1320 lines
64 KiB
TeX
1320 lines
64 KiB
TeX
%==============================================================================
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\documentclass{llncs}
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||
%------------------------------------------------------------------------------
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\usepackage[latin1]{inputenc}
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\usepackage{a4wide}
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\usepackage{float}
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||
\usepackage{alltt}
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||
\usepackage{xspace}
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\usepackage{epsfig}
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\usepackage{wrapfig}
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\usepackage{subfigure}
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|
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\renewcommand{\rmdefault}{ptm}
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%------------------------------------------------------------------------------
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\floatstyle{ruled}
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||
\newfloat{Algorithm}{ht}{lop}
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%------------------------------------------------------------------------------
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\newcommand{\wamcodesize}{scriptsize}
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\newcommand{\code}[1]{\texttt{#1}}
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\newcommand{\instr}[1]{\textsf{#1}}
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||
\newcommand{\try}{\instr{try}\xspace}
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\newcommand{\retry}{\mbox{\instr{retry}}\xspace}
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\newcommand{\trust}{\instr{trust}\xspace}
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\newcommand{\TryRetryTrust}{\mbox{\instr{try-retry-trust}}\xspace}
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||
\newcommand{\fail}{\instr{fail}\xspace}
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\newcommand{\jump}{\instr{jump}\xspace}
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\newcommand{\jitiSTAR}{\mbox{\instr{dindex\_on\_*}}\xspace}
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\newcommand{\switchSTAR}{\mbox{\instr{switch\_on\_*}}\xspace}
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\newcommand{\jitiONterm}{\mbox{\instr{dindex\_on\_term}}\xspace}
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\newcommand{\jitiONconstant}{\mbox{\instr{dindex\_on\_constant}}\xspace}
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\newcommand{\jitiONstructure}{\mbox{\instr{dindex\_on\_structure}}\xspace}
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\newcommand{\switchONterm}{\mbox{\instr{switch\_on\_term}}\xspace}
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\newcommand{\switchONconstant}{\mbox{\instr{switch\_on\_constant}}\xspace}
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\newcommand{\switchONstructure}{\mbox{\instr{switch\_on\_structure}}\xspace}
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\newcommand{\getcon}{\mbox{\instr{get\_constant}}\xspace}
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\newcommand{\proceed}{\instr{proceed}\xspace}
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\newcommand{\Cline}{\cline{2-3}}
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\newcommand{\JITI}{demand-driven indexing\xspace}
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%------------------------------------------------------------------------------
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\newcommand{\bench}[1]{\textbf{\textsf{#1}}}
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\newcommand{\tcLio}{\bench{tc\_l\_io}\xspace}
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\newcommand{\tcRio}{\bench{tc\_r\_io}\xspace}
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\newcommand{\tcDio}{\bench{tc\_d\_io}\xspace}
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\newcommand{\tcLoo}{\bench{tc\_l\_oo}\xspace}
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\newcommand{\tcRoo}{\bench{tc\_r\_oo}\xspace}
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||
\newcommand{\tcDoo}{\bench{tc\_d\_oo}\xspace}
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||
\newcommand{\compress}{\bench{compress}\xspace}
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\newcommand{\sgCyl}{\bench{sg\_cyl}\xspace}
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\newcommand{\muta}{\bench{mutagenesis}\xspace}
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\newcommand{\pta}{\bench{pta}\xspace}
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\newcommand{\tea}{\bench{tea}\xspace}
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%------------------------------------------------------------------------------
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\newcommand{\BreastCancer}{\bench{BreastCancer}\xspace}
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\newcommand{\Carcino}{\bench{Carcinogenesis}\xspace}
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\newcommand{\Choline}{\bench{Choline}\xspace}
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\newcommand{\GeneExpr}{\bench{GeneExpression}\xspace}
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\newcommand{\IEProtein}{\bench{IE-Protein\_Extraction}\xspace}
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%\newcommand{\Krki}{\bench{Krki}\xspace}
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%\newcommand{\KrkiII}{\bench{Krki~II}\xspace}
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\newcommand{\Mesh}{\bench{Mesh}\xspace}
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\newcommand{\Pyrimidines}{\bench{Pyrimidines}\xspace}
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\newcommand{\Susi}{\bench{Susi}\xspace}
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\newcommand{\Thermolysin}{\bench{Thermolysin}\xspace}
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%------------------------------------------------------------------------------
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\newenvironment{SmallProg}{\begin{tt}\begin{small}\begin{tabular}[b]{l}}{\end{tabular}\end{small}\end{tt}}
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\newenvironment{ScriptProg}{\begin{tt}\begin{scriptsize}\begin{tabular}[b]{l}}{\end{tabular}\end{scriptsize}\end{tt}}
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\newenvironment{FootProg}{\begin{tt}\begin{footnotesize}\begin{tabular}[c]{l}}{\end{tabular}\end{footnotesize}\end{tt}}
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\newcommand{\TODOcomment}[2]{%
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\stepcounter{TODOcounter#1}%
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{\scriptsize\bf$^{(\arabic{TODOcounter#1})}$}%
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\marginpar[\fbox{
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\parbox{2cm}{\raggedleft
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\scriptsize$^{({\bf{\arabic{TODOcounter#1}{#1}}})}$%
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\scriptsize #2}}]%
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{\fbox{\parbox{2cm}{\raggedright
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\scriptsize$^{({\bf{\arabic{TODOcounter#1}{#1}}})}$%
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\scriptsize #2}}}
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}%
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\newcounter{TODOcounter}
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\newcommand{\TODO}[1]{\TODOcomment{}{#1}}
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%------------------------------------------------------------------------------
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\title{Demand-Driven Indexing of Prolog Clauses}
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\titlerunning{Demand-Driven Indexing of Prolog Clauses}
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\author{V\'{\i}tor Santos Costa\inst{1} \and Konstantinos
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Sagonas\inst{2} \and Ricardo Lopes\inst{1}}
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\authorrunning{V. Santos Costa, K. Sagonas and R. Lopes}
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\institute{
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LIACC- DCC/FCUP, University of Porto, Portugal
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\and
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National Technical University of Athens, Greece
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}
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\pagestyle{plain} % For the submission only
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\begin{document}
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\maketitle
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\begin{abstract}
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As logic programming applications grow in size, Prolog systems need
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to efficiently access larger and larger data sets and the need for
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any- and multi-argument indexing becomes more and more profound.
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Static generation of multi-argument indexing is one alternative, but
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applications often rely on features that are inherently dynamic
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(e.g., generating hypotheses for ILP data sets during runtime) which
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makes static techniques inapplicable or inaccurate. Another
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alternative, which has not been investigated so far, is to employ
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dynamic schemes for flexible demand-driven indexing of Prolog
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clauses. We propose such schemes and discuss issues that need to be
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addressed for their efficient implementation in the context of
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WAM-based Prolog systems. We have implemented demand-driven indexing
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in two different Prolog systems and have been able to obtain
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non-negligible performance speedups: from a few percent up to orders
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of magnitude. Given these results, we see very little reason for
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Prolog systems not to incorporate some form of dynamic indexing
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based on actual demand. In fact, we see demand-driven indexing as
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the first step towards effective runtime optimization of Prolog
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programs.
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\end{abstract}
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\section{Introduction}
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%=====================
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The WAM~\cite{Warren83} has mostly been a blessing but occasionally
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also a curse for Prolog systems. Its ingenious design has allowed
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implementors to get byte code compilers with decent performance --- it
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is not a fluke that most Prolog systems are still based on the WAM. On
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the other hand, \emph{because} the WAM gives good performance in many
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cases, implementors have not incorporated in their systems many
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features that drastically depart from WAM's basic characteristics.
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%
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For example, first argument indexing is sufficient for many Prolog
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applications. However, it is clearly sub-optimal for applications
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accessing large data sets; for a long time now, the database community
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has recognized that good indexing is the basis for fast query
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processing.
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As logic programming applications grow in size, Prolog systems need to
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efficiently access larger and larger data sets and the need for any-
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and multi-argument indexing becomes more and more profound. Static
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generation of multi-argument indexing is one alternative. The problem
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is that this alternative is often unattractive because it may
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drastically increase the size of the generated byte code and do so
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unnecessarily. Static analysis can partly address this concern, but in
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applications that rely on features which are inherently dynamic (e.g.,
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generating hypotheses for inductive logic programming data sets during
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runtime) static analysis is inapplicable or grossly inaccurate.
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Another alternative, which has not been investigated so far, is to do
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flexible indexing on demand during program execution.
