SIMD Binary Heap Operations
12 days ago
- #binary-heap
- #vectorization
- #performance
- Binary heap is a binary tree data structure with an array-friendly memory layout, maintaining a parent-child invariant where parent nodes are greater than their children.
- The article discusses two procedures related to heaps: `is_heap` and `push_heap`. `is_heap` is vectorizable and benefits from SIMD instructions, while `push_heap` can be expressed with gather and scatter operations but performs poorly.
- A vectorized approach for `is_heap` involves loading vectors of parent and child nodes, comparing them, and checking the heap invariant efficiently using AVX2 instructions.
- The `push_heap` procedure adds a new element to the heap and adjusts the heap by comparing and swapping elements up to the root. A vectorized approach for `push_heap` is described but noted to be impractical due to significant slowdowns.
- Benchmark results show that vectorized implementations of `is_heap` (using SSE, AVX2, and AVX-512) outperform scalar implementations, with AVX-512 providing the best performance.
- The article includes C++ code snippets for both scalar and vectorized implementations, highlighting the advantages and limitations of each approach.