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US20100153654A1 - Data processing method and device - Google PatentsData processing method and device Download PDF
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In a data-processing method, first result data may be obtained using a plurality of configurable coarse-granular elements, the first result data may be written into a memory that includes spatially separate first and second memory areas and that is connected via a bus to the plurality of configurable coarse-granular elements, the first result data may be subsequently read out from the memory, and the first result data may be subsequently processed using the plurality of configurable coarse-granular elements. In a first configuration, the first memory area may be configured as a write memory, and the second memory area may be configured as a read memory. Subsequent to writing to and reading from the memory in accordance with the first configuration, the first memory area may be configured as a read memory, and the second memory area may be configured as a write memory.
- The present invention relates to methods of operating and optimum use of reconfigurable arrays of data processing elements.
- The limitations of conventional processors are becoming more and more evident. The growing importance of stream-based applications makes coarse-grain dynamically reconfigurable architectures an attractive alternative. See, e.g., R. Hartenstein, R. Kress, & H. Reinig, "A new FPGA architecture for word-oriented datapaths," Proc. FPL '94, Springer LNCS, September 1994, at 849; E. Waingold et al., "Baring it all to software: Raw machines," IEEE Computer, September 1997, at 86-93; PACT Corporation, "The XPP Communication System," Technical Report 15 (2000); see generally http://www.pactcorp.com. They combine the performance of ASICs, which are very risky and expensive (development and mask costs), with the flexibility of traditional processors. See, for example, J. Becker, "Configurable Systems-on-Chip (CSoC)," (Invited Tutorial), Proc. of 9th Proc. of XV Brazilian Symposium on Integrated Circuit, Design (SBCCI 2002), (September 2002).
- The datapaths of modern microprocessors reach their limits by using static instruction sets. In spite of the possibilities that exist today in VLSI development, the basic concepts of microprocessor architectures are the same as 20 years ago. The main processing unit of modern conventional microprocessors, the datapath, in its actual structure follows the same style guidelines as its predecessors. Although the development of pipelined architectures or superscalar concepts in combination with data and instruction caches increases the performance of a modern microprocessor and allows higher frequency rates, the main concept of a static datapath remains. Therefore, each operation is a composition of basic instructions that the used processor owns. The benefit of the processor concept lies in the ability of executing strong control dominant application. Data or stream oriented applications are not well suited for this environment. The sequential instruction execution isn't the right target for that kind of application and needs high bandwidth because of permanent retransmitting of instruction/data from and to memory. This handicap is often eased by use of caches in various stages. A sequential interconnection of filters, which perform data manipulation without writing back the intermediate results would get the right optimisation and reduction of bandwidth. Practically, this kind of chain of filters should be constructed in a logical way and configured during runtime. Existing approaches to extend instruction sets use static modules, not modifiable during runtime.
- Customized microprocessors or ASICs are optimized for one special application environment. It is nearly impossible to use the same microprocessor core for another application without loosing the performance gain of this architecture.
- A new approach of a flexible and high performance datapath concept is needed, which allows for reconfiguring the functionality and for making this core mainly application independent without losing the performance needed for stream-based applications.
- When using a reconfigurable array, it is desirable to optimize the way in which the array is coupled to other units, e.g., to a processor if the array is used as a coprocessor. It is also desirable to optimize the way in which the array is configured.
- Further, WO 00/49496 discusses a method for execution of a computer program using a processor that includes a configural functional unit capable of executing reconfigurable instructions, which can be redefined at runtime. A problem with conventionable processor architectures exists if a coupling of, for example, sequentional processors is needed and/or technologies such as a data-streaming, hyper-threading, multi-threading, multi-tasking, execution of parts of configurations, etc., are to be a useful way for enhancing performance. Techniques discussed in prior art, such as WO 02/50665 A1, do not allow for a sufficiently efficient way of providing for a data exchange between the ALU of a CPU and the configurable data processing logic cell field, such as an FPGA, DSP, or other such arrangement. In the prior art, the data exchange is effected via registers. In other words, it is necessary to first write data into a register sequentially, then retrieve them sequentially, and restore them sequentially as well.
- Another problem exists if an external access to data is requested in known devices used, inter alia, to implement functions in the configurable data processing logic cell field, DFP, FPGA, etc., that cannot be processed sufficiently on a CPU-integrated ALU. Accordingly, the data processing logic cell field is practically used to allow for user-defined opcodes that can process data more efficiently than is possible on the ALU of the CPU without further support by the data processing logic cell field. In the prior art, the coupling is generally word-based, not block-based. A more efficient data processing, in particular more efficient than possible with a close coupling via registers, is highly desirable.
- Another method for the use of logic cell fields that include coarse- and/or fine-granular logic cells and logic cell elements provides for a very loose coupling of such a field to a conventional CPU and/or a CPU-core in embedded systems. In this regard, a conventional sequential program can be executed on the CPU, for example a program written in C, C++, etc., wherein the instantiation or the data stream processing by the fine- and/or coarse-granular data processing logic cell field is effected via that sequential program. However, a problem exists in that for programming said logic cell field, a program not written in C or another sequential high-level language must be provided for the data stream processing. It is desirable to allow for C-programs to run both on a conventional CPU-architecture as well as on the data processing logic cell field operated therewith, in particular, despite the fact that a quasi-sequential program execution should maintain the capability of data-streaming in the data processing logic cell fields, whereas simultaneously the capability exists to operate the CPU in a not too loosely coupled way.
- It is already known to provide for sequential data processing within a data processing logic cell field. See, for example, DE 196 51 075, WO 98/26356, DE 196 54 846, WO 98/29952, DE 197 04 728, WO 98/35299, DE 199 26 538, WO 00/77652, and DE 102 12 621. Partial execution is achieved within a single configuration, for example, to reduce the amount of resources needed, to optimize the time of execution, etc. However, this does not lead automatically to allowing a programmer to translate or transfer high-level language code automatically onto a data processing logic cell field as is the case in common machine models for sequential processes. The compilation, transfer, or translation of a high-level language code onto data processing logic cell fields according to the methods known for models of sequentially executing machines is difficult.
- In the prior art, it is further known that configurations that effect different functions on parts of the area respectively can be simultaneously executed on the processing array and that a change of one or some of the configuration(s) without disturbing other configurations is possible at run-time. Methods and hardware-implemented means for the implementation are known to ensure that the execution of partial configurations to be loaded onto the array is possible without deadlock. Reference is made to DE 196 54 593, WO 98/31102, DE 198 07 872, WO 99/44147, DE 199 26538, WO 00/77652, DE 100 28 397, and WO 02/13000. This technology allows in a certain way a certain parallelism and, given certain forms and interrelations of the configurations or partial configurations for a certain way of multitasking/multi-threading, in particular in such a way that the planning, i.e., the scheduling and/or the planning control for time use, can be provided for. Furthermore, from the prior art, time use planning control means and methods are known that, at least under a corresponding interrelation of configurations and/or assignment of configurations to certain tasks and/or threads to configurations and/or sequences of configurations, allow for a multi-tasking and/or multi-threading.
- Embodiments of the present invention may improve upon the prior art with respect to optimization of the way in which a reconfigurable array is coupled to other units and/or the way in which the array is configured.
- A way out of limitations of conventional microprocessors may be a dynamic reconfigurable processor datapath extension achieved by integrating traditional static datapaths with the coarse-grain dynamic reconfigurable XPP-architecture (eXtreme Processing Platform). Embodiments of the present invention introduce a new concept of loosely coupled implementation of the dynamic reconfigurable XPP architecture from PACT Corp. into a static datapath of the SPARC compatible LEON processor. Thus, this approach is different from those where the XPP operates as a completely separate (master) component within one Configurable System-on-Chip (CsoC), together with a processor core, global/local memory topologies, and efficient multi-layer Amba-bus interfaces. See, for example, J. Becker & M. Vorbach, "Architecture, Memory and Interface Technology Integration of an Industrial/Academic Configurable System-on-Chip (CSoC)," IEEE Computer Society Annual Workshop on VLSI (WVLSI 2003), (February 2003). From the programmer's point of view, the extended and adapted datapath may seem like a dynamic configurable instruction set. It can be customized for a specific application and can accelerate the execution enormously. Therefore, the programmer has to create a number of configurations that can be uploaded to the XPP-Array at run time. For example, this configuration can be used like a filter to calculate stream-oriented data. It is also possible to configure more than one function at the same time and use them simultaneously. These embodiments may provide an enormous performance boost and the needed flexibility and power reduction to perform a series of applications very effective.
- Embodiments of the present invention may provide a hardware framework, which may enable an efficient integration of a PACT XPP core into a standard RISC processor architecture.
- Embodiments of the present invention may provide a compiler for a coupled RISC+XPP hardware. The compiler may decide automatically which part of a source code is executed on the RISC processor and which part is executed on the PACT XPP core.
- In an example embodiment of the present invention, a C Compiler may be used in cooperation with the hardware framework for the integration of the PACT XPP core and RISC processor.
- In an example embodiment of the present invention, the proposed hardware framework may accelerate the XPP core in two respects. First, data throughput may be increased by raising the XPP's internal operating frequency into the range of the RISC's frequency. This, however, may cause the XPP to run into the same pit as all high frequency processors, i.e., memory accesses may become very slow compared to processor internal computations. Accordingly, a cache may be provided for use. The cache may ease the memory access problem for a large range of algorithms, which are well suited for an execution on the XPP. The cache, as a second throughput increasing feature, may require a controller. A programmable cache controller may be provided for managing the cache contents and feeding the XPP core. It may decouple the XPP core computations from the data transfer so that, for instance, data preload to a specific cache sector may take place while the XPP is operating on data located in a different cache sector.
- A problem which may emerge with a coupled RISC+XPP hardware concerns the RISC's multitasking concept. It may become necessary to interrupt computations on the XPP in order to perform a task switch. Embodiments of the present invention may provided for hardware and a compiler that supports multitasking. First, each XPP configuration may be considered as an uninterruptible entity. This means that the compiler, which generates the configurations, may take care that the execution time of any configuration does not exceed a predefined time slice. Second, the cache controller may be concerned with the saving and restoring of the XPP's state after an interrupt. The proposed cache concept may minimize the memory traffic for interrupt handling and frequently may even allow avoiding memory accesses at all.
- In an example embodiment of the present invention, the cache concept may be based on a simple internal RAM (IRAM) cell structure allowing for an easy scalability of the hardware. For instance, extending the XPP cache size, for instance, may require not much more than the duplication of IRAM cells.
- In an embodiment of the present invention, a compiler for a RISC+XPP system may provide for compilation for the RISC+XPP system of real world applications written in the C language. The compiler may remove the necessity of developing NML (Native Mapping Language) code for the XPP by hand. It may be possible, instead, to implement algorithms in the C language or to directly use existing C applications without much adaptation to the XPP system. The compiler may include the following three major components to perform the compilation process for the XPP:
- 1. partitioning of the C source code into RISC and XPP parts;
- 2. transformations to optimize the code for the XPP; and
- 3. generating of NML code.
- The generated NML code may be placed and routed for the XPP.
- The partitioning component of the compiler may decide which parts of an application code can be executed on the XPP and which parts are executed on the RISC. Typical candidates for becoming XPP code may be loops with a large number of iterations whose loop bodies are dominated by arithmetic operations. The remaining source code—including the data transfer code—may be compiled for the RISC.
- The compiler may transform the XPP code such that it is optimized for NML code generation. The transformations included in the compiler may include a large number of loop transformations as well as general code transformations. Together with data and code analysis the compiler may restructure the code so that it fits into the XPP array and so that the final performance may exceed the pure RISC performance. The compiler may generate NML code from the transformed program. The whole compilation process may be controlled by an optimization driver which selects the optimal order of transformations based on the source code.
- Discussed below with respect to embodiments of the present invention are case studies, the basis of the selection of which is the guiding principle that each example may stand for a set of typical real-world applications. For each example is demonstrated the work of the compiler according to an embodiment of the present invention. For example, first partitioning of the code is discussed. The code transformations, which may be done by the compiler, are shown and explained. Some examples require minor source code transformations which may be performed by hand. These transformations may be either too expensive, or too specific to make sense to be included in the proposed compiler. Dataflow graphs of the transformed codes are constructed for each example, which may be used by the compiler to generate the NML code. In addition, the XPP resource usages are shown. The case studies demonstrate that a compiler containing the proposed transformations can generate efficient code from numerical applications for the XPP. This is possible because the compiler may rely on the features of the suggested hardware, like the cache controller.
- Other embodiments of the present invention pertain to a realization that for data-streaming data-processing, block-based coupling is highly preferable. This is in contrast to a word-based coupling discussed above with respect to the prior art.
- Further, embodiments of the present invention provide for the use of time use planning control means, discussed above with respect to their use in the prior art, for configuring and management of configurations for the purpose of scheduling of tasks, threads, and multi- and hyper-threads.
FIG. 1illustrates components of a LEON architecture.
FIG. 2shows the pipelined datapath structure of the LEON integer unit.
FIG. 3illustrates components of a typical PAE.
FIG. 4is a diagram that illustrates an extended datapath according to an example embodiment of the present invention.
FIG. 5illustrates transmission of data to an extended XPP-based datapath by passing the data through an IO-Port, according to an example embodiment of the present invention.
FIG. 6illustrates an extended LEON instruction pipeline, according to an example embodiment of the present invention.
FIG. 7is a graph that shows that the benefit brought by XPP rises with the number of iDCT blocks computed by it before reconfiguration.
FIG. 8is a block diagram of an MPEG-4 decoding algorithm, according to an example embodiment of the present invention.
FIG. 9is a block diagram illustrating components of an example embodiment of the present invention, where an XPP core and a RISC core share a memory hierarchy.
FIG. 10shows an IRAM and configuration cache controller data structures and a usage example, according to an example embodiment of the present invention.
