# Coarse Grained SIMD Architecture Computer Science Essay

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The study of architectures for applications in which the nature of the computing evolves from fine grain parallelism (massive parallel SIMD highly pipelined computing) to coarse grain computing (MIMD computing). Although this phenomenon is apparent in many scientific computing problems, it is most evident in image processing, where the computing activity evolves from global filtering over the image, to operations only involving the structures in the image-objects, object features-, to operations only involving the measured attributes of the structures and their manual relations. This can be considered as an evolution of abstraction level, whereas each abstraction level works on different data-structures and has another granularity. Not to be confused with multi-resolution processing (pyramidal processing, e.g., split and merge techniques), where the processing takes place on another resolution of similar data in a similar data structure. Quite common are algorithms that use feedback from higher abstraction levels to lower abstraction levels, to adapt and control the performance of the lower levels. The author reports the investigation on new computational models and principles of computer architectures that smoothly support efficient processing on each of the granularity levels of an application's task. It proposes a mixed SIMD/MIMD architecture with an emphasis on the interface between these two paradigms. The use of the architecture is elucidated using the distance transform, a path search algorithm and region growing as application examples.

To understand the fundamental architecture, scalability and interconnection network of multiprocessor based computing platforms.

INTRODUCTION

Multiprocessors and parallel computers have made significant impact in high-end computer applications especially those requiring real-time processing. Various coarse-grained and fine-grained architectures with reference to SIMD and MIMD designs will also be studied. Case studies based on modern commercial as well as research machines such as Cray X and T series, IBM Blue Gene, Earth Simulator (Japan), MIT Alewife, Stanford FLASH etc. will also be discussed. The course format will be a mixture of lecture and discussions and will incorporate student research and presentations on advanced topics.

FPGAs (Field-Programmable Gate Arrays) have been widely used as coprocessors to boost the performance of data-intensive applications. However, there are several challenges to further boost FPGA performance: the communication overhead between the host workstation and the FPGAs can be substantial; large-scale applications cannot fit in a single FPGA because of its limited capacity; mapping an application algorithm to FPGAs still remains a daunting job in configurable system design. To circumvent these problems, we propose in this paper the FPGA-based Hierarchical-SIMD (H-SIMD) machine with its codesign of the Pyramidal Instruction Set Architecture (PISA). PISA comprises high-level instructions implemented as FPGA functions of coarse-grain SIMD (Single-Instruction, Multiple-Data) tasks to facilitate ease of program development, code portability across different H-SIMD implementations and high performance. Multiple FPGA chips can work in unison at a higher SIMD level, if needed, controlled by the host. Additionally, by using a memory switching scheme and the high-level PISA to partition applications into coarse-grain tasks, host-FPGA communication overheads can be hidden. We enlist the two-dimensional Fast Fourier Transform to test the effectiveness of H-SIMD. The test results show sustained high performance for this problem.

Keywords: configurable computing, FPGA, SIMD, parallel processing, memory switching, FFT, hardware-software codesign.

## Design and Implementation of a Rendering Algorithm in a SIMD Reconfigurable Architecture

We analyze a 3D image rendering algorithm and the different mapping schemes to implement

it in a SIMD reconfigurable architecture. 3D image render is highly computational and has an important restriction in execution time due to the requirement to get interactive results. We demonstrate that the execution of this algorithm in MorphoSys can take advantage of the available parallel resources, as well as of the possibility of one cycle configuration change. In this paper we show that it is possible to implement the rendering algorithm in our coarse grain reconfigurable architecture, obtaining values over 100 fps.

Reconfigurable architectures have had an important growth in the last years as academic as commercial level. The reconfigurable systems consist of a programmable hardware controlled by different control and configuration points, which decide the hardware functionality required in

each moment to execute different applications. The coarse grain reconfigurable architectures consist of a matrix with some functional units, which can work to word level instead of bit level, like FPGAs (fine grain). This granularity reduces the architecture area, consumed power, delays and configuration times compared with FPGAs. For more than one decade ago, different coarse grain reconfigurable architectures have appeared. Examples of those architectures are: Morphosys [4] targe architecture of this work; RAPID which uses linear arrays and it can be programmed through a high level language, like C. PACT XXP [6] including one AMBA bus as communication channel. REMARC which consists of one MIPS-II RISC processor and an 8x8 array, made with 16 bits nano-processors, each one of them with a little memory. All the nano-processors are connected to a global control unit. CHAMALEON architecture is made up of a reconfigurable unit, a programmable processor and in/out device. ADRES is a coarse grain reconfigurable

Architecture developed at IMEC. All these architectures have common characteristics as one cycle context changing, array of reconfigurable cells with a rich interconnectivity, on-chip data memory. All these features have been optimized to execute multimedia and signal processing applications.

