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The Potential of the Cell Broadband Engine for Data Mining

Gregory Buehrer

The Ohio State University Columbus, OH, USA

Srinivasan Parthasarathy

The Ohio State University Columbus, OH, USA

buehrer@cse.ohio-state.edu

srini@cse.ohio-state.edu

ABSTRACT

In this article we examine the performance of key data mining kernels on the STI Cell Broadband Engine architecture. This architecture represents an interesting design point along the spectrum of chipsets with multiple processing elements. The STI Cell has one main processor and eight support processing elements (SPEs), and while it represents a more general purpose architecture when compared to graphics processor units, memory management is explicit. Thus while it is easier to program than GPUs it is not as easy to program as current day dual and quad-core processors designed by AMD and Intel. We investigate the performance of three key kernels, namely clustering, classication, and outlier detection on the STI Cell along the axes of performance, programming complexity and algorithm designs. Specically, we formulate SIMD algorithms for these workloads and evaluate them in detail to determine both the benets of Cell processor, as well as its inherent bottlenecks. As part of our comparative analysis we juxtapose these algorithms with similar ones implemented on modern architectures including the Itanium, AMD Opteron and Pentium architectures. For the workloads we consider, the Cell processor is up to 34 times more ecient than competing technologies. An important outcome of the study, beyond the results on these particular algorithms, is that we answer several higher level questions designed explicitly to provide a fast and reliable estimate for how well other data mining workloads will scale on the Cell processor.

1.

INTRODUCTION

Every so often, humankind makes a leap in its ability to collect and store knowledge. From the carvings on pottery in 3500 BC, to Chinese paper in 100 AD, we have found that maintaining knowledge aids in the improvement and advancement of civilization. When this knowledge is lost, sociThis work is supported in part by NSF grants #CAREERIIS-0347662, #RI-CNS-0403342, and #NGS-CNS-0406386.

Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, to post on servers or to redistribute to lists, requires a fee and/or special permission from the publisher, ACM. VLDB '07, September 23-28, 2007, Vienna, Austria. Copyright 2007 VLDB Endowment, ACM 978-1-59593-649-3/07/09.

ety is set back considerably, at times for thousands of years. Take for example, the Roman Empire. Their engineering efforts produced such improvements as hydraulic cement and the grain reaper. During the Dark Ages, both inventions were lost. Farmers used a simple blade for nearly 2000 years, until the reaper was reinvented by an Irish-American inventor named Cyrus McCormick in 1834. In eorts to avoid losing knowledge, and also to gain a competitve edge, organizations collect and store large volumes of data. In fact, even a simple home PC may contain 500GB or more of data. In an eort to harness this information, organizations have turned to data mining. Data mining is the process of converting vast amounts of this information into insight or knowledge in a semi-automated fashion. A fundamental challenge is that the cost of extracting this information often grows exponentially with the size of the data. As data mining is an interactive process, short response times for querying and processing data sets is crucial. Researchers address long execution times along two avenues. First, the amount of computation can be pruned via cleverly short circuiting the search space, or via intelligent indices and other data structures. Second, algorithm designers restructure and tune computations to improve the utilization of the underlying hardware. As hardware designers adapt to the ever-challenging workloads present in modern computing, maintaining a high utilization of the hardware is quite dicult. For example, recent projects by the database community have leveraged the general purpose nature of newer graphics cards for the TeraSort[10] project. One such recent advancement in microprocessor design is chip multiprocessing (CMP). CMP designs exhibit multiple processing cores on one chip. CMPs arise in part because of the inherent challenges with increasing clock frequencies. The increase in processor frequencies over the past several years has required a signicant increase in voltage, which has increased power consumption and heat dissipation. In addition, increased frequencies require considerable extensions to instruction pipeline depths. Finally, since memory latency has not decreased proportionally to the increase in clock frequency, higher frequencies are often not benecial due to poor memory performance. By incorporating thread level parallelism, chip vendors can continue to improve IPC by exploiting parallelism without raising frequencies. As these low cost parallel chips become mainstream, designing data mining algorithms to leverage them becomes an important task. Current dual core chips include Intel's Pentium D, AMD's Opteron, and IBM's Power4. A joint venture

by Sony, Toshiba and IBM (STI) has produced a nine core architecture called the Cell BDEA. As a result of this advancement, parallel algorithm designs will become increasingly important, even for mainstream commodity applications, in order to realize performance that is commensurate with such emerging processors. The spectrum of emerging chipsets in this arena span different points on the design spectrum, ranging from graphics processor units on one end to commercial general purpose POSIX-style multicore CPUs from Intel, SUN and AMD. The Cell chip is of particular interest because of its high number of cores, its 200+ GFLOPs of compute power, and its 25GB/s o chip bandwidth. All three values represent breakthroughs in commodity processing. Cell is expected to be used in high end super computing systems1 as kernel accelerators. The layout of the Cell chip lies somewhere between other modern CMP chips and a high end GPU, since in some views the eight SPUs mimic pixel shader units. Unlike GPUs, however, the Cell can chain its processors in any order, or have them operate independently. Target applications include medical imaging, physical model simulation, and consumer HDTV equipment. While the Cell chip is quite new, several workloads seem quite amenable to its architecture. For example, high oating point workloads with streaming access patterns are of particular interest. These workloads could leverage the large oating point throughput. In addition, because their access pattern is known a priori, they can use software-managed caches for good bandwidth utilization. This work seeks to map several important data mining tasks onto the Cell, namely clustering, classication and outlier detection. These are three fundamental data mining tasks, often used independently or as precursors to solve multi-step data mining challenges. In addition, all three tasks have ecient solutions which leverage distance computations. Specically, we seek to make the following contributions to the community. Our rst goal is to pinpoint the bottlenecks in scalability and performance when mapping these workloads to this platform. We believe future streaming architectures could benet from this study as well. We port these three tasks to the Cell, and present the reader with a detailed study regarding their performance. More importantly, our second goal is to answer the following higher level questions for data mining applications. Can these applications leverage the Cell to eciently process large data sets? Specically, does the small local store prohibit mining large data sets? Will channel transfer time (bandwidth) limit scalability? If not, what is the greatest bottleneck? Which data mining workloads can leverage SIMD instructions for signicant performance gains? What metrics can a programmer use to quickly gage whether an algorithm is amenable to the Cell? At what cost to programming development are these gains aorded? The outline of this paper is as follows. Related work is presented in Section 2. A description of the Cell architecture is given in Section 3. A background on the workloads in

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question is presented in Section 4. In Section 5, we present our Cell formulations of these workloads. We empirically evaluate these approaches, and discuss our ndings in Sections 6 and 7. Finally, concluding remarks are presented in Section 8.

