52c4cfb18f
git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@1814 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
876 lines
42 KiB
TeX
876 lines
42 KiB
TeX
%==============================================================================
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\documentclass{llncs}
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%------------------------------------------------------------------------------
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\usepackage{a4wide}
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\usepackage{float}
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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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\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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\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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\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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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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\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 been both a blessing and a curse for
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Prolog systems. Its ingenious design has allowed implementors to get
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byte code compilers with decent performance --- it is not a fluke that
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most Prolog systems are still based on the WAM. On the other hand,
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\emph{because} the WAM gives good performance in many cases,
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implementors have felt reluctant to explore alternatives that
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drastically depart from its basic philosophy.
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%
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For example, first argument indexing makes sense for many Prolog
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applications. For applications accessing large databases though is
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clearly sub-optimal; for long time now, the database community has
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recognized that good indexing mechanisms are 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. However,
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this alternative is often unattractive because it may drastically
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increase the size of the generated byte code unnecessarily. Static
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analysis techniques 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) they are inapplicable or grossly inaccurate. Another
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alternative, which has not been investigated so far, is to do flexible
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indexing on demand during program execution.
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This is precisely what we advocate in this paper. More specifically,
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we present a minimal 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. In our
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experience these schemes pay off. We have implemented \JITI in two
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different Prolog systems (Yap and XXX) and have obtained non-trivial
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speedups, ranging from a few percent to orders of magnitude, across a
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wide range of applications. Given these results, we see very little
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reason for Prolog systems not to incorporate some form of indexing
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based on actual demand from queries. In fact, we see \JITI as only the
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first step towards effective runtime 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, and discuss their implementation in two Prolog systems and
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the performance benefits they bring (Sect.~\ref{sec:perf}). The paper
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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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Even nowadays, some Prolog systems are still influenced by the WAM and
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only support indexing on the main functor symbol of the first
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argument. Some others, like YAP~\cite{YAP}, can look inside compound
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terms. 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 like
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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 in general we disagree with their
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conclusion because they underestimate the benefits of indexing on
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large datasets. 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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like 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 like 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 like 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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big demands for effective indexing since they need to efficiently
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access big datasets and on the other they are very 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 Prolog 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 providing effective indexing
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during runtime. Naturally, we will base our technique on the existing
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support for indexing that the WAM provides, but we will extend this
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support with the technique of \JITI that we describe in the next
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sections.
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%\begin{itemize}
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%\item Just-In-Time and dynamic compilation techniques (VITOR, IS THERE
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% ANYTHING FOR PROLOG?)
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%\end{itemize}
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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 performs a sequential backtracking search of
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the clauses using a \TryRetryTrust chain of instructions. The \try
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instruction sets up a choice point, the \retry instructions (if any)
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update 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 we will not consider them here. This is not a
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problem since the above scheme handles all cases. Also, we will feel
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free to do some minor modifications and optimizations when this
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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 well-known 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 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 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 will index ($r_1$). The 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 $L_1$ \\
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\retry $L_2$ \\
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\retry $L_3$ \\
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\retry $L_4$ \\
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\trust $L_5$ \\
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\\
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\begin{tabular}[b]{r|c@{\ }|l|}
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\Cline
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$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
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\ & d1 & \try $L_1$ \\
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\ & & \trust $L_2$ \\ \Cline
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\ & d2 & \try $L_3$ \\
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\ & & \trust $L_4$ \\ \Cline
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\ & d3 & \jump $L_5$ \\
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\Cline
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\end{tabular}
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\subfigure[Code for the clauses\label{fig:carc:clauses}]{%
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\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}[b]{rl}
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$L_1$: & \getcon $r_1$ d1 \\