FIG. 11shows an asynchronous pipeline of an XPP, according to an example embodiment of the present invention.
FIG. 12is a diagram that illustrates tasks of an XPP cache controller as states, according to an example embodiment of the present invention.
FIG. 13shows simultaneous multithreading according to an example embodiment of the present invention.
FIG. 14shows an example of a cache structure according to an example embodiment of the present invention.
FIG. 15is a control-flow graph of a piece of a program, according to an example embodiment of the present invention.
FIG. 16illustrates a code and diagram of an example of a true dependence with distance 0 on array 'a', according to an example embodiment of the present invention.
FIG. 17illustrates a code and diagram of an example of an anti-dependence with distance 0 on array 'b', according to an example embodiment of the present invention.
FIG. 18illustrates a code and diagram of an example of an output dependence with distance 0 on array 'a', according to an example embodiment of the present invention.
FIG. 19illustrates a code and diagram of an example of a dependence with direction vector (=,=) between S1 and S2 and a dependence with direction vector (=,=,<) between S2 and S2, according to an example embodiment of the present invention.
FIG. 20illustrates a code and diagram of an example of an anti-dependence with distance vector (0,2), according to an example embodiment of the present invention.
FIG. 21is a graph illustrating information of a flow-sensitive alias analysis versus a flow insensitive alias analysis, according to an example embodiment of the present invention.
FIG. 22is a diagram that illustrates aligned and misaligned memory accesses.
FIG. 23illustrates merging of arrays, according to an example embodiment of the present invention.
FIG. 24is a flowchart that illustrates a global view of a compiling procedure, according to an example embodiment of the present invention.
FIG. 25is a flowchart that illustrates a detailed architecture and an internal processing of an XPP Compiler.
FIG. 26is a diagram that illustrates details of XPP loop optimizations, including their organization, according to an example embodiment of the present invention.
FIG. 27is an expression tree of an edge 3×3 inner loop body, according to an example embodiment of the present invention.
FIG. 28is an expression tree showing the interchanging of operands of commutative add expressions to reduce an overall tree depth, according to an example embodiment of the present invention.
FIG. 29shows a main calculation network of an edge 3×3 configuration, according to an example embodiment of the present invention.
FIG. 30shows a case of synthesized shift registers, according to an example embodiment of the present invention.
FIG. 31is a data dependency graph relating to a FIR filter, according to an example embodiment of the present invention.
FIG. 32is a dataflow graph that is achieved in an instance where values of x needed for computation of y are kept in registers, according to an example embodiment of the present invention.
FIG. 33is a dataflow graph representing an inner loop with loop unrolling, according to an example embodiment of the present invention.
FIG. 34is a data dependency graph for matrix multiplication, according to an example embodiment of the present invention.
FIG. 35is a visualization of array access sequences prior to optimization according to an example embodiment of the present invention.
FIG. 36is a visualization of array access sequences subsequent to optimization according to an example embodiment of the present invention.
FIG. 37is a dataflow graph of a synthesized configuration and shows matrix multiplication after unroll and jam, according to an example embodiment of the present invention.
FIG. 38is a data flow graph corresponding to a butterfly loop, according to an example embodiment of the present invention.
FIG. 39is a data flow graph showing modifications to code corresponding to the graph of FIG. 38, according to an example embodiment of the present invention.
FIG. 40illustrates a splitting network, according to an example embodiment of the present invention.
FIG. 41is a diagram that illustrates how short values are handled, according to an example embodiment of the present invention.
FIG. 42is a diagram that illustrates how a merge is done, according to an example embodiment of the present invention.
FIG. 43illustrates a changing of values of a block row by row before processing of columns.
FIG. 44illustrates a possible implementation for saturate (val,n) as an NML schematic using two ALUs, according to an example embodiment of the present invention.
FIG. 45is a data flow graph for IDCTCOLUMN_CONFIG.
FIG. 46is a diagram that illustrates use of two counter macros for address generation, according to an example embodiment of the present invention.
FIG. 47is a diagram that illustrates an idling of units of a deep pipeline.
FIG. 48illustrates a loop interchange, according to an example embodiment of the present invention.
FIG. 49illustrates use of output IRAM of Config A as input IRAM of Config B to bypass a memory interface for bandwidth optimization, according to an example embodiment of the present invention.
FIG. 50illustrates block offsets inside tiles generated by a SUIP counter, according to an example embodiment of the present invention.
FIG. 51illustrates a difference in efficiency between an instance where there is no data duplication and instance where there is data duplication according to an example embodiment of the present invention.
FIG. 52illustrates IDCTROW_CONFIG, IDCTCOLUMN_CONFIG, and REORDER_CONFIG of an example embodiment of the present invention.
FIG. 53is a dataflow graph of loop bodies of wavelet after performance of a step of tree balancing, according to an example embodiment of the present invention.
FIG. 54is a graphical representation of functions for processing data and event packets that can be configured into an RDFP.
FIGS. 55-69each illustrates a CDFG according to a respective embodiment of the present invention.
- Instruction datapaths of modern microprocessors are constrained by certain limitations because they use static instruction sets driven by the traditional von Neumann or Harvard architectural principles. These limitations may be avoided via a dynamic reconfigurable processor datapath extension achieved by integrating traditional static datapaths with the coarse-grain dynamic reconfigurable XPP architecture. Therefore, a loosely asynchronous coupling mechanism of the corresponding instruction datapath or datapath units has been developed and integrated onto a CMOS 0.13 μm standard cell technology from UMC. In embodiments of the present invention, the SPARC compatible LEON RISC processor may be used, with its static pipelined instruction datapath extended to be configured and personalized for specific applications. This compiler-compatible instruction set extension allows various and efficient uses, e.g., in streaming application domains like MPEG-4, digital filters, mobile communication modulation, etc. Discussed below is a coupling technique by flexible dual-clock FIFO interfaces that allows asynchronous concurrency of the additionally configured compound instructions, which are integrated into the programming and compilation environment of the LEON processor, and that allows adaption of the frequency of the configured XPP datapath, dependent on actual performance requirements, e.g., for avoiding unneeded cycles and reducing power consumption.
- The coupling technique of embodiments of the present invention discussed below combines the flexibility of a general purpose microprocesser with the performance and power consumption of coarse-grain reconfigurable datapath structures, nearly comparable to ASIC performance. Two programming and computing paradigms (control-driven von Neumann and transport-triggered XPP) are unified within one hybrid architecture with the option of two clock domains. The ability to reconfigure the transport-triggered XPP makes the system independent from standards or specific applications. This concept creates potential to develop multi-standard communication devices like software radios by using one extended processor architecture with adapted programming and compilation tools. Thus, new standards can be easily implemented through software updates. The system is scalable during design time through the scalable array-structure of the used XPP extension. This extends the range of suitable applications from products with less multimedia functions to complex high performance systems.
- Embodiments of the present invention may be implemented using a 32-bit SPARC V8 compatible LEON microprocessor. See SPARC International Inc., The SPARC Architecture Manual, Version 8, at http://www.sparc.com; Jiri Gaisler, The LEON Processor User's Manual, at http://www.gaisler.com. This microprocessor is a synthesisable, freely available VHDL model which has a load/store architecture and has a five stages pipeline implementation with separated instruction and data caches.
FIG. 1illustrates components of a LEON architecture. The LEON may be provided with a full implementation of an AMBA 2.0 AHB and APB on-chip bus (1000, 1002), a hardware multiplier and divider, programmable 8/16/32-bit memory controller 1005 for external PROM, static RAM and SDRAM, and several on-chip peripherals such as timers 1010, UARTs 1012, an interrupt controller 1014, and a 16-bit I/O port 1016. A simple power down mode may be implemented as well.
- LEON is developed by the European Space Agency (ESA) for future space missions. The performance of LEON is close to an ARM19 series but does not have a memory management unit (MMU) implementation, which limits the use to single memory space applications.
FIG. 2shows the pipelined datapath structure of the LEON integer unit.
- eXtreme Processing Platform—XPP
- Embodiments of the present invention may be implemented using the XPP architecture. Regarding the XPP architecture, see http://www.pactcorp.com; "The XPP Communication System," supra; and V. Baumgarte et al., "A Self-Reconfigurable Data Processing Architecture," The 1st Intl. Conference of Engineering of Reconfigurable Systems and Algorithms (ERSA '01), Las Vegas, Nev. (June 2001). The XPP architecture is based on a hierarchical array of coarse-grain, adaptive computing elements called Processing Array Elements (PAEs) and a packet-oriented communication network. The strength of the XPP technology originates from the combination of array processing with unique, powerful run-time reconfiguration mechanisms. Since configuration control is distributed over a Configuration Manager (CM) embedded in the array, PAEs can be configured rapidly in parallel while neighboring PAEs are processing data. Entire applications can be configured and run independently on different parts of the array. Reconfiguration may be triggered externally or even by special event signals originating within the array, enabling self-reconfiguring designs. By utilizing protocols implemented in hardware, data and event packets may be used to process, generate, decompose and merge streams of data.
- The XPP has some similarities with other coarse-grain reconfigurable architectures like the KressArray (see R. Hartenstein et al., supra) or Raw Machines (see E. Waingold et al., supra), which are specifically designed for stream-based applications. XPP's main distinguishing features are its automatic packet-handling mechanisms and its sophisticated hierarchical configuration protocols for runtime and self reconfiguration.
- Array Structure
- A CM may include a state machine and internal RAM for configuration caching. The PAE itself (see top right-hand side of
FIG. 3) may include a configuration bus which connects the CM with PAEs and other configurable objects. Horizontal busses may carry data and events. They can be segmented by configurable switch-objects, and can be connected to PAEs and special I/O objects at the periphery of the device.
- A PAE is a collection of PAE objects.
FIG. 3illustrates components of a typical PAE, which may include a BREG object (back registers) 1100 and an FREG object (forward registers) 1102, which are used for vertical routing, as well as an ALU object 1104 which performs the actual computations. The ALU 1104 may perform common fixed-point arithmetical and logical operations as well as several special three input opcodes, such as multiply-add, sort, and counters. Events generated by ALU objects depend on ALU results or exceptions, very similar to the state flags of a conventional microprocessor. A counter, e.g., generates a special event only after it has terminated. How these events are used is discussed below. Another PAE object implemented in the XPP is a memory object which can be used in FIFO mode or as RAM for lookup tables, intermediate results, etc. However, any PAE object functionality can be included in the XPP architecture.
- Packet Handling and Synchronization
- PAE objects, as defined above, may communicate via a packet-oriented network. Two types of packets may be sent through the array: data packets and event packets. Data packets have a uniform bit width specific to the device type. In normal operation mode, PAE objects are self-synchronizing. An operation is performed as soon as all necessary data input packets are available. The results are forwarded as soon as they are available, provided the previous results have been used. Thus, it is possible to map a signal-flow graph directly to ALU objects. Event packets are one bit wide. They transmit state information which controls ALU execution and packet generation.
- Configuration
- Every PAE stores locally its current configuration state, i.e., if it is part of a configuration or not (states "configured" or "free"). Once a PAE is configured, it changes its state to "configured." This prevents the CM from reconfiguring a PAE which is still used by another application. The CM caches the configuration data in its internal RAM until the required PAEs become available.
- While loading a configuration, all PAEs start to compute their part of the application as soon as they are in state "configured." Partially configured applications are able to process data without loss of packets. This concurrency of configuration and computation hides configuration latency.
- XPP Application Mapping
- The NML language, a PACT proprietary structural language with reconfiguration primitives, was developed by PACT to map applications to the XPP array. It gives the programmer direct access to all hardware features.
- In NML, configurations consist of modules which are specified as in a structural hardware description language, similar to, for example, structural VHDL. PAE objects are explicitly allocated, optionally placed, and their connections specified. Hierarchical modules allow component reuse, especially for repetitive layouts. Additionally, NML includes statements to support configuration handling. A complete NML application program may include one or more modules, a sequence of initially configured modules, differential changes, and statements which map event signals to configuration and prefetch requests. Thus, configuration handling is an explicit part of the application program.
- XPP-based architectures and development tools, such as the PACT XPP Development Suite (XDS) are discussed in detail at http://www.pactcorp.com.
- LEON and XPP should be able to communicate with each other in a simple and high performance manner. While the XPP is a dataflow orientated device, the LEON is a general purpose processor, suitable for handling control flow. See, for example, The SPARC Architecture Manual, supra; Jiri Gaisler, supra. Therefore, LEON may be used for system control. To do this, the XPP is integrated into the datapath of the LEON integer unit, which is able to control the XPP.
FIG. 4is a diagram that illustrates this extended datapath.
- Due to unpredictable operation time of the XPP algorithm, integration of XPP into LEON data-path is done in a loosely-coupled way. Thus, the XPP array can operate independently of the LEON, which is able to control and reconfigure the XPP during runtime. Since the configuration of XPP is handled by LEON, the CM 1106 of the XPP is unnecessary and can be left out of the XPP array. The configuration codes are stored in the LEON RAM. LEON transfers the needed configuration from its system RAM into the XPP and creates the needed algorithm on the array.
- To enable a maximum of independence of XPP from LEON, all ports of the XPP —input ports as well as output ports—are buffered using dual clock FIFOs. Dual-clocked FIFOs are implemented into the IO-Ports between LEON and XPP. To transmit data to the extended XPP-based datapath, the data are passed through an IO-Port as shown in
FIG. 5. In addition to the FIFO, the IO-Ports include logic to generate handshake signals and an interrupt request signal. The IO-Port for receiving data from XPP is similar to FIG. 5except with a reversed direction of the data signals. This enables XPP to perform completely independently of LEON as long as there are input data available in the input port FIFOs and free space for result date in the output port FIFOs. There are a number of additional features implemented in the LEON pipeline to control the data transfer between LEON and XPP.