2. RELATED WORK

Several researchers have investigated improving the eciency of kMeans clustering [18]. Alsabti, Ranka and Singh[1] use geometry trees to reduce runtimes by lowering the number of distance calculations required. Pelleg and Moore[19] also employed a kd-tree in a similar fashion to improve the kMeans clustering algorithm. These techniques dene regions in n-dimensional space to cluster points. Then, all the points in a space can be assigned to a particular center. Subsequent assignment calculations essentially need only to verify the point lies within the bounding box. However, Weber and Zezula found that bounding trees do not scale well with increasing dimensions [22], failing completely with as little as 16 dimensions. They show that simple scans of the data set greatly outperform geometric meta structures such as bounding trees. Elkan [6] leverages a knowledge cache from previous iterations to lower execution times. Jin and Agrawal have several works targeted at solving parallel data mining workloads [13, 14] on both shared memory and distributed systems. They implement a framework called FREERIDE for fast prototyping of data mining workloads on shared memory systems. A focus of the work is on locking cost reduction, which does not appear to be the bottleneck for the platforms targeted in this work. k Nearest Neighbors [11] is used in many domains, such as biology [12], chemistry, nance, and is the basis for many machine learning techniques. Many researchers have investigated eciency improvements for kN N , we mention several of the most relevent [3, 20]. Wang and Wang [21] develop a multi-level approximation scheme to query for nearest neighbors in high dimensional data at remote sites. Liao, Lopez and Leutenegger [17] redistribute data points in a B-tree to improve execution times for nearest neighbor queries for high-dimensional data, but their results are approximate. Kulkarni and Orlandic [15] use clustering to aggregate points into regions, thus allowing the algorithm to prune unnecessary distance calculations. The method maintains exact neighbors. Zaki, Ho and Agrawal [25] parallelized decision tree construction for classication. It is not clear that their approach is readily portable to the Cell, since the construction process uses signicant main memory for the meta structures, and the SPUs have limited memory. Mining for outliers in high dimensional data has been of recent interest. ORCA [2] uses a threshold to prune distance calculations, and will be presented in Section 4. Chaudhary, Szalay, and Moore [4] use kd-trees to improve execution times when searching for outliers. Their approach is similar to those employed by Alsabti, Ranka and Singh when clustering with kMeans. Angiulli and Pizzuti dene a metric called weight to aid on nding outliers. They term weight as the sum of the distances to the top K nearest neighbors. This metric could be used in our algorithms without a signicant modication.

The IBM/DOE RoadRunner

Kunzman, et al [16] adapted their parallel runtime framework CHARM++, a parallel object-oriented C++ library, to provide portability between the Cell and other platforms. In particular, they proposed the Ooad API, a general-purpose API to prefetch data, encapsulate data, and peek into the work queue. Algorithm 1 kMeans Input: Dataset D Input: k, the number of centers Output: Each d ∈ D ← closest center c ∈ C 1: while true do 2: changed=0 3: for each data point di ∈ D do 4: assignedCenter = di .center 5: for each center cj ∈ C do 6: d = dist(di ,cj ) 7: if d < di .Center then 8: di .centerDistance = d 9: di .center = j 10: end if 11: end for 12: if di .center <> assignedCenter then 13: changed++ 14: end if 15: end for 16: for each center cj ∈ C do 17: cj = Mean of points i where ci =j 18: end for 19: if changed==0 then 20: break 21: end if 22: end while Several sorting algorithms leverage SIMD programming, and are relevant; we mention several here. Govindaraju et al developed an ecient SIMD sorting network for GPUs called TeraSort. It leverages the rasterization engine to execute bitonic sort. Zagha and Blelloch [24] developed a dataparallel SIMD version of Radix sort for the Y-MP. Furtak, Amaral and Niewiadomski [8] describe several methods to improve the performance of sorting networks using SIMD instructions. They describe a two-pass approach, which rst approximately sorts using SIMD registers, and then uses traditional sorting such as merge sort to complete the process. Among their results, they show that the branch reductions aorded by a competing one pass vector sort improves overall execution times signicantly. We are not aware of existing work which attempts to marry the Cell BDEA with data mining. Williams [23] et al investigate the performance of the Cell for scientic workloads. They nd that it provides a many-fold reduction in execution times when compared to other processors. In particular, they show speedups for GEMM, Fast Fourier Transform, and Stencil computations. They also suggest a data path modication to improve the computational throughput on double-precision workloads.

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

256K 50 GB/s SPE 3.2GHz 128 reg 25 GB/s

EIB 200 GB/s 25 GB/s PPE 3.2GHz 128 reg 50 GB/s 32K L1 Memory 50 GB/s 512K L2 25 GB/s M/C 25 GB/s

I/O C

25 GB/s 25 GB/s 35 GB/s

Figure 1: The layout and bandwidth of the Cell processor. tion 3 gaming console. The chip is also available in commercial blade servers through Mercury Computer Systems. Highly tauted, it was the winner of the Microprocessor Best Technology Award in 20042 . It is surmised by the high performance community that the Cell's commercial uses will allow it to be produced in sucient quantities so as to support a low price tag. This thought, in conjunction with the Cell's signicant oating point computational throughput and high o chip bandwidth, have led to discussion regarding utilizing the chip in large scale clusters. The architecture features one general-purpose processing element called the Power Processing Element (PPE) and eight support processors called Synergistic Processing Elements (SPEs). It is depicted in Figure 1. The PPE is a twoway SMT multithreaded Power 970 architecture compliant core, while all SPEs are single threaded. All processors are interconnected with a high-bandwidth ring network called the EIB. The Cell's design is one that favors bandwidth over latency, as the memory model does not include a hierarchical cache. In addition, it favors performance over programming simplicity. The memory model is software controlled. For example, all memory accesses must be performed by the programmer through DMA transfers calls, and the local cache at each SPE is managed explicitly by the programmer. Although this imparts a complexity on the programmer, it also aords the potential for very ecient bandwidth use, since each byte transferred is specically requested by user software. There is no separate instruction cache; the program shares the local store with the data. Also, software memory management lowers required on-chip hardware requirements, thus lowering power consumption. At 3.2 GHz, an SPE uses only 4 watts per core; as a comparison, a 1.4GHz Itanium consumes about 130 watts. Each SPE [7] contains an SPU and an SPF. The SPF consists of a DMA (direct memory access) controller, and an MMU (memory management unit) to interact with the common interconnect bus (EIB). Bandwidth from an SPE to the EIB is about 25GB/s, both upstream and downstream (see Figure 1). SPEs are SIMD, capable of operating on eight 16 bit operands in one instruction (or four 32 bit operands). The oating point unit supports multiplication and subsequent accumulation in one instruction, (spu madd()), which

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3.