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This is precisely what we advocate with this paper. More specifically,
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we present a small extension to the WAM that allows for flexible
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indexing of Prolog clauses during runtime based on actual demand. For
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static predicates, the scheme we propose is partly guided by the
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compiler; for dynamic code, besides being demand-driven by queries,
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the method needs to cater for code updates during runtime. Where our
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schemes radically depart from current practice is that they generate
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new byte code during runtime, in effect doing a form of just-in-time
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compilation. In our experience these schemes pay off. We have
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implemented \JITI in two different Prolog systems (YAP and XXX) and
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have obtained non-trivial speedups, ranging from a few percent to
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orders of magnitude, across a wide range of applications. Given these
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results, we see very little reason for Prolog systems not to
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incorporate some form of indexing based on actual demand from queries.
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In fact, we see \JITI as only the first step towards effective runtime
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optimization of Prolog programs.
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This paper is structured as follows. After commenting on the state of
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the art and related work concerning indexing in Prolog systems
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(Sect.~\ref{sec:related}) we briefly review indexing in the WAM
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(Sect.~\ref{sec:prelims}). We then present \JITI schemes for static
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(Sect.~\ref{sec:static}) and dynamic (Sect.~\ref{sec:dynamic})
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predicates, their implementation in two Prolog systems
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(Sect.~\ref{sec:impl}) and the performance benefits they bring
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(Sect.~\ref{sec:perf}). The paper ends with some concluding remarks.
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\section{State of the Art and Related Work} \label{sec:related}
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%==============================================================
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% Indexing in Prolog systems:
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To the best of our knowledge, many Prolog systems still only support
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indexing on the main functor symbol of the first argument. Some
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others, such as YAP version 4, can look inside some compound
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terms~\cite{YAP}. SICStus Prolog supports \emph{shallow
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backtracking}~\cite{ShallowBacktracking@ICLP-89}; choice points are
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fully populated only when it is certain that execution will enter the
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clause body. While shallow backtracking avoids some of the performance
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problems of unnecessary choice point creation, it does not offer the
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full benefits that indexing can provide. Other systems such as
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BIM-Prolog~\cite{IndexingProlog@NACLP-89}, SWI-Prolog~\cite{SWI} and
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XSB~\cite{XSB} allow for user-controlled multi-argument indexing (via
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an \code{:-~index} directive). Notably, ilProlog~\cite{ilProlog} uses
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compile-time heuristics and generates code for multi-argument indexing
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automatically. In all these systems, this support comes with various
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implementation restrictions. For example, in SWI-Prolog at most four
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arguments can be indexed; in XSB the compiler does not offer
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multi-argument indexing and the predicates need to be asserted
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instead; we know of no system where multi-argument indexing looks
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inside compound terms. More importantly, requiring users to specify
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arguments to index on is neither user-friendly nor guarantees good
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performance results.
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% Trees, tries and unification factoring:
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Recognizing the need for better indexing, researchers have proposed
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more flexible index mechanisms for Prolog. For example, Hickey and
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Mudambi proposed \emph{switching trees}~\cite{HickeyMudambi@JLP-89},
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which rely on the presence of mode information. Similar proposals were
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put forward by Van Roy, Demoen and Willems who investigated indexing
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on several arguments in the form of a \emph{selection tree}~\cite{VRDW87}
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and by Zhou et al.\ who implemented a \emph{matching tree} oriented
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abstract machine for Prolog~\cite{TOAM@ICLP-90}. For static
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predicates, the XSB compiler offers support for \emph{unification
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factoring}~\cite{UnifFact@POPL-95}; for asserted code, XSB can
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represent databases of facts using \emph{tries}~\cite{Tries@JLP-99}
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which provide left-to-right multi-argument indexing. However, in XSB
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none of these mechanisms is used automatically; instead the user has
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to specify appropriate directives.
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% Comparison with static analysis techniques and Mercury:
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Long ago, Kliger and Shapiro argued that such tree-based indexing
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schemes are not cost effective for the compilation of Prolog
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programs~\cite{KligerShapiro@ICLP-88}. Some of their arguments make
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sense for certain applications, but, as we shall show, in general
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they underestimate the benefits of indexing on EDB predicates.
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Nevertheless, it is true that unless the modes of
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predicates are known we run the risk of doing indexing on output
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arguments, whose only effect is an unnecessary increase in compilation
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times and, more importantly, in code size. In a programming language
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such as Mercury~\cite{Mercury@JLP-96} where modes are known the compiler
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can of course avoid this risk; indeed in Mercury modes (and types) are
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used to guide the compiler generate good indexing tables. However, the
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situation is different for a language such as Prolog. Getting accurate
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information about the set of all possible modes of predicates requires
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a global static analyzer in the compiler --- and most Prolog systems
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do not come with one. More importantly, it requires a lot of
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discipline from the programmer (e.g., that applications use the module
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system religiously and never bypass it). As a result, most Prolog
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systems currently do not provide the type of indexing that
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applications require. Even in systems such as Ciao~\cite{Ciao@SCP-05},
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which do come with built-in static analysis and more or less force
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such a discipline on the programmer, mode information is not used for
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multi-argument indexing.
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% The grand finale:
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The situation is actually worse for certain types of Prolog
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applications. For example, consider applications in the area of
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inductive logic programming. These applications on the one hand have
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high demands for effective indexing since they need to efficiently
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access big datasets and on the other they are unfit for static
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analysis since queries are often ad hoc and generated only during
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runtime as new hypotheses are formed or refined.
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%
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Our thesis is that the abstract machine should be able to adapt
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automatically to the runtime requirements of such or, even better, of
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all applications by employing increasingly aggressive forms of dynamic
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compilation. As a concrete example of what this means in practice, in
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this paper we will attack the problem of satisfying the indexing needs
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of applications during runtime. Naturally, we will base our technique
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on the existing support for indexing that the WAM provides, but we
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will extend this support with the technique of \JITI that we describe
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in the next sections.
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\section{Indexing in the WAM} \label{sec:prelims}
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%================================================
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To make the paper relatively self-contained we briefly review the
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indexing instructions of the WAM and their use. In the WAM, the first
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level of dispatching involves a test on the type of the argument. The
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\switchONterm instruction checks the tag of the dereferenced value in
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the first argument register and implements a four-way branch where one
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branch is for the dereferenced register being an unbound variable, one
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for being atomic, one for (non-empty) list, and one for structure. In
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any case, control goes to a (possibly empty) bucket of clauses. In the
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buckets for constants and structures the second level of dispatching
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involves the value of the register. The \switchONconstant and
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\switchONstructure instructions implement this dispatching: typically
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with a \fail instruction when the bucket is empty, with a \jump
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instruction for only one clause, with a sequential scan when the
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number of clauses is small, and with a hash lookup when the number of
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clauses exceeds a threshold. For this reason the \switchONconstant and
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\switchONstructure instructions take as arguments the hash table
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\instr{T} and the number of clauses \instr{N} the table contains (or
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equivalently, \instr{N} is the size of the hash table). In each bucket
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of this hash table and also in the bucket for the variable case of
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\switchONterm the code sequentially backtracks through the clauses
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using a \TryRetryTrust chain of instructions. The \try instruction
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sets up a choice point, the \retry instructions (if~any) update
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certain fields of this choice point, and the \trust instruction
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removes it.
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The WAM has additional indexing instructions (\instr{try\_me\_else}
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and friends) that allow indexing to be interspersed with the code of
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clauses. For simplicity of presentation we will not consider them
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here. This is not a problem since the above scheme handles all programs.
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Also, we will feel free to do some minor modifications and
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optimizations when this simplifies things.
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We present an example. Consider the Prolog code shown in
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Fig.~\ref{fig:carc:facts}. It is a fragment of the machine
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learning dataset \textit{Carcinogenesis}~\cite{Carcinogenesis@ILP-97}.
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The five clauses get compiled to the WAM code shown in
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Fig.~\ref{fig:carc:clauses}. The first argument indexing code
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that a Prolog compiler generates is shown in
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Fig.~\ref{fig:carc:index}. This code is typically placed before the
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code for the clauses and the \switchONconstant instruction is the
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entry point of the predicate. Note that compared with vanilla WAM this
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instruction has an extra argument: the register on the value of which
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we index ($r_1$). This extra argument will allow us to go beyond
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first argument indexing. Another departure from the WAM is that if
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this argument register contains an unbound variable instead of a
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constant then execution will continue with the next instruction; in
|
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effect we have merged part of the functionality of \switchONterm into
|
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the \switchONconstant instruction. This small change in the behavior
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of \switchONconstant will allow us to get \JITI. Let's see how.
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%------------------------------------------------------------------------------
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\begin{figure}[t]
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\centering
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\subfigure[Some Prolog clauses\label{fig:carc:facts}]{%
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\begin{ScriptProg}
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has\_property(d1,salmonella,p).\\
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has\_property(d1,salmonella\_n,p).\\
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has\_property(d2,salmonella,p). \\
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has\_property(d2,cytogen\_ca,n).\\
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has\_property(d3,cytogen\_ca,p).
