David Cohn, Satinder Singh
Predictions oflifetimes of dynamically allocated objects can be used to improve time and space efficiency of dynamic memory manage(cid:173) ment in computer programs. Barrett and Zorn  used a simple lifetime predictor and demonstrated this improvement on a variety of computer programs. In this paper, we use decision trees to do lifetime prediction on the same programs and show significantly better prediction . Our method also has the advantage that during training we can use a large number of features and let the decision tree automatically choose the relevant subset.
INTELLIGENT MEMORY ALLOCATION
Dynamic memory allocation is used in many computer applications. The appli(cid:173) cation requests blocks of memory from the operating system or from a memory manager when needed and explicitly frees them up after use. Typically, all of these requests are handled in the same way, without any regard for how or for how long the requested block will be used. Sometimes programmers use runtime profiles to analyze the typical behavior of their program and write special purpose memory management routines specifically tuned to dominant classes of allocation events. Machine learning methods offer the opportunity to automate the process of tuning memory management systems.
In a recent study, Barrett and Zorn  used two allocators: a special allocator for objects that are short-lived, and a default allocator for everything else. They tried a simple prediction method on a number of public-domain , allocation-intensive programs and got mixed results on the lifetime prediction problem. Nevertheless, they showed that for all the cases where they were able to predict well, their strategy of assigning objects predicted to be short-lived to the special allocator led to savings
D. A. Cohn and S. Singh
in program running times. Their results imply that if we could predict well in all cases we could get similar savings for all programs. We concentrate on the lifetime prediction task in this paper and show that using axis-parallel decision trees does indeed lead to significantly better prediction on all the programs studied by Zorn and Grunwald and some others that we included. Another advantage of our approach is that we can use a large number of features about the allocation requests and let the decision tree decide on their relevance. There are a number of advantages of using lifetime predictions for intelligent mem(cid:173) ory management. It can improve CPU usage, by using special-purpose allocators, e.g., short-lived objects can be allocated in small spaces by incrementing a pointer and deallocated together when they are all dead. It can decrease memory fragmen(cid:173) tation, because the short-lived objects do not pollute the address space of long lived objects. Finally, it can improve program locality, and thus program speed, because the short-lived objects are all allocated in a small part of the heap.
The advantages of prediction must be weighed against the time required to examine each request and make that prediction about its intended use. It is frequently argued that, as computers and memory become faster and cheaper, we need to be less concerned about the speed and efficiency of machine learning algorithms. When the purpose of the algorithm is to save space and computation, however, these concerns are paramount.
1.1 RELATED WORK
Traditionally, memory management has been relegated to a single, general-purpose allocator. When performance is critical, software developers will frequently build a custom memory manager which they believe is tuned to optimize the performance of the program. Not only is this hand construction inefficient in terms of the pro(cid:173) gramming time required, this "optimization" may seriously degrade the program's performance if it does not accurately reflect the program's use [Wilson et al., 1995]. Customalloc [Grunwald and Zorn, 1992] monitors program runs on benchmark in(cid:173) puts to determine the most commonly requested block sizes. It then produces a set of memory allocation routines which are customized to efficiently allocate those block sizes. Other memory requests are still handled by a general purpose allocator.
Barrett and Zorn  studied lifetime prediction based on benchmark inputs. At each allocation request, the call graph (the list of nested procedure/function calls in effect at the time) and the object size was used to identify an allocation site. If all allocations from a particular site were short-lived on the benchmark inputs, their algorithm predicted that future allocations would also be short-lived. Their method produced mixed results at lifetime prediction, but demonstrated the savings that such predictions could bring.
In this paper, we discuss an approach to lifetime prediction which uses learned decision trees. In the next section, we first discuss the identification of relevant state features by a decision tree. Section 3 discusses in greater detail the problem of lifetime prediction. Section 4 describes the empirical results of applying this approach to several benchmark programs, and Section 5 discusses the implications of these results and directions for future work.
Predicting Lifetimes in Dynamically Allocated Memory
2 FEATURE SELECTION WITH A DECISION TREE
Barrett and Zorn 's approach captures state information in the form of the program's call graph at the time of an allocation request, which is recorded to a fixed pre(cid:173) determined depth. This graph, plus the request size, specifies an allocation "site"; statistics are gathered separately for each site. A drawback of this approach is that it forces a division for each distinct call graph, preventing generalization across ir(cid:173) relevant features. Computationally, it requires maintaining an explicit call graph (information that the program would not normally provide), as well as storing a potentially large table of call sites from which to make predictions. It also ignores other potentially useful information, such as the parameters of the functions on the call stack, and the contents of heap memory and the program registers at the time of the request.
Ideally, we would like to examine as much of the program state as possible at the time of each allocation request, and automatically extract those pieces of informa(cid:173) tion that best allow predicting how the requested block will be used. Decision tree algorithms are useful for this sort of task. A decision tree divides inputs on basis of how each input feature improves "purity" of the tree's leaves. Inputs that are statistically irrelevant for prediction are not used in any splits; the tree's final set of decisions examine only input features that improve its predictive performance.
Regardless of the parsimony of the final tree however, training a tree with the entire program state as a feature vector is computationally infeasible. In our experiments, detailed below, we arbitrarily used the top 20 words on the stack, along with the request size, as an approximate indicator of program state. On the target machine (a Sparcstation) , we found that including program registers in the feature set made no significant difference, and so dropped them from consideration for efficiency.
3 LIFETIME PREDICTION
The characteristic of memory requests that we would like to predict is the lifetime of the block - how long it will be before the requested memory is returned to the central pool. Accurate lifetime prediction lets one segregate memory into short(cid:173) term, long-term and permanent storage. To this end, we have used a decision tree learning algorithm to derive rules that distinguish "short-lived" and "permanent" allocations from the general pool of allocation requests.
For short-lived blocks, one can create a very simple and efficient allocation scheme [Barrett and Zorn, 1993]. For "permanent" blocks, allocation is also simple and cheap, because the allocator does not need to compute and store any of the infor(cid:173) mation that would normally be required to keep track of the block and return it to the pool when freed .
One complication is that of unequal loss for different types of incorrect predictions. An appropriately routed memory request may save dozens of instruction cycles, but an inappropriately routed one may cost hundreds. The cost in terms of memory may also be unequal: a short-lived block that is incorrectly predicted to be "per(cid:173) manent" will permanently tie up the space occupied by the block (if it is allocated via a method that can not be freed). A "permanent" block, however, that is in(cid:173) correctly predicted to be short-lived may pollute the allocator's short-term space by preventing a large segment of otherwise free memory from being reclaimed (see Barrett and Zorn for examples).
These risks translate into a time-space tradeoff that depends on the properties of
D. A. Cohn and S. Singh
the specific allocators used and the space limitations of the target machine. For our experiments, we arbitrarily defined false positives and false negatives to have equal loss, except where noted otherwise. Other cases may be handled by reweighting the splitting criterion, or by rebalancing the training inputs (as described in the following section).