THE CELL BROADBAND ENGINE

The Cell Broadband Engine Architecture [5] (Cell) was designed over a four year period primarily for the PlaySta-

http://www.power.org/news/besttechaward.pdf

can be issued every cycle (with a latency of 6 cycles). This equates to about 25 GFLOPs per SPE, or 200 GFLOPs for eight SPEs, a number far greater than competing commodity processors. Each SPU has a low-latency mailbox channel to the PPU which can send one word (32 bits) at a time and receive four words. SPEs have no branch predictors. All branching is predicted statically at compile time, and a misprediction requires about 20 cycles to load the new instruction stream. Finally, the SPE supports in-order instruction issue only. Thus, the programmer must provide sucient instruction level parallelism so that compile-time techniques can order instructions in a manner which minimizes pipeline stalls.

label of its k closest neighbors. In the worst case, the algorithm requires a distance calculation between each two data points. The method is considered lazy because a model is not built a priori; instead the training data is inspected only when a point is classied. In addition to avoiding model construction, kN N requires essentially no parameters and scales with data dimensionality. The data set is typically a collection of n-dimensional points, and the similarity measure is Euclidean distance. A sketch of the algorithm is presented as Algorithm 2.

4.3 Outlier Detection

Automatically detecting outliers in large data sets is a data mining task which has received signicant attention in recent years [2, 4, 9]. Outlier detection can be used to nd network intrusions, system alarm conditions, physical simulation defects, noise in data, and many other anomalies. The premise is that most data t well to a model, save a few points. These few points are then classied as outliers. As with classication, there are two common techniques, namely model-based approaches and distance-based methods. Model approaches build a model of the data, and then output data which does not t the model. Distance-based approaches dene a distance calculation, and label points without nearby neighbors as outliers. Also like classication, distance-based detections schemes are well received because model construction is avoided, which is often a bottleneck with high-dimensional data. Algorithm 2 kNearestNeighbors Input: Dataset D Input: k, number of neighbors Output: di ∈ D, di .neighbors = closest k points to di 1: for each data point di ∈ D do 2: di .neighbors = 3: for each data point dj ∈ D where di <> dj do 4: dis = dist(di ,dj ) 5: if |di .neighbors| < k then 6: di .neighbors = di .neighbors = ∪dj 7: else 8: if max(di .neighbors) > dis then 9: Remove farthest point in di .neighbors 10: di .neighbors = di .neighbors = ∪dj 11: end if 12: end if 13: di .class = class most seen in di .neighbors 14: end for 15: end for ORCA[2] is an ecient distance-based outlier detection algorithm developed by Bay and Schwabacher. It uses the nearest k neighbors as a basis for determining an outlier. The insight provided by ORCA is that once a point has k neighbors which are closer to it than the kth nearest neighbor of the weakest outlier, the point cannot be an outlier. Therefore, processing of the data point is terminated. To illustrate, consider the outliers in Table 1. This data represents the top 5 outliers, with the number of neighbors k = 4. Thus, an outlier is determined by the distance to his 4th neighbor. The weakest outlier is the outlier with the smallest 4th neighbor, in this case outlier 5. The threshold is then 255.1, since if any data point has four neighbors closer than 255.1, that point cannot be an outlier. Often times, k near

4.

DATA MINING WORKLOADS

In this section, we briey sketch the workloads under study.

4.1 Clustering

Clustering is a process by which data points are grouped together based on similarity. Objects assigned to the same group should have high similarity, and objects between groups should have low similarity. Clustering has many practical applications, such as species grouping in biology, grouping documents on the web, grouping commodities in nance and grouping molecules in chemistry. It is considered an unsupervised learning algorithm, since user input is minimal and classes or group labels need not be determined a priori. There are many dierent mechanisms by which objects of a data set can be clustered, such as distance-based clustering, divisive clustering, agglomerative clustering, and probabilistic clustering. kMeans [18] is a widely popular distancebased clustering algorithm, and is the chosen algorithm for our study. As its name implies, the kMeans algorithm uses the average of all the points assigned to a center to represent that center. The algorithm proceeds as follows. First, each data object is assigned to one of the k centers at random. In the second step, the centers are calculated by averaging the points assigned to them. Third, each point is checked against each center, to verify the point is assigned to the center closest to it. If any point required reassignment, the algorithm loops back to step two. The algorithm terminates when a scan of the data set yields no reassignments. A sketch is presented as Algorithm 1.

4.2 Classication

Classication is a common data mining task, whereby the label or class of a data object is predicted. For example, a classication algorithm may be used to predict whether a loan applicant should be approved or rejected. Classication is said to be supervised since classes are known and a training data set is provided, where each object in the set has been labeled with the appropriate class. There are many methods to predict labels. Examples include Bayesian networks, neural networks, nearest neighbors algorithms, and decision tree algorithms. Algorithm designers are faced with several challenges when designing these solutions, including noise reduction, the curse of dimensionality, and scalability with increasing data set size. One of the most widely used classiers is the k Nearest Neighbors algorithm (kN N ). kN N is said to work by analogy. A data object is classied by the most represented

Neighbors → Outlier 1 Outlier 2 Outlier 3 Outlier 4 Outlier 5

1st 147.6 342.2 100.0 87.2 31.0

2nd 151.2 387.5 131.4 89.8 151.2

3rd 179.1 409.9 219.1 107.3 179.1

4th 655.1 458.2 325.1 210.0 255.1

data transfer mechanism to move data from from main memory to the local store. Third, we must restructure the algorithm to leverage the Single Instruction Multiple Data (SIMD) intrinsics available. In this section, we detail these components.