In the last years, many multimedia interactive applications have been implemented in different platforms like cell phones or PDAs. Among the applications that are having bigger growth, we can find 3D image processing applications. They are present in games, museums or virtual shop. They process a large amount of data, and they have a strong computational work. Moreover, these applications have an important inherent parallelism that makes them perfect candidates for being executed in reconfigurable architectures. Particularly, renderization algorithm [9], it is one of the most used in many applications to represent in the screen (2D) the 3D target scene. This algorithm is usually implemented in PC graphic cards. Obtaining excellent results in execution time, but these cards are not frequently used to execute other kind of applications. However, the reconfigurable architectures have demonstrate that can executed many of the multimedia and DSP applications obtaining a competitive performance, as well as some graphic applications. Therefore, the coarse grain reconfigurable architectures are the perfect candidates to executed one of the most used algorithm in graphics, renderization, as this paper demonstrates.

The paper is organized as follow. Morphosys architecture where we implement the rendering algorithm.

## Morphosys

MorphoSys is a coarse grain reconfigurable architecture developing in the University of California, Irvine. Current demand on speed of multimedia applications execution makes MorphoSys reconfigurable architecture an interesting alternative.

## Figure: MorphoSys Architecture

Its architectural scheme is shown in Figure. The RC Array is the most important part of the reconfigurable module. It is composed by 64 reconfigurable cells, placed in 8 rows by 8 columns array. The RCs (Reconfigurable Cells) have a set of interconnections for communicating. The RC Array is divided into four 4x4 quadrants. Each cell is connected with four nearest neighbors in each quadrant and also with all the cells of its row and its column. There are interquadrant connections too. Each reconfigurable cell seems a data-path of a microprocessor. It has an ALU-multiplier, a shift unit of 32 bits, multiplexers that select ALU input, a register bank and a context register. The Context Memory (CM) stores the different configurations (contexts) that the architecture needs for executing the application. Then the cell in the same row or column share at one time the same context, it is a SIMD system but letting execution of different configurations in each row or columns at one time. This method lets to reduce the size of the context memory because it has to store one configuration for all the cells in the same column or row. It also reduces the time of loading contexts and the complexity of the interconnection network. Configuration load penalty is minimum because the contexts are stored in the CM, which is an internal memory. The context is loaded into the RC internal context registers in one cycle, which allows dynamic configuration. Furthermore, it is possible loading contexts into context memory at the same time that one configuration is executed in the RC Array.

The Frame Buffer (FB) is the internal memory of the reconfigurable module. It stores the application input data and results. The FB has two memory banks. This division lets loading output data to one bank at the same time the other bank loads data to reconfigurable cells without

increasing execution time. The DMA Controller controls traffic between main memory and Frame Buffer or Context Memory but it does not allow simultaneous transfers of data and contexts. TinyRISC is a 32 bits RISC processor that controls the system. It has an instructions set as a MIPS, adding control instructions of MorphoSys. TinyRISC loads contexts in the CM, loads data from main memory to the FB, stores Morphosys results into main memory, and controls the DMA and RC Array. It decides which configuration is executed at each time.

We have added another internal memory to the original MorphoSys model, the Z-buffer; it was designed for executing graphic applications. We store depth information of screen pixels into it. Data is structured as an array with the same number of rows and columns as the width and height of the screen. Each pixel is stored into Z-buffer only if it has lower depth than the stored pixels. So, we only store pixels of the visible objects, not of the hidden parts.

