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Sum cosine distances and vec_normalize() in double #338

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109 changes: 74 additions & 35 deletions sqlite-vec.c
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Original file line number Diff line number Diff line change
Expand Up @@ -185,6 +185,9 @@ static f32 l2_sqr_float_neon(const void *pVect1v, const void *pVect2v,
return sqrt(sum_scalar);
}

// Sums are kept in double, as distance_cosine_float() keeps them: each
// float32x4 load is widened to two float64x2 halves before it is multiplied
// and added.
static f32 cosine_float_neon(const void *pVect1v, const void *pVect2v,
const void *qty_ptr) {
f32 *pVect1 = (f32 *)pVect1v;
Expand All @@ -193,53 +196,83 @@ static f32 cosine_float_neon(const void *pVect1v, const void *pVect2v,
size_t qty16 = qty >> 4;
const f32 *pEnd1 = pVect1 + (qty16 << 4);

float32x4_t dot0 = vdupq_n_f32(0), dot1 = vdupq_n_f32(0);
float32x4_t dot2 = vdupq_n_f32(0), dot3 = vdupq_n_f32(0);
float32x4_t amag0 = vdupq_n_f32(0), amag1 = vdupq_n_f32(0);
float32x4_t amag2 = vdupq_n_f32(0), amag3 = vdupq_n_f32(0);
float32x4_t bmag0 = vdupq_n_f32(0), bmag1 = vdupq_n_f32(0);
float32x4_t bmag2 = vdupq_n_f32(0), bmag3 = vdupq_n_f32(0);
float64x2_t dot0 = vdupq_n_f64(0), dot1 = vdupq_n_f64(0);
float64x2_t dot2 = vdupq_n_f64(0), dot3 = vdupq_n_f64(0);
float64x2_t amag0 = vdupq_n_f64(0), amag1 = vdupq_n_f64(0);
float64x2_t amag2 = vdupq_n_f64(0), amag3 = vdupq_n_f64(0);
float64x2_t bmag0 = vdupq_n_f64(0), bmag1 = vdupq_n_f64(0);
float64x2_t bmag2 = vdupq_n_f64(0), bmag3 = vdupq_n_f64(0);

while (pVect1 < pEnd1) {
float32x4_t v1, v2;
float64x2_t a, b;

v1 = vld1q_f32(pVect1); pVect1 += 4;
v2 = vld1q_f32(pVect2); pVect2 += 4;
dot0 = vfmaq_f32(dot0, v1, v2);
amag0 = vfmaq_f32(amag0, v1, v1);
bmag0 = vfmaq_f32(bmag0, v2, v2);
a = vcvt_f64_f32(vget_low_f32(v1));
b = vcvt_f64_f32(vget_low_f32(v2));
dot0 = vfmaq_f64(dot0, a, b);
amag0 = vfmaq_f64(amag0, a, a);
bmag0 = vfmaq_f64(bmag0, b, b);
a = vcvt_high_f64_f32(v1);
b = vcvt_high_f64_f32(v2);
dot0 = vfmaq_f64(dot0, a, b);
amag0 = vfmaq_f64(amag0, a, a);
bmag0 = vfmaq_f64(bmag0, b, b);

v1 = vld1q_f32(pVect1); pVect1 += 4;
v2 = vld1q_f32(pVect2); pVect2 += 4;
dot1 = vfmaq_f32(dot1, v1, v2);
amag1 = vfmaq_f32(amag1, v1, v1);
bmag1 = vfmaq_f32(bmag1, v2, v2);
a = vcvt_f64_f32(vget_low_f32(v1));
b = vcvt_f64_f32(vget_low_f32(v2));
dot1 = vfmaq_f64(dot1, a, b);
amag1 = vfmaq_f64(amag1, a, a);
bmag1 = vfmaq_f64(bmag1, b, b);
a = vcvt_high_f64_f32(v1);
b = vcvt_high_f64_f32(v2);
dot1 = vfmaq_f64(dot1, a, b);
amag1 = vfmaq_f64(amag1, a, a);
bmag1 = vfmaq_f64(bmag1, b, b);

v1 = vld1q_f32(pVect1); pVect1 += 4;
v2 = vld1q_f32(pVect2); pVect2 += 4;
dot2 = vfmaq_f32(dot2, v1, v2);
amag2 = vfmaq_f32(amag2, v1, v1);
bmag2 = vfmaq_f32(bmag2, v2, v2);
a = vcvt_f64_f32(vget_low_f32(v1));
b = vcvt_f64_f32(vget_low_f32(v2));
dot2 = vfmaq_f64(dot2, a, b);
amag2 = vfmaq_f64(amag2, a, a);
bmag2 = vfmaq_f64(bmag2, b, b);
a = vcvt_high_f64_f32(v1);
b = vcvt_high_f64_f32(v2);
dot2 = vfmaq_f64(dot2, a, b);
amag2 = vfmaq_f64(amag2, a, a);
bmag2 = vfmaq_f64(bmag2, b, b);

