Describe the bug

For input vectors that are highly co-linear, their cosine distance may be computed to be negative due to numerical error.

Steps to reproduce

import simsimd
import numpy as np

u = np.array([-0.30039746, -0.13594460, 0.58292344])
v = np.array([-0.65563949, -0.29700866, 1.27146813])
print(simsimd.cosine(u, v))

Expected behavior

Cosine distance should be between 0 and 2. But I don't know if returning a negative result is a material issue in practice.

43 describes a similar issue related to numerical inaccuracy of the cosine distance. (Probably due to the use of RSQRT.)

A possible workaround is to clip the result within $[0,2]$, but that may have a negative impact on the performance (which could be more significant for short vectors are increasing negligible for longer vectors).

SimSIMD version

v5.4.3

Operating System

macOS Sonoma

Hardware architecture

Arm

Which interface are you using?

Python bindings

Contact Details

No response

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Is there an existing issue for this?

[X] I have searched the existing issues

Code of Conduct

[X] I agree to follow this project's Code of Conduct

ashvardanian / SimSIMD

Bug: Cosine distance may be negative #195