5.1 KMeans on the Cell

Parallelization of kMeans is straightforward. We partition the data set (which resides in main memory) such that two conditions hold. First, the number of records assigned to each processor is as balanced as possible. Second, the start boundary of the each processor's segment is aligned on a 16 byte boundary 3 . This can be achieved by placing the rst record on a 16 byte boundary, and then verifying that the number of records assigned to a processor satises the constraint below. records dim sizeof (f loat) % 16 == 0 (2)

Table 1: An example set of outliers, where outlier 5 is the weakest. neighbors can be found by scanning just a small percentage of the data set. A sketch of the algorithm is provided as Algorithm 3. For all three workloads we implement the Euclidean distance as our similarity metric, which is a special case (p=2) of the Minkowski metric (given below). D2 (xi , xj ) = (∑d (xi,k xj,k )2 )1/2 k=1 (1)

In practice, since the square root function maintains the total order on positive reals, most implementations do not take the square root of the distance. Based on our ndings, we believe any distance calculation which touches every byte loaded will have similar results as those presented in Section 6. Algorithm 3 ORCA Input: Dataset D Input: n, number of outliers Input: k, number of neighbors Output: O = top n outliers 1: O = 2: Threshold = 0 3: for each data point di ∈ D do 4: di .N eighbors = 5: for each data point dj ∈ D where di <> dj do 6: d = dist(di ,dj ); 7: if d < max(O) or |di .N eighbors| < k then 8: di .neighbors = di .neighbors ∪ dj 9: end if 10: if |di .N eighbors| = k and max(di .N eighbors) > T hreshold then 11: break; 12: end if 13: if |O| < n then 14: O = O ∪ di 15: else 16: if minDistance(O) then 17: Remove weakest outlier from O 18: O = O ∪ di 19: end if 20: end if 21: end for 22: Threshold = kth value from weakest(O).neighbor 23: end for

We simply assign the processor an even share of records, and add a record until it is properly aligned. If after adding a user-dened threshold of additional records, it is still not 16 byte aligned, then we pad it with the necessary bytes. Ecient data transfer for kMeans is achieved by calculating a chunk size which results in landing on a record boundary, is a multiple of 16, and is about 6KB. At values below 6KB, the startup cost to retrieve the rst byte is not suciently amortized. The maximum DMA call permitted by the Cell is 16KB, but we found smaller values aorded better load balancing opportunities. This chunk size can be calculated by simple doubling as shown in Algorithm 4. Algorithm 4 SPU GetChunksize Input: M , the number of dimensions Output: chunkSize is properly aligned 1: int chunkSize=sizeof(oat)*M 2: int recordsToGet=1 3: while chunkSize < 4096 do 4: chunkSize*=2; 5: recordsToGet*=2; 6: end while Restructuring kMeans to allow for SIMD distance calculations can be achieved by a) calculating the distance to multiple centers at once, b) calculating the distance between a center and multiple data points at once, and c) calculating multiple dimensions at once. We make use of two intrinsics, namely v3 = spu sub(v1, v2) and v4 = spu madd(v1, v2, v3). The former subtracts each element of vector v1 from v2 and stores the result in v3. The latter multiples the elements of v1 to v2, adds the result to v3 and stores it in v4. This second instruction eectively executes 8 oating point operations in a single instruction, with a 6 cycle latency. The latency can be avoided by calculating multiple points. The strategy for calculating distances is shown in Algorithm 5. It is clear that the number of distance calculations in the inner loop can be expanded to improve throughput by further unrolling until each center in the chunk size is accommodated. In the case that the number of centers or dimensions is not modulo the largest desired block, a simple iterative halving ow of control is used to nish the calculation.

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5.

ALGORITHMS

Developing algorithms for the proposed workloads on the Cell requires three components. First we must parallelize the workload. This is direct, as at least two of the three workloads are members of the embarrassingly parallel class of data mining algorithms. Second, we require an ecient

The Cell's DMA controller requires 16-byte boundaries.

Note that these will have branching, which incurs a 20 cycle penalty. Fortunately, the intrinsic builtin expect(cond, 0) can be employed to avoid penalty in the common case. Note that the function spu extract(v, pos) extracts a scaler from vector v at position pos. The if /then constructs after the looping are replaced by spu sel() by the compiler, which removes simple branching. The SPUs send the number of reassigned data points back to the PPU through mailboxes. If any SPU reassigned a data point, the centers are recalculated and the SPUs are sent a message to perform another iteration; otherwise the SPUs are sent a message to terminate. The pseudo code for the kM eans is shown in Algorithms 6 and 7. An important issue when using the Cell is that any meta data which grows with the size of the data set cannot be stored locally. In the case of kM eans, the center assignment are an example of this type of data. The solution is to preallocate storage with each record when the data is read from disk. When each record is loaded from main memory to the SPU, the meta data is loaded as well, and when the record is purged from the SPU, the meta data is written to main memory with the record. This allows the algorithm to scale to large data sets.

Algorithm 6 kMeans PPU Input: Dataset D Input: P , the number of processors Input: k, the number of centers Output: Each d ∈ D ← closest center c ∈ C 1: Assign each d ∈ D a random center 2: Partition D among P SPUs 3: Spawn P SPU Threads 4: while true do 5: int changed=0 6: for each processor p do 7: changed += p.mailbox 8: end for 9: for each center cj ∈ C do 10: cj = Mean of points i where ci = j 11: end for 12: if changed==0 then 13: p ∈ P, p.mailbox ← 0 14: break; 15: else 16: p ∈ P, p.mailbox ← 1 17: end if 18: end while

Algorithm 5 AssignCenter Input: Data record with M dimensions Input: Centers C Output: record.center ← closest center c ∈ C 1: vector v1 = (vector oat*)record 2: for i=0 to |C| step 2 do 3: vector v2=(vector oat*)Center[i] 4: vector v3=(vector oat*)Center[i+1] 5: vector oat total,total2=0,0,0,0 6: for j = 0 to M/4 do 7: vector oat res= spu sub(v1[j],v2[j]) 8: vector oat res2= spu sub(v1[j],v2[j]) 9: total = spu madd(res,res,total) 10: total2 = spu madd(res2,res2,total2) 11: end for 12: if builtin expect(M % 4<>0,0) then 13: int k=j 14: for j = 0 to M % 4 do 15: oat val1=(record[k*4+j]-center[i][k*4+j]) 16: total +=val1*val1 17: oat val2=(record[k*4+j]-center[i+1][k*4+j]) 18: total2 +=val2*val2 19: end for 20: end if 21: oat distance = spu extract(total,0) + ... (total,4) 22: oat distance2 = spu extract(total2,0) + ... (total2,4) 23: if distance < record.centerDistance then 24: record.center=i 25: record.centerDistance=distance 26: end if 27: if distance2 < record.centerDistance then 28: record.center=i+1 29: record.centerDistance=distance2 30: end if 31: end for