- When LEON tries to write to an TO-Port containing a full FIFO or read from an IO-Port containing an empty FIFO, a trap is generated. This trap can be handled through a trap handler. A further mechanism, e.g., pipeline-holding, may be implemented to allow LEON to hold the pipeline and wait for free FIFO space during XPP write access or wait for a valid FIFO value during XPP read access. When using pipeline-holding, the software developer has to avoid reading from an IO-Port with an empty FIFO while the XPP, or the XPP input IO-Ports, includes no data to produce output. In this case a deadlock will occur requiring a reset of the complete system.
- XPP can generate interrupts for the LEON when trying to read a value from an empty FIFO port or to write a value to a full FIFO port. The occurrence of interrupts indicates that the XPP array cannot process the next step because it has either no input values or it cannot output the result value. The interrupts generated by the XPP are maskable.
- The interface provides information about the FIFOs. LEON can read the number of valid values that are in the FIFO.
FIG. 6illustrates an extended LEON instruction pipeline. The interface, shown in FIG. 6, to the XPP appears to the LEON as a set of special registers. These XPP registers can be divided into a communication register category and a status register category.
- For data exchange, the XPP communication registers are used. Since XPP provides three different types of communication ports, there are also three types of communication registers each type is split into an input part and an output part.
- Communication Registers
- The data for the process are accessed through XPP data registers. The number of data input and data output ports, as well as the data bit-width depends on the implemented XPP array.
- XPP can generate and consume events. Events are one bit signals. The number of input events and output events also depends on the implemented XPP array.
- Configuration of the XPP is done through the XPP configuration register. LEON reads the required configuration value from a file stored in its system RAM and writes it to the XPP configuration register.
- Status Resisters
- There are a number of XPP status registers implemented to control the behavior and get status information of the interface. Switching between the usage of trap handling and pipeline holding can be done in the hold register. An XPP clock register includes a clock frequency ratio between LEON and XPP. By writing to this register, LEON software can set the XPP clock relative to the LEON clock. This allows adaptation of the XPP clock frequency to the required XPP performance and consequently allows for influencing the power consumption of the system. Writing zero to the XPP clock register turns off the XPP. There is also a status register for every FIFO including the number of valid values actually available in the FIFO.
- This status registers provide a high degree of flexibility in communication between LEON and XPP and enables different communication modes.
- Modes
- If there is only one application running on the system at a particular time, software may be developed in pipeline-hold mode. In this instance, LEON initiates data read or write from or to XPP. If there is no value to read or no value to write, LEON pipeline will be stopped until read or write is possible. This can be used to reduce power consumption of the LEON part.
- In interrupt mode, XPP can influence the LEON program flow. Thus, the IO-Ports generate an interrupt depending on the actual number of values available in the FIFO. The communication between LEON and XPP is via interrupt service routines.
- Polling mode is a way to access the XPP. Initiated by a timer event, LEON reads XPP ports including data and writes to XPP ports including free FIFO space. Between these phases, LEON can compute other calculations.
- It is possible to switch between these strategies anytime within one application.
- A conventional XPP includes a configuration manager to handle configuration and reconfiguration of the array. However, in combination with the LEON, the configuration manager is dispensable because the configuration as well as any reconfiguration is controlled by the LEON through the XPP configuration register. All XPP configurations used for an application are stored in the LEON's system RAM.
- To make the new XPP registers accessible through software, the LEON's SPARC 8 instruction set (see The SPARC Architecture Manual, supra) is extended by a new subset of instructions. These instructions are based on the SPARC instruction format, but do not conform to the SPARC V8 standard. Corresponding to the SPARC conventions of a load/store architecture, the instruction subset can be divided into two categories. Load/store instructions can exchange data between the LEON memory and the XPP communication registers. The number of cycles per instruction is similar to the standard load/store instructions of the LEON. Read/write instructions are used for communications between LEON registers. Since the LEON register-set is extended by the XPP registers, the read/write instructions are also extended to access XPP registers. Status registers can only be accessed with read/write instructions. Execution of arithmetic instructions on XPP registers are not possible. Values have to be written to standard LEON registers before they can be targets of arithmetic operations.
- The complete system can still execute any SPARC V8 compatible code. Doing this, the XPP is completely unused.
- The LEON is provided with the LECCS cross compiler system (see LEON/ERC32 Crass Compilation System (LECCS) at http://www.gaisler.com/cms4—5—3/index.php?option=com_content&task=view&id=62&Itemid=149) under the terms of LGPL. This system includes modified-versions of the binutils 2.11 and gcc 2.95.2. To make the new instruction subset available to software developers, the assembler of the binutils has been extended by a number of instructions according to the implemented instruction subset. The new instructions have the same mnemonic as the regular SPARC V8 load, store, read, and write instructions. Only the new XPP registers have to be used as a source or target operand. Since the modifications of LECCS are straightforward extensions, the cross compiler system is backward compatible to the original version. The availability of the source code of LECCS has allowed for extending the tools by the new XPP operations in the described way.
- The development of the XPP algorithms have to be done with separate tools, provided by PACT Corp.
- As a first analysis application, an inverse Discrete Cosine Transform (DCT) applied to an 8×8 pixel block was implemented. For all simulations, a 2.50 MHz clock frequency for the LEON processor and a 50 MHZ clock frequency for XPP was used. The usage of XPP accelerates the computation of the iDCT by about a factor of four, depending on the communication mode. However, XPP has to be configured before computing the iDCT on it. The following table shows the configuration time for this algorithm.
LEON with XPP LEON with XPP LEON with XPP LEON alone in IRQ Mode in Poll Mode in Hold Mode Configuration — 71.308 ns 84.364 ns 77.976 ns of XPP 17.827 cycles 21.091 cycles 19.494 cycles 2D iDCT (8 × 8) 14.672 ns 3.272 ns 3.872 ns 3.568 ns 3.668 cycles 818 cycles 968 cycles 892 cycles
- As shown in
FIG. 7, the benefit brought by XPP rises with the number of iDCT blocks computed by it before reconfiguration. Accordingly, the number of reconfigurations during complex algorithms should be minimized.
- A first complex application implemented on the system is MPEG-4 decoding. The optimization of the algorithm partitioning on LEON and XPP is still in progress.
FIG. 8is a block diagram of the MPEG-4 decoding algorithm. Frames with 320×240 pixels were decoded. LEON, by using SPARC V8 standard instructions, decodes one frame in 23.46 seconds. In a first implementation of MPEG-4 using the XPP, only the iDCT is computed by XPP. The rest of the MPEG-4 decoding is still done with LEON. With the help of XPP, one frame is decoded in 17.98s. This is a performance boost of more then twenty percent. Since the XPP performance gain by accelerating the iDCT algorithm only is very low at the moment, we work on XPP implementations of Huffmann-decoding, dequantization, and prediction decoding. So the performance boost of this implementation against the standalone LEON will be increased.
- For integration of the XPP core as a functional unit into a standard RISC core, some system parameters may be reconsidered as follows:
- Pipelining/Concurrency/Synchronicity
- RISC instructions of totally different type (Ld/St, ALU, MuL/Div/MAC, FPALU, FPMul, etc.) may be executed in separate specialized functional units to increase the fraction of silicon that is busy on average. Such functional unit separation has led to superscalar RISC designs that exploit higher levels of parallelism.
- Each functional unit of a RISC core may be highly pipelined to improve throughput. Pipelining may overlap the execution of several instructions by splitting them into unrelated phases, which may be executed in different stages of the pipeline. Thus, different stages of consecutive instructions can be executed in parallel with each stage taking much less time to execute. This may allow higher core frequencies.
- With an approximate subdivision of the pipelines of all functional units into sub-operations of the same size (execution time), these functional units/pipelines may execute in a highly synchronous manner with complex floating point pipelines being the exception.
- Since the XPP core uses data flow computation, it is pipelined by design. However, a single configuration usually implements a loop of the application, so the configuration remains active for many cycles, unlike the instructions in every other functional unit, which typically execute for one or two cycles at most. Therefore, it is still worthwhile to consider the separation of several phases, (e.g., Ld/Ex/Store), of an XPP configuration, (i.e., an XPP instruction), into several functional units to improve concurrency via pipelining on this coarser scale. This also may improve throughput and response time in conjunction with multi tasking operations and implementations of simultaneous multithreading (SMT).
- The multi cycle execution time may also forbid a strongly synchronous execution scheme and may rather lead to an asynchronous scheme, e.g., like for floating point square root units. This in turn may necessitate the existence of explicit synchronization instructions.
- Core Frequency/Memory Hierarchy
- As a functional unit, the XPP's operating frequency may either be half of the core frequency or equal to the core frequency of the RISC. Almost every RISC core currently on the market exceeds its memory bus frequency with its core frequency by a larger factor. Therefore, caches are employed, forming what is commonly called the memory hierarchy, where each layer of cache is larger but slower than its predecessors.
- This memory hierarchy does not help to speed up computations which shuffle large amounts of data, with little or no data reuse. These computations are called "bounded by memory bandwidth." However, other types of computations with more data locality (another term for data reuse) may gain performance as long as they fit into one of the upper layers of the memory hierarchy. This is the class of applications that gains the highest speedups when a memory hierarchy is introduced.
- Classical vectorization can be used to transform memory-bounded algorithms, with a data set too big to fit into the upper layers of the memory hierarchy. Rewriting the code to reuse smaller data sets sooner exposes memory reuse on a smaller scale. As the new data set size is chosen to fit into the caches of the memory hierarchy, the algorithm is not memory bounded anymore, yielding significant speed-ups.
- Software/Multitasking Operating Systems
- As the XPP is introduced into a RISC core, the changed environment—higher frequency and the memory hierarchy—may necessitate, not only reconsideration of hardware design parameters, but also a reevaluation of the software environment.
- Memory Hierarchy
- The introduction of a memory hierarchy may enhance the set of applications that can be implemented efficiently. So far, the XPP has mostly been used for algorithms that read their data sets in a linear manner, applying some calculations in a pipelined fashion and writing the data back to memory. As long as all of the computation fits into the XPP array, these algorithms are memory bounded. Typical applications are filtering and audio signal processing in general.
- But there is another set of algorithms that have even higher computational complexity and higher memory bandwidth requirements. Examples are picture and video processing, where a second and third dimension of data coherence opens up. This coherence is, e.g., exploited by picture and video compression algorithms that scan pictures in both dimensions to find similarities, even searching consecutive pictures of a video stream for analogies. These algorithms have a much higher algorithmic complexity as well as higher memory requirements. Yet they are data local, either by design or by transformation, thus efficiently exploiting the memory hierarchy and the higher clock frequencies of processors with memory hierarchies.
- Multi Tasking
- The introduction into a standard RISC core makes it necessary to understand and support the needs of a multitasking operating system, as standard RISC processors are usually operated in multitasking environments. With multitasking, the operating system may switch the executed application on a regular basis, thus simulating concurrent execution of several applications (tasks). To switch tasks, the operating system may have to save the state, (e.g., the contents of all registers), of the running task and then reload the state of another task. Hence, it may be necessary to determine what the state of the processor is, and to keep it as small as possible to allow efficient context switches.
- Modern microprocessors gain their performance from multiple specialized and deeply pipelined functional units and high memory hierarchies, enabling high core frequencies. But high memory hierarchies mean that there is a high penalty for cache misses due to the difference between core and memory frequency. Many core cycles may pass until the values are finally available from memory. Deep pipelines incur pipeline stalls due to data dependencies as well as branch penalties for mispredicted conditional branches. Specialized functional units like floating point units idle for integer-only programs. For these reasons, average functional unit utilization is much too low.
- The newest development with RISC processors, Simultaneous MultiThreading (SMT), adds hardware support for a finer granularity (instruction/functional unit level) switching of tasks, exposing more than one independent instruction stream to be executed. Thus, whenever one instruction stream stalls or doesn't utilize all functional units, the other one can jump in. This improves functional unit utilization for today's processors.
- With SMT, the task (process) switching is done in hardware, so the processor state has to be duplicated in hardware. So again it is most efficient to keep the state as small as possible. For the combination of the PACT XPP and a standard RISC processor, SMT may be very beneficial, since the XPP configurations may execute longer than the average RISC instruction. Thus, another task can utilize the other functional units, while a configuration is running. On the other hand, not every task will utilize the XPP, so while one such non-XPP task is running, another one will be able to use the XPP core.
- The following are several possible embodiments that are each a possible hardware implementation for accessing memory.
- Streaming
- Since streaming can only support (number_of_IO_ports*width_of_IO_port) bits per cycle, it may be well suited for only small XPP arrays with heavily pipelined configurations that feature few inputs and outputs. As the pipelines take a long time to fill and empty while the running time of a configuration is limited (as described herein with respect to "context switches"), this type of communication does not scale well to bigger XPP arrays and XPP frequencies near the RISC core frequency.
- Streaming from the RISC Core
- In this setup, the RISC may supply the XPP array with the streaming data. Since the RISC core may have to execute several instructions to compute addresses and load an item from memory, this setup is only suited if the XPP core is reading data with a frequency much lower than the RISC core frequency.
- Streaming via DMA
- In this mode the RISC core only initializes a DMA channel which may then supply the data items to the streaming port of the XPP core.
- Shared Memory (Main Memory)
- In this configuration, the XPP array configuration may use a number of PAEs to generate an address that is used to access main memory through the IO ports. As the number of IO ports may be very limited, this approach may suffer from the same limitations as the previous one, although for larger XPP arrays there is less impact of using PAEs for address generation. However, this approach may still be useful for loading values from very sparse vectors.
- Shared Memory (IRAM)
- This data access mechanism uses the IRAM elements to store data for local computations. The IRAMs can either be viewed as vector registers or as local copies of main memory.
- The following are several ways in which to fill the IRAMs with data:
- 1. The IRAMs may be loaded in advance by a separate configuration using streaming.
