For the complete documentation index, see llms.txt. Markdown versions of all pages are available by appending .md to any URL (e.g. /get-started.md).

Mojo module

reduce_op

Reduction monoid traits — the device-agnostic author surface.

A reduction algorithm is authored as a struct conforming to ReduceOp: inlined state fields, __init__ (identity), accumulate[w] (SIMD-tile fold), join (sequential combine), and optionally join_parallel[R: Reducer] (parallel combine). How participants cooperate and how the parallel scope is defined live in the Reducer impls.

Structs

• ​ArgMax: Argmax reduction monoid: tracks the (value, axis-index) pair with the largest value. Ties break to the lower index.
• ​ArgMin: Argmin reduction monoid: mirrors ArgMax with </ge comparison (see ArgMax for the algorithm + design notes).
• ​MinMax: Fused min+max reduction monoid: tracks both min(self, x) and max(self, x) in one state. Cuts the axis walk in half vs running separate ReduceMin + ReduceMax.
• ​OnlineLogSumExp: Online (flash-style) log-sum-exp monoid (Milakov & Gimelshein, 2018) — the reduction half of softmax.
• ​ReduceMax: Max reduction monoid: (self, x) -> max(self, x).
• ​ReduceMin: Min reduction monoid: (self, x) -> min(self, x).
• ​ReduceProduct: Product reduction monoid: (self, x) -> self * x.
• ​ReduceSum: Sum reduction monoid: (self, x) -> self + x.
• ​Welford: Welford's online mean/variance monoid (Welford 1962, Chan et al. 1979 for the combine) — the reduction half of layer_norm / group_norm.

Traits

• ​ReduceOp: Trait for an associative reduction monoid (identity + associative join).
• ​Reducer: Parallel scalar reducer over the closed set of associative ops.