Algorithm 7 KMeans SPU Input: Dataset D, Address A Input: M ,the number of dimensions Input: k, the number of centers Output: Each d ∈ D ← closest center c ∈ C 1: GetChunksize(Dp , I, K) 2: message=1 3: totalData = |D| 4: while message==1 do 5: Load centers C into local store via DMA call(s) 6: while totalData > 0 do 7: Load data Da into local store via DMA call 8: totalData = totalData - recordsToGet 9: for each data point dj ∈ Da do 10: assignedCenter = di .Center 11: AssignCenter(dj ,C) 12: if di .Center <> assignedCenter then 13: Changed++; 14: end if 15: end for 16: end while 17: p.mailBox ← changed 18: message ← p.mailbox 19: end while

5.2 kNN on the Cell

The main dierence in construction between kM eans and kN N is that with kM eans two streams are required4 . The rst stream is the test data set (the data to be labeled) and the second stream is the training data set (the prelabeled data). The same chunk size is used for both streams, and is calculated with Algorithm 4. However, the record size is the dimensionality of the data plus k, where k is the number of neighbors to store. This allocation allows the SPU to store

4 If the centers in kMeans do not t in the local store, then both algorithms use two streams.

the IDs of the neighbors with the record, and limit local meta data. This can be doubled if the user requires the actual distances as well; otherwise only one array of size k is kept on the local store to maintain this information and is cleared after each data point completes. This is a fundamental point when data mining on the Cell, which is to say that meta data must be stored with the record, to allow the Cell's SPUs to process large data. Synchronization only occurs at the completion of the algorithm. Pseudo code for kN N has been omitted due to space constraints.

5.3 ORCA on the Cell

The ORCA construction is also similar to that of kM eans. ORCA presents an additional challenge, however, because the eectiveness of computation pruning is a function of the threshold value. Without eective pruning, the algorithm grows in average case complexity from O(nlgn) to O(n2 ). )As the threshold increases, more pruning occurs. Partitioning the data set evenly may result in an uneven outlier distribution among the SPUs, thus the computation time per SPU becomes unbalanced. We can correct this by sharing local outliers between SPUs periodically. The strategy is to synchronize often early in the computation, and less frequently later in the computation. In the early stages, each data point has a higher probability to increase the threshold, since the set of outliers is incomplete. Recall that the threshold is the neighbor in the weakest outlier with the greatest distance. With all the SPUs maintaining separate outlier tables, their thresholds will vary. In most cases the thresholds will all be dierent, with the largest threshold being the best pruner. However, if all the SPUs share their data, the new threshold is most likely larger than any single SPU's current threshold. This is because the top ve outliers from all the sets of outliers (one from each SPU) are the true outliers. Therefore, frequent synchronization early in the computation will support sifting these outliers to the top. Partitioning the data set proceeds as it did for the previous two workloads. However, the chunk size initially is set at the rst record size satisfying Equation 2 greater than 512 bytes. Each successive data movement is increased, until a chunk size of about 4K is reached, which is optimal. As we will see in Section 6, chunk sizes larger than 4K result in a greater number of distance calculations. At each synchronization point, each SPU writes its outliers to main memory. The synchronization is initiated by each SPU writing 1 to its mailbox to the PPU. When all SPUs have written to their mailboxes, the PPU then takes the top n outliers from these eight sets and copies them back to main memory. When the SPUs start the next chunk, they also load the new outlier list, and with it the maximum threshold. When an SPU is nished with its portion of the data set, it writes a 0 to its mailbox. The algorithm terminates when all SPUs have written 0 to their mailboxes.

vides the programmer with only six SPUs, as one is unavailable (rumored to be for improved yield) and another is dedicated to the game console's security features. It houses 256MB of main memory, of which about 175MB is available. Performance-level simulation data, such as cycle counts, was provided by the IBM Full System Simulator (Mambo), available in the IBM Cell SDK 5 . Data was synthetically generated (32 bit oats). This allowed us to vary the number of data points, number of training points, dimensionality, and the number of outliers. Results on representative real data sets for the target applications are very similar to the corresponding synthetic data sets in our study. As a comparison, we provide execution times for other processors as well, as shown in Table 2. Therefore, a few notes on these implementations. First, the only other multithreaded implementation is that for Intel's PentiumD processor, which has two processing cores. All other implementations were on single chip processors and use only one thread. Compiler ags had a large impact on performance, which is a topic in its own right. These implementations were compiled with a variety of dierent ags, and the best performing binaries are reported. For example, the Itanium performed best with icc -f ast, and for the Xeon processor, the best performance was found with icc -xW which vectorized the code. In interesting cases, we provide two runtimes, one for Intel's compiler (icc) and another for the public gcc compiler (at least -O3 ag). We also experimented with providing the PPU with work, which in principle is comparable to adding another SPU. Speedups were the same as adding an additional SPU. The columns of Tables 4, 7 and 8 are as follows. The rst column lists the trial number. The next four columns (ve for kN N and ORCA) are input parameters, as shown in the headings. Each data point is an array of 32 bit oats. Columns 6-11 are the cycle statistics of the SPUs as a results of executing the program on the IBM simulator. Column 6 displays the Cycles required Per Instruction (CPI). Column 7 shows the percentage of the time that a single instruction is issued. Recall that the Cell SPU has two pipelines. Column 8 shows the percentage of the cycles that an instruction is issued on both pipelines. If this column were 100%, then all other columns would be 0% and the eective CPI would be 0.5, which is optimal. Columns 9-11 display the reason that there is not 100% double issue. Thus, columns 7-11 should sum to 100%. Branch stalls are due to branch mispredictions. Dependency stalls are due to a variety of reasons, for these workloads the common case is to stall on FP6, the oating point unit. This typically suggests that an instruction is waiting on the result of the previous instruction. Another common case is to stall waiting on a load instruction, which requires six cycles and moves the data from the local store to a register. Channel stalls are cycles lost waiting on DMA calls to load data chunks to the local store. Finally, the last column represents real execution time on the PS3.

6.

EVALUATION

In this section we present a detailed evaluation of the proposed workloads and their optimizations on the Cell processor.