- This method can be implemented with the current XPP architecture. The IRAMs act as vector registers. As explicated above, this may limit the performance of the XPP array, especially as the IRAMs will always be part of the externally visible state and hence must be saved and restored on context switches.
- 2. The IRAMs may be loaded in advance by separate load-instructions.
- This is similar to the first method. Load-instructions may be implemented in hardware which loads the data into the IRAMs. The load-instructions can be viewed as a hard coded load configuration. Therefore, configuration reloads may be reduced. Additionally, the special load instructions may use a wider interface to the memory hierarchy. Therefore, a more efficient method than streaming can be used.
- 3. The IRAMs can be loaded by a "burst preload from memory" instruction of the cache controller. No configuration or load-instruction is needed on the XPP. The IRAM load may be implemented in the cache controller and triggered by the RISC processor. But the IRAMs may still act as vector registers and may be therefore included in the externally visible state.
- 4. The best mode, however, may be a combination of the previous solutions with the extension of a cache:
- A preload instruction may map a specific memory area defined by starting address and size to an IRAM. This may trigger a (delayed, low priority) burst load from the memory hierarchy (cache). After all IRAMs are mapped, the next configuration can be activated. The activation may incur a wait until all burst loads are completed. However, if the preload instructions are issued long enough in advance and no interrupt or task switch destroys cache locality, the wait will not consume any time.
- To specify a memory block as output-only IRAM, a "preload clean" instruction may be used, which may avoid loading data from memory. The "preload clean" instruction just indicates the IRAM for write back.
- A synchronization instruction may be needed to make sure that the content of a specific memory area, which is cached in IRAM, is written back to the memory hierarchy. This can be done globally (full write back), or selectively by specifying the memory area, which will be accessed.
- 1. The IRAMs may be loaded in advance by a separate configuration using streaming.
- As discussed above, the size of the state may be crucial for the efficiency of context switches. However, although the size of the state may be fixed for the XPP core, whether or not they have to be saved may depend on the declaration of the various state elements.
- The state of the XPP core can be classified as:
- 1. Read only (instruction data)
- configuration data, consisting of PAE configuration and routing configuration data; and
- the contents of the data registers and latches of the PAEs, which are driven onto the busses
- the contents of the IRAM elements.
- Limiting Memory Traffic
- There are several possibilities to limit the amount of memory traffic during context switches, as follows:
- Do Not Save Read-Only Data
- This may avoid storing configuration data, since configuration data is read only. The current configuration may be simply overwritten by the new one.
- Save Less Data
- If a configuration is defined to be uninterruptible (non pre-emptive), all of the local state on the busses and in the PAEs can be declared as scratch. This means that every configuration may get its input data from the IRAMs and may write its output data to the IRAMs. So after the configuration has finished, all information in the PAEs and on the buses may be redundant or invalid and saving of the information might not be required.
- Save Modified Data Only
- To reduce the amount of R/W data which has to be saved, the method may keep track of the modification state of the different entities. This may incur a silicon area penalty for the additional "dirty" bits.
- Use Caching to Reduce the Memory Traffic
- The configuration manager may handle manual preloading of configurations. Preloading may help in parallelizing the memory transfers with other computations during the task switch. This cache can also reduce the memory traffic for frequent context switches, provided that a Least Recently Used (LRU) replacement strategy is implemented in addition to the preload mechanism.
- The IRAMs can be defined to be local cache copies of main memory as discussed above under the heading "Shared Memory (IRAM)." Then each IRAM may be associated with a starting address and modification state information. The IRAM memory cells may be replicated. An IRAM PAE may contain an IRAM block with multiple IRAM instances. It may be that only the starting addresses of the IRAMs have to be saved and restored as context. The starting addresses for the IRAMs of the current configuration select the IRAM instances with identical addresses to be used.
- If no address tag of an IRAM instance matches the address of the newly loaded context, the corresponding memory area may be loaded to an empty IRAM instance.
- If no empty IRAM instance is available, a clean (unmodified) instance may be declared empty (and hence it may be required for it to be reloaded later on).
- If no clean IRAM instance is available, a modified (dirty) instance may be cleaned by writing its data back to main memory. This may add a certain delay for the write back.
- This delay can be avoided if a separate state machine (cache controller) tries to clean inactive IRAM instances by using unused memory cycles to write back the IRAM instances' contents.
- Usually a processor is viewed as executing a single stream of instructions. But today's multi-tasking operating systems support hundreds of tasks being executed on a single processor. This is achieved by switching contexts, where all, or at least the most relevant parts, of the processor state which belong to the current task—the task's context—is exchanged with the state of another task, that will be executed next.
- There are three types of context switches: switching of virtual processors with simultaneous multithreading (SMT, also known as HyperThreading), execution of an Interrupt Service Routine (ISR), and a Task Switch.
- SMT Virtual Processor Switch
- This type of context switch may be executed without software interaction, totally in hardware. Instructions of several instruction streams are merged into a single instruction stream to increase instruction level parallelism and improve functional unit utilization. Hence, the processor state cannot be stored to and reloaded from memory between instructions from different instruction streams. For example, in an instance of alternating instructions from two streams and hundreds to thousands of cycles might be needed to write the processor state to memory and read in another state.
- Hence hardware designers have to replicate the internal state for every virtual processor. Every instruction may be executed within the context (on the state) of the virtual processor whose program counter was used to fetch the instruction. By replicating the state, only the multiplexers, which have to be inserted to select one of the different states, have to be switched.
- Thus the size of the state may also increase the silicon area needed to implement SMT, so the size of the state may be crucial for many design decisions.
- Interrupt Service Routine
- This type of context switch may be handled partially by hardware and partially by software. It may be required for all of the state modified by the ISR to be saved on entry and it may be required for it to be restored on exit.
- The part of the state which is destroyed by the jump to the ISR may be saved by hardware, (e.g., the program counter). It may be the ISR's responsibility to save and restore the state of all other resources, that are actually used within the ISR.
- The more state information to be saved, the slower the interrupt response time may be and the greater the performance impact may be if external events trigger interrupts at a high rate.
- The execution model of the instructions may also affect the tradeoff between short interrupt latencies and maximum throughput. Throughput may be maximized if the instructions in the pipeline are finished and the instructions of the ISR are chained. This may adversely affect the interrupt latency. If, however, the instructions are abandoned (pre-empted) in favor of a short interrupt latency, it may be required for them to be fetched again later, which may affect throughput. The third possibility would be to save the internal state of the instructions within the pipeline, but this may require too much hardware effort. Usually this is not done.
- Task Switch
- This type of context switch may be executed totally in software. It may be required for all of a task's context (state) to be saved to memory, and it may be required for the context of the new task to be reloaded. Since tasks are usually allowed to use all of the processor's resources to achieve top performance, it may be required to save and restore all of the processor state. If the amount of state is excessive, it may be required for the rate of context switches to be decreased by less frequent rescheduling, or a severe throughput degradation may result, as most of the time may be spent in saving and restoring task contexts. This in turn may increase the response time for the tasks.
- In an example embodiment of the present invention, an XPP integration may be provided as an asynchronously pipelined functional unit for the RISC. An explicitly preloaded cache may be provided for the IRAMs, on top of the memory hierarchy existing within the RISC (as discussed above under the heading "Shared Memory (IRAM)." Additionally a de-centralized explicitly preloaded configuration cache within the PAE array may be employed to support preloading of configurations and fast switching between configurations.
- Since the IRAM content is an explicitly preloaded memory area, a virtually unlimited number of such IRAMs can be used. They may be identified by their memory address and their size. The IRAM content may be explicitly preloaded by the application. Caching may increase performance by reusing data from the memory hierarchy. The cached operation may also eliminate the need for explicit store instructions; they may be handled implicitly by cache write back operations but can also be forced to synchronize with the RISC.
- The pipeline stages of the XPP functional unit may be Load, Execute, and Write Back (Store). The store may be executed delayed as a cache write back. The pipeline stages may execute in an asynchronous fashion, thus hiding the variable delays from the cache preloads and the PAE array.
- The XPP functional unit may be decoupled of the RISC by a FIFO fed with the XPP instructions. At the head of this FIFO, the XPP PAE may consume and execute the configurations and the preloaded IRAMs. Synchronization of the XPP and the RISC may be done explicitly by a synchronization instruction.
- Instructions
- Embodiments of the present invention may require certain instruction formats. Data types may be specified using a C style prototype definition. The following are example instruction formats which may be required, all of which execute asynchronously, except for an XPPSync instruction, which can be used to force synchronization.
- XPPPreloadConfig (void *ConfigurationStartAddress)
- The configuration may be added to the preload FIFO to be loaded into the configuration cache within the PAE array.
- Note that speculative preloads is possible since successive preload commands overwrite the previous.
- The parameter is a pointer register of the RISC pointer register file. The size is implicitly contained in the configuration.
- XPPPreload (int IRAM, void *StartAddress, int Size)
- XPPPreloadClean (int IRAM, void *StartAddress, int Size)
- This instruction may specify the contents of the IRAM for the next configuration execution. In fact, the memory area may be added to the preload FIFO to be loaded into the specified IRAM.
- The first parameter may be the IRAM number. This may be an immediate (constant) value.
- The second parameter may be a pointer to the starting address. This parameter may be provided in a pointer register of the RISC pointer register file.
- The third parameter may be the size in units of 32 bit words. This may be an integer value. It may reside in a general purpose register of the RISC's integer register file.
- The first variant may actually preload the data from memory.
- The second variant may be for write-only accesses. It may skip the loading operation. Thus, it may be that no cache misses can occur for this IRAM. Only the address and size are defined. They are obviously needed for the write back operation of the IRAM cache.
- Note that speculative preloads are possible since successive preload commands to the same IRAM overwrite each other (if no configuration is executed in between). Thus, only the last preload command may be actually effective when the configuration is executed.
- XPPExecute ( )
- This instruction may execute the last preloaded configuration with the last preloaded IRAM contents. Actually, a configuration start command may be issued to the FIFO. Then the FIFO may be advanced. This may mean that further preload commands will specify the next configuration or parameters for the next configuration.
- Whenever a configuration finishes, the next one may be consumed from the head of the FIFO; if its start command has already been issued.
- XPPSync (void *StartAddress, int Size)
- This instruction may force write back operations for all IRAMs that overlap the given memory area. If overlapping IRAMs are still in use by a configuration or preloaded to be used, this operation will block. Giving an address of NULL (zero) and a size of MAX INT (bigger than the actual memory), this instruction can also be used to wait until all issued configurations finish.
- A Basic Implementation
- As shown in
FIG. 9, the XPP core 102 may share a memory hierarchy with the RISC core 112 using a special cache controller 125-130.
FIG. 10shows an IRAM and configuration cache controller data structures and a usage example (instructions).
- The preload-FIFOs in
FIG. 10may contain the addresses and sizes for already issued IRAM preloads, exposing them to the XPP cache controller. The FIFOs may have to be duplicated for every virtual processor in an SMT environment. "Tag" is the typical tag for a cache line containing starting address, size, and state (empty/clean/dirty I in-use). The additional in-use state signals usage by the current configuration. The cache controller cannot manipulate these IRAM instances.
- The execute configuration command may advance all preload FIFOs, copying the old state to the newly created entry. This way the following preloads may replace the previously used IRAMs and configurations. If no preload is issued for an IRAM before the configuration is executed, the preload of the previous configuration may be retained. Therefore, it may be that it is not necessary to repeat identical preloads for an IRAM in consecutive configurations.
- Each configuration's execute command may have to be delayed (stalled) until all necessary preloads are finished, either explicitly by the use of a synchronization command or implicitly by the cache controller. Hence the cache controller (XPP Ld/St unit) 125 may have to handle the synchronization and execute commands as well, actually starting the configuration as soon as all data is ready. After the termination of the configuration, dirty IRAMs may be written back to memory as soon as possible if their content is not reused in the same IRAM. Therefore the XPP PAE array (XPP core 102) and the XPP cache controller 125 can be seen as a single unit since they do not have different instruction streams. Rather, the cache controller can be seen as the configuration fetch (CF), operand fetch (OF) (IRAM preload) and write back (WB) stage of the XPP pipeline, also triggering the execute stage (EX) (PAE array).
FIG. 11shows the asynchronous pipeline of the XPP 100.
- Due to the long latencies, and their non-predictability (cache misses, variable length configurations), the stages can be overlapped several configurations wide using the configuration and data preload FIFO, (i.e., pipeline), for loose coupling. If a configuration is executing and the data for the next has already been preloaded, the data for the next but one configuration may be preloaded. These preloads can be speculative. The amount of speculation may be the compiler's trade-off. The reasonable length of the preload FIFO can be several configurations. It may be limited by diminishing returns, algorithm properties, the compiler's ability to schedule preloads early and by silicon usage due to the IRAM duplication factor, which may have to be at least as big as the FIFO length. Due to this loosely coupled operation, the interlocking (to avoid data hazards between IRAMs) cannot be done optimally by software (scheduling), but may have to be enforced by hardware (hardware interlocking). Hence the XPP cache controller and the XPP PAE array can be seen as separate but not totally independent functional units.
- The XPP cache controller may have several tasks. These are depicted as states in
FIG. 12. State transitions may take place along the edges between states, whenever the condition for the edge is true. As soon as the condition is not true any more, the reverse state transition may take place. The activities for the states may be as follows.
- At the lowest priority, the XPP cache controller 125 may have to fulfill already issued preload commands, while writing back dirty IRAMs as soon as possible.
- As soon as a configuration finishes, the next configuration can be started. This is a more urgent task than write backs or future preloads. To be able to do that, all associated yet unsatisfied preloads may have to be finished first. Thus, they may be preloaded with the high priority inherited from the execute state.