## Rendering algorithm

Rendering is the process of generating an image from a model. The model is a description of three dimensional objects; it would contain geometry, viewpoint, texture and lighting information. Then, rendering algorithm target is to project a 3D scene in a graphic device (2D). It is one of the major sub-topics of 3D computer graphics. In the 'graphics pipeline' it is the last major step, giving the final appearance to the models and animation. It has uses in: computer games, simulators, movies special effects, and design visualisation. Each one employs a different balance of features and techniques. As a product, a wide variety of renders are available. The rendering algorithm used in our work transforms a 3D scene made up of triangles in a 2D representation. The algorithm processes all the triangles in the scene, and it transforms their 3D points coordinates (vertex) in the corresponding projection coordinates, and these last coordinates are the screen pixels in the graphic device (Figure 2). The implemented rendering algorithm is the scan line rendering [9], it works on a point-by-point basis rather than polygon-by-polygon basis. Some point in a line is calculated, followed by successive points in the line. When the line is finished, rendering proceeds to the next line. This kind of algorithm can be easily integrated with the Phong reflection model and Z-buffer algorithm

## Figure. Parallel projection of one triangle

The rendering algorithm repeats the following steps for each triangle that compose the scene:

- It orders the triangles points (x0,y0,z0), (x1,y1,z1) and (x2,y2,z2), using the 'y' coordinate from smaller to bigger, in such a way that the A vertex correspond with the smallest 'y' value and the C vertex with the greatest one. It is done to make triangle filling easier.

-These vertexes are projected into the screen.

-Triangles pixels are drawn in two stages for each 'y' line of pixels. The algorithm calculates first the edge pixels of the line, these are the pixels of the lines AB, AC and BC. And later, the pixels in between these two edges are drawn.

- After drawn one line, the 'y' coordinate is increased by one, and the new edges are calculated. Later the pixels in between these two edges are also computed. The algorithm continues till drawn the whole triangle.

- The z value of each pixel, which is required for the depth test, is calculated through linear extrapolation from the z0, z1 and z2 vertex values. In order to facilitate the triangle edge calculation the render can divide the triangle into two sub-triangles. Firstly, the pixels between AB and AC are drawn until the 'y' coordinate is greater than the 'y' value for vertex B. Then, the algorithm draws the pixels between lines BC and AC. It is always possible to divide the triangle into two pieces because we have ordered the triangle vertex before they are drawn. In order to obtain an image with enough realism we apply to each pixel a Gouraud shading algorithm. We calculate the light intensity in each triangle vertex applying which is the intensity of diffused light given by Lambert's Law.

## Id = IiKdcosÎ±

Ii stands for the intensity of the light source, Î± is the angle between the surface normal and a line from the surface point to the light source (it varies between 0 and 90 degrees), and Kd is a constant between 0 and 1, which is an approximation to the diffuse reflectivity which depends on the nature of the material and the wavelength of the incident light. This equation can be also written as the dot product of two unit vector:

## Figure (a): filling pixels between AB and AC.

## (b): filling pixels between BC and AC.

## Id = IiKd(L·N)

Where N is the surface normal vector and L is the direction of vector from the light source to the point on the surface. We calculate this value for the three vertex of the triangle, and then, we realize a linear interpolation form this point to compute the light intensity in each pixel of that triangle. This method produces results with high quality in a reduced computation time. Finally, the algorithm checks the parts of the image visible, deleting the hidden ones. The 3D scene is composed by several objects, described as a set of triangles; some objects may occlude the others in the final 2D image. We use the Z-Buffer algorithm to compute the visible part of the image. In this case, the algorithm has to draw in the screen the lower depth pixels, those closer to the screen. The Z-Buffer is represented in a matrix structure, like screen pixels matrix. This matrix stores the 'z' value and the colour of the current pixel in the position 'x' and 'y', its coordinates. When a new triangle is rendered the new pixel colours and 'z' value is only stored if this new 'z' coordinate is smaller than the current 'z' in the 'x' and 'y' position of the Z-Buffer.

We have chosen a simple rendering algorithm, but it obtains, as experimental results demonstrate, a high quality images in an interactive execution time. Moreover, we will be able to add improvements incrementally, adding new rendering characteristic to the algorithm pipeline.

