Bug: Distance is negative

[alexbarev]

Describe the bug

Shouldn't distances for all metrics be non-negative? When I used the Inner Product as a distance measure, I found that it could produce negative values when using Index.search().

The same behavior is observed in the C# binding, so I suspect the same will occur when using the C99 interface.

Steps to reproduce

import numpy as np
from usearch.index import Index, Matches

index = Index(
    ndim=3, 
    metric='ip', 
    dtype='f32', 
)

keys = np.arange(5)
vectors = np.array(
    [
        [1, 1, 1],
        [-1, -1, -1],
        [1, 2, 3],
        [-1, -2, -3],
        [1, -2, -3],
    ], 
    dtype=np.float32
)
search_vector = np.array([1, 1, 1], dtype=np.float32)

index.add(keys, vectors)
matches: Matches = index.search(search_vector, 4)

for match in matches:
    assert(match.distance > -1e-6), f"Negative distance {match.distance}"

Expected behavior

Distance is always >= -epsilon, where epsilon is very small.

USearch version

v2.3.1

Operating System

Ubuntu 22.04

Hardware architecture

x86

Which interface are you using?

Python bindings

Contact Details

No response

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• [X] I have searched the existing issues

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[ashvardanian]

It might be a bit counter-intuitive, but your vectors aren’t normalized in any way, so you shouldn’t expect the inner products to be in the 0-1 range.