6.2 Instruction Mix

The instruction mixes for each workload are presented in Table 3. From our description of these workloads, it is clear that the distance calculation dominates execution times, which is expected. Recall that our data sets are 32-bit oats, and the Cell executes on 128-bit registers. For many

5

6.1 Experimental Setup

We execute the programs on a Playstation3 gaming console with Fedora Core 5 (PPC) installed. The PS3 pro-

http://www-128.ibm.com/developerworks/power/cell/

Processor Itanium 2 (g) Itanium 2 (i) Xeon (g) Xeon (i) Opteron 250 Pentium D Pentium D 2 Cell SPU Cell 6 SPU Cell 8 SPU (sim)

Watts 130 130 110 110 89 95 95 4 24 32

MHz 1400 1400 2400 2400 2400 2800 2800 3200 3200 3200

Threads 1 1 1 1 1 1 2 1 6 8

Compiler gcc icc gcc icc gcc icc icc IBM SDK 2 IBM SDK 2 IBM SDK 2

Processor Itanium 2 g Itanium 2 i Xeon g Xeon i Opteron 250 Pentium D Pentium D 2 Cell SPU Cell 6 SPU Cell 8 SPU (sim)

Time (sec) 66 29 31 12 19 16 9 7.4 1.25 0.95

Slowdown 51 22 24 10 15 13 7 5.9 – –

Table 2: Processors used for the evaluation. kMeans 35% 17% 24% 10% 11% 3% kNN 34% 13% 26% 11% 9% 5% ORCA 31% 23% 17% 13% 6% 9%

Table 5: kMeans execution time comparison for various processors.

FP ALU SHIFT LD/ST LOGICAL BRANCH

Table 3: Instruction mixes for the Cell processor implementations. oating point operations, this equates to 4 ops per instruction. However, about 30% of our operations are spu madd() instructions, which multiply and add four 32-bit values in a single instruction. Therefore, although only 35% of the instructions are oating point, in actuality this is closer to 65% of the eective operations in a non-vectorized implementation. ORCA has the largest number of branch instructions at 9%. This is primarily because the threshold may eliminate the need for a distance calculation for a given point, and force the loop to terminate prematurely. Both ORCA and kNN have more branching than kMeans because the nearest neighbors are stored in a sorted array, which inherently adds branching. All three workloads have a signicant amount of loads and stores, which are required to bring the data from the local store to a register. Load and store instructions have a six cycle latency (not accounting for the channel costs to bring data chunks into the local store).

6.3 kMeans

The cycle statistics for kMeans is presented in Table 4 for various parameters. We xed all trials to execute 30 iterations, to ease in comparisons. Interestingly, each iteration has the exact same statistics, since the computation is xed and the SPU's mechanics are deterministic (no dynamic branch prediction, no cache eects, in-order issue, etc.). From Table 4, we can see that only when the number of centers is very low is there any appreciable channel delay. Thus for kMeans it can be concluded that moving data to and from the local store is not the bottleneck. In fact, most of the slowdown with the rst trials is not due to the channel, but because the number of dimensions is suciently low to stall the pipeline on loop boundaries. This can be addressed with vector pipelining, albeit painstakingly so. Also, it would likely require padding, depending on the dimensionality of the data. Rather than use the memory space

(the PS3 only has 256MB) we chose to use looping. As seen, when the number of dimensions increases, the SIMD instructions can be issued in succession, improving CPI (and FLOPs). For example, trial 1 uses 2 dimensions and has a CPI of 2.0. Trial 5 increases the dimensions to 40, and the resulting CPI drops to 1.21. Double issue rates rise from 9% to 20%. Our initial implementation did not use SIMD instructions, and the CPI was quite low. Since each oating point instruction performed only one operation, each loop in the distance calculation used many instructions, and the issue rate was high. After SIMD instructions were used, the CPI increased, but execution execution times lowered. The scalability is healthy from 1 to 6 SPUs. For example, in trials 13 and 14, one SPU required 13.97 seconds and 6 SPUs required 2.38 seconds, for a speedup of 5.86. This near 6-fold speedup when moving from 1 to 6 SPUs is consistent in the other trials as well. Varying data set size behaved as expected, namely that twice as many points required about twice as much time (given the number of centers was far smaller than the number of data points). A nal point to mention is that CPI and other statistics was generally xed for a set of input parameters, regardless of the number of SPUs used. This is because, as long as there are sucient data points to ll one DMA load, and the channel contention is low, the SPUs will be performing independently. Table 5 illustrates the performance advantage of the Cell executing kM eans as compared to other commodity processors. The parameters were DataPoints=200K, Dimensions=60, and Centers=24. The second best performance was aorded by the PentiumD, which is also a CMP. Because we do not have access to a real 8 core Cell, the slowdown column uses only our 6 core PS3 execution times.

6.4 kNN

The cycle statistics for kNN are provided in Table 7 for varying parameters. As with kMeans, kN N does not exhibit channel latency issues. Also, it can be seen that scalability is near linear. For example at 10 neighbors and 80 dimensions (trials 5 and 6), the execution time is reduced from 12.29 to 2.06 seconds, a 5.95-fold reduction when moving from 1 SPU to 6 SPUs. Also, in trials 2 and 6, the CPI is reduced from 1.53 to 1.02 when the workload rises from 10 neighbors and 12 dimensions to 10 neighbors and 80 dimensions. A larger number of dimensions results in longer record vectors, thus allowing more SIMD instructions per loop. Increasing the number of neighbors degrades performance. This can be seen between the rst trial and the third trial,

Trial Centers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 10 10 10 10 10 10 20 20 20 20 40 40 40 40 40 40

Input Dimensions 2 2 10 10 40 40 40 40 100 100 100 100 100 100 100 100

Data Points 200000 200000 200000 200000 200000 200000 200000 200000 200000 200000 100000 100000 200000 200000 400000 400000

SPUs 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6

CPI 2.00 2.00 1.32 1.32 1.21 1.21 1.17 1.18 1.16 1.16 1.05 1.05 1.05 1.05 1.05 1.05

% Single Issue 32 33 40 40 42 41 43 43 44 44 49 49 49 49 48 49

% Dble Issue 9 9 18 18 20 20 21 20 21 21 23 23 23 23 23 22

Output % Branch % Dep. Stalls Stalls 16 40 17 38 18 20 18 19 14 24 14 25 13 23 13 23 7 28 7 27 5 23 5 23 5 23 5 23 5 24 5 23

%Channel Stalls 0 3 0 1 0 1 0 1 0 1 0 0 0 0 0 1

Exec. Time(sec) 1.17 0.20 2.18 0.37 3.49 0.77 4.87 0.84 8.91 1.54 6.98 1.19 13.9 2.38 28.1 4.97

Table 4: Statistics for Kmeans on the Cell processor. Processor Itanium 2 g Itanium 2 i Xeon g Xeon i Opteron 250 Pentium D Pentium D (2) Cell SPU Cell 6 SPU Cell 8 SPU (sim) Time (sec) 24 9.46 9.44 8.02 6.79 8.7 4.64 1.65 0.28 0.21 Slowdown 86 34 34 28 24 31 16 5.9 – – Processor Itanium 2 g Itanium 2 i Xeon g Xeon i Opteron 250 Pentium D Pentium D Cell SPU Cell 6 SPU Cell 8 SPU (sim) Time (sec) 138 148 147 128 131 126 71 46 7.1 5.3 Slowdown 19 21 21 18 18 18 10 6.5 – –

Table 6: Execution time comparison for various processors running K nearest neighbors.