v1 = vld1q_f32(pVect1); pVect1 += 4;
v2 = vld1q_f32(pVect2); pVect2 += 4;
dot3 = vfmaq_f32(dot3, v1, v2);
amag3 = vfmaq_f32(amag3, v1, v1);
bmag3 = vfmaq_f32(bmag3, v2, v2);
}

f32 dot_s = vaddvq_f32(vaddq_f32(vaddq_f32(dot0, dot1), vaddq_f32(dot2, dot3)));
f32 amag_s = vaddvq_f32(vaddq_f32(vaddq_f32(amag0, amag1), vaddq_f32(amag2, amag3)));
f32 bmag_s = vaddvq_f32(vaddq_f32(vaddq_f32(bmag0, bmag1), vaddq_f32(bmag2, bmag3)));
a = vcvt_f64_f32(vget_low_f32(v1));
b = vcvt_f64_f32(vget_low_f32(v2));
dot3 = vfmaq_f64(dot3, a, b);
amag3 = vfmaq_f64(amag3, a, a);
bmag3 = vfmaq_f64(bmag3, b, b);
a = vcvt_high_f64_f32(v1);
b = vcvt_high_f64_f32(v2);
dot3 = vfmaq_f64(dot3, a, b);
amag3 = vfmaq_f64(amag3, a, a);
bmag3 = vfmaq_f64(bmag3, b, b);
}

double dot_s = vaddvq_f64(vaddq_f64(vaddq_f64(dot0, dot1), vaddq_f64(dot2, dot3)));
double amag_s = vaddvq_f64(vaddq_f64(vaddq_f64(amag0, amag1), vaddq_f64(amag2, amag3)));
double bmag_s = vaddvq_f64(vaddq_f64(vaddq_f64(bmag0, bmag1), vaddq_f64(bmag2, bmag3)));

const f32 *pEnd2 = pVect1 + (qty - (qty16 << 4));
while (pVect1 < pEnd2) {
dot_s += *pVect1 * *pVect2;
amag_s += *pVect1 * *pVect1;
bmag_s += *pVect2 * *pVect2;
dot_s += (double)*pVect1 * (double)*pVect2;
amag_s += (double)*pVect1 * (double)*pVect1;
bmag_s += (double)*pVect2 * (double)*pVect2;
pVect1++; pVect2++;
}

return 1.0f - (dot_s / (sqrtf(amag_s) * sqrtf(bmag_s)));
return 1 - (dot_s / (sqrt(amag_s) * sqrt(bmag_s)));
}

static f32 l2_sqr_int8_neon(const void *pVect1v, const void *pVect2v,
Expand Down Expand Up @@ -492,13 +525,17 @@ static f32 distance_cosine_float(const void *pVect1v, const void *pVect2v,
f32 *pVect2 = (f32 *)pVect2v;
size_t qty = *((size_t *)qty_ptr);

f32 dot = 0;
f32 aMag = 0;
f32 bMag = 0;
// Accumulate in double: the square of a small (or large) f32 element
// underflows (or overflows) f32, which made the magnitude 0 (or Inf) and
// the distance +-Inf, NaN or plain wrong for nonzero finite vectors. Every
// f32 product is representable in double.
double dot = 0;
double aMag = 0;
double bMag = 0;
for (size_t i = 0; i < qty; i++) {
dot += *pVect1 * *pVect2;
aMag += *pVect1 * *pVect1;
bMag += *pVect2 * *pVect2;
dot += (double)*pVect1 * (double)*pVect2;
aMag += (double)*pVect1 * (double)*pVect1;
bMag += (double)*pVect2 * (double)*pVect2;
pVect1++;
pVect2++;
}
Expand Down Expand Up @@ -2047,9 +2084,11 @@ static void vec_normalize(sqlite3_context *context, int argc,

f32 *v = (f32 *)vector;

f32 norm = 0;
// Accumulate in double so that squaring small or large f32 elements does
// not underflow or overflow, see distance_cosine_float().
double norm = 0;
for (size_t i = 0; i < dimensions; i++) {
norm += v[i] * v[i];
norm += (double)v[i] * (double)v[i];
}
norm = sqrt(norm);
for (size_t i = 0; i < dimensions; i++) {
Expand Down
89 changes: 87 additions & 2 deletions tests/test-loadable.py
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Original file line number Diff line number Diff line change
Expand Up @@ -273,13 +273,48 @@ def check(a, b, dtype=np.float32):
b = np.array(b, dtype=dtype)

x = vec_distance_cosine(a, b, a=transform, b=transform)
y = npy_cosine(a, b)
# the reference in float64: numpy sums int8 products in int8
y = npy_cosine(a.astype(np.float64), b.astype(np.float64))
assert isclose(x, y, abs_tol=1e-6)

check([1.2, 0.1], [0.4, -0.4])
check([-1.2, -0.1], [-0.4, 0.4])
check([1, 2, 3], [-9, -8, -7], dtype=np.int8)
assert vec_distance_cosine("[1.1, 1.0]", "[1.2, 1.2]") == 0.001131898257881403
assert vec_distance_cosine("[1.1, 1.0]", "[1.2, 1.2]") == 0.0011318627512082458

