Algorithmic differentiation for domain specific languages in C++ with expression templates

TL;DR

This paper introduces a novel algorithmic differentiation approach for C++ domain-specific languages that preserves memory structure and leverages domain operations for improved performance.

Contribution

A new AD tool tailored for domain-specific languages in C++ that maintains primal data structure and enhances optimization capabilities.

Findings

Performance comparable to specialized AD tools.

Run-time factor below reverse AD theoretical limit.

Effective handling of linear algebra operations.

Abstract

The application of operator overloading algorithmic differentiation (AD) to computer programs in order to compute the derivative is quite common. But, the replacement of the underlying computational floating point type with the specialized type of an AD tool has two problems. First, the memory structure of the program is changed and floating-point data is interleaved with identifiers from AD. This prevents the compiler from performing optimizations such as SIMD optimizations. Second, the AD tool does not see any domain-specific operations, e.,g. linear algebra operations, that the program uses. This prevents the AD tool from using specialized algorithms in such places. We propose a new AD tool that is tailored to such situations. The memory structure of the primal data is retained by associating an identifier with each entity, e.,g. matrix, and not with each floating point value, e.,g. element of the matrix. Operations on such entities can then be annotated and a generator is used to create the AD overloads. We demonstrate that this approach provides performance comparable to that of other specializations. In addition, the run-time factor is below the theoretical 4.5 of reverse AD for programs that are written purely with linear algebra entities and operations.