Fix empty-index BLAS search results (#5528)

Summary:
- initialize result handlers when an exhaustive search has no database vectors
- process empty results in the configured query block size, preserving bounded temporary memory for large query batches
- cover L2 and inner-product search across top-1, heap, and reservoir result handlers

## Problem

Searching an empty `IndexFlat` produced correct sentinel values for small query batches, but could leave the caller's distance and label buffers untouched once `nq * d` selected the BLAS path. The BLAS helpers return early for `ny == 0` before the result handler's `begin_multiple` / `end_multiple` lifecycle initializes and finalizes the output.

This change handles an empty database before choosing the sequential or BLAS implementation. It uses the existing result-handler lifecycle so each handler supplies its own correct neutral distance and `-1` label semantics.

Fixes https://github.com/facebookresearch/faiss/issues/3830.

## Validation

- `python -m unittest test_index.TestIndexFlat_ARM_NEON.test_empty_index_with_blas`
- `python -m unittest test_index` (49 tests passed)
- `faiss_test --gtest_brief=1` (290 passed, 1 platform-specific skip)
- `clang-format 21 --dry-run --Werror faiss/utils/distances.cpp`

## Verification of the regression test

We confirmed `test_empty_index_with_blas` is a true regression test by running it with and without the `utils/distances.cpp` change:

| State | Result |
|-------|--------|
| Fix applied | 1 passed, 0 failed |
| `utils/distances.cpp` reverted to parent, test retained | 6 failed |

The 6 failures are every subtest (2 metrics x 3 values of `k`), covering the `Top1`, `Heap`, and `Reservoir` result handlers. The failure output reports `ACTUAL: array([[42., 42., ...` against `DESIRED: array(-3.402823e+38)`. The test pre-fills `D` with `42` and `I` with `99`, so this confirms the output buffers are never written without the fix, rather than written with incorrect values. The passing run is clean under ASan and UBSan.

## Note for issue #3830

The repro in the issue (`d=1`, `nq=20`) no longer reproduces on `main`. When the issue was filed, `distance_compute_blas_threshold` defaulted to `20` and the branch condition was `nx < threshold`, which put `nq=19` on the sequential path (correct sentinels) and `nq=20` on the BLAS path (uninitialized output). The threshold is now dimension-aware (`nx * d < distance_compute_blas_threshold`, default `128000`), so `d=1` requires `nq >= 128000` to select BLAS. The defect was relocated, not fixed. A repro that still holds today is:

```
faiss.IndexFlatL2(128).search(np.random.random((1000, 128)).astype('float32'), 1)  # nx * d == 128000
```

This change removes the defect at its source, for all `nx`, all `d`, both metrics, and all three result handlers. The `k > ntotal` case with `ntotal > 0` was never affected: `begin_multiple` already initializes all `k` slots, so the unfilled tail is correctly padded.

Pull Request resolved: https://github.com/facebookresearch/faiss/pull/5528

Reviewed By: mnorris11, trang-nm-nguyen

Differential Revision: D116650117

Pulled By: alibeklfc

fbshipit-source-id: b40bdf7ade7640b2e433765b3877e2cea3546cf2

faiss/utils/distances.cpp

@@ -563,7 +563,11 @@ struct Run_search_inner_product {
            size_t d,
            size_t nx,
            size_t ny) {
-        if (res.sel ||
+        // ny == 0 goes to the sequential path: it guards only on nx, so its
+        // per-query begin()/end() still runs and each handler writes its own
+        // neutral distance and -1 label. The BLAS path instead returns early
+        // on ny == 0, before the handler is initialized.
+        if (res.sel || ny == 0 ||
             nx * d < static_cast<size_t>(distance_compute_blas_threshold)) {
             exhaustive_inner_product_seq(x, y, d, nx, ny, res);
         } else {
@@ -582,7 +586,8 @@ struct Run_search_L2sqr {
            size_t nx,
            size_t ny,
            const float* y_norm2) {
-        if (res.sel ||
+        // See the note on ny == 0 in Run_search_inner_product.
+        if (res.sel || ny == 0 ||
             nx * d < static_cast<size_t>(distance_compute_blas_threshold)) {
             exhaustive_L2sqr_seq(x, y, d, nx, ny, res);
         } else {

tests/test_index.py

@@ -137,6 +137,32 @@ class TestIndexFlat(unittest.TestCase):
                     lims, np.zeros(1, dtype=np.int64)
                 )
 
+    def test_empty_index_with_blas(self):
+        # The threshold is what makes this a regression test: it puts the
+        # search in a configuration that would otherwise select the BLAS path,
+        # which returns early on an empty database without ever initializing
+        # the result handler. k covers the Top1, heap, and reservoir handlers.
+        saved_threshold = faiss.cvar.distance_compute_blas_threshold
+        faiss.cvar.distance_compute_blas_threshold = 1
+        try:
+            xq = np.arange(5, dtype="float32").reshape(-1, 1)
+            for metric_type in (faiss.METRIC_L2, faiss.METRIC_INNER_PRODUCT):
+                expected_distance = (
+                    np.finfo("float32").max
+                    if metric_type == faiss.METRIC_L2
+                    else np.finfo("float32").min
+                )
+                index = faiss.IndexFlat(1, metric_type)
+                for k in (1, 10, 150):
+                    with self.subTest(metric_type=metric_type, k=k):
+                        D = np.full((len(xq), k), 42, dtype="float32")
+                        I = np.full((len(xq), k), 99, dtype="int64")
+                        index.search(xq, k, D=D, I=I)
+                        np.testing.assert_array_equal(D, expected_distance)
+                        np.testing.assert_array_equal(I, -1)
+        finally:
+            faiss.cvar.distance_compute_blas_threshold = saved_threshold
+
 
 @for_all_simd_levels
 class TestDbParallelSearch(unittest.TestCase):