Table 9: Execution time comparison for various processors running ORCA.

where every parameter is held constant except for the number of neighbors, which is increased from 10 to 100. The subsequent CPI drops from 1.53 to 1.75, and branch stalls increase from 14% to 18%. Whenever a point dj is found to be closer to the point being processed di , dj must be added to di 's neighbor list. This requires removing the weakest neighbor from the list and inserting dj in sorted order. A larger neighbor list requires more search time, because a point is more likely to be a neighbor, and because adding that neighbor will be more costly. Recall that each (statically) mispredicted branch is a 20 cycle penalty. An execution time comparison for kN N is provided in Table 6. The parameters were TrainingPoints=20K, TestPoints=2K, Dimensions=24, and Neighbors=10. As was the case with kM eans, the PentiumD's two execution cores afford it the second lowest execution times.

in trials 2 and 8. The dimensions is increased from 12 to 60, but the execution time only increases 21%. The increased dimensions improve the CPI. While the CPI only drops from 1.47 to 1.28, we point out that each additional FP instruction executes approximately 6 operations, and these operations are only 31% of the workload. Doubling the data set size from 100K to 200K requires 2.5-fold longer running times. This not surprising, since the worst case performance of the underlying algorithm is O(n2 ). The execution times for running ORCA on the Cell are compared with the other processors in Table 9. The parameters are DataPoints=200K, Dimensions=32, Outliers=10, and Neighbor=40. The PentiumD is competitive, as the increased branching degrades the Cell's performance. Still, the Cell is several times quicker than the others, at least 6.5 times faster than the PentiumD.

6.5 ORCA

The cycle statistics for ORCA, collected from the simulator, are presented in Table 8. As with the previous two workloads, scalability from 1 to 6 SPUs is excellent. The CPI clearly drops when the number of neighbors increases, because we have more branch misprediction due to inserting and sorting into a longer neighbor list. Branch stalls increase from 12% to 24% when increasing the neighbor list from 10 to 100 (trials 1 and 3). This also occurred with kN N . The algorithm handles increasing dimensions well, as seen

6.6 Channel Stalls

If a signicant amount of an algorithm's time is spent waiting for data transfers, the potential speedup of multiple execution threads may not be realized. In this experiment, we vary the data transfer size from 64 bytes to 8192 bytes for ORCA, in an eort to gain insight on channel stalls on a real machine, since our earlier channel stall data was given by the simulator. All values for this experiment are taken from trials on the PS3, and all trials use six SPUs to maximize DMA contention. Recall that the exact chunk size must be a) a multiple

Trial Neighbors (k) 10 10 100 100 10 10 10 10 10 10 Dim 12 12 12 12 80 80 80 80 80 80

1 2 3 4 5 6 7 8 9 10

Input Train Points 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000

Test Points 1000 1000 1000 1000 1000 1000 2000 2000 5000 5000

SPUs 1 6 1 6 1 6 1 6 1 6

CPI 1.53 1.53 1.75 1.69 0.99 1.02 1.00 1.00 0.99 0.99

% Single Issue 41 41 39 39 49 48 48 49 48 48

% Dble Issue 12 12 9 10 26 25 26 25 27 27

Output % Branch % Dep. Stalls Stalls 14 32 14 33 18 33 17 33 4 21 5 22 6 20 4 22 5 20 4 21

%Channel Stalls 0 0 0 0 0 0 0 0 0 0

Exec. Time(sec) 3.05 0.51 3.78 0.59 12.29 2.06 24.58 4.11 61.5 10.56

Table 7: Statistics for k Nearest Neighbors on the Cell processor.

Trial Neighbors (k) 10 10 100 100 10 10 10 10 10 10 10 10 Dim. 12 12 12 12 24 24 60 60 60 60 24 24 Input Outliers 10 10 10 10 10 10 10 10 10 10 100 100 Data Points 100000 100000 100000 100000 100000 100000 100000 100000 200000 200000 100000 100000 SPUs 1 6 1 6 1 6 1 6 1 6 1 6 CPI 1.40 1.47 1.96 1.94 1.36 1.38 1.28 1.28 1.27 1.27 1.36 1.38 % Single Issue 49 48 35 36 53 52 59 59 59 60 53 52 % Dble Issue 11 10 8 8 10 10 9 9 9 9 10 10 Output % Branch % Dep. Stalls Stalls 12 28 12 27 24 22 23 22 10 27 11 27 6 26 6 25 6 25 5 26 10 27 9 28 %Channel Stalls 0 0 0 0 0 0 0 1 0 1 0 1 Exec. Time(sec) 15.8 2.69 65.31 11.39 15.36 2.56 19.36 3.28 48.26 8.21 28.2 4.77

1 2 3 4 5 6 7 8 9 10 11 12

Table 8: Statistics for ORCA on the Cell processor. of 16 bytes, and b) on a record boundary. Thus for this experiment we let a record be four single precision oats. The size of the data set is 80,000 records, the number of centers, neighbors and outliers are 10. As can be seen in Table 10, very small chunk sizes degrade performance signicantly. However, at 64 bytes, only approximately 50% of the slowdown is attributed to cycles waiting on the channel load to complete. The balance is due to a) the decrease in SIMD parallelization (only a few calculations can be vectorized at once) and the increased number of instructions to set up channel transfers. Although in our previous experiments transfer sizes were about 6K, this experiment shows that if they are suciently small, channel stalls can be rather costly. The break in the curve occurs with transfers of at least 256 bytes. At this value, the number of DMA loads required to process the data set dropped from 175 million to only 9.6 million, and the cost of each transfer only increased from 1216 cycles to 1504 cycles. The end execution time dropped from 28 seconds to 4.31 seconds. The lowest execution time occurs at a transfer size of 4096 bytes. The reason is that transfers larger than 4096 have only a marginal improvement in transfer time per byte, but incur a signicant increase in the number of computations made. Recall that each synchronization allows SPUs to share their largest outliers and threshold values. These synchronizations generally increase the average threshold at the SPUs and aord improved pruning. Also we note that the cycles stalls per byte continually decreases as the size of the transfer is increased. eciently process large data sets? The answer for the applications considered is yes. The small local store of the SPU did not pose a practical limitation. In most cases, only two buers were needed, each of which was the size of an ecient data transfer (near 6KB). Only with kMeans did we use more than 15KB, since the full set of centers was kept on the SPU. Note that even here we could have avoided this extra buer space – see for example our approach with kNearest Neighbors. Basically, the O(n2 ) comparisons among the centers and the loaded points amortize the data loads to a suciently inexpensive cost. The overall insight here is that any meta data associated with a record can be inlined with that record, and moved to main memory when the record is ejected from the local store. For example, calculating k neighbors for D records requires k D 4 bytes. With low dimensional data, the number of records a DMA call can transfer becomes signicant, and the local storage to maintain the k neighbors locally becomes the storage bottleneck. By simply inlining the k neighbors with the record, this storage requirement is mitigated (at the cost of lower cross-computational throughput per transfer). However, the local store size may be of greater concern with very large programs, since the instruction store and data store are shared. Will channel transfer time (bandwidth) limit scalability? If not, what is the greatest bottleneck? From our experience (not just limited to this study), workloads which touch every loaded byte require less execution time on the Cell than on competing processors, regardless of the oating point computation requirements. For many data mining applications, this will be the case. Several studies, including one by Williams et al [23] recommend double buering to reduce channel delays. For our workloads the channel stall times were relatively nominal when compared to other issues, such as branch and dependency stalls. For

