# Case study: a latent bug the verification harness caught

This documents a real defect that the verification work found **on the very
first run** of the new `make verify` target — before any of the heavier layers
(TLA+, Gobra) were even involved. It is a good illustration of *why* wiring
these checks into a gate pays off: the bug had been sitting in the repository
undetected because the existing tests could never trigger it.

## TL;DR

- **Where:** `search/hash.go`, the `Hash.hash` method.
- **What:** `key << 10`, where `key` has a generic integer type, silently
  evaluates to `0` for narrow key types (`int8`/`uint8`), discarding a whole
  term of the hash mix.
- **Who found it:** `go vet`'s shift analyzer, run as part of `make verify`.
- **Why the tests missed it:** every test instantiates the hash with 64-bit
  `int` keys, where the shift is perfectly fine — so the bug is *latent*.
- **Fix:** compute the mix in a full-width `int64`.

## The offending code

Before:

```go
func (h *Hash[K,V]) hash(key K) int {
	i := key + key*2 + key<<10 + key>>2
	if i < 0 {
		i = -i
	}
	return int(i) % h.capacity
}
```

`K` is a type parameter constrained by `ds.Integer` (`ds/types.go`), which
embeds `constraints.Integer` — i.e. `K` may be **any** of `int, int8, int16,
int32, int64, uint, uint8, …`. The intent of `key<<10` is clearly to spread the
key's low bits up into the high bits so that keys differing only in their low
bits land in different buckets.

## What the tool reported

```
$ make verify
go vet ./...
search/hash.go:29:21: key (may be 8 bits) too small for shift of 10
```

`go vet` bundles a *shift* analyzer that is, in effect, a lightweight formal
check: for every shift expression it computes a conservative lower bound on the
bit width of the left operand and flags any shift whose count is `>=` that
width. Here the narrowest type `K` can take is `int8` (8 bits), and `10 >= 8`,
so the analyzer proves that *for at least one legal instantiation* the shift is
degenerate.

## Why it is genuinely a bug (Go shift semantics)

This is not a false positive. The Go specification defines non-constant left
shifts operationally:

> Shifts behave as if the left operand is shifted `n` times by 1 for a shift
> count of `n`. […] There is no upper limit on the shift count.

For an 8-bit value, shifting "one bit at a time" ten times pushes **every**
original bit out of the value's width. The result is therefore always `0`. So
for `K = int8`/`uint8`:

```
key<<10  ==  0    // always, for every key
```

and the hash silently collapses to `key + key*2 + key>>2` — the high-bit mixing
the author intended is simply gone.

Two subtleties worth recording:

1. **It is width-dependent, not universally broken.** For `int16` the count
   `10 < 16`, so the term is fine; for 32-/64-bit types it is obviously fine.
   `go vet` still (correctly) flags the expression because it must be sound for
   *all* instantiations, and `int8` is in the constraint set. The narrowest
   type is what governs safety.

2. **It is a quality/portability bug, not a memory-safety or a Set-contract
   violation.** The hash table stays *functionally correct* even for `int8`
   keys: `Put`, `Get`, and `Del` all call the same `hash`, and collisions are
   resolved by chaining in the per-bucket `Elementary` list. What degrades is
   the *distribution* — more keys collide into the same bucket, turning the
   intended O(1) operations toward O(n). So the failure mode is silent
   performance rot for narrow-key instantiations, exactly the kind of thing that
   never shows up as a failing assertion.

## Why no test caught it

Every instantiation in the test suite uses `int` keys:

```go
test[int,int](NewHash[int,int](i*2), i, t)   // search/search_test.go
```

`int` is 64 bits on this platform, so `key<<10` behaves as intended and all
tests pass. There is no `Hash[int8, …]` anywhere, so the degenerate path is
never exercised. A property test or a fuzz run over `int` keys would *also* miss
it — the bug lives in the *type dimension*, not the value dimension, and only a
tool that reasons about the type (like `go vet`) or an actual narrow-type
instantiation can surface it. This is precisely the class of latent defect that
static analysis is good at and dynamic testing is blind to.

## The fix

Perform the mixing in a full-width `int64`, then reduce:

```go
func (h *Hash[K,V]) hash(key K) int {
	// Mix the key in a full-width int64 rather than in K. K is any ds.Integer,
	// so for a narrow type (e.g. int8) the "key<<10" term would shift past the
	// type width and vanish to 0, destroying the intended high-bit mixing (and
	// go vet rightly flags it). Widening to int64 first keeps the result
	// identical for 64-bit int keys while making the mix well-defined for every
	// integer width.
	i := int64(key)
	i = i + i*2 + i<<10 + i>>2
	if i < 0 {
		i = -i
	}
	return int(i) % h.capacity
}
```

Why this is the right fix:

- **Behavior-preserving for the code that exists.** For `K = int` (64-bit), the
  arithmetic is byte-for-byte identical to before — `int64(key)` is a no-op
  widening, and every operation stays in 64 bits — so every existing test still
  passes unchanged.
- **Correct for the code that might exist.** For narrow `K`, the key is widened
  *before* the shift, so `i<<10` now mixes real bits instead of vanishing. The
  hash finally does for `int8` keys what it always did for `int` keys.
- **It silences the analyzer for the right reason.** `int64` is 64 bits, `10 <
  64`, so the shift is provably well-defined for the actual operand type. We are
  not suppressing the warning; we are removing the condition that made it true.

An `int64` cast rather than the value's own width also documents intent: "this
mixing is meant to happen in a wide register, independent of the key type."

> Residual note, left as-is: `if i < 0 { i = -i }` still has the classic
> `-math.MinInt64` overflow corner. It predates this change, is astronomically
> unlikely for these inputs, and is out of scope here — recorded for honesty.

## How this maps to the verification layers

This defect was caught by **Layer 2** of the harness (see
[`verification.md`](verification.md)) — `go vet` inside `make verify`. It is the
cheapest layer, and it found a bug that the paper proofs (Layer 0, which focus
on the sorts) and the property tests (Layer 1, which only ever run `int`) did
not. The lesson is the ordering of the layers is not the ordering of their
value: a one-line static check surfaced a real, shipped-in latent bug that no
amount of value-space testing would have. Cheap, broad checks first; deep proofs
where they earn their keep.