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\ & \getcon $r_2$ salmonella \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_2$: & \getcon $r_1$ d1 \\
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\ & \getcon $r_2$ salmonella\_n \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_3$: & \getcon $r_1$ d2 \\
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\ & \getcon $r_2$ salmonella \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_4$: & \getcon $r_1$ d2 \\
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\ & \getcon $r_2$ cytogen\_ca \\
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\ & \getcon $r_3$ n \\
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\ & \proceed \\
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$L_5$: & \getcon $r_1$ d3 \\
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\ & \getcon $r_2$ cytogen\_ca \\
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\ & \getcon $r_3$ p \\
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\ & \proceed
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\subfigure[Any arg indexing\label{fig:carc:jiti_single:before}]{%
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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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\jitiONconstant $r_2$ 5 3 \\
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\jitiONconstant $r_3$ 5 3 \\
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\try $L_1$ \\
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\retry $L_2$ \\
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\retry $L_3$ \\
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\retry $L_4$ \\
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\trust $L_5$ \\
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\\
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\begin{tabular}[b]{r|c@{\ }|l|}
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\Cline
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$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
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\ & \code{d1} & \try $L_1$ \\
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\ & & \trust $L_2$ \\ \Cline
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\ & \code{d2} & \try $L_3$ \\
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\ & & \trust $L_4$ \\ \Cline
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\ & \code{d3} & \jump $L_5$ \\
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\Cline
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\end{tabular}
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\caption{Part of the Carcinogenesis dataset and WAM code that a byte
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code compiler generates}
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\label{fig:carc}
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\end{figure}
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%------------------------------------------------------------------------------
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\section{Demand-Driven Indexing of Static Predicates} \label{sec:static}
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%=======================================================================
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For static predicates the compiler has complete information about all
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clauses and shapes of their head arguments. It is both desirable and
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possible to take advantage of this information at compile time and so
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we treat the case of static predicates separately.
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%
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We will do so with schemes of increasing effectiveness and
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implementation complexity.
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\subsection{A simple WAM extension for any argument indexing}
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%------------------------------------------------------------
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Let us initially consider the case where the predicates to index
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consist only of Datalog facts. This is commonly the case for all
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extensional database predicates where indexing is most effective and
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called for.
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Refer to the example in Fig.~\ref{fig:carc}.
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%
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The indexing code of Fig.~\ref{fig:carc:index} incurs a small cost for
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a call where the first argument is a variable (namely, executing the
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\switchONconstant instruction) but the instruction pays off for calls
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where the first argument is bound. On the other hand, for calls where
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the first argument is a free variable and some other argument is
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bound, a choice point will be created, the \TryRetryTrust chain will
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be used, and execution will go through the code of all clauses. This
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is clearly inefficient, more so for larger data sets.
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%
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We can do much better with the relatively simple scheme shown in
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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 will
|
|
scan the WAM code of the clauses and create 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.
|
|
Also, 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 will get transformed to a
|
|
\switchONconstant. Again this is straightforward because of the two
|
|
instructions have similar layouts in memory. Execution of the
|
|
abstract machine will continue 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, even 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.
|
|
|
|
\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 (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 an argument 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 arguments 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, we 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
|
|
instruction 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 an 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.}
|
|
Complexity-wise, dynamic index construction does not add any overhead
|
|
to program 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 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. One pass over the list of $\langle c, L
|
|
\rangle$ pairs suffices. After index construction, execution will
|
|
visit only 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 extremely unlikely in practice. On the other hand, \JITI can
|
|
change the complexity of evaluating a predicate call 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 like \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 only needs to understand
|
|
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 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 all argument combinations. In applications where it
|
|
becomes a problem or when running in an environment where memory is
|
|
limited, we can easily put a bound on the size of index tables, either
|
|
globally or for each predicate separately. 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 space for some tables that are no longer in use. This is easy to
|
|
do by reverting the corresponding \jitiSTAR instructions back to
|
|
\switchSTAR instructions. If the indices are needed again, they can
|
|
simply be regenerated.
|
|
|
|
|
|
\section{Demand-Driven Indexing of Dynamic Predicates} \label{sec:dynamic}
|
|
%=========================================================================
|
|
|
|
|
|
\section{Performance Evaluation} \label{sec:perf}
|
|
%================================================
|
|
|
|
|
|
\section{Concluding Remarks}
|
|
%===========================
|
|
\begin{itemize}
|
|
\item Mention the non-trivial speedups in actual applications; also
|
|
that it is important to realize that certain applications have ad
|
|
hoc query patterns (e.g., ILP) are not amenable to static analyses
|
|
\end{itemize}
|
|
|
|
%==============================================================================
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|
\bibliographystyle{splncs}
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|
\bibliography{lp}
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|
%==============================================================================
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|
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|
\end{document}
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