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\end{ScriptProg}
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}%
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\subfigure[WAM indexing\label{fig:carc:index}]{%
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||
\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}[b]{l}
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\switchONconstant $r_1$ 5 $T_1$ \\
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||
\try $L_1$ \\
|
||
\retry $L_2$ \\
|
||
\retry $L_3$ \\
|
||
\retry $L_4$ \\
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||
\trust $L_5$ \\
|
||
\\
|
||
\begin{tabular}[b]{r|c@{\ }|l|}
|
||
\Cline
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||
$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & d1 & \try $L_1$ \\
|
||
\ & & \trust $L_2$ \\ \Cline
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||
\ & d2 & \try $L_3$ \\
|
||
\ & & \trust $L_4$ \\ \Cline
|
||
\ & d3 & \jump $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
\end{tabular}
|
||
\end{\wamcodesize}
|
||
\end{sf}
|
||
}%
|
||
\subfigure[Code for the clauses\label{fig:carc:clauses}]{%
|
||
\begin{sf}
|
||
\begin{\wamcodesize}
|
||
\begin{tabular}[b]{rl}
|
||
$L_1$: & \getcon $r_1$ d1 \\
|
||
\ & \getcon $r_2$ salmonella \\
|
||
\ & \getcon $r_3$ p \\
|
||
\ & \proceed \\
|
||
$L_2$: & \getcon $r_1$ d1 \\
|
||
\ & \getcon $r_2$ salmonella\_n \\
|
||
\ & \getcon $r_3$ p \\
|
||
\ & \proceed \\
|
||
$L_3$: & \getcon $r_1$ d2 \\
|
||
\ & \getcon $r_2$ salmonella \\
|
||
\ & \getcon $r_3$ p \\
|
||
\ & \proceed \\
|
||
$L_4$: & \getcon $r_1$ d2 \\
|
||
\ & \getcon $r_2$ cytogen\_ca \\
|
||
\ & \getcon $r_3$ n \\
|
||
\ & \proceed \\
|
||
$L_5$: & \getcon $r_1$ d3 \\
|
||
\ & \getcon $r_2$ cytogen\_ca \\
|
||
\ & \getcon $r_3$ p \\
|
||
\ & \proceed
|
||
\end{tabular}
|
||
\end{\wamcodesize}
|
||
\end{sf}
|
||
}%
|
||
\subfigure[Any arg indexing\label{fig:carc:jiti_single:before}]{%
|
||
\begin{sf}
|
||
\begin{\wamcodesize}
|
||
\begin{tabular}[b]{l}
|
||
\switchONconstant $r_1$ 5 $T_1$ \\
|
||
\jitiONconstant $r_2$ 5 3 \\
|
||
\jitiONconstant $r_3$ 5 3 \\
|
||
\try $L_1$ \\
|
||
\retry $L_2$ \\
|
||
\retry $L_3$ \\
|
||
\retry $L_4$ \\
|
||
\trust $L_5$ \\
|
||
\\
|
||
\begin{tabular}[b]{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{d1} & \try $L_1$ \\
|
||
\ & & \trust $L_2$ \\ \Cline
|
||
\ & \code{d2} & \try $L_3$ \\
|
||
\ & & \trust $L_4$ \\ \Cline
|
||
\ & \code{d3} & \jump $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
\end{tabular}
|
||
\end{\wamcodesize}
|
||
\end{sf}
|
||
}%
|
||
\caption{Part of the Carcinogenesis dataset and WAM code that a byte
|
||
code compiler generates}
|
||
\label{fig:carc}
|
||
\end{figure}
|
||
%------------------------------------------------------------------------------
|
||
|
||
|
||
\section{Demand-Driven Indexing of Static Predicates} \label{sec:static}
|
||
%=======================================================================
|
||
For static predicates the compiler has complete information about all
|
||
clauses and shapes of their head arguments. It is both desirable and
|
||
possible to take advantage of this information at compile time and so
|
||
we treat the case of static predicates separately.
|
||
%
|
||
We will do so with schemes of increasing effectiveness and
|
||
implementation complexity.
|
||
|
||
\subsection{A simple WAM extension for any argument indexing}
|
||
%------------------------------------------------------------
|
||
Let us initially consider the case where the predicates to index
|
||
consist only of Datalog facts. This is commonly the case for all
|
||
extensional database predicates where indexing is most effective and
|
||
called for.
|
||
|
||
Refer to the example in Fig.~\ref{fig:carc}.
|
||
%
|
||
The indexing code of Fig.~\ref{fig:carc:index} incurs a small cost for
|
||
a call where the first argument is a variable (namely, executing the
|
||
\switchONconstant instruction) but the instruction pays off for calls
|
||
where the first argument is bound. On the other hand, for calls where
|
||
the first argument is a free variable and some other argument is
|
||
bound, a choice point will be created, the \TryRetryTrust chain will
|
||
be used, and execution will go through the code of all clauses. This
|
||
is clearly inefficient, more so for larger data sets.
|
||
%
|
||
We can do much better with the relatively simple scheme shown in
|
||
Fig.~\ref{fig:carc:jiti_single:before}. Immediately after the
|
||
\switchONconstant instruction, we can statically generate
|
||
\jitiONconstant (demand indexing) instructions, one for each remaining
|
||
argument. Recall that the entry point of the predicate is the
|
||
\switchONconstant instruction. The \jitiONconstant $r_i$ \instr{N A}
|
||
instruction works as follows:
|
||
\begin{itemize}
|
||
\item if the argument register $r_i$ is a free variable, then
|
||
execution continues with the next instruction;
|
||
\item otherwise, \JITI kicks in as follows. The abstract machine
|
||
scans the WAM code of the clauses and creates an index table for the
|
||
values of the corresponding argument. It can do so because the
|
||
instruction takes as arguments the number of clauses \instr{N} to
|
||
index and the arity \instr{A} of the predicate. (In our example, the
|
||
numbers 5 and 3.) For Datalog facts, this information is sufficient.
|
||
Because the WAM byte code for the clauses has a very regular
|
||
structure, the index table can be created very quickly. Upon its
|
||
creation, the \jitiONconstant instruction gets transformed to a
|
||
\switchONconstant. Again this is straightforward because of the two
|
||
instructions have similar layouts in memory. Execution of the
|
||
abstract machine then continues with the \switchONconstant
|
||
instruction.
|
||
\end{itemize}
|
||
Figure~\ref{fig:carg:jiti_single:after} shows the index table $T_2$
|
||
which is created for our example and how the indexing code looks after
|
||
the execution of a call with mode \code{(out,in,?)}. Note that the
|
||
\jitiONconstant instruction for argument register $r_2$ has been
|
||
appropriately patched. The call that triggered \JITI and subsequent
|
||
calls of the same mode will use table $T_2$. The index for the second
|
||
argument has been created.
|
||
%------------------------------------------------------------------------------
|
||
\begin{figure}
|
||
\centering
|
||
\begin{sf}
|
||
\begin{\wamcodesize}
|
||
\begin{tabular}{c@{\hspace*{2em}}c@{\hspace*{2em}}c}
|
||
\begin{tabular}{l}
|
||
\switchONconstant $r_1$ 5 $T_1$ \\
|
||
\switchONconstant $r_2$ 5 $T_2$ \\
|
||
\jitiONconstant $r_3$ 5 3 \\
|
||
\try $L_1$ \\
|
||
\retry $L_2$ \\
|
||
\retry $L_3$ \\
|
||
\retry $L_4$ \\
|
||
\trust $L_5$ \\
|
||
\end{tabular}
|
||
&
|
||
\begin{tabular}{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{d1} & \try $L_1$ \\
|
||
\ & & \trust $L_2$ \\ \Cline
|
||
\ & \code{d2} & \try $L_3$ \\
|
||
\ & & \trust $L_4$ \\ \Cline
|
||
\ & \code{d3} & \jump $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
&
|
||
\begin{tabular}{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_2$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{salmonella} & \try $L_1$ \\
|
||
\ & & \trust $L_3$ \\ \Cline
|
||
\ & \code{salmonella\_n} & \jump $L_2$ \\ \Cline
|
||
\ & \code{cytrogen\_ca} & \try $L_4$ \\
|
||
\ & & \trust $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
\end{tabular}
|
||
\end{\wamcodesize}
|
||
\end{sf}
|
||
\caption{WAM code after demand-driven indexing for argument 2;
|
||
table $T_2$ is generated dynamically}
|
||
\label{fig:carg:jiti_single:after}
|
||
\end{figure}
|
||
%------------------------------------------------------------------------------
|
||
|
||
The main advantage of this scheme is its simplicity. The compiled code
|
||
(Fig.~\ref{fig:carc:jiti_single:before}) is not significantly bigger
|
||
than the code which a WAM-based compiler would generate
|
||
(Fig.~\ref{fig:carc:index}) and, if \JITI turns out unnecessary
|
||
during runtime (e.g. execution encounters only open calls or with only
|
||
the first argument bound), the extra overhead is minimal: the
|
||
execution of some \jitiONconstant instructions for the open call only.