# lengths past the SIMD kernels' thresholds, with and without a remainder
# past their 16-element blocks
rng = np.random.default_rng(324)
for n in [17, 31, 32, 40, 127, 768]:
check(rng.uniform(-1, 1, n), rng.uniform(-1, 1, n))
check(rng.integers(-128, 128, n), rng.integers(-128, 128, n), dtype=np.int8)


def test_vec_distance_cosine_extreme_magnitudes():
# squaring very small or very large f32 elements used to underflow or
# overflow the f32 magnitude accumulators, returning +-Inf, NaN or a wrong
# distance for nonzero finite vectors
# https://github.com/asg017/sqlite-vec/issues/324
vec_distance_cosine = lambda a, b: db.execute(
"select vec_distance_cosine(?, ?)", [_f32(a), _f32(b)]
).fetchone()[0]

# the same 2-element vectors padded to 40 elements, past the SIMD kernels'
# threshold, with a remainder past their 16-element blocks
for pad in [0, 38]:
z = [0] * pad
for scale in [1e-45, 1e-30, 1e-25, 1e-20, 1.0, 1e20, 3e38]:
# cosine distance is invariant under positive scaling
assert vec_distance_cosine([1, 0] + z, [scale, 0] + z) == 0.0
assert vec_distance_cosine([scale, 0] + z, [1, 0] + z) == 0.0
assert vec_distance_cosine([scale, 0] + z, [scale, 0] + z) == 0.0
assert vec_distance_cosine([1, 0] + z, [-scale, 0] + z) == 2.0
assert vec_distance_cosine([1, 0] + z, [0, scale] + z) == 1.0
assert isclose(
vec_distance_cosine([1, 0] + z, [scale, scale] + z),
1 - 1 / np.sqrt(2),
abs_tol=1e-6,
)


def test_vec_distance_hamming():
Expand Down Expand Up @@ -482,6 +517,18 @@ def test_vec_normalize():
-0.6324555277824402,
]

# small and large nonzero vectors are normalized rather than treated as
# zero-magnitude or returned as a zero vector, the squared magnitude used
# to underflow/overflow f32
# https://github.com/asg017/sqlite-vec/issues/324
for scale in [1e-45, 1e-30, 1e-25, 1e-22, 1e-20, 1e20, 3e38]:
assert vec_normalize(_f32([scale, 0])) == _f32([1, 0])
assert vec_normalize(_f32([0, -scale])) == _f32([0, -1])
assert np.allclose(
np.frombuffer(vec_normalize(_f32([scale, scale])), dtype=np.float32),
[1 / np.sqrt(2)] * 2,
)


def test_vec_slice():
vec_slice = lambda *args, f="?": db.execute(
Expand Down Expand Up @@ -2183,6 +2230,44 @@ def test_vec0_distance_metric():
]


def test_vec0_cosine_extreme_magnitudes():
# tiny or huge nonzero vectors used to get +-Inf, NaN or wrong cosine
# distances, which ranked them ahead of (or behind) the true nearest
# neighbors
# https://github.com/asg017/sqlite-vec/issues/324
db = connect(EXT_PATH)
db.execute("create virtual table v using vec0(a float[2] distance_metric=cosine)")
db.executemany(
"insert into v(rowid, a) values (?, ?)",
[
(1, _f32([0.9, 0.1])),
(2, _f32([1e-25, 0])),
(3, _f32([1e-25, 1e-25])),
(4, _f32([-1e-25, 0])),
(5, _f32([1e-30, 0])),
(6, _f32([3e38, 3e38])),
],
)

expected = [
{"rowid": 2, "distance": 0.0},
{"rowid": 5, "distance": 0.0},
{"rowid": 1, "distance": 0.006116265896707773},
{"rowid": 3, "distance": 0.2928932309150696},
{"rowid": 6, "distance": 0.2928932309150696},
{"rowid": 4, "distance": 2.0},
]
for query in ([1, 0], [1e-25, 0], [3e38, 0]):
rows = execute_all(
db,
"select rowid, distance from v where a match ? and k = 6",
[_f32(query)],
)
# the order of equidistant rows is unspecified
assert sorted(rows, key=lambda r: (r["distance"], r["rowid"])) == expected
assert [r["distance"] for r in rows] == [r["distance"] for r in expected]


def test_vec0_vacuum():
db = connect(EXT_PATH)
db.execute("create virtual table vec_t using vec0(a float[1]);")
Expand Down