## Implementation Strategies

There are several possible implementation strategies for the rendering algorithm into MorphoSys. The strategy finally chosen must minimize the execution time. It can be achieved by minimizing the period of time in which the reconfigurable cells are idle and reducing the time wasted in data transfers not overlapped with computation. The rendering algorithm implemented was described in the section above. From that description and taking into account the MorphoSys architecture we must find the different macro-tasks (kernels) that compose it. We can transfers the existence of 4 different kernels. The 3D scene, described by triangles, is stored in the FB. The "Vertex Ordering" kernel orders the tree triangles vertex.

The "Edge Pixel" kernel finds the edge pixels of the corresponding triangle edges. The "z-buffer" kernel sends the pixels found to the z-buffer. This kernel has to send the pixels obtained by the "edge pixels" kernel and also by the "line pixels" kernel. The internal pixels are calculated by the "line pixel" kernel, which found one by one the pixels in the x-line between the two edges. When the algorithm ends one x-line, it has to calculate the new edges of the upper x-line. The control point 2 (Figure 4) checks if the last pixel founded is the last on the x-line. We also need a control point to check if the triangle is completely render (control point 1, Figure 4). Moreover, the final pixel colour, and all the environment effects can be added to the diagram flow after the edge and line pixels kernels.

## Figure: Flow Diagram of the Rendering Algorithm

The kernels' internal loops and if-then-else structures are easily solved by pseudo-branch contexts, which were previously used for mapping, for example, the ray-tracing algorithm. The problem appears when we try to mapping the control points 1 and 2 at Figure 4, in a SIMD reconfigurable architecture, as MorphoSys. For example, the control point 2 checks if all the pixels between the two edges of the line have been rendered. Then it is very likely that several reconfigurable cells have ended the line rendering process, while the others require render more pixels. In that case, the RCs that have ended that process are idle while the others are executing the loop, due to the SIMD execution model. In the other control point, control point 1, it checks if the triangle is completely render. The triangles sizes and positions are completely random, so in the most of the cases we would have a great number of RCs idle. The implementation finally chosen must minimize this effect.

## There several possible strategies:

- The first one implies the execution of one triangle in each RC. This means the parallel execution of 64 triangles of different sizes, with an important problem of coherence. Beside that, there is also a problem of memory bandwidth due to the triangles concurrent execution. The 64 cells are sending to the z-buffer 64 possible pixels at the same time that could address the same pixel in memory. This occurs when two cells obtain the same pixel but with different 'z' values (different depth).

- Other possible strategy involves the execution of one kernel per row (or column) of the RC Array, since MorphoSys can be configured per rows. It can be done if the different rows configurations are known at compilation time. This solution could be performed executing the first kernel in the first row, the second in the second one, and go on. An improvement of this solution would imply the usage of one column to perform the "z-buffer" kernel. We could map 2x8 rendering pipelines. However, the kernels have very different execution time, then the most part of the computation time is being spent in the execution of the "line pixels" kernel while the rest of the RC Array (6 rows of 8 RCs) is idle. Although we could think of use the idle rows to perform "line pixels", this is not possible because the position and color of the next pixel in the line is calculated through the current pixel.

- The vertex ordering allows us to execute each half of the triangle independently. Therefore, we can map half triangle in each RC. There are two differences between this solution and the first one which make it more suitable for MorphoSys. First, it only renders 32 triangles which make the possibility of differences among them lower. But, we are not increasing the execution time because ideally, as it processes half triangle, it takes half the time. Second in the first solution we should send pixels one by one to the z-buffer to avoid incoherencies. In this case we can send two pixels at times, because they belong to the same triangle, then they cannot address the same pixel in the screen, so the same address in the z-buffer.

However, there is still a problem with z-buffer kernel, because it still takes for the third strategy 32 cycles. During this time the 96% of the RCs are idle.

## The z-buffer bottleneck

From the above discussion is clearly that the transfer of pixels' data to the z-buffer is the application bottleneck. In this section we discuss the different approaches to reduce its effect.