|
||
%
|
||
In short, this is a simple scheme that allows for \JITI on \emph{any
|
||
single} argument. At least for big sets of Datalog facts, we see
|
||
little reason not to use this indexing scheme.
|
||
|
||
\paragraph*{Optimizations.}
|
||
Because we are dealing with static code, there are opportunities for
|
||
some easy optimizations. Suppose we statically determine that there
|
||
will never be any calls with \code{in} mode for some arguments or that
|
||
these arguments are not discriminating enough.\footnote{In our example,
|
||
suppose the third argument of \code{has\_property/3} had the atom
|
||
\code{p} as value throughout.} Then we can avoid generating
|
||
\jitiONconstant instructions for them. Also, suppose we detect or
|
||
heuristically decide that some arguments are most likely than others
|
||
to be used in the \code{in} mode. Then we can simply place the
|
||
\jitiONconstant instructions for these arguments \emph{before} the
|
||
instructions for other arguments. This is possible since all indexing
|
||
instructions take the argument register number as an argument; their
|
||
order does not matter.
|
||
|
||
\subsection{From any argument indexing to multi-argument indexing}
|
||
%-----------------------------------------------------------------
|
||
The scheme of the previous section gives us only single argument
|
||
indexing. However, all the infrastructure we need is already in place.
|
||
We can use it to obtain any fixed-order multi-argument \JITI in a
|
||
straightforward way.
|
||
|
||
Note that the compiler knows exactly the set of clauses that need to
|
||
be tried for each query with a specific symbol in the first argument.
|
||
This information is needed in order to construct, at compile time, the
|
||
hash table $T_1$ of Fig.~\ref{fig:carc:index}. For multi-argument
|
||
\JITI, instead of generating for each hash bucket only \TryRetryTrust
|
||
instructions, the compiler can prepend appropriate demand indexing
|
||
instructions. We illustrate this on our running example. The table
|
||
$T_1$ contains four \jitiONconstant instructions: two for each of the
|
||
remaining two arguments of hash buckets with more than one
|
||
alternative. For hash buckets with none or only one alternative (e.g.,
|
||
for \code{d3}'s bucket) there is obviously no need to resort to \JITI
|
||
for the remaining arguments. Figure~\ref{fig:carc:jiti_multi} shows
|
||
the state of the hash tables after the execution of queries
|
||
\code{has\_property(C,salmonella,T)}, which creates table $T_2$, and
|
||
\code{has\_property(d2,P,n)} which creates the $T_3$ table and
|
||
transforms the \jitiONconstant instruction for \code{d2} and register
|
||
$r_3$ to the appropriate \switchONconstant instruction.
|
||
|
||
%------------------------------------------------------------------------------
|
||
\begin{figure}[t]
|
||
\centering
|
||
\begin{sf}
|
||
\begin{\wamcodesize}
|
||
\begin{tabular}{@{}cccc@{}}
|
||
\begin{tabular}{l}
|
||
\switchONconstant $r_1$ 5 $T_1$ \\
|
||
\switchONconstant $r_2$ 5 $T_2$ \\
|
||
\jitiONconstant $r_3$ 5 3 \\
|
||
\try $L_1$ \\
|
||
\retry $L_2$ \\
|
||
\retry $L_3$ \\
|
||
\retry $L_4$ \\
|
||
\trust $L_5$ \\
|
||
\end{tabular}
|
||
&
|
||
\begin{tabular}{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{d1} & \jitiONconstant $r_2$ 2 3 \\
|
||
\ & & \jitiONconstant $r_3$ 2 3 \\
|
||
\ & & \try $L_1$ \\
|
||
\ & & \trust $L_2$ \\ \Cline
|
||
\ & \code{d2} & \jitiONconstant $r_2$ 2 3 \\
|
||
\ & & \switchONconstant $r_3$ 2 $T_3$ \\
|
||
\ & & \try $L_3$ \\
|
||
\ & & \trust $L_4$ \\ \Cline
|
||
\ & \code{d3} & \jump $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
&
|
||
\begin{tabular}{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_2$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{salmonella} & \jitiONconstant $r_3$ 2 3 \\
|
||
\ & & \try $L_1$ \\
|
||
\ & & \trust $L_3$ \\ \Cline
|
||
\ & \code{salmonella\_n} & \jump $L_2$ \\ \Cline
|
||
\ & \code{cytrogen\_ca} & \jitiONconstant $r_3$ 2 3 \\
|
||
\ & & \try $L_4$ \\
|
||
\ & & \trust $L_5$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
&
|
||
\begin{tabular}{r|c@{\ }|l|}
|
||
\Cline
|
||
$T_3$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
|
||
\ & \code{p} & \jump $L_3$ \\ \Cline
|
||
\ & \code{n} & \jump $L_4$ \\
|
||
\Cline
|
||
\end{tabular}
|
||
\end{tabular}
|
||
\end{\wamcodesize}
|
||
\end{sf}
|
||
\caption{\JITI for all argument combinations;
|
||
table $T_1$ is static; $T_2$ and $T_3$ are generated dynamically}
|
||
\label{fig:carc:jiti_multi}
|
||
\end{figure}
|
||
%------------------------------------------------------------------------------
|
||
|
||
\paragraph{Implementation issues.}
|
||
In the \jitiONconstant instructions of Fig.~\ref{fig:carc:jiti_multi}
|
||
notice the integer 2 which denotes the number of clauses that the
|
||
instruction will index. Using this number an index table of
|
||
appropriate size will be created, such as $T_3$. To fill this table we
|
||
need information about the clauses to index and the symbols to hash
|
||
on. The clauses can be obtained by scanning the labels of the
|
||
\TryRetryTrust instructions following \jitiONconstant; the symbols by
|
||
looking at appropriate byte code offsets (based on the argument
|
||
register number) from these labels. In our running example, the
|
||
symbols can be obtained by looking at the second argument of the
|
||
\getcon instruction whose argument register is $r_2$. In the loaded
|
||
bytecode, assuming the argument register is represented in one byte,
|
||
these symbols are found $sizeof(\getcon) + sizeof(opcode) + 1$ bytes
|
||
away from the clause label; see Fig.~\ref{fig:carc:clauses}. Thus,
|
||
multi-argument \JITI is easy to get and the creation of index tables
|
||
can be extremely fast when indexing Datalog facts.
|
||
|
||
\subsection{Beyond Datalog and other implementation issues}
|
||
%----------------------------------------------------------
|
||
Indexing on demand clauses with function symbols is not significantly
|
||
more difficult. The scheme we have described is applicable but
|
||
requires the following extensions:
|
||
\begin{enumerate}
|
||
\item Besides \jitiONconstant we also need \jitiONterm and
|
||
\jitiONstructure instructions. These are the \JITI counterparts of
|
||
the WAM's \switchONterm and \switchONstructure.
|
||
\item Because the byte code for the clause heads does not necessarily
|
||
have a regular structure, the abstract machine needs to be able to
|
||
``walk'' the byte code instructions and recover the symbols on which
|
||
indexing will be based. Writing such a code walking procedure is not
|
||
hard.\footnote{In many Prolog systems, a procedure with similar
|
||
functionality often exists for the disassembler, the debugger, etc.}
|
||
\item Indexing on a position that contains unconstrained variables
|
||
for some clauses is tricky. The WAM needs to group clauses in this
|
||
case and without special treatment creates two choice points for
|
||
this argument (one for the variables and one per each group of
|
||
clauses). However, this issue and how to deal with it is well-known
|
||
by now. Possible solutions to it are described in a 1987 paper by
|
||
Carlsson~\cite{FreezeIndexing@ICLP-87} and can be readily adapted to
|
||
\JITI. Alternatively, in a simple implementation, we can skip \JITI
|
||
for positions with variables in some clauses.
|
||
\end{enumerate}
|
||
Before describing \JITI more formally, we remark on the following
|
||
design decisions whose rationale may not be immediately obvious:
|
||
\begin{itemize}
|
||
\item By default, only table $T_1$ is generated at compile time (as in
|
||
the WAM) and the additional index tables $T_2, T_3, \ldots$ are
|
||
generated dynamically. This is because we do not want to increase
|
||
compiled code size unnecessarily (i.e., when there is no demand for
|
||
these indices).
