A common application of generative programming is building high-performance computational kernels highly tuned to the problem at hand. A typical linear algebra kernel is specialized to the numerical domain (rational, float, double, etc.), loop unrolling factors, array layout and a priori knowledge (e.g., the matrix being positive definite). It is tedious and error prone to specialize by hand, writing numerous variations of the same algorithm.
The widely used generators such as ATLAS and SPIRAL reliably produce highly tuned specialized code but are difficult to extend. In ATLAS, which generates code using printf, even balancing parentheses is a challenge. According to the ATLAS creator, debugging is nightmare.
A typed staged programming language such as MetaOCaml lets us state a general, obviously correct algorithm and add layers of specializations in a modular way. By ensuring that the generated code always compiles and letting us quickly test it, MetaOCaml makes writing generators less daunting and more productive.
The readers will see it for themselves in this hands-on tutorial. Assuming no prior knowledge of MetaOCaml and only a basic familiarity with functional programming, we will eventually implement a simple domain-specific language (DSL) for linear algebra, with layers of optimizations for sparsity and memory layout of matrices and vectors, and their algebraic properties. We will generate optimal BLAS kernels. We shall get the taste of the ``Abstraction without guilt''.
As any other monograph in now's Foundations and Trends (TM) series,
``Reconciling Abstraction with High Performance: A MetaOCaml approach''
is published in three formats: journal, e-book and print book.
DOI: 10.1561/2500000038
The tutorial on systematic generation of optimal numeric kernels with MetaOCaml was first presented at the tutorial session of the conference of Commercial Users of Functional Programming (CUFP 13) on September 23, 2013 in Boston, USA. It was reprised at IFL 2017 (Bristol, UK).
This page describes the structure of the book and points to the accompanying code.
The stress on high-performance applications and on modular optimizations and generators sets this tutorial apart from Taha's very accessible, gentle introductions to the `classical' partial evaluation and staging, focused on turning an interpreter of a generally higher-order language into a compiler. We also get to see this classical area in Chap. 6; however, we pay less attention to lambda-calculus and more to image processing. Furthermore, this tutorial mentions recent additions to MetaOCaml such as offshoring and let-insertion.
The source code for the tutorial is available as a supplement (Accompanying Code).
The recent ``Stream Fusion, to Completeness'' enforces the lesson, on the `industrial strength' stream processing. The strymonas library designed in the paper lets us build pipelines by freely nesting and plugging in the components such as maps, filters, joins, etc. The result is the highly imperative code, whose performance not just approaches but matches the hand-written code (in the cases where the hand-written code was feasible to write).
Building even complicated generators is simple if we take advantage of abstraction and types. OCaml's excellent abstraction facilities -- from higher-order functions to module system -- let us write and debug generators in small pieces, and compose optimizations from separate layers. As we keep saying, with code generation, the abstraction comes with no cost. We may abstract with abandon.
Staged types are of particularly great help. They help ensure that compiling the generated code produces no errors. Problematic generators are reported with helpful error messages that refer to the generator (rather than generated) code. Furthermore, on many occasions we have seen that to stage code, we merely need to give it the desired signature, submit the code to the type checker and fix the reported errors. The type checker actively helps us write the code.
This tutorial has covered the part of MetaOCaml that has been stable
for a decade and is expected to remain so. MetaOCaml is an actively
developed project, with more, experimental features such as offshoring
and genlet, which have been mentioned only in passing. They all help
write generators easily and produce faster code while maintaining
confidence in the result.
oleg-at-okmij.org
Your comments, problem reports, questions are very welcome!
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