One possible solution would imply the usage of one row of RCs to discriminate the different pixels. Each row of the architecture sends its corresponding pixels to this row, and it performs the z-buffer algorithm deleting those pixels that have the same position in the screen and greater depth. However, it is impracticable because the time required to check 56 pixels is huge compared with pixel kernels calculation. For example the "line pixels" kernel only takes 18 cycles. Then, there would be 7 rows the majority of the time idle. An improvement to this solution involves a kind of row sequential strategy. We propose to execute the whole algorithm in each row, keeping one row to execute the z-buffer kernel, but with several cycles delay for different rows. Therefore, the row dedicated to perform the z-buffer only has to compare 8 pixels at time. Even so, it takes at least 16 cycles. This solution is completely inefficient, above all because it takes more time than send one pixel a time to the z-buffer by the row that produce them, which takes 8 cycles. It is clear from the above discussion that a specific row for help the z-buffer is not required. Moreover, if we apply row sequential to the third strategy, the algorithm only takes 4 cycles per row to send the pixels, because the two pixels from the same triangle cannot belong to the same pixel, so they can be sent at a time.

## Different snapshots of the RC-Array for the execution

Therefore, the final strategy chosen is: execute the algorithm in rows sequentially, where each row also performs "z-buffer" kernel. The rows in white are idle; the rendering algorithm is executed over the first row, after the fourth cycle the rendering algorithm begins to be executed in the second row. 4 cycles later it begins to be executed in the third row and go on. Then after 'N' cycles, depends on the final render chosen, the first row send its pixels in four cycles (we call this the "z-buffer" kernel), and so, 'N+4' cycles later the second row send its pixels.

The previous solution has a problem depending on the" edge pixels" and "line pixels" execution times. It is because after these two kernels the "z-buffer" kernel is executed, then, it can occur that when one row is sending the pixels after the edge kernel other row, at the same time, is sending pixels after the line kernel. In order to avoid this situation we must add idle cycles to each row after the first execution of the z-buffer kernel. For our implementation we know that the idle cycles we should be five, but the algorithm dedicate 3 cycles to check the control point 1, so finally the rows are only two cycles idle. For example, in the Figure 6.a in the next cycle the "line pixels" kernel begins on row one. In the Figure 6.b in the next cycle the first row will begin to send the pixel, meanwhile in this cycle the last row is ending these transfers.

## Experimental Results

MorphoSys is designed to be running at 450MHz. It has 512x16 internal RC-RAM, 4x16Kx16 FB, 64Kx16 Z-buffer, 8x1Kx32 Context Memory, and 16 internal registers in each RC. The chip size is less than 30mm2 using 0.13um CMOS technology. Thus, MorphoSys is more power efficient than general-purpose processors.

The algorithm was translated into MorphoSys Assembly and then into machine code. The Simulation is run on MorphoSys processor simulator "Mulate" [4]. Table 1 shows the experimental results obtained with the different strategies over the example of (Stanford's bunny). These results demonstrate that the strategy with the lowest execution time is the third with the z-buffer optimization we have also rendered several images with different number of triangles. The largest one corresponds to Thorax and hip with more than one million of triangles, we obtain 79 fps as Table 2 shows. In the case of figures of lower number of triangles our implementation reaches more than 600 fps which demonstrate that interactivity is possible in MorphoSys. This also indicates that we can improve the rendering algorithm in order to obtain a better quality images because we have enough frame per second.

If we compare our results with commercial render architectures, we have obtained similar results in triangle per second. For example, "Chromium" [15], which is a cluster of 32x2 Pentium III render images a rate of 71 million of triangles per second; the NVIDIA GeForce FX 5200 [10], that is a standard graphic card, render images as a rate of 81 million of triangles per second. Moreover, MorphoSys architecture can also be used to implement a wide range of multimedia and DSP algorithms obtained competitive results.

## Image Triangles fps T/s

## Table 2. Frame per second (fps) and triangles per second (T/s) for different images.

We have demonstrated that is possible to get 3D image representations and interacting with them. Algorithm has been implemented against a coarse-grained reconfigurable hardware device with a SIMD execution model. In this implementation we have found all cells are doing useful job most part of the time. The render can be easily improved adding more realistic effects and keeping interactive results. At architectural level we could improve the use of z-buffer in the way of using a smaller size memory than screen pixels.