|
||
\item On the other hand, we generate \jitiSTAR instructions at compile
|
||
time for the head arguments.\footnote{The \jitiSTAR instructions for
|
||
the $T_1$ table can be generated either by the compiler or by the
|
||
loader.} This does not noticeably increase the generated byte code
|
||
but it greatly simplifies code loading. Notice that a nice property
|
||
of the scheme we have described is that the loaded byte code can be
|
||
patched \emph{without} the need to move any instructions.
|
||
% The indexing tables are typically not intersperced with the byte code.
|
||
\item Finally, one may wonder why the \jitiSTAR instructions create
|
||
the dynamic index tables with an additional code walking pass
|
||
instead of piggy-backing on the pass which examines all clauses via
|
||
the main \TryRetryTrust chain. Main reasons are: 1) in many cases
|
||
the code walking can be selective and guided by offsets and 2) by
|
||
first creating the index table and then using it we speed up the
|
||
execution of the queries encountered during runtime and often avoid
|
||
unnecessary choice point creations.
|
||
\end{itemize}
|
||
This is \JITI as we have implemented it.
|
||
% in one of our Prolog systems.
|
||
However, we note that these decisions are orthogonal to the main idea
|
||
and are under compiler control. If, for example, analysis determines
|
||
that some argument sequences will never demand indexing we can simply
|
||
avoid generation of \jitiSTAR instructions for these. Similarly, if we
|
||
determine that some argument sequences will definitely demand indexing
|
||
we can speed up execution by generating the appropriate index tables
|
||
at compile time instead of at runtime.
|
||
|
||
\subsection{Demand-driven index construction and its properties}
|
||
%---------------------------------------------------------------
|
||
The idea behind \JITI can be captured in a single sentence: \emph{we
|
||
can generate every index we need during program execution when this
|
||
index is demanded}. Subsequent uses of these indices can speed up
|
||
execution considerably more than the time it takes to construct them
|
||
(more on this below) so this runtime action makes sense.\footnote{In
|
||
fact, because choice points are expensive in the WAM, \JITI can speed
|
||
up even the execution of the query that triggers the process, not only
|
||
subsequent queries.}
|
||
%
|
||
We describe the process of demand-driven index construction.
|
||
|
||
% \subsubsection{Demand-driven index construction}
|
||
%-------------------------------------------------
|
||
Let $p/k$ be a predicate with $n$ clauses.
|
||
%
|
||
At a high level, its indices form a tree whose root is the entry point
|
||
of the predicate. For simplicity, assume that the root node of the
|
||
tree and the interior nodes corresponding to the index table for the
|
||
first argument have been constructed at compile time. Leaves of this
|
||
tree are the nodes containing the code for the clauses of the
|
||
predicate and each clause is identified by a unique label \mbox{$L_i,
|
||
1 \leq i \leq n$}. Execution always starts at the first instruction of
|
||
the root node and follows Algorithm~\ref{alg:construction}. The
|
||
algorithm might look complicated but is actually quite simple.
|
||
%
|
||
Each non-leaf node contains a sequence of byte code instructions with
|
||
groups of the form \mbox{$\langle I_1, \ldots, I_m, T_1, \ldots, T_l
|
||
\rangle, 0 \leq m \leq k, 1 \leq l \leq n$} where each of the $I$
|
||
instructions, if any, is either a \switchSTAR or a \jitiSTAR
|
||
instruction and the $T$ instructions are either a sequence of
|
||
\TryRetryTrust instructions (if $l > 1$) or a \jump instruction (if
|
||
\mbox{$l = 1$}). Step~2.2 dynamically constructs an index table $\cal
|
||
T$ whose buckets are the newly created interior nodes in the tree.
|
||
Each bucket associated with a single clause contains a \jump to the
|
||
label of that clause. Each bucket associated with many clauses starts
|
||
with the $I$ instructions which are yet to be visited and continues
|
||
with a \TryRetryTrust chain pointing to the clauses. When the index
|
||
construction is done, the instruction mutates to a \switchSTAR WAM
|
||
instruction.
|
||
%-------------------------------------------------------------------------
|
||
\begin{Algorithm}[t]
|
||
\caption{Actions of the abstract machine with \JITI}
|
||
\label{alg:construction}
|
||
\begin{enumerate}
|
||
\item if the current instruction $I$ is a \switchSTAR, \try, \retry,
|
||
\trust or \jump, the action is as in the WAM;
|
||
\item if the current instruction $I$ is a \jitiSTAR with arguments $r,
|
||
l$, and $k$ where $r$ is a register then
|
||
\begin{enumerate}
|
||
\item[2.1] if register $r$ contains a variable, the action is simply to
|
||
\instr{goto} the next instruction in the node;
|
||
\item[2.2] if register $r$ contains a value $v$, the action is to
|
||
dynamically construct the index as follows:
|
||
\begin{itemize}
|
||
\item[2.2.1] collect the subsequent instructions in a list $\cal I$
|
||
until the next instruction is a \try;\footnote{Note that there
|
||
will always be a \try following a \jitiSTAR instruction.}
|
||
\item[2.2.2] for each label $L$ in the \TryRetryTrust chain
|
||
inspect the code of the clause with label $L$ to find the
|
||
symbol~$c$ associated with register $r$ in the clause; (This
|
||
step creates a list of $\langle c, L \rangle$ pairs.)
|
||
\item[2.2.3] create an index table $\cal T$ out of these pairs as
|
||
follows:
|
||
\begin{itemize}
|
||
\item if $I$ is a \jitiONconstant or a \jitiONstructure then
|
||
create an index table for the symbols in the list of pairs;
|
||
each entry of the table is identified by a symbol $c$ and
|
||
contains:
|
||
\begin{itemize}
|
||
\item the instruction \jump $L_c$ if $L_c$ is the only label
|
||
associated with $c$;
|
||
\item the sequence of instructions obtained by appending to
|
||
$\cal I$ a \TryRetryTrust chain for the sequence of labels
|
||
$L'_1, \ldots, L'_l$ that are associated with $c$
|
||
\end{itemize}
|
||
\item if $I$ is a \jitiONterm then
|
||
\begin{itemize}
|
||
\item partition the sequence of labels $\cal L$ in the list
|
||
of pairs into sequences of labels ${\cal L}_c, {\cal L}_l$
|
||
and ${\cal L}_s$ for constants, lists and structures,
|
||
respectively;
|
||
\item for each of the four sequences ${\cal L}, {\cal L}_c,
|
||
{\cal L}_l, {\cal L}_s$ of labels create code as follows:
|
||
\begin{itemize}
|
||
\item the instruction \fail if the sequence is empty;
|
||
\item the instruction \jump $L$ if $L$ is the only label in
|
||
the sequence;
|
||
\item the sequence of instructions obtained by appending to
|
||
$\cal I$ a \TryRetryTrust chain for the current sequence
|
||
of labels;
|
||
\end{itemize}
|
||
\end{itemize}
|
||
\end{itemize}
|
||
\item[2.2.4] transform the \jitiSTAR $r, l, k$ instruction to
|
||
a \switchSTAR $r, l, {\cal T}$ instruction; and
|
||
\item[2.2.5] continue execution with this instruction.
|
||
\end{itemize}
|
||
\end{enumerate}
|
||
\end{enumerate}
|
||
\end{Algorithm}
|
||
%-------------------------------------------------------------------------
|
||
|
||
\paragraph*{Complexity properties.}
|
||
Index construction during runtime does not change the complexity of
|
||
query execution. First, note that each demanded index table will be
|
||
constructed at most once. Also, a \jitiSTAR instruction will be
|
||
encountered only in cases where execution would examine all clauses in
|
||
the \TryRetryTrust chain.\footnote{This statement is possibly not
|
||
valid in the presence of Prolog cuts.} The construction visits these
|
||
clauses \emph{once} and then creates the index table in time linear in
|
||
the number of clauses as one pass over the list of $\langle c, L
|
||
\rangle$ pairs suffices. After index construction, execution will
|
||
visit a subset of these clauses as the index table will be consulted.
|
||
%% Finally, note that the maximum number of \jitiSTAR instructions
|
||
%% that will be visited for each query is bounded by the maximum
|
||
%% number of index positions (symbols) in the clause heads of the
|
||
%% predicate.
|
||
Thus, in cases where \JITI is not effective, execution of a query will
|
||
at most double due to dynamic index construction. In fact, this worst
|
||
case is pessimistic and extremely unlikely in practice. On the other
|
||
hand, \JITI can change the complexity of query evaluation from $O(n)$
|
||
to $O(1)$ where $n$ is the number of clauses.
|
||
|
||
\subsection{More implementation choices}
|
||
%---------------------------------------
|
||
The observant reader has no doubt noticed that
|
||
Algorithm~\ref{alg:construction} provides multi-argument indexing but
|
||
only for the main functor symbol of arguments. For clauses with
|
||
compound terms that require indexing in their sub-terms we can either
|
||
employ a program transformation such as \emph{unification
|
||
factoring}~\cite{UnifFact@POPL-95} at compile time or modify the
|
||
algorithm to consider index positions inside compound terms. This is
|
||
relatively easy to do but requires support from the register allocator
|
||
(passing the sub-terms of compound terms in appropriate argument
|
||
registers) and/or a new set of instructions. Due to space limitations
|
||
we omit further details.
