# HPTT: A High-Performance Tensor Transposition C++ Library

## TL;DR

HPTT is an open-source C++ library that efficiently performs tensor transpositions at runtime, with optimizations and autotuning, significantly improving tensor contraction performance across architectures.

## Contribution

Introduces HPTT, a modular, architecture-portable tensor transposition library with autotuning, enabling high-performance tensor operations in runtime applications.

## Key findings

- Achieves bandwidth comparable to SAXPY.
- Yields up to 3.1x speedup in tensor contractions.
- Performs well across diverse architectures.

## Abstract

Recently we presented TTC, a domain-specific compiler for tensor transpositions. Despite the fact that the performance of the generated code is nearly optimal, due to its offline nature, TTC cannot be utilized in all the application codes in which the tensor sizes and the necessary tensor permutations are determined at runtime. To overcome this limitation, we introduce the open-source C++ library High-Performance Tensor Transposition (HPTT). Similar to TTC, HPTT incorporates optimizations such as blocking, multi-threading, and explicit vectorization; furthermore it decomposes any transposition into multiple loops around a so called micro-kernel. This modular design---inspired by BLIS---makes HPTT easy to port to different architectures, by only replacing the hand-vectorized micro-kernel (e.g., a 4x4 transpose). HPTT also offers an optional autotuning framework---guided by a performance model---that explores a vast search space of implementations at runtime (similar to FFTW). Across a wide range of different tensor transpositions and architectures (e.g., Intel Ivy Bridge, Intel Knights Landing, ARMv7, IBM Power7), HPTT attains a bandwidth comparable to that of SAXPY, and yields remarkable speedups over Eigen's tensor transposition implementation. Most importantly, the integration of HPTT into the Cyclops Tensor Framework (CTF) improves the overall performance of tensor contractions by up to 3.1x.