- A preload in turn can be blocked by an overlapping in-use or dirty IRAM instance in a different block or by the lack of empty IRAM instances in the target IRAM block. The former can be resolved by waiting for the configuration to finish and/or by a write back. To resolve the latter, the least recently used clean IRAM can be discarded, thus becoming empty. If no empty or clean IRAM instance exists, a dirty one may have to be written back to the memory hierarchy. It cannot occur that no empty, clean, or dirty IRAM instances exist, since only one instance can be in-use and there should be more than one instance in an IRAM block; otherwise, no caching effect is achieved.
- In an SMT environment the load FIFOs may have to be replicated for every virtual processor. The pipelines of the functional units may be fed from the shared fetch/reorder/issue stage. All functional units may execute in parallel. Different units can execute instructions of different virtual processors.
FIG. 13shows adding of simultaneous multithreading.
- So the following design parameters, with their smallest initial value, may be obtained:
- IRAM length: 128 words
- The longer the IRAM length, the longer the running time of the configuration and the less influence the pipeline startup has.
- FIFO length: 1
- This parameter may help to hide cache misses during preloading. The longer the FIFO length, the less disruptive is a series of cache misses for a single configuration.
- IRAM duplication factor: (pipeline stages+caching factor)*virtual processors: 3
- Pipeline stages is the number of pipeline stages LD/EX/WB plus one for every FIFO stage above one: 3
- Caching factor is the number of IRAM duplicates available for caching: 0
- Virtual processors is the number of virtual processors with SMT: 1
- IRAM length: 128 words
- The size of the state of a virtual processor is mainly dependent on the FIFO length. It is
- FIFO length*#IRAM ports*(32 bit (Address)+32 bit (Size)).
- This may have to be replicated for every virtual processor.
- The total size of memory used for the IRAMs may be:
- #IRAM ports * IIRAM duplication factor* IRAM length * 32 bit.
- A first implementation will probably keep close to the above-stated minimum parameters, using a FIFO length of one, an IRAM duplication factor of four, an IRAM length of 128 and no simultaneous multithreading.
- Implementation Improvements
- Write Pointer
- To further decrease the penalty for unloaded IRAMs, a simple write pointer may be used per IRAM, which may keep track of the last address already in the IRAM. Thus, no stall is required, unless an access beyond this write pointer is encountered. This may be especially useful if all IRAMs have to be reloaded after a task switch. The delay to the configuration start can be much shorter, especially, if the preload engine of the cache controller chooses the blocking IRAM next whenever several IRAMs need further loading.
- Longer FIFOs
- The frequency at the bottom of the memory hierarchy (main memory) cannot be raised to the same extent as the frequency of the CPU core. To increase the concurrency between the RISC core 112 and the PACT XPP core 102, the prefetch FIFOs in
FIG. 13can be extended. Thus, the IRAM contents for several configurations can be preloaded, like the configurations themselves. A simple convention makes clear which IRAM preloads belong to which configuration. The configuration execute switches to the next configuration context. This can be accomplished by advancing the FIFO write pointer with every configuration execute, while leaving it unchanged after every preload. Unassigned IRAM FIFO entries may keep their contents from the previous configuration, so every succeeding configuration may use the preceding configuration's IRAMx if no different IRAMx was preloaded.
- If none of the memory areas to be copied to IRAMs is in any cache, extending the FIFOs does not help, as the memory is the bottleneck. So the cache size should be adjusted together with the FIFO length.
- A drawback of extending the FIFO length is the increased likelihood that the IRAM content written by an earlier configuration is reused by a later one in another IRAM. A cache coherence protocol can clear the situation. Note, however, that the situation can be resolved more easily. If an overlap between any new IRAM area and a currently dirty IRAM contents of another IRAM bank is detected, the new IRAM is simply not loaded until the write back of the changed IRAM has finished. Thus, the execution of the new configuration may be delayed until the correct data is available.
- For a short (single entry) FIFO, an overlap is extremely unlikely, since the compiler will usually leave the output IRAM contents of the previous configuration in place for the next configuration to skip the preload. The compiler may do so using a coalescing algorithm for the IRAMs I vector registers. The coalescing algorithm may be the same as used for register coalescing in register allocation.
- Read Only IRAMS
- Whenever the memory that is used by the executing configuration is the source of a preload command for another IRAM, an XPP pipeline stall may occur. The preload can only be started when the configuration has finished and, if the content was modified, the memory content has been written to the cache. To decrease the number of pipeline stalls, it may be beneficial to add an additional read only IRAM state. If the IRAM is read only, the content cannot be changed, and the preload of the data to the other IRAM can proceed without delay. This may require an extension to the preload instructions. The XppPreload and the XppPreloadClean instruction formats can be combined to a single instruction format that has two additional bits stating whether the IRAM will be read and/or written. To support debugging, violations should be checked at the IRAM ports, raising an exception when needed.
- Support for Data Distribution and Data Reorganization
- The IRAMs may be block-oriented structures, which can be read in any order by the PAE array. However, the address generation may add complexity, reducing the number of PAEs available for the actual computation. Accordingly, the IRAMs may be accessed in linear order. The memory hierarchy may be block oriented as well, further encouraging linear access patterns in the code to avoid cache misses.
- As the IRAM read ports limit the bandwidth between each IRAM and the PAE array to one word read per cycle, it can be beneficial to distribute the data over several IRAMs to remove this bottleneck. The top of the memory hierarchy is the source of the data, so the number of cache misses never increases when the access pattern is changed, as long as the data locality is not destroyed.
- Many algorithms access memory in linear order by definition to utilize block reading and simple address calculations. In most other cases and in the cases where loop tiling is needed to increase the data bandwidth between the IRAMs and the PAE array, the code can be transformed in a way that data is accessed in optimal order. In many of the remaining cases, the compiler cam modify the access pattern by data layout rearrangements, (e.g., array merging), so that finally the data is accessed in the desired pattern. If none of these optimizations can be used because of dependencies, or because the data layout is fixed, there are still two possibilities to improve performance, which are data duplication and data reordering.
- Data Duplication
- Data may be duplicated in several IRAMs. This may circumvent the IRAM read port bottleneck, allowing several data items to be read from the input every cycle.
- Several options are possible with a common drawback. Data duplication can only be applied to input data. Output IRAMs obviously cannot have overlapping address ranges.
- Using several IRAM preload commands specifying just different target IRAMs:
- This way cache misses may occur only for the first preload. All other preloads may take place without cache misses. Only the time to transfer the data from the top of the memory hierarchy to the IRAMs is needed for every additional load. This is only beneficial if the cache misses plus the additional transfer times do not exceed the execution time for the configuration.
- Using an IRAM preload instruction to load multiple IRAMs concurrently:
- As identical data is needed in several IRAMs, they can be loaded concurrently by writing the same values to all of them. This amounts to finding a clean IRAM instance for every target IRAM, connecting them all to the bus, and writing the data to the bus. The problem with this instruction may be that it requires a bigger immediate field for the destination (16 bits instead of 4 for the XPP 64). Accordingly, this instruction format may grow at a higher rate when the number of IRAMs is increased for bigger XPP arrays.
- Using several IRAM preload commands specifying just different target IRAMs:
- The interface of this instruction is for example:
- XPPPreloadMultiple (int IRAMS, void *StartAddress, int Size).
- This instruction may behave as the XPPPreload/XPPPreloadClean instructions with the exception of the first parameter. The first parameter is IRAMS. This may be an immediate (constant) value. The value may be a bitmap. For every bit in the bitmap, the IRAM with that number may be a target for the load operation.
- There is no "clean" version, since data duplication is applicable for read data only.
- Data Reordering
- Data reordering changes the access pattern to the data only. It does not change the amount of memory that is read. Thus, the number of cache misses may stay the same.
- Adding additional functionality to the hardware:
- A stride (displacement between two elements in memory) may be used in vector load operations to load, e.g., a column of a matrix into a vector register.
- This is still a linear access pattern. It can be implemented in hardware by giving a stride to the preload instruction and adding the stride to the IRAM identification state. One problem with this instruction may be that the number of possible cache misses per IRAM load rises. In the worst case it can be one cache miss per loaded value if the stride is equal to the cache line size and all data is not in the cache. But as already stated, the total number of misses stays the same. Just the distribution changes. Still, this is an undesirable effect.
- The other problem may be the complexity of the implementation and a possibly limited throughput, as the data paths between the layers of the memory hierarchy are optimized for block transfers. Transferring non-contiguous words will not use wide busses in an optimal fashion.
- The interface of the instruction is for example:
- XPPPreloadStride (int IRAN, void *StartAddress, int Size, int Stride)
- XPPPreloadCleanStride (int IRAN, void *StartAddress, int Size, int Stride).
- This instruction may behave as the XPPPreload/XPPPreloadClean instructions with the addition of another parameter. The fourth parameter is the vector stride. This may be an immediate (constant) value. It may tell the cache controller to load only every nth value to the specified IRAM.
- Reordering the data at run time, introducing temporary copies.
- The RISC can copy data at a maximum rate of one word per cycle for simple address computations and at a somewhat lower rate for more complex ones.
- With a memory hierarchy, the sources may be read from memory (or cache, if they were used recently) once and written to the temporary copy, which may then reside in the cache, too. This may increase the pressure in the memory hierarchy by the amount of memory used for the temporaries. Since temporaries are allocated on the stack memory, which may be re-used frequently, the chances are good that the dirty memory area is redefined before it is written back to memory. Hence the write back operation to memory is of no concern.
- Via an XPP configuration:
- The PAE array can read and write one value from every IRAM per cycle. Thus, if half of the IRAMs are used as inputs and half of the IRAMs are used as outputs, up to eight (or more, depending on the number of IRAMs), values can be reordered per cycle, using the PAE array for address generation. As the inputs and outputs reside in IRAMs, it does not matter if the reordering is done before or after the configuration that uses the data. The IRAMs can be reused immediately.
- Adding additional functionality to the hardware:
- IRAM Chaining
- If the PAEs do not allow further unrolling, but there are still IRAMs left unused, it may be possible to load additional blocks of data into these IRAMs and chain two IRAMs via an address selector. This might not increase throughput as much as unrolling would do, but it still may help to hide long pipeline startup delays whenever unrolling is not possible.
- According to the design parameter changes and the corresponding changes to the hardware, according to embodiments of the present invention, the hardware/software interface has changed. In the following, some prominent changes and their handling are discussed.
- Explicit Cache
- The proposed cache is not a usual cache, which would be, without considering performance issues, invisible to the programmer/compiler, as its operation is transparent. The proposed cache is an explicit cache. Its state may have to be maintained by software.
- Cache Consistency and Pipelining of Preload/Configuration/Write back
- The software may be responsible for cache consistency. It may be possible to have several IRAMs caching the same or overlapping memory areas. As long as only one of the IRAMs is written, this is perfectly ok. Only this IRAM will be dirty and will be written back to memory. If, however, more than one of the IRAMs is written, which data will be written to memory is not defined. This is a software bug (non-deterministic behavior).
- As the execution of the configuration is overlapped with the preloads and write backs of the IRAMs, it may be possible to create preload/configuration sequences that contain data hazards. As the cache controller and the XPP array can be seen as separate functional units, which are effectively pipelined, these data hazards are equivalent to pipeline hazards of a normal instruction pipeline. As with any ordinary pipeline, there are two possibilities to resolve this, which are hardware interlocking and software interlocking.
- Hardware interlocking:
- Interlocking may be done by the cache controller. If the cache controller detects that the tag of a dirty or in-use item in IRAMx overlaps a memory area used for another IRAM preload, it may have to stall that preload, effectively serializing the execution of the current configuration and the preload.
- Software interlocking:
- If the cache controller does not enforce interlocking, the code generator may have to insert explicit synchronize instructions to take care of potential interlocks. Inter-procedural and inter-modular alias and data dependency analyses can determine if this is the case, while scheduling algorithms may help to alleviate the impact of the necessary synchronization instructions.
- In either case, as well as in the case of pipeline stalls due to cache misses, SMT can use the computation power that would be wasted otherwise.
- Code Generation for the Explicit Cache
- Apart from the explicit synchronization instructions issued with software interlocking, the following instructions may have to be issued by the compiler.
- Configuration preload instructions, preceding the IRAM preload instructions, that will be used by that configuration. These should be scheduled as early as possible by the instruction scheduler.
- IRAM preload instructions, which should also be scheduled as early as possible by the instruction scheduler.
- Configuration execute instructions, following the IRAM preload instructions for that configuration. These instructions should be scheduled between the estimated minimum and the estimated maximum of the cumulative latency of their preload instructions.
- IRAM synchronization instructions, which should be scheduled as late as possible by the instruction scheduler. These instructions must be inserted before any potential access of the RISC to the data areas that are duplicated and potentially modified in the IRAMs. Typically, these instructions will follow a long chain of computations on the XPP, so they will not significantly decrease performance.
- Asynchronicity to Other Functional Units
- An XppSync( ) must be issued by the compiler, if an instruction of another functional unit (mainly the Ld/St unit) can access a memory area that is potentially dirty or in-use in an IRAM. This may force a synchronization of the instruction streams and the cache contents, avoiding data hazards. A thorough inter-procedural and inter-modular array alias analysis may limit the frequency of these synchronization instructions to an acceptable level.
- For the previous design, the IRAMs are existent in silicon, duplicated several times to keep the pipeline busy. This may amount to a large silicon area, that is not fully busy all the time, especially, when the PAE array is not used, but as well whenever the configuration does not use all of the IRAMs present in the array. The duplication may also make it difficult to extend the lengths of the IRAMs, as the total size of the already large IRAM area scales linearly.
- For a more silicon efficient implementation, the IRAMs may be integrated into the first level cache, making this cache bigger. This means that the first level cache controller is extended to feed all IRAM ports of the PAE array. This way the XPP and the RISC may share the first level cache in a more efficient manner. Whenever the XPP is executing, it may steal as much cache space as it needs from the RISC. Whenever the RISC alone is running it will have plenty of additional cache space to improve performance.