|
||
|
||
Algorithm~\ref{alg:construction} relies on a procedure that inspects
|
||
the code of a clause and collects the symbols associated with some
|
||
particular index position (step~2.2.2). If we are satisfied with
|
||
looking only at clause heads, this procedure needs to understand only
|
||
the structure of \instr{get} and \instr{unify} instructions. Thus, it
|
||
is easy to write. At the cost of increased implementation complexity,
|
||
this step can of course take into account other information that may
|
||
exist in the body of the clause (e.g., type tests such as
|
||
\code{var(X)}, \code{atom(X)}, aliasing constraints such as \code{X =
|
||
Y}, numeric constraints such as \code{X > 0}, etc).
|
||
|
||
A reasonable concern for \JITI is increased memory consumption during
|
||
runtime due to the creation of index tables. In our experience, this
|
||
does not seem to be a problem in practice since most applications do
|
||
not have demand for indexing on many argument combinations. In
|
||
applications where it does become a problem or when running in an
|
||
environment with limited memory, we can easily put a bound on the size
|
||
of index tables, either globally or for each predicate separately. For
|
||
example, the \jitiSTAR instructions can either become inactive when
|
||
this limit is reached, or better yet we can recover the space of some
|
||
tables. To do so, we can employ any standard recycling algorithm
|
||
(e.g., least recently used) and reclaim the memory of index tables
|
||
that are no longer in use. This is easy to do by reverting the
|
||
corresponding \switchSTAR instructions back to \jitiSTAR instructions.
|
||
If the indices are demanded again at a time when memory is available,
|
||
they can simply be regenerated.
|
||
|
||
|
||
\section{Demand-Driven Indexing of Dynamic Predicates} \label{sec:dynamic}
|
||
%=========================================================================
|
||
We have so far lived in the comfortable world of static predicates,
|
||
where the set of clauses to index is fixed and the compiler can take
|
||
advantage of this knowledge. Dynamic code introduces several
|
||
complications:
|
||
\begin{itemize}
|
||
\item We need mechanisms to update multiple indices when new clauses
|
||
are asserted or retracted. In particular, we need the ability to
|
||
expand and possibly shrink multiple code chunks after code updates.
|
||
\item We do not know a priori which are the best index positions and
|
||
cannot determine whether indexing on some arguments is avoidable.
|
||
\item Supporting the so-called logical update (LU) semantics of the
|
||
ISO Prolog standard becomes harder.
|
||
\end{itemize}
|
||
We will briefly discuss possible ways of addressing these issues.
|
||
However, we note that Prolog systems typically provide indexing for
|
||
dynamic predicates and thus already deal in some way or another with
|
||
these issues; \JITI makes the problems more involved but not
|
||
fundamentally different than those with only first argument indexing.
|
||
|
||
The first complication suggests that we should allocate memory for
|
||
dynamic indices in separate chunks, so that these can be expanded and
|
||
deallocated independently. Indeed, this is what we do.
|
||
%
|
||
Regarding the second complication, in the absence of any other
|
||
information, the only alternative is to generate indices for all
|
||
arguments. As optimizations, we can avoid indexing for predicates with
|
||
only one clause (these are often used to simulate global variables)
|
||
and we can exclude arguments where some clause has a variable.
|
||
|
||
Under logical update semantics calls to dynamic predicates execute in a
|
||
``snapshot'' of the corresponding predicate. In other words, each call
|
||
sees the clauses that existed at the time when the call was made, even if
|
||
some of the clauses were later deleted or new clauses were asserted.
|
||
If several calls are alive in the stack, several snapshots will be
|
||
alive at the same time. The standard solution to this problem is to
|
||
use time stamps to tell which clauses are \emph{live} for which calls.
|
||
%
|
||
This solution complicates freeing index tables because: (1) an index
|
||
table holds references to clauses, and (2) the table may be in use,
|
||
that is, it may be accessible from the execution stacks. An index
|
||
table thus is killed in several steps:
|
||
\begin{enumerate}
|
||
\item Detach the index table from the indexing tree.
|
||
\item Recursively \emph{kill} every child of the current table:
|
||
if the current table is killed, so are its children.
|
||
\item Wait until the table is not in use, that is, it is not pointed
|
||
to by anywhere.
|
||
\item Walk the table and release any references it may hold.
|
||
\item Physically recover space.
|
||
\end{enumerate}
|
||
%% It is interesting to observe that at the end of an \emph{itemset-node}
|
||
%% the emulator can remove references to the current index, hence freeing
|
||
%% the code it is currently executing. This happens on the last member of
|
||
%% the \emph{itemset-node}, so the emulator reads all the instruction's
|
||
%% arguments before executing the instruction.
|
||
|
||
|
||
\section{Implementation in XXX and in YAP} \label{sec:impl}
|
||
%==========================================================
|
||
The implementation of \JITI in XXX follows a variant of the scheme
|
||
presented in Sect.~\ref{sec:static}. The compiler uses heuristics to
|
||
determine the best argument to index on (i.e., this argument is not
|
||
necessarily the first) and employs \switchSTAR instructions for this
|
||
task. It also statically generates \jitiONconstant instructions for
|
||
other arguments that are good candidates for \JITI.
|
||
Currently, an argument is considered a good candidate if it has only
|
||
constants or only structure symbols in all clauses. Thus, XXX uses
|
||
only \jitiONconstant and \jitiONstructure instructions, never a
|
||
\jitiONterm. Also, XXX does not perform \JITI inside structure
|
||
symbols.\footnote{Instead, it prompts its user to request unification
|
||
factoring for predicates that look likely to benefit from indexing
|
||
inside compound terms. The user can then use the appropriate compiler
|
||
directive for these predicates.} For dynamic predicates, \JITI is
|
||
employed only if they consist of Datalog facts; if a clause which is
|
||
not a Datalog fact is asserted, all dynamically created index tables
|
||
for the predicate are simply removed and the \jitiONconstant
|
||
instruction becomes a \instr{noop}. All this is done automatically,
|
||
but the user can disable \JITI in compiled code using an appropriate
|
||
compiler option.
|
||
|
||
YAP implements \JITI since version 5. The current implementation
|
||
supports static code, dynamic code, and the internal database. It
|
||
differs from the algorithm presented in Sect.~\ref{sec:static} in that
|
||
\emph{all indexing code is generated on demand}. Thus, YAP cannot
|
||
assume that a \jitiSTAR instruction is followed by a \TryRetryTrust
|
||
chain. Instead, by default YAP has to search the whole predicate for
|
||
clauses that match the current position in the indexing code. Doing so
|
||
for every index expansion was found to be very inefficient for larger
|
||
relations: in such cases YAP will maintain a list of matching clauses
|
||
at each \jitiSTAR node. Indexing dynamic predicates in YAP follows
|
||
very much the same algorithm as static indexing: the key idea is that
|
||
most nodes in the index tree must be allocated separately so that they
|
||
can grow or shrink independently. YAP can index arguments where some
|
||
clauses have unconstrained variables, but only for static predicates,
|
||
as in dynamic code this would complicate support for logical update
|
||
semantics.
|
||
|
||
YAP uses the term JITI (Just-In-Time Indexing) to refer to \JITI. In
|
||
the next section we will take the liberty to use this term as a
|
||
convenient abbreviation.
|
||
|
||
\section{Performance Evaluation} \label{sec:perf}
|
||
%================================================
|
||
We evaluate \JITI on a set of benchmarks and applications.
|
||
Throughout, we compare performance of JITI with first argument
|
||
indexing. For the benchmarks of Sect.~\ref{sec:perf:ineffective}
|
||
and~\ref{sec:perf:effective} which involve both systems, we used a
|
||
2.4~GHz P4-based laptop with 512~MB of memory running Linux.
|
||
% and report times in milliseconds.
|
||
For the benchmarks of Sect.~\ref{sec:perf:ILP} which involve
|
||
YAP~5.1.2 only, we used a 8-node cluster, where each node is a
|
||
dual-core AMD~2600+ machine with 2GB of memory.
|
||
% and report times in seconds.
|
||
|
||
\subsection{Performance of \JITI when ineffective} \label{sec:perf:ineffective}
|
||
%------------------------------------------------------------------------------
|
||
In some programs, \JITI does not trigger\footnote{In XXX only; as
|
||
mentioned in Sect.~\ref{sec:impl} even 1st argument indexing is
|
||
generated on demand when JITI is used in YAP.} or might trigger but
|
||
have no effect other than an overhead due to runtime index
|
||
construction. We therefore wanted to measure this overhead.
