title: Compiler Support for Operator Overloading and Algorithmic Differentiation in C++
Creators: name: Hück, Alexander
Publisher: name: UNSPECIFIED
Year: 2020

description: Multiphysics software needs derivatives for, e.g., solving a system of non-linear equations, conducting model verification, or sensitivity studies. In C++, algorithmic differentiation (AD), based on operator overloading (overloading), can be used to calculate derivatives up to machine precision. To that end, the built-in floating-point type is replaced by the user-defined AD type. It overloads all required operators, and calculates the original value and the corresponding derivative based on the chain rule of calculus. While changing the underlying type seems straightforward, several complications arise concerning software and performance engineering. This includes (1) fundamental language restrictions of C++ w.r.t. user-defined types, (2) type correctness of distributed computations with the Message Passing Interface (MPI) library, and (3) identification and mitigation of AD induced overheads. To handle these issues, AD experts may spend a significant amount of time to enhance a code with AD, verify the derivatives and ensure optimal application performance. Hence, in this thesis, we propose a modern compiler-based tooling approach to support and accelerate the AD-enhancement process of C++ target codes. In particular, we make contributions to three aspects of AD. The initial type change - While the change to the AD type in a target code is conceptually straightforward, the type change often leads to a multitude of compiler error messages. This is due to the different treatment of built-in floating-point types and user-defined types by the C++ language standard. Previously legal code constructs in the target code subsequently violate the language standard when the built-in floating-point type is replaced with a user-defined AD type. We identify and classify these problematic code constructs and their root cause is shown. Solutions by localized source transformation are proposed. To automate this rather mechanical process, we develop a static code analyser and source transformation tool, called OO-Lint, based on the Clang compiler framework. It flags instances of these problematic code constructs and applies source transformations to make the code compliant with the requirements of the language standard. To show the overall relevance of complications with user-defined types, OO-Lint is applied to several well-known scientific codes, some of which have already been AD enhanced by others. In all of these applications, except the ones manually treated for AD overloading, problematic code constructs are detected. Type correctness of MPI communication - MPI is the de-facto standard for programming high performance, distributed applications. At the same time, MPI has a complex interface whose usage can be error-prone. For instance, MPI derived data types require manual construction by specifying memory locations of the underlying data. Specifying wrong offsets can lead to subtle bugs that are hard to detect. In the context of AD, special libraries exist that handle the required derivative book-keeping by replacing the MPI communication calls with overloaded variants. However, on top of the AD type change, the MPI communication routines have to be changed manually. In addition, the AD type fundamentally changes memory layout assumptions as it has a different extent than the built-in types. Previously legal layout assumptions have, thus, to be reverified. As a remedy, to detect any type-related errors, we developed a memory sanitizer tool, called TypeART, based on the LLVM compiler framework and the MPI correctness checker MUST. It tracks all memory allocations relevant to MPI communication to allow for checking the underlying type and extent of the typeless memory buffer address passed to any MPI routine. The overhead induced by TypeART w.r.t. several target applications is manageable. AD domain-specific profiling - Applying AD in a black-box manner, without consideration of the target code structure, can have a significant impact on both runtime and memory consumption. An AD expert is usually required to apply further AD-related optimizations for the reduction of these induced overheads. Traditional profiling techniques are, however, insufficient as they do not reveal any AD domain-specific metrics. Of interest for AD code optimization are, e.g., specific code patterns, especially on a function level, that can be treated efficiently with AD. To that end, we developed a static profiling tool, called ProAD, based on the LLVM compiler framework. For each function, it generates the computational graph based on the static data flow of the floating-point variables. The framework supports pattern analysis on the computational graph to identify the optimal application of the chain rule. We show the potential of the optimal application of AD with two case studies. In both cases, significant runtime improvements can be achieved when the knowledge of the code structure, provided by our tool, is exploited. For instance, with a stencil code, a speedup factor of about 13 is achieved compared to a naive application of AD and a factor of 1.2 compared to hand-written derivative code.