- The PAE array may have the ability to read one word and write one word to each IRAM port every cycle. This can be limited to either a read or a write access per cycle, without limiting programmability. If data has to be written to the same area in the same cycle, another IRAM port can be used. This may increase the number of used IRAM ports, but only under rare circumstances.
- This leaves sixteen data accesses per PAE cycle in the worst case. Due to the worst case of all sixteen memory areas for the sixteen IRAM ports mapping to the same associative bank, the minimum associativity for the cache may be a 16-way set associativity. This may avoid cache replacement for this rare, but possible, worst-case example.
- Two factors may help to support sixteen accesses per PAE array cycle:
- The clock frequency of the PAE array generally has to be lower than for the RISC by a factor of two to four. The reasons lie in the configurable routing channels with switch matrices which cannot support as high a frequency as solid point-to-point aluminum or copper traces.
- This means that two to four IRAM port accesses can be handled serially by a single cache port, as long as all reads are serviced before all writes, if there is a potential overlap. This can be accomplished by assuming a potential overlap and enforcing a priority ordering of all accesses, giving the read accesses higher priority.
- A factor of two, four, or eight is possible by accessing the cache as two, four, or eight banks of lower associativity cache.
- For a cycle divisor of four, four banks of four-way associativity will be optimal. During four successive cycles, four different accesses can be served by each bank of four way associativity. Up to four-way data duplication can be handled by using adjacent IRAM ports that are connected to the same bus (bank). For further data duplication, the data may have to be duplicated explicitly, using an XppPreloadMultiple( ) cache controller instruction. The maximum data duplication for sixteen read accesses to the same memory area is supported by an actual data duplication factor of four—one copy in each bank. This does not affect the RAM efficiency as adversely as an actual data duplication of 16 for the embodiment discussed above under the heading "A Load Store Architecture."
FIG. 14shows an example of a cache structure according to an example embodiment of the present invention. The cache controller may run at the same speed as the RISC. The XPP may run at a lower, (e.g., quarter), speed. Accordingly, in the worst case, sixteen read requests from the PAE array may be serviced in four cycles of the cache controller, with an additional four read requests from the RISC. Accordingly, one bus at full speed can be used to service four IRAM read ports. Using four-way associativity, four accesses per cycle can be serviced, even in the case that all four accesses go to addresses that map to the same associative block.
- a) The RISC still has a 16-way set associative view of the cache, accessing all four four-way set associative banks in parallel. Due to data duplication, it is possible that several banks return a hit. This may be taken care of with a priority encoder, enabling only one bank onto the data bus.
- b) The RISC is blocked from the banks that service IRAM port accesses. Wait states are inserted accordingly.
- c) The RISC shares the second cache access port of a two-port cache with the RAM interface, using the cycles between the RAM transfers for its accesses.
- d) The cache is extended by a fifth 4-way set associative bank, used exclusively by the RISC. (The other banks are only accessed when they are not used by the current XPP configuration. PROBLEM: dirty line in a blocked bank).
- With respect to a 2 port RAM, concurrent reads may be accommodated. Concurrent R/W to a same cache line may be avoided by software synchronization/hardware arbiter.
- A problem is that a read could potentially address the same memory location as a write. The value read may depend on the order of the operation so that the order is fixed, i.e., all writes have to take place after all reads, but before the reads of the next cycle, except, if the reads and writes actually do not overlap. This can only be a problem with data duplication, when only one copy of the data is actually modified. Therefore, modifications are forbidden with data duplication.
- Programming Model Changes
- Data Interference
- According to an example embodiment of the present invention that is without dedicated IRAMs, it is not possible anymore to load input data to the IRAMs and write the output data to a different IRAM, which is mapped to the same address, thus operating on the original, unaltered input data during the whole configuration.
- As there are no dedicated IRAMs anymore, writes directly modify the cache contents, which will be read by succeeding reads. This changes the programming model significantly. Additional and more in-depth compiler analyses are accordingly necessary.
- Hiding Implementation Details
- The actual number of bits in the destination field of the XppPreloadMultiple instruction is implementation dependent. It depends on the number of cache banks and their associativity, which are determined by the clock frequency divisor of the XPP PAE array relative to the cache frequency. However, this can be hidden by the assembler, which may translate IRAM ports to cache banks, thus reducing the number of bits from the number of IRAM ports to the number of banks. For the user, it is sufficient to know that each cache bank services an adjacent set of IRAM ports starting at a power of two. Thus, it may be best to use data duplication for adjacent ports, starting with the highest power of two greater than the number of read ports to the duplicated area.
- Analyses may be performed on programs to describe the relationships between data and memory location in a program. These analyses may then be used by different optimizations. More details regarding the analyses are discussed in Michael Wolfe, "High Performance Compilers for Parallel Computing" (Addison-Wesley 1996); Hans Zima & Barbara Chapman, "Supercompilers for parallel and vector computers" (Addison-Wesley 1991); and Steven Muchnick, "Advanced Compiler Design and Implementation" (Morgan Kaufmann 1997).
- Data-Flow Analysis
- Data-flow analysis examines the flow of scalar values through a program to provide information about how the program manipulates its data. This information can be represented by dataflow equations that have the following general form for object i, that can be an instruction or a basic block, depending on the problem to solve:
- This means that data available at the end of the execution of object i, Ex[I], are either produced by i, Prod[i] or were alive at the beginning of i, In[i], but were not deleted during the execution of i, Supp[i].
- These equations can be used to solve several problems, such as, e.g.,
- the problem of reaching definitions;
- the Def-Use and Use-Def chains, describing respectively, for a definition, all uses that can be reached from it, and, for a use, all definitions that can reach it;
- the available expressions at a point in the program; and/or
- the live variables at a point in the program,
whose solutions are then used by several compilation phases, analysis, or optimizations.
- For example, with respect to a problem of computing the Def-Use chains of the variables of a program, this information can be used for instance by the data dependence analysis for scalar variables or by the register allocation. A Def-Use chain is associated to each definition of a variable and is the set of all visible uses from this definition. The data-flow equations presented above may be applied to the basic blocks to detect the variables that are passed from one block to another along the control flow graph. In
FIG. 15, which shows a control-flow graph of a piece of a program, two definitions for variable x are produced: S1 in B1 and S4 in B3. Hence, the variable that can be found at the exit of B1 is Ex(B1)={x(S1)}; and at the exit of B4 is Ex(B4)={x(S4)}. Moreover, Ex(B2)=Ex(B1) as no variable is defined in B2. Using these sets, it is the case that the uses of x in S2 and S3 depend on the definition of x in B1 and that the use of x in S5 depends on the definitions of x in B1 and B3. The Def-use chains associated with the definitions are then D(S1)={S2, S3, S5} and D(S4)={S5}.
- Data Dependence Analysis
- A data dependence graph represents the dependencies existing between operations writing or reading the same data. This graph may be used for optimizations like scheduling, or certain loop optimizations to test their semantic validity. The nodes of the graph represent the instructions, and the edges represent the data dependencies. These dependencies can be of three types: true (or flow) dependence when a variable is written before being read, anti-dependence when a variable is read before being written, and output dependence when a variable is written twice. A more formal definition is provided in Hans Zima et al., supra and is presented below.
- Let S and S′ be two statements. Then S′ depends on S, noted SδS′ iff:
- (1) S is executed before S′
- (2)
- (3) There is no statement T such that S is executed before T and T is executed before S′, and ν ε DEF(T),
where VAR is the set of the variables of the program, DEF(S) is the set of the variables defined by instruction S, and USE(S) is the set of variables used by instruction S.
- Moreover, if the statements are in a loop, a dependence can be loop independent or loop carried. This notion introduces the definition of the distance of a dependence. When a dependence is loop independent, it occurs between two instances of different statements in the same iteration, and its distance is equal to 0. By contrast, when a dependence is loop carried, it occurs between two instances in two different iterations, and its distance is equal to the difference between the iteration numbers of the two instances.
- The notion of direction of dependence generalizes the notion of distance, and is generally used when the distance of a dependence is not constant, or cannot be computed with precision. The direction of a dependence is given by < if the dependence between S and S′ occurs when the instance of S is in an iteration before the iteration of the instance of S′,=if the two instances are in the same iteration, and > if the instance of S is in an iteration after the iteration of the instance of S′.
- In the case of a loop nest, there are distance and direction vector, with one element for each level of the loop nest.
FIGS. 16 to 20illustrate these definitions. FIG. 16illustrates a code and diagram of an example of a true dependence with distance 0 on array 'a'. FIG. 17illustrates a code and diagram of an example of an anti-dependence with distance 0 on array 'b'. FIG. 18illustrates a code and diagram of an example of an output dependence with distance 0 on array 'a'. FIG. 19illustrates a code and diagram of an example of a dependence with direction vector (=,=) between S1 and S2 and a dependence with direction vector (=,=,<) between S2 and S2. FIG. 20illustrates a code and diagram of an example of an anti-dependence with distance vector (0,2).
- The data dependence graph may be used by a lot of optimizations, and may also be useful to determine if their application is valid. For instance, a loop can be vectorized if its data dependence graph does not contain any cycle.
- Interprocedural Alias Analysis
- An aim of alias analysis is to determine if a memory location is aliased by several objects, e.g., variables or arrays, in a program. It may have a strong impact on data dependence analysis and on the application of code optimizations. Aliases can occur with statically allocated data, like unions in C where all fields refer to the same memory area, or with dynamically allocated data, which are the usual targets of the analysis. A typical case of aliasing where p alias b is:
int b[100], *p; for (p=b;p < &b[100];p++) *p=0;
- Alias analysis can be more or less precise depending on whether or not it takes the control-flow into account. When it does, it is called flow-sensitive, and when it does not, it is called flow insensitive. Flow-sensitive alias analysis is able to detect in which blocks along a path two objects are aliased. As it is more precise, it is more complicated and more expensive to compute. Usually flow insensitive alias information is sufficient. This aspect is illustrated in
FIG. 21where a flow-insensitive analysis would find that p alias b, but where a flow-sensitive analysis would be able to find that p alias b only in block B2.
- Furthermore, aliases are classified into must-aliases and may-aliases. For instance, considering flow-insensitive may-alias information, x alias y, iff x and y may, possibly at different times, refer to the same memory location. Considering flow-insensitive must-alias information, x alias y, iff x and y must, throughout the execution of a procedure, refer to the same storage location. In the case of
FIG. 21, if flow-insensitive may-alias information is considered, p alias b holds, whereas if flow-insensitive must-alias information is considered, p alias b does not hold. The kind of information to use depends on the problem to solve. For instance, if removal of redundant expressions or statements is desired, must-aliases must be used, whereas if build of a data dependence graph is desired, may-aliases are necessary.
- Finally this analysis must be interprocedural to be able to detect aliases caused by non-local variables and parameter passing. The latter case is depicted in the code below, which is an example for aliasing parameter passing, where i and j are aliased through the function call where k is passed twice as parameter.
void foo (int *i, int* j) { *i = *j+1; } . . . foo (&k, &k);
- Interprocedural Value Range Analysis
- This analysis can find the range of values taken by the variables. It can help to apply optimizations like dead code elimination, loop unrolling and others. For this purpose, it can use information on the types of variables and then consider operations applied on these variables during the execution of the program. Thus, it can determine, for instance, if tests in conditional instruction are likely to be met or not, or determine the iteration range of loop nests.
- This analysis has to be interprocedural as, for instance, loop bounds can be passed as parameters of a function, as in the following example. It is known by analyzing the code that in the loop executed with array 'a', N is at least equal to 11, and that in the loop executed with array 'b', N is at most equal to 10.
void foo (int *c, int N) { int i; for (i=O; i<N; i++) c[i] = g(i,2); } . . . if (N > 10) foo (a,N); else foo (b,N);
- The value range analysis can be supported by the programmer by giving further value constraints which cannot be retrieved from the language semantics. This can be done by pragmas or a compiler known assert function.
- Alignment Analysis
- Alignment analysis deals with data layout for distributed memory architectures. As stated by Saman Amarasinghe, "Although data memory is logically a linear array of cells, its realization in hardware can be viewed as a multi-dimensional array. Given a dimension in this array, alignment analysis will identify memory locations that always resolve to a single value in that dimension. For example, if the dimension of interest is memory banks, alignment analysis will identify if a memory reference always accesses the same bank." This is the case in the second part of
FIG. 22, which is a reproduction of a figure that can be found in Sam Larsen, Emmet Witchel & Saman Amarasinghe, "Increasing and Detecting Memory Address Congruence," Proceedings of the 2002 IEEE International Conference on Parallel Architectures and Compilation Techniques (PACT '02), 18-29 (September 2002). All accesses, depicted in dark squares, occur to the same memory bank, whereas in the first part, the accesses are not aligned. Saman Amarasinghe adds that "Alignment information is useful in a variety of compiler-controlled memory optimizations leading to improvements in programmability, performance, and energy consumption."
- Alignment analysis, for instance, is able to help find a good distribution scheme of the data and is furthermore useful for automatic data distribution tools. An automatic alignment analysis tool can be able to automatically generate alignment proposals for the arrays accessed in a procedure and thus simplifies the data distribution problem. This can be extended with an interprocedural analysis taking into account dynamic realignment.
- Alignment analysis can also be used to apply loop alignment that transforms the code directly rather than the data layout in itself, as discussed below. Another solution can be used for the PACT XPP, relying on the fact that it can handle aligned code very efficiently. It includes adding a conditional instruction testing if the accesses in the loop body are aligned followed by the necessary number of peeled iterations of the loop body, then the aligned loop body, and then some compensation code. Only the aligned code is then executed by the PACT XPP. The rest may be executed by the host processor. If the alignment analysis is more precise (inter-procedural or inter-modular), less conditional code has to be inserted.