|
||
%
|
||
As both systems support tabling, we decided to use tabling benchmarks
|
||
because they are small and easy to understand, and because they are a
|
||
bad case for JITI in the following sense: tabling avoids generating
|
||
repetitive queries and the benchmarks operate over extensional
|
||
database (EDB) predicates of size approximately equal to the size of
|
||
the program. We used \compress, a tabled program that solves a puzzle
|
||
from an ICLP Prolog programming competition. The other benchmarks are
|
||
different variants of tabled left, right and doubly recursive
|
||
transitive closure over an EDB predicate forming a chain of size shown
|
||
in Table~\ref{tab:ineffective} in parentheses. For each variant of
|
||
transitive closure, we issue two queries: one with mode
|
||
\code{(in,out)} and one with mode \code{(out,out)}.
|
||
%
|
||
For YAP, indices on the first argument and \TryRetryTrust chains are
|
||
built on all benchmarks under \JITI.
|
||
%
|
||
For XXX, \JITI triggers on no benchmark but the \jitiONconstant
|
||
instructions are executed for the three \bench{tc\_?\_oo} benchmarks.
|
||
%
|
||
As can be seen in Table~\ref{tab:ineffective}, \JITI, even when
|
||
ineffective, incurs a runtime overhead that is at the level of noise
|
||
and goes mostly unnoticed.
|
||
%
|
||
We also note that our aim here is \emph{not} to compare the two
|
||
systems, so the \textbf{YAP} and \textbf{XXX} columns should be read
|
||
separately.
|
||
|
||
\vspace*{-0.5em}
|
||
\subsection{Performance of \JITI when effective} \label{sec:perf:effective}
|
||
%--------------------------------------------------------------------------
|
||
On the other hand, when \JITI is effective, it can significantly
|
||
improve runtime performance. We use the following programs and
|
||
applications:
|
||
%% \TODO{For the journal version we should also add FSA benchmarks
|
||
%% (\bench{k963}, \bench{dg5} and \bench{tl3})}
|
||
%------------------------------------------------------------------------------
|
||
\begin{small}
|
||
\begin{description}
|
||
\item[\sgCyl] The same generation DB benchmark on a $24 \times 24
|
||
\times 2$ cylinder. We issue the open query.
|
||
\item[\muta] A computationally intensive application where most
|
||
predicates are defined intentionally.
|
||
\item[\pta] A tabled logic program implementing Andersen's points-to
|
||
analysis~\cite{anderson-phd}. A medium-sized imperative program is
|
||
encoded as a set of facts (about 16,000) and properties of interest
|
||
are encoded using rules. Program properties can then be determined
|
||
by checking the closure of these rules.
|
||
\item[\tea] Another analyzer using tabling to implement Andersen's
|
||
points-to analysis. The analyzed program, the \texttt{javac} SPEC
|
||
benchmark, is encoded in a file of 411,696 facts (62,759,581 bytes
|
||
in total). As its compilation exceeds the limits of the XXX compiler
|
||
(w/o JITI), we run this benchmark only in YAP.
|
||
\end{description}
|
||
\end{small}
|
||
%------------------------------------------------------------------------------
|
||
|
||
%------------------------------------------------------------------------------
|
||
\begin{table}[t]
|
||
\centering
|
||
\caption{Performance of some benchmarks with 1st vs. \JITI (times in msecs)}
|
||
\setlength{\tabcolsep}{2.5pt}
|
||
\subfigure[When JITI is ineffective]{
|
||
\label{tab:ineffective}
|
||
\begin{tabular}[b]{|l||r|r||r|r|} \hline
|
||
& \multicolumn{2}{|c||}{\bf YAP} & \multicolumn{2}{|c|}{\bf XXX} \\
|
||
\cline{2-5}
|
||
Benchmark & 1st & JITI & 1st & JITI \\
|
||
\hline
|
||
\tcLio (8000) & 13 & 14 & 4 & 4 \\
|
||
\tcRio (2000) & 1445 & 1469 & 614 & 615 \\
|
||
\tcDio ( 400) & 3208 & 3260 & 2338 & 2300 \\
|
||
\tcLoo (2000) & 3935 & 3987 & 2026 & 2105 \\
|
||
\tcRoo (2000) & 2841 & 2952 & 1502 & 1512 \\
|
||
\tcDoo ( 400) & 3735 & 3805 & 4976 & 4978 \\
|
||
\compress & 3614 & 3595 & 2875 & 2848 \\
|
||
\hline
|
||
\end{tabular}
|
||
}
|
||
\subfigure[When \JITI is effective]{
|
||
\label{tab:effective}
|
||
\begin{tabular}[b]{|l||r|r|r||r|r|r|} \hline
|
||
& \multicolumn{3}{|c||}{\bf YAP} & \multicolumn{3}{|c|}{\bf XXX} \\
|
||
\cline{2-7}
|
||
Benchmark & 1st & JITI &{\bf ratio}& 1st & JITI &{\bf ratio}\\
|
||
\hline
|
||
\sgCyl & 2,864 & 24 & $119\times$& 2,390 & 28 & $85\times$\\
|
||
\muta & 30,057 &16,782 &$1.79\times$&26,314 &21,574 &$1.22\times$\\
|
||
\pta & 5,131 & 188 & $27\times$& 4,442 & 279 & $16\times$\\
|
||
\tea &1,478,813 &54,616 & $27\times$& --- & --- & --- \\
|
||
\hline
|
||
\end{tabular}
|
||
}
|
||
\end{table}
|
||
%------------------------------------------------------------------------------
|
||
|
||
As can be seen in Table~\ref{tab:effective}, \JITI significantly
|
||
improves the performance of these applications. In \muta, which spends
|
||
most of its time in recursive predicates, the speed up is only $79\%$
|
||
in YAP and~$22\%$ in XXX. The remaining benchmarks execute several
|
||
times (from~$16$ up to~$119$) faster. It is important to realize that
|
||
\emph{these speedups are obtained automatically}, i.e., without any
|
||
programmer intervention or by using any compiler directives, in all
|
||
these applications.
|
||
|
||
We analyze the \sgCyl program that has the biggest speedup in both
|
||
systems and is the only one whose code is small enough to be shown.
|
||
With the open call to \texttt{same\_generation/2}, most work in this
|
||
benchmark consists of calling \texttt{cyl/2} facts in three different
|
||
modes: with both arguments unbound, with the first argument bound, or
|
||
with only the second argument bound. Demand-driven indexing improves
|
||
performance in the last case only, but this improvement makes a big
|
||
difference in this benchmark.
|
||
|
||
\begin{alltt}\small
|
||
same_generation(X,X) :- cyl(X,_).
|
||
same_generation(X,X) :- cyl(_,X).
|
||
same_generation(X,Y) :- cyl(X,Z), same_generation(Z,W), cyl(Y,W).\end{alltt}
|
||
|
||
%% Our experience with the indexing algorithm described here shows a
|
||
%% significant performance improvement over the previous indexing code in
|
||
%% our system. Quite often, this has allowed us to tackle applications
|
||
%% which previously would not have been feasible.
|
||
|
||
\subsection{Performance of \JITI on ILP applications} \label{sec:perf:ILP}
|
||
%-------------------------------------------------------------------------
|
||
The need for \JITI was originally noticed in inductive logic
|
||
programming applications. These applications tend to issue ad hoc
|
||
queries during execution and thus their indexing requirements cannot
|
||
be determined at compile time. On the other hand, they operate on lots
|
||
of data, so memory consumption is a reasonable concern. We evaluate
|
||
JITI's time and space performance on some learning tasks using the
|
||
Aleph system~\cite{ALEPH} and the datasets of
|
||
Fig.~\ref{fig:ilp:datasets} which issue simple queries in an
|
||
extensional database. Several of these datasets are standard in the
|
||
Machine Learning literature.
|
||
|
||
\paragraph*{Time performance.}
|
||
We compare times for 10 runs of the saturation/refinement cycle of the
|
||
ILP system; see Table~\ref{tab:ilp:time}.
|
||
%% The \Krki datasets have small search spaces and small databases, so
|
||
%% they achieve the same performance under both versions: there is no
|
||
%% slowdown.
|
||
The \Mesh and \Pyrimidines applications are the only ones that do not
|
||
benefit much from indexing in the database; they do benefit through
|
||
from indexing in the dynamic representation of the search space, as
|
||
their running times improve somewhat with \JITI.