7.

DISCUSSION

In this section, we revisit the questions posed in the Section 1. Can data mining applications leverage the Cell to

Bytes Execution time (sec) DMA Loads (Millions) Calculations (Millions) Cycles per DMA Load Channel wait time (sec)

64 28.2 175 216 1216 11.1

128 13.7 78 218 1332 5.01

256 4.31 29 222 1483 1.89

512 2.78 9.6 226 1504 0.64

1024 1.82 3.3 228 1950 0.26

2048 1.45 1.0 243 2130 0.11

4096 1.20 0.36 264 3960 0.07

8192 1.40 0.10 303 7550 0.04

Table 10: Channel costs as a function of data chunk size for 6 SPEs. example, from Table 4 we can see that in kM eans only 10 centers and 2 dimensions was sucient to reduce channel stalls to 3% of the cycle time. As a test, we implemented a simple GetM ax() program, which sifts through an array for the largest value. It was three times faster on the Cell than on the Xeon, with no special buering or SIMD instructions. The lost time waiting on channel stalls was overcome by the fact that each SPU only searched 1/8th the data. As shown in Tables 4, 7 and 8, branching is a signicant bottleneck. From our experience, it is a penalty which can be dicult to avoid. Using select() instructions will only remove the simplest cases. Dependency stalls appear high as well, but these costs can be lowered with additional loop unrolling and SIMD vectorization, and in fact were more than twice as high before we unrolled the outer loops. Branching is a natural programming concept and is used frequently. Eliminating branches, particularly when each ow of control requires complex operations, is not trivial and often cannot be amortized. For example, in our simple merge sort algorithm, up to 20% of the stall time was due to branching. In another test application, we implemented merge sort. We found it to be almost twice as fast as any other processor in our study, without using SIMD instructions. The Cell's benet was the multiple concurrent cores. However, branching stalls were quite high. Also, the nal merge was done such that each successive stage used only have the processors, with the last merge performed by the PPU. We are in the process of improving its performance, a topic for future work. Which data mining workloads can leverage SIMD instructions for signicant performance gains? Any distance-based algorithm has the potential for signicant gains. This work targets data mining workloads which are, in some senses, the best case for the Cell. An algorithm designer can leverage the Cell's high GFLOP throughput to churn the extensive oating point calculations of these workloads. Also, the predictable nature of the access patterns (namely streaming) allow for large data transfers, where each byte in the transfer will be used in an operation. In these situations, the Cell can be extremely ecient. In many trials, our results from the Cell's real execution times via the PS3 exhibit many-fold GFLOP improvements over the theoretical maximums for all other processors in this study. This is due to the 25+ GFLOPs aorded by each SPU. We are currently designing pattern mining algorithms for the Cell, which do not have distance calculations. Our initial ndings suggest that these algorithms also stand to benet, primarily due to the additional threads of program control. What metrics can a programmer use to quickly gauge whether an algorithm is amenable to the Cell? There are two questions to pose when evaluating the applicability of the Cell to workload. First, is the access pattern predictable? If so, then it is likely that chunks of data can be transferred to an SPU and most of those chunks will be involved in a computation. Second, is the workload parallelizable? In our experience, this question is often easily answered. Data mining applications in particular exhibit signicant data-level parallelism, since it is common that each data object must be inspected. At what cost to programming development are these gains aorded? Parallel programming is challenging, regardless of the target platform. For someone with parallel programming experience, the programming model aorded by the Cell is somewhat more dicult than conventional CMPs, such as Intel's PentiumD processors. The programmer must explicitly move data to and from main memory as necessary. However, after about a month of programming the Cell, we did not nd this cumbersome. Several sources compare the Cell processor to GPGPUs. Both own multiple small processing elements which can be pipelined, both support SIMD instructions, and both require explicit data movement by the programmer. However, the Cell supports a very typical programming environment. The programmer uses everyday C functions, such as malloc(), and spawns threads in the same manner as traditional pthread models. An added benet of choosing the Cell as a development platform is that the Mambo Simulator is quite useful when tuning implementations. It provides cycle-level accuracy for the SPUs, and allows one to step through assembly level executions a cycle at a time. The programmer clearly sees which instruction stall the pipelines. In this regard, while prototype-level programs are unnaturally dicult to implement, highly ecient implementations may in fact be easier. A natural future direction then is to develop a framework which allows the programmer to specify data mining computations in a higher level language for fast prototyping. We are currently investigating such a platform.

8. CONCLUSION

In this work, we design and develop data mining algorithms and strategies for the Cell BDEA. Specically, we illustrate that clustering, classication, and outlier detection can leverage the available bandwidth and oating point throughput to experience many-fold execution time reductions, when compared with similar codes on other commodity processors. In addition, we provide insight into the nature of a larger class of algorithms which can be executed eciently on such a CMP platform. We believe that the ndings in this eort are applicable to other domains which are considering the Cell processor as well. The structure of the general purpose CPU is in state of marked reconstruction, and future algorithm designers must consider these new platforms to see maximum utilization. As part of ongoing and future work, we are investigating data mining algorithms which make use of complex pointerbased meta structures. Our initial experience suggests that

such algorithm would be rather cumbersome, and not overly ecient if implemented on the Cell. The local store does not have sucient space to store the tree, which would require excessive transfers. Our observations in this study imply it is unlikely these transfers would be ecient.

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