- Discussion regarding many of the optimizations and transformations discussed below can be found in detail in David F. Bacon, Susan L. Graham & Oliver J. Sharp, "Compiler Transformations for High-Performance Computing," ACM Computing Surveys, 26(4):325-420 (1994); Michael Wolfe, supra; Hans Zima et al., supra; and Steven Muchnick, supra.
- General Transformations
- Discussed below are a few general optimizations that can be applied to straightforward code and to loop bodies. These are not the only ones that appear in a compiler.
- Constant Propagation
- A constant propagation may propagate the values of constants into the expressions using them throughout the program. This way a lot of computations can be done statically by the compiler, leaving less work to be done during the execution. This part of the optimization is also known as constant folding.
- An example of constant propagation is:
N = 256; for(i=O; i<=256; i++) c = 3; a[i] = b [i] + 3; for (i=0; i<=N; i++) a[i] = b[i] + c;
- Copy Propagation
- A copy propagation optimization may simplify the code by removing redundant copies of the same variable in the code. These copies can be produced by the programmer or by other optimizations. This optimization may reduce the register pressure and the number of register-to-register move instructions.
- An example of copy propagation is:
t = i*4; t = i*4; r = t; for (i=0; i<=N; i++) for (i=0; i<=N; i++) a[t] = b[t] + a[i]; a[r] = b[r] + a[i];
- Dead Code Elimination
- A dead code elimination optimization may remove pieces of code that will never be executed. Code is never executed if it is in the branch of a conditional statement whose condition is always evaluated to true or false, or if it is a loop body, whose number of iterations is always equal to 0.
- Code updating variables that are never used is also useless and can be removed as well. If a variable is never used, then the code updating it and its declaration can also be eliminated.
- An example of dead code elimination is:
for (i=0; i<=N; i++){ for (i=0; i<=N; i++){ for (j=0; j<O; j++) for (j=0; j<10; j++) a[j] = b[j] + a[i]; a[j+1] = a[j] + b[j]; for (j=0; j<10; j++) } a[j+1] = a[j] + b[j]; }
- Forward Substitution
- A forward substitution optimization is a generalization of copy propagation. The use of a variable may be replaced by its defining expression. It can be used for simplifying the data dependency analysis and the application of other transformations by making the use of loop variables visible.
- An example of forward substitution is:
c = N + 1; for (i=0; i<=N; i++) for (i=0; i<= N; i++) a[N+1] = b[N+1] + a[i]; a[c] = b[c] + a[i];
- Idiom Recognition
- An idiom recognition transformation may recognize pieces of code and can replace them by calls to compiler known functions, or less expensive code sequences, like code for absolute value computation.
- An example of idiom recognition is:
for (i=0; i<N; i++){ for (i=0; i<N; i++){ c = a[i] − b[i]; c = a[i] − b[i]; if (c<0) c = abs(c); c = −c; d[i] = c; d[i] = c; } }
- Loop Transformations
- Loop Normalization
- A loop normalization transformation may ensure that the iteration space of the loop is always with a lower bound equal to 0 or 1 (depending on the input language), and with a step of 1. The array subscript expressions and the bounds of the loops are modified accordingly. It can be used before loop fusion to find opportunities, and ease inter-loop dependence analysis, and it also enables the use of dependence tests that need a normalized loop to be applied:
- An example of loop normalization is:
for (i=2; i<N; i=i+2) for (i=0; i<(N−2)/2; i++) a[i] = b[i]; a[2*i+2] = b[2*i+2];
- Loop Reversal
- A loop reversal transformation may change the direction in which the iteration space of a loop is scanned. It is usually used in conjunction with loop normalization and other transformations, like loop interchange, because it changes the dependence vectors.
- An example of loop reversal is:
for (i=N; i>=0; i−−) for (i=0; i<=N; i++) a[i] = b[i]; a[i] = b[i];
- Strength Reduction
- A strength reduction transformation may replace expressions in the loop body by equivalent but less expensive ones. It can be used on induction variables, other than the loop variable, to be able to eliminate them.
- An example of strength reduction is:
for (i=0; i<N; i++) t = c; a[i] = b[i] + c*i; for (i=0; i<N; i++){ a[i] = b[i] + t; t = t + c; }
- Variable Elimination
- An induction variable elimination transformation can use strength reduction to remove induction variables from a loop, hence reducing the number of computations and easing the analysis of the loop. This may also remove dependence cycles due to the update of the variable, enabling vectorization.
- An example of induction variable elimination is:
for (i=0; i<=N; i++){ for (i=0; i<=N; i++){ k = k+3; a[i] = b[i] + a[k+(i+1)*3]; a[i] = b[i] + a[k]; } } k = k + (N+1)*3;
- Loop-Invariant Code Motion
- A loop-invariant code motion transformation may move computations outside a loop if their result is the same in all iterations. This may allow a reduction of the number of computations in the loop body. This optimization can also be conducted in the reverse fashion in order to get perfectly nested loops, that are easier to handle by other optimizations.
- An example of loop-invariant code motion is:
for (i=0; i<N; i++) if (N >= 0) a [i] = b[i] + x*y; c = x*y; for (i=0; i<N; i++) a[i] = b[i] + c;
- Loop Unswitching
- A loop unswitching transformation may move a conditional instruction outside of a loop body if its condition is loop invariant. The branches of the condition may then be made of the original loop with the appropriate original statements of the conditional statement. It may allow further parallelization of the loop by removing control-flow in the loop body and also removing unnecessary computations from it.
- An example of loop unswitching is:
for (i=0; i<N; i++){ if (x > 2) a[i] = b[i] + 3; for (i=0; i<N; i++){ if (x > 2) a[i] = b[i] + 3; b[i] = c[i] + 2; b[i] = c[i] +2; else } b[i]=c[i] − 2; else } for (i=0; i<N; i++){ a[i] = b[i] + 3; b[i] = c[i] − 2; }
- If-Conversion
- An if-conversion transformation may be applied on loop bodies with conditional instructions. It may change control dependencies into data dependencies and allow then vectorization to take place. It can be used in conjunction with loop unswitching to handle loop bodies with several basic blocks. The conditions where array expressions could appear may be replaced by boolean terms called guards. Processors with predicated execution support can execute directly such code.
- An example of if-conversion is:
for (i=0; i<N; i++){ for (i=0; i<N; i++){ a[i] = a[i] + b[i]; a[i] = a[i] + b[i]; if (a[i] != 0) c2 = (a[i] != 0); if (a[i] > c[i]) if (c2) c4 = (a[i] > c[i]); a[i] = a[i] − 2; if (c2 && c4) a[i] = a[i] − 2; else if (c2 && ! c4) a[i] = a[i] + 1; a[i] = a[i] + 1; d[i] = a[i] * 2; d[i] = a[i] * 2; } }
- Strip-Mining
- A strip-mining transformation may enable adjustment of the granularity of an operation. It is commonly used to choose the number of independent computations in the inner loop nest. When the iteration count is not known at compile time, it can be used to generate a fixed iteration count inner loop satisfying the resource constraints. It can be used in conjunction with other transformations like loop distribution or loop interchange. It is also called loop sectioning. Cycle shrinking, also called stripping, is a specialization of strip-mining.
- An example of strip-mining is:
for (i=0; i<N; i++) up = (N/16)*16; a [i] = b[i] + C; for(i=0; i<up; i = i + 16) a[i:1+16] = b[i:i+16] + c; for (j=i+1; j<N; j++) a[i] = b[i] + c;
- Loop Tiling
- A loop tiling transformation may modify the iteration space of a loop nest by introducing loop levels to divide the iteration space in tiles. It is a multi-dimensional generalization of strip-mining. It is generally used to improve memory reuse, but can also improve processor, register, TLB, or page locality. It is also called loop blocking.
- The size of the tiles of the iteration space may be chosen so that the data needed in each tile fit in the cache memory, thus reducing the cache misses. In the case of coarse-grain computers, the size of the tiles can also be chosen so that the number of parallel operations of the loop body fits the number of processors of the computer.
- An example of loop tiling is:
for (i=0; i<N; i++) for (ii=0; ii<N; ii = ii+16) for (j=0; j<N; j++) for (jj=0; jj<N; jj = jj+16) a[i][j] = b[j][i]; for (i=ii; i<min(ii+15,N); j++) for (j=jj; j<min(jj+15,N); j++) a[i][j] = b[j][i];
- Loop Interchange
- A loop interchange transformation may be applied to a loop nest to move inside or outside (depending on the searched effect) the loop level containing data dependencies. It can:
- enable vectorization by moving inside an independent loop and outside a dependent loop,
- improve vectorization by moving inside the independent loop with the largest range,
- deduce the stride,
- increase the number of loop-invariant expressions in the inner-loop, or
- improve parallel performance by moving an independent loop outside of a loop nest to increase the granularity of each iteration and reduce the number of barmier synchronizations.
- An example of a loop interchange is:
for (i=0; i<N; i++) for (j=0; j<N; j++) for (j=0; j<N; j++) for (i=0; i<N; i++) a[i] = a[i] + b[i][j]; a[i] = a[i] + b[i][j];
- Loop Coalescing/Collapsing
- A loop coalescing/collapsing transformation may combine a loop nest into a single loop. It can improve the scheduling of the loop, and also reduces the loop overhead. Collapsing is a simpler version of coalescing in which the number of dimensions of arrays is reduced as well. Collapsing may reduce the overhead of nested loops and multidimensional arrays. Collapsing can be applied to loop nests that iterate over memory with a constant stride.
- Otherwise, loop coalescing may be a better approach. It can be used to make vectorizing profitable by increasing the iteration range of the innermost loop.
- An example of loop coalescing is:
for (i=0; i<N; i++) for (k=O; k<N*M; k++) { for (j=0; j<M; j++) i = ((k−1)/m)*m+1; a[i][j] = a[i][j] + c; j = ((T−1)%m) + 1; a[i][j] = a[i][j] + c; }
- Loop Fusion
- A loop fusion transformation, also called loop jamming, may merge two successive loops. It may reduce loop overhead, increases instruction-level parallelism, improves register, cache, TLB or page locality, and improves the load balance of parallel loops. Alignment can be taken into account by introducing conditional instructions to take care of dependencies.
- An example of loop fusion is:
for (i=0; i<N; i++) for (i=0; i<N; i++){ a[i] = b[i] + c; a[i] = b[i] + c; for (i=0; i<N; i++) d[i] = e[i] + c; d[i] = e[i] + c; }
- Loop Distribution
- A loop distribution transformation, also called loop fission, may allow to split a loop in several pieces in case the loop body is too big, or because of dependencies. The iteration space of the new loops may be the same as the iteration space of the original loop. Loop spreading is a more sophisticated distribution.
- An example of loop distribution is:
for (i=0; i<N; i++){ for (i=0; i<N; i++) a[i] = b[i] + c; a[i] = b[i] + c; d[i] = e[i] + c; for (i=0; i<N; i++) } d[i] = e[i] + c;
- Loop Unrolling/Unroll-and-Jam
- A loop unrolling/unroll-and-jam transformation may replicate the original loop body in order to get a larger one. A loop can be unrolled partially or completely. It may be used to get more opportunity for parallelization by making the loop body bigger. It may also improve register or cache usage and reduces loop overhead. Loop unrolling the outer loop followed by merging the induced inner loops is referred to as unroll-and-jam.
- An example of loop unrolling is:
for (i=0; i<N; i++) for (i=0; i<N; i = i+2){ a[i] = b[i] + c; a[i] = b[i] + c; a[i+1] = b[i+1] + c; } if ((N−1)%2) == 1) a[N−1] = b[N−1] + c;
- Loop Alignment
- A loop alignment optimization may transform the code to get aligned array accesses in the loop body. Its effect may be to transform loop-carried dependencies into loop-independent dependencies, which allows for extraction of more parallelism from a loop. It can use different transformations, like loop peeling or introduce conditional statements, to achieve its goal. This transformation can be used in conjunction with loop fusion to enable this optimization by aligning the array accesses in both loop nests. In the example below, all accesses to array 'a' become aligned.
- An example of loop alignment is:
for (i=2; i<=N; i++){ for (i=1; i<=N; i++){ a[i] = b[i] + c[i]; if (i>1) a[i] = b[i] + c[i]; d[i] = a[i−1] * 2; if (i<N) d[i+1] = a[i] * 2; e[i] = a[i−1] + d[i+1]; if (i<N) e[i+1] = a[i] + d[i+2]; } }
- Loop Skewing
- A loop skewing transformation may be used to enable parallelization of a loop nest. It may be useful in combination with loop interchange. It may be performed by adding the outer loop index multiplied by a skew factor, f, to the bounds of the inner loop variable, and then subtracting the same quantity from every use of the inner loop variable inside the loop.
- An example of loop skewing is:
for (i=1; i<=N; i++){ for (i=1; i<=N; i++){ for (j=1; j<=N; j++) for (j=i+1; j<=i+N; j++) a[i] = a[i+j] + c; a[i] = a[j] + c;
- Loop Peeling
- A loop peeling transformation may remove a small number of beginning or ending iterations of a loop to avoid dependences in the loop body. These removed iterations may be executed separately. It can be used for matching the iteration control of adjacent loops to enable loop fusion.
- An example of loop peeling is:
for (i=0; i<=N; i++) a[0][N] = a[0][N] + a[N][N]; a[i][N] = a[0][N] + a[N][N]; for (i=1; i<=N−1; i++) a[i][N] = a[0][N] + a[N][N]; a[N][N] = a[0][N] + a[N][N];
- Loop Splitting
- A loop splitting transformation may cut the iteration space in pieces by creating other loop nests. It is also called Index Set Splitting and is generally used because of dependencies that prevent parallelization. The iteration space of the new loops may be a subset of the original one. It can be seen as a generalization of loop peeling.
