# Parallell Processing Systems1 Chapter 4 Vector Processors.

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Parallell Processing Systems1 Chapter 4 Vector Processors

Parallell Processing Systems2 Introduction  Typical operations on array-oriented data  One or more vectors ==> a scalar result  two vectors ==> a vector  a scalar and a vector ==> a vector  a combination of the above three operations

Parallell Processing Systems3 Introduction(continued)  Three architectures suitable for the vector processing environments  pipelined vector processors  parallel array processors  systolic array architectures

Parallell Processing Systems4 Introduction (continued)  Pipelined vector processors  They utilize one or more pipelined ALUs to achieve high computation throughput.  Parallel array processors  They adopt a multiplicity of CPUs that operate on elements of arrays in parallel.  Systolic array architectures  They use extensive pipelining and parallel processing.

Parallell Processing Systems5 Introductions(continued)  Vector processors are supercomputers optimized for fast execution of long groups of vectorizable scientific code.  Vector processors are extensively pipelined architectures designed to operate on array-oriented data.

Parallell Processing Systems6 4.1 Vector Processor Models  Figure 4.1 shows a vector computational model.  Start-up time: the number of clock cycles required prior to the generation of the first result.  The time to complete N-element vector operation in a pipeline Start-up time + (N-1) X Initiation rate

Parallell Processing Systems7 4.1 Vector Processor Models (continued)  Note that the start-up time adds a considerable overhead for small value of N and the effect of start-up time is negligible for large value of N.  Example 4.1

Parallell Processing Systems8 4.1 Vector Processor Models (continued)  Memory-Oriented Vector Processor (Figure 4.2) versus Register-Oriented Vector Processor (Figure 4.3)  The characteristics of vector processors contributing to the high performance  High-speed memory  A large number of registers  Instruction set  Multiplicity of overlapped processing levels

Parallell Processing Systems9 4.2 Memory Design Considerations  Memory bandwidth  the average number of words that can be accessed from the memory per second.  Memory bandwidth must match the demand of multiple pipelined vector processors.  Memory system configuration  the number of memory modules  bus width  addressing decoding structure

Parallell Processing Systems10 4.2 Memory Design Considerations(cont.)  Memory module characteristics  Size  Access time  Cycle time

Parallell Processing Systems11 Example 4.2  Consider a vector processor with four 32-bit floating point processors, each requiring two 32- bit operands every clock cycle and producing one 32-bit result. Assume that one 32-bit instruction is fetched for each arithmetic operation.  Total traffic per cycle?  If the memory cycle time is 1.28  s and the processor cycle time is 40 ns, how can we match the demand?

Parallell Processing Systems12 4.2 Memory Design Considerations(con.)  How to match the demand rate between memory system and processors.  Configuring with multiple memory modules allowing simultaneous access (Figure 4.4)  Inserting fast intermediate memories.

Parallell Processing Systems13 Example 4.3  C i = A i + B i, 1  i  N  Figure 4.5 shows the data structure in a memory system with 8 modules.  Figure 4.6 shows the reservation table for the addition using a 3-stage pipelined adder and memory with 8 modules.  1 delay on A

Parallell Processing Systems14 Example 4.4  An architecture with a 6-modules memory, 3-stage pipelined adder, memory access time equivalent to two processor cycle times.  Figure 4.7 shows the reservation table.  3 delays in A  3 delays on output

Parallell Processing Systems15 Example 4.5  C[I] = A[I] + b[I], 1  I  N Assume N=64 and vector register length =64 The time unit for floating point addition is six clock periods. Including one clock period for transferring data from vector registers to additional unit and one clock cycle period to store the result into another vector register. In scalar mode: 64x8=512 clock periods In vector mode: 8+63 = 71 clock periods If N < 64? If N > 64?

Parallell Processing Systems16 4.2 Memory Design Considerations(con.)  Figure 4.8 shows the general structure of the vector processor with delay elements inserted in the input and output.  A common method of further increasing the memory system bandwidth is to insert high speed intermediate memory between main memory and the processor pipeline.

Parallell Processing Systems17 4.3 Architecture of the Cray Series  Cray X-MP/4(Figure 4.9): successor of Cray-1  Memory: is built out of several sections, each divided into banks.  25 to 100 Gbps  4 ports  Memory conflict solution may require wait states to be inserted  Solid state device is used as an exceptional fast access disk devices.

Parallell Processing Systems18 4.3 Architecture of the Cray Series(continued)  Cray X-MP/4(Figure 4.9)  Processor interconnection  The interconnection of CPUs assumed a coarse- grained multiprocessing environment.  Central Processor(Figure 4.10)  Each CPU is a register-oriented vector processor.  Table 4.1 shows the functional unit characteristics.  Strip mining  Chaining  Cray Y-MP, Cray-3, Cray-4

Parallell Processing Systems19 4.4 Two Other Architectures  Convex C series  From FPS(Floating-Point Systems, Inc.)  C1, C2, C3  Figure 4.15 shows the architecture of Convex C120 system  FPS 5000 Series  Figure 4.18 shows the FPS 5000 Series architecture.

Parallell Processing Systems20 4.5 Performance Evaluation  Major characteristics to affect supercomputer architecture  Clock speed  Instruction issue rate  Size and number of registers  Memory size  Number of concurrent paths to memory  Ability to fetch/store vectors efficiently  Number of duplicate arithmetic functional units  Whether function can be chained together  Indirect addressing capability  Handling of conditional blocks of code

Parallell Processing Systems21 4.5 Performance Evaluation (continued)  The sustained performance depends on the following factors:  Level of vectorization  Average vector length  Possibility of vector chaining  Overlap of scalar, vector, memory load/store operations possible  Memory contention resolution mechanism adopted.

Parallell Processing Systems22 4.5 Performance Evaluation (continued)  The Amdal ’ s law  Speed-up = where s is the ratio the speed of the vector unit to that of scalar unit.  The execution time of a vector loop with N element, T N = T memory + (N-1) T cycle, where T memory is the time to initialize starting address for each vector.,,,  R  =, where F is the floating-point operation included in the loop

Parallell Processing Systems23 4.6 Programming Vector Processors  Programming facilities  Development of programming facilities  Development of compiler  In general, it is not possible to completely vectorize a sequential program.  In general, an algorithm that is considered efficient for scalar computation need not be efficient for a vector environment. Modifications are then needed to take advantage of the vector hardware.

Parallell Processing Systems24 4.6 Programming Vector Processors(continued)  Several techniques adopted by vector processor environment:  Scalar renaming  Scalar expansion  Loop unrolling  Loop fusion or jamming  Loop distribution  Force maximum work into inner loop  Subprogram in-lining  Eliminate ambiguity using the PARAMETER statement  Positioning frequently executed scalar conditional block first