Compiling Diderot: From Tensor Calculus to C

TL;DR

This paper presents a compiler approach for Diderot, a language for scientific image analysis, translating high-level tensor calculus into efficient C code using a novel intermediate representation called EIN.

Contribution

The paper introduces EIN, an intermediate representation that enables efficient compilation of Diderot's tensor calculus to C, reducing manual derivations and implementation effort.

Findings

EIN improves compiler efficiency and code quality.

The approach effectively lowers tensor calculus to C.

Compilation avoids combinatorial explosion in IR size.

Abstract

Diderot is a parallel domain-specific language for analysis and visualization of multidimensional scientific images, such as those produced by CT and MRI scanners. In particular, it supports algorithms where tensor fields (i.e., functions from 3D points to tensor values) are used to represent the underlying physical objects that were scanned by the imaging device. Diderot supports higher-order programming where tensor fields are first-class values and where differential operators and lifted linear-algebra operators can be used to express mathematical reasoning directly in the language. While such lifted field operations are central to the definition and computation of many scientific visualization algorithms, to date they have required extensive manual derivations and laborious implementation. The challenge for the Diderot compiler is to effectively translate the high-level mathematical concepts that are expressible in the surface language to a low-level and efficient implementation in C. This paper describes our approach to this challenge, which is based around the careful design of an intermediate representation (IR), called EIN, and a number of compiler transformations that lower the program from tensor calculus to C while avoiding combinatorial explosion in the size of the IR. We describe the challenges in compiling a language like Diderot, the design of EIN, and the transformation used by the compiler. We also present an evaluation of EIN with respect to both compiler efficiency and quality of generated code.