *testing.T) {
+	p := randomPrint(70, printLen)
+	q := randomPrint(71, printLen)
+	hash := []byte("identical")
+	cands := []fingerprintCandidate{
+		{ID: "p1", DurationMs: 200000, Chromaprint: p},
+		{ID: "p2", DurationMs: 201000, Chromaprint: withBitNoise(p, 0.04, 72)},
+		{ID: "q1", DurationMs: 150000, Chromaprint: q},
+		{ID: "q2", DurationMs: 150500, Chromaprint: withBitNoise(q, 0.02, 73)},
+		{ID: "h1", DurationMs: 90000, StreamSHA256: hash},
+		{ID: "h2", DurationMs: 90000, StreamSHA256: hash},
+		{ID: "lone", DurationMs: 200000, Chromaprint: randomPrint(74, printLen)},
+	}
+	want := groupDuplicates(cands, defaultAcousticMaxBitErrorRate)
+	if len(want.Groups) != 3 {
+		t.Fatalf("fixture broken: %d groups, want 3 (p, q, h)", len(want.Groups))
+	}
+	r := rand.New(rand.NewPCG(75, 76))
+	for range 20 {
+		shuffled := append([]fingerprintCandidate(nil), cands...)
+		r.Shuffle(len(shuffled), func(i, j int) { shuffled[i], shuffled[j] = shuffled[j], shuffled[i] })
+		if got := groupDuplicates(shuffled, defaultAcousticMaxBitErrorRate); !reflect.DeepEqual(got, want) {
+			t.Fatalf("input order changed the result:\n got  %+v\n want %+v", got, want)
+		}
+	}
+}