Representation|Metric|Exact core operator|SQL operator|Order for nearest-first search|Current SQL lifecycle dense|L2|`DistanceMetric::L2::distance`|`<->`|ascending distance|stable dense|Inner product|`DistanceMetric::InnerProduct::distance`|`inner_product` helper|descending raw similarity|stable dense|Negative inner product|`DistanceMetric::NegativeInnerProduct::distance`|`<#>`|ascending distance|stable dense|Cosine distance|`DistanceMetric::Cosine::distance`|`<=>`|ascending distance|stable dense|L1|`DistanceMetric::L1::distance`|`<+>`|ascending distance|stable half|L2|`DistanceMetric::L2::distance_half`|`<->`|ascending distance|experimental half|Inner product|`DistanceMetric::InnerProduct::distance_half`|`halfvec_inner_product` helper|descending raw similarity|experimental half|Negative inner product|`DistanceMetric::NegativeInnerProduct::distance_half`|`<#>`|ascending distance|experimental half|Cosine distance|`DistanceMetric::Cosine::distance_half`|`<=>`|ascending distance|experimental half|L1|`DistanceMetric::L1::distance_half`|`<+>`|ascending distance|experimental sparse|L2|`DistanceMetric::L2::distance_sparse`|`<->`|ascending distance|experimental sparse|Inner product|`DistanceMetric::InnerProduct::distance_sparse`|`sparsevec_inner_product` helper|descending raw similarity|experimental sparse|Negative inner product|`DistanceMetric::NegativeInnerProduct::distance_sparse`|`<#>`|ascending distance|experimental sparse|Cosine distance|`DistanceMetric::Cosine::distance_sparse`|`<=>`|ascending distance|experimental sparse|L1|`DistanceMetric::L1::distance_sparse`|`<+>`|ascending distance|experimental bit|Hamming|`BitVector::hamming_distance`|`<~>`|ascending distance|experimental bit|Jaccard distance|`BitVector::jaccard_distance`|`<%>`|ascending distance|experimental