Functions to compute L1 distance

[MBkkt]

Manhattan distance sometimes useful

https://github.com/google-research/google-research/tree/master/scann/scann/distance_measures/one_to_one
https://github.com/ydb-platform/ydb/tree/main/library/cpp/l1_distance

Already done for bit (hamming)

[ashvardanian]

This might be interesting for i8 inputs and any other low-capacity integral types, and might be related to #100 for sparse distances

[raulod]

l1 is picking momentum is many high dimensional usage where l2 distances are unstable.

[ashvardanian]

It seems like L1 is still very niche and L2 & Angular distances are mostly used.

Would be great to see some more user requests before switching the attention from matrix multiplications.

[rvalavi]

Is there any chance that L1 distance will be added for f32 or bf16?

[ashvardanian]

Yes, but depends on the demand. Where do you plan to use it, @rvalavi?

[rvalavi]

Thanks for the quick response, @ashvardanian!

L1 distance is pretty common in ecology and environmental modeling, especially when you’re working with multidimensional distances. E.g.: https://github.com/fitzLab-AL/gdm

I’m in the process of writing a Rust crate for this kind of application (private for now, but planning to make it public soon), and I wanted to try this out. In another application I worked on, I couldn’t get Rust anywhere close to the performance of a C++ implementation using Eigen with SIMD enabled, which is why having support for things like L1 here matters to me.

It’d be great to have L1 distance supported, since it comes up a lot in real-world use cases like this. I really appreciate you taking a look.