|
||
|
||
The \BreastCancer and \GeneExpr applications use data in 1NF (i.e.,
|
||
unstructured data). The speedup here is mostly from multiple argument
|
||
indexing. \BreastCancer is particularly interesting. It consists of 40
|
||
binary relations with 65k elements each, where the first argument is
|
||
the key. We know that most calls have the first argument bound, hence
|
||
indexing was not expected to matter much. Instead, the results show
|
||
\JITI to improve running time by more than an order of magnitude. Like in
|
||
\sgCyl, this suggests that even a small percentage of badly indexed
|
||
calls can end up dominating runtime.
|
||
|
||
\IEProtein and \Thermolysin are example applications that manipulate
|
||
structured data. \IEProtein is the largest dataset we consider, and
|
||
indexing is absolutely critical. The speedup is not just impressive;
|
||
it is simply not possible to run the application in reasonable time
|
||
with only first argument indexing. \Thermolysin is smaller and
|
||
performs some computation per query, but even so, \JITI improves its
|
||
performance by an order of magnitude. The remaining benchmarks improve
|
||
from one to more than two orders of magnitude.
|
||
|
||
%------------------------------------------------------------------------------
|
||
\begin{table}[t]
|
||
\centering
|
||
\caption{Time and space performance of JITI
|
||
on Inductive Logic Programming datasets}
|
||
\label{tab:ilp}
|
||
\setlength{\tabcolsep}{3pt}
|
||
\subfigure[Time (in seconds)]{\label{tab:ilp:time}
|
||
\begin{tabular}{|l||r|r|r||} \hline
|
||
& \multicolumn{3}{|c||}{Time} \\
|
||
\cline{2-4}
|
||
Benchmark & 1st & JITI &{\bf ratio} \\
|
||
\hline
|
||
\BreastCancer & 1,450 & 88 & $16\times$ \\
|
||
\Carcino & 17,705 & 192 & $92\times$ \\
|
||
\Choline & 14,766 & 1,397 & $11\times$ \\
|
||
\GeneExpr & 193,283 & 7,483 & $26\times$ \\
|
||
\IEProtein & 1,677,146 & 2,909 & $577\times$ \\
|
||
%% \Krki & 0.3 & 0.3 & $1$ \\
|
||
%% \KrkiII & 1.3 & 1.3 & $1$ \\
|
||
\Mesh & 4 & 3 & $1.3\times$ \\
|
||
\Pyrimidines & 487,545 & 253,235 & $1.9\times$ \\
|
||
\Susi & 105,091 & 307 & $342\times$ \\
|
||
\Thermolysin & 50,279 & 5,213 & $10\times$ \\
|
||
\hline
|
||
\end{tabular}
|
||
}
|
||
\subfigure[Memory usage (in KB)]{\label{tab:ilp:memory}
|
||
\begin{tabular}{||r|r|r|r||} \hline
|
||
\multicolumn{2}{||c|}{Static code}
|
||
& \multicolumn{2}{|c||}{Dynamic code} \\
|
||
\hline
|
||
\multicolumn{1}{||c|}{Clauses} & \multicolumn{1}{c}{Index}
|
||
& \multicolumn{1}{|c|}{Clauses} & \multicolumn{1}{c||}{Index}\\
|
||
\hline
|
||
60,940 & 46,887 & 630 & 14 \\
|
||
1,801 & 2,678 & 13,512 & 942 \\
|
||
666 & 174 & 3,172 & 174 \\
|
||
46,726 & 22,629 & 116,463 & 9,015 \\
|
||
146,033 & 129,333 & 53,423 & 1,531 \\
|
||
%% 678 & 117 & 2,047 & 24 \\
|
||
%% 1,866 & 715 & 2,055 & 26 \\
|
||
802 & 161 & 2,149 & 109 \\
|
||
774 & 218 & 25,840 & 12,291 \\
|
||
5,007 & 2,509 & 4,497 & 759 \\
|
||
2,317 & 929 & 116,129 & 7,064 \\
|
||
\hline
|
||
\end{tabular}
|
||
}
|
||
\end{table}
|
||
%------------------------------------------------------------------------------
|
||
|
||
%------------------------------------------------------------------------------
|
||
\begin{figure}
|
||
\hrule \ \\[-2em]
|
||
\begin{description}
|
||
%% \item[\Krki] tries to learn rules from a small database of chess end-games;
|
||
\item[\GeneExpr] learns rules for yeast gene activity given a
|
||
database of genes, their interactions, and micro-array gene
|
||
expression data; %~\cite{Regulatory@ILP-06};
|
||
\item[\BreastCancer] processes real-life patient reports towards
|
||
predicting whether an abnormality may be
|
||
malignant; %~\cite{DavisBDPRCS@IJCAI-05-short};
|
||
\item[\IEProtein] processes information extraction from paper
|
||
abstracts to search proteins;
|
||
\item[\Susi] learns from shopping patterns;
|
||
\item[\Mesh] learns rules for finite-methods mesh design;
|
||
\item[\Carcino, \Choline, \Pyrimidines] try to predict chemical
|
||
properties of compounds and store them as tables, given their
|
||
chemical composition and major proprerties;
|
||
\item[\Thermolysin] also manipulates chemical compounds but learns
|
||
from the 3D-structure of a molecule's conformations.
|
||
\end{description}
|
||
\hrule
|
||
\caption{Description of the ILP datasets used in the performance
|
||
comparison of Table~\ref{tab:ilp}}
|
||
\label{fig:ilp:datasets}
|
||
\end{figure}
|
||
%------------------------------------------------------------------------------
|
||
|
||
\paragraph*{Space performance.}
|
||
Table~\ref{tab:ilp:memory} shows memory usage when using \JITI. The
|
||
table presents data obtained at a point near the end of execution;
|
||
memory usage should be at or close to the maximum. These applications
|
||
use a mixture of static and dynamic predicates and we show their
|
||
memory usage separately. On static predicates, memory usage varies
|
||
widely, from only 10\% to the worst case, \Carcino, where the index
|
||
tables take more space than the original program. Hash tables dominate
|
||
usage in \IEProtein and \Susi, whereas \TryRetryTrust chains dominate
|
||
in \BreastCancer. In most other cases no single component dominates
|
||
memory usage. Memory usage for dynamic data is shown in the last two
|
||
columns; note that dynamic data is mostly used to store the search
|
||
space. One can observe that there is a much lower overhead in this
|
||
case. A more detailed analysis shows that most space is occupied by
|
||
the hash tables and by internal nodes of the tree, and that relatively
|
||
little space is occupied by \TryRetryTrust chains, suggesting that
|
||
\JITI is behaving well in practice.
|
||
|
||
|
||
\section{Concluding Remarks}
|
||
%===========================
|
||
Motivated by the needs of applications in the areas of inductive
|
||
logic programming, program analysis, deductive databases, etc.\ to
|
||
access large datasets efficiently, we have described a novel but also
|
||
simple idea: \emph{indexing Prolog clauses on demand during program
|
||
execution}.
|
||
%
|
||
Given the impressive speedups this idea can provide for many LP
|
||
applications, we are a bit surprised similar techniques have not been
|
||
explored before. In general, Prolog systems have been reluctant to
|
||
perform code optimizations during runtime and our feeling is that LP
|
||
implementation has been left a bit behind. We hold that this
|
||
should change.
|
||
%
|
||
Indeed, we see \JITI as only a first, very successful, step towards
|
||
effective runtime optimization of logic programs.\footnote{The good
|
||
results obtained with JITI have motivated recent work on
|
||
Just-In-Time compilation of Prolog~\cite{yapc}.}
|
||
|
||
As presented, \JITI is a hybrid technique: index generation occurs
|
||
during runtime but is partly guided by the compiler, because we want
|
||
to combine it with compile-time WAM-style indexing. More flexible
|
||
schemes are of course possible. For example, index generation can be
|
||
fully dynamic (as in YAP), combined with user declarations, or driven
|
||
by static analysis to be even more selective or go beyond fixed-order
|
||
indexing.
|
||
%
|
||
Last, observe that \JITI fully respects Prolog semantics. Better
|
||
performance can be achieved in the context of one solution
|
||
computations, or in the context of tabling where order of clauses and
|
||
solutions does not matter and repeated solutions are discarded.
|
||
|
||
\paragraph{Acknowledgments}
|
||
|
||
This work is dedicated to the memory of our friend and colleague
|
||
Ricardo Lopes. We miss you! V\'{\i}tor Santos Costa was partially
|
||
supported by CNPq and would like to acknowledge support received while
|
||
visiting at UW-Madison and the support of the YAP user community.
|
||
This work has been partially supported by MYDDAS (POSC/EIA/59154/2004)
|
||
and by funds granted to LIACC through the Programa de Financiamento
|
||
Plurianual, Funda<64><61>o para a Ci<43>ncia e Tecnologia and Programa POSC.
|
||
|
||
%==============================================================================
|
||
\bibliographystyle{splncs}
|
||
\bibliography{lp}
|
||
%==============================================================================
|
||
|
||
\end{document}
|