- An example of loop splitting is:
for (i=0; i<=N; i++) for (i=0; i<(N+1)/2; i++) a[i] = a[N−i+1] + c; a[i] = a[N−i+1] + c; for (i = (N+1)/2; i<=N; i++) a[i] = a[N−i+1] + c;
- Node Splitting
- A node splitting transformation may split a statement in pieces. It may be used to break dependence cycles in the dependence graph due to the too high granularity of the nodes, thus enabling vectorization of the statements.
- An example of node splitting is:
for (i=0; i<N; i++){ for (i=0; i<N; i++){ b[i] = a[i] + c[i] * d[i]; t1[i] = c[i] * d[i]; a[i+1] = b[i] * (d[i] − c[i]); t2[i] = d[i] − c[i]; } b[i] = a[i] + t1[i]; a[i+1] = b[i] * t2[i]; }
- Scalar Expansion
- A scalar expansion transformation may replace a scalar in a loop by an array to eliminate dependencies in the loop body and enable parallelization of the loop nest. If the scalar is used after the loop, a compensation code must be added.
- An example of scalar expansion is:
for (i=0; i<N; i++){ for (i=0; i<N; i++){ c = b[i]; tmp[i] = b[i]; a[i] = a[i] + c; a[i] = a[i] + tmp[i]; } } c = tmp[N−1];
- Array Contraction/Array Shrinking
- An array contraction/array shrinking transformation is the reverse transformation of scalar expansion. It may be needed if scalar expansion generates too many memory requirements.
- An example of array contraction is:
for (i=0; i<N; i++) for (i=0; i<N; i++) for (j=0; j<N; j++){ for (j=0; j<N; j++){ t[i][j] = a[i][j] * 3; t[j] = a[i][j] * 3; b[i][j] = t[i][j] + c[j]; b[i][j] = t[j] + c[j]; } }
- Scalar Replacement
- A scalar replacement transformation may replace an invariant array reference in a loop by a scalar. This array element may be loaded in a scalar before the inner loop and stored again after the inner loop if it is modified. It can be used in conjunction with loop interchange.
- An example of scalar replacement is:
for (i=0; i<N; i++) for (i=0; i<N; i++){ for (j=0; j<N; j++) tmp = a[i]; a[i] = a[i] + b[i][j]; for (j=0; j<N; j++) tmp = tmp + b[i][j]; a[i] = tmp; }
- Reduction Recognition
- A reduction recognition transformation may allow handling of reductions in loops. A reduction may be an operation that computes a scalar value from arrays. It can be a dot product, the sum or minimum of a vector for instance. A goal is then to perform as many operations in parallel as possible. One way may be to accumulate a vector register of partial results and then reduce it to a scalar with a sequential loop. Maximum parallelism may then be achieved by reducing the vector register with a tree, i.e., pairs of dements are summed; then pairs of these results are summed; etc.
- An example of reduction recognition is:
for (i=0; i<N; i++) for (i=0; i<N; i=i+64) s = s + a[i]; tmp[0:63] = tmp[0:63] + a[i:i+63]; for (i=0; i<64;i++) s = s + tmp[i];
- Loop Pushing/Loop Embedding
- A loop pushing/loop embedding transformation may replace a call in a loop body by the loop in the called function. It may be an interprocedural optimization. It may allow the parallelization of the loop nest and eliminate the overhead caused by the procedure call. Loop distribution can be used in conjunction with loop pushing.
- An example of loop pushing is:
for (i=0; i<N; i++) f2(x) f(x,i); void f2(int* a){ void f(int* a, int j){ for (i=0; i<N; i++) a[j] = a[j] + c; a[i] = a[i] + c; } }
- Procedure Inlining
- A procedure inlining transformation replaces a call to a procedure by the code of the procedure itself. It is an interprocedural optimization. It allows a loop nest to be parallelized, removes overhead caused by the procedure call, and can improve locality.
- An example of procedure inlining is:
for (i=0; i<N; i++) for(i=0; i<N; i++) f(a,i); a[i] = a[i] + c; void f(int* x, int j){ x[j] = x[j] + c; }
- Statement Reordering
- A statement reordering transformation schedules instructions of the loop body to modify the data dependence graph and enable vectorization.
- An example of statement reordering is:
for (i=0; i<N; i++){ for(i=0; i<N; i++){ a[i] = b[i] * 2; c[i] = a[i−1] − 4; c[i] = a[i−1] − 4; a[i] = b[i] * 2; } }
- Software Pipelining
- A software pipelining transformation may parallelize a loop body by scheduling instructions of different instances of the loop body. It may be a powerful optimization to improve instruction-level parallelism. It can be used in conjunction with loop unrolling. In the example below, the preload commands can be issued one after another, each taking only one cycle. This time is just enough to request the memory areas. It is not enough to actually load them. This takes many cycles, depending on the cache level that actually has the data. Execution of a configuration behaves similarly. The configuration is issued in a single cycle, waiting until all data are present. Then the configuration executes for many cycles. Software pipelining overlaps the execution of a configuration with the preloads for the next configuration. This way, the XPP array can be kept busy in parallel to the Load/Store unit.
- An example of software pipelining is:
Issue Cycle Command XPPPreloadConfig (CFG1); for (i=0; i<100; ++i){ 1: XPPPreload (2,a+10*i,10); 2: XPPPreload (5,b+20*i,20); 3: 4: //delay 5: 6: XPPExecute (CFG1); } Issue Cycle Command Prologue XPPPreloadConfig (CFG1); XPPPreload (2,a,10); XPPPreload (5,b,20); // delay for (i=1; i<100; ++i){ Kernel 1: XPPExecute (CFG1); 2: XPPPreload (2,a+10*i,10); 3: XPPPreload (5,b+20*i,20); 4: } XPPExecute (CFG1); Epilog // delay
- Vector Statement Generation
- A vector statement generation transformation may replace instructions by vector instructions that can perform an operation on several data in parallel.
- An example of vector statement generation is:
for (i=0; i<N; i++) [0:N] = b[0:N]; [i] = b[i];
- Data-Layout Optimizations
- Optimizations may modify the data layout in memory in order to extract more parallelism or prevent memory problems like cache misses. Examples of such optimizations are scalar privatization, array privatization, and array merging.
- Scalar Privatization
- A scalar privatization optimization may be used in multi-processor systems to increase the amount of parallelism and avoid unnecessary communications between the processing elements. If a scalar is only used like a temporary variable in a loop body, then each processing element can receive a copy of it and achieve its computations with this private copy.
- An example of scalar privatization is:
for (i=0; i<=N; i++){ c = b[i]; a[i] = a[i] + c; }
- Array Privatization
- An array privatization optimization may be the same as scalar privatization except that it may work on arrays rather than on scalars.
- Array Merging
- An array merging optimization may transform the data layout of arrays by merging the data of several arrays following the way they are accessed in a loop nest. This way, memory cache misses can be avoided. The layout of the arrays can be different for each loop nest. The example code for array merging presented below is an example of a cross-filter, where the accesses to array 'a' are interleaved with accesses to array 'b'.
FIG. 23illustrates a data layout of both arrays, where blocks of 'a' (the dark highlighted portions) are merged with blocks of 'b' (the lighter highlighted portions). Unused memory space is represented by the white portions. Thus, cache misses may be avoided as data blocks containing arrays 'a' and 'b' are loaded into the cache when getting data from memory. More details can be found in Daniela Genius & Sylvain Lelait, "A Case for Array Merging in Memory Hierarchies," Proceedings of the 9th International Workshop on Compilers for Parallel Computers, CPC '01 (June 2001).
for (j=1; j<=N−1; i++) for (j=1; j<=N; j++) b[i][j] = 0.25*(a[i−1][j]+a[i][j−1]+a[i+1][j]+a[i][j+1]);
- Example of Application of the Optimizations
- In accordance with that which is discussed above, it will be appreciated that a lot of optimizations can be performed on loops before and also after generation of vector statements. Finding a sequence of optimizations that would produce an optimal solution for all loop nests of a program is still an area of research. Therefore, in an embodiment of the present invention, a way to use these optimizations is provided that follows a reasonable heuristic to produce vectorizable loop nests. To vectorize the code, the Allen-Kennedy algorithm, that uses statement reordering and loop distribution before vector statements are generated, can be used. It can be enhanced with loop interchange, scalar expansion, index set splitting, node splitting, loop peeling. All these transformations are based on the data dependence graph. A statement can be vectorized if it is not part of a dependence cycle. Hence, optimizations may be performed to break cycles or, if not completely possible, to create loop nests without dependence cycles.
- The whole process may be divided into four majors steps. First, the procedures may be restructured by analyzing the procedure calls inside the loop bodies. Removal of the procedures may then be tried. Then, some high-level dataflow optimizations may be applied to the loop bodies to modify their control-flow and simplify their code. The third step may include preparing the loop nests for vectorization by building perfect loop nests and ensuring that inner loop levels are vectorizable. Then, optimizations can be performed that target the architecture and optimize the data locality. It should also be noted that other optimizations and code transformations can occur between these different steps that can also help to further optimize the loop nests.
- Hence, the first step may apply procedure inlining and loop pushing to remove the procedure calls of the loop bodies. Then, the second step may include loop-invariant code motion, loop unswitching, strength reduction and idiom recognition. The third step can be divided in several subsets of optimizations. Loop reversal, loop normalization and if-conversion may be initially applied to get normalized loop nests. This may allow building of the data dependency graph. Then, if dependencies prevent the loop nest to be vectorized, transformations may be applied. For instance, if dependencies occur only on certain iterations, loop peeling or loop splitting may be applied. Node splitting, loop skewing, scalar expansion or statement reordering can be applied in other cases. Then, loop interchange may move inwards the loop levels without dependence cycles. A goal is to have perfectly nested loops with the loop levels carrying dependence cycles as much outwards as possible. Then, loop fusion, reduction recognition, scalar replacement/array contraction, and loop distribution may be applied to further improve the following vectorization. Vector statement generation can be performed at last using the Allen-Kennedy algorithm for instance. The last step can include optimizations such as loop tiling, strip-mining, loop unrolling and software pipelining that take into account the target processor.
- The number of optimizations in the third step may be large, but it may be that not all of them are applied to each loop nest. Following the goal of the vectorization and the data dependence graph, only some of them are applied. Heuristics may be used to guide the application of the optimizations that can be applied several times if needed. The following code is an example of this:
void f(int** a, int** b, int *c, int i, int j){ a[i][j] = a[i] [j−1] − b[i+1][j−1]; } void g(int* a , int* c, int i){ a[i] = c[i] + 2; } for(i=0; i<N; i++){ for (j=1; j<9; j=j++){ if (k>0) f(a, b, i, j); else g(d, c, j); } d[i] = d[i+1] + 2; } for (i=0; i<N; i++) a[i][i] = b[i] + 3;
- The first step will find that inlining the two procedure calls is possible. Then loop unswitching can be applied to remove the conditional instruction of the loop body. The second step may begin by applying loop normalization and analyses of the data dependence graph. A cycle can be broken by applying loop interchange as it is only carried by the second level. The two levels may be exchanged so that the inner level is vectorizable. Before that or also after, loop distribution may be applied. Loop fusion can be applied when the loop on i is pulled out of the conditional instruction by a traditional redundant code elimination optimization. Finally, vector code can be generated for the resulting loops.
- In more detail, after procedure inlining, the following may be obtained:
for (i=0; i<N; i++){ for (j=1; j<9; j=j++) if (k>0) a[i][j] = a[i][j−1] − b[i+1][j−1]; else d[j] = c[j] + 2; } d[i] = d[i+1] + 2; } for (i=0; i<N; i++) a[i][i] = b [i] + 3;
- After loop unswitching, the following may be obtained:
if (k>0) for (i=0; i<N; i++){ for (j=1; j<9; j=j++) a[i][j] = a[i][j−1] − b[i+1][j−1]; d[i] = d[i+1] + 2; } else for (i=0; i<N; i++){ for (j=1; j<9; j=j++) d[j] = c[j] + 2; d[i] = d[i+1] + 2; } for (i=0; i<N; i++) a[i][i] = b[i] + 3;
- After loop normalization, the following may be obtained:
if (k>0) for (i=0; i<N; i++){ for (j=0; j<8; j=j++) a[i][j+1] = a[i][j] − b[i+1][j]; d[i] = d[i+1] + 2; } else for (i=0; i<N; i++){ for (j=0; j<8; j = j++) d[j] = c[j+1] + 2; d[i] = d[i+1] + 2; } for (i=0; i<N; i++) a[i][i] = b[i] + 3;
- After loop distribution and loop fusion, the following may be obtained:
if (k>0) for(i=0; i<N; i++) for (j=0; j<8; j=j++) a[i][j+1] = a[i][j] − b[i+1][j]; else for (i=0; i<N; i++) for (j=0; j<8; j=j++) d[j] = c[j+1] + 2; for (i=0; i<N; i++){ d[i] = d[i+1] + 2; a[i][i] = b[i] + 3; }
- After loop interchange, the following may be obtained:
if (k>0) for (j=0; j<8; j=j++) for (i=0; i<N; i++) a[i][j+1] = a[i][j] − b[i+1][j]; else for (i=0; i<N; i++) for (j=0; j<8; j=j++) d[j] = c[j+1] + 2; for (i=0; i<N; i++){ d[i] = d[i+1] + 2; a[i][i] = b[i] + 3; }
- After vector code generation, the following may be obtained:
if (k>0) for (j−0; j<8; j=j++) a[0:N−1][j+1] = a[0:N−1][j] − b[0:N][j]; else for (i=0; i<N; i++) d[0:8] = c[1:9] + 2; d[0:N−1] = d[1:N] + 2; a[0:N−1][0:N−1] = b[0:N] + 3;
- A cached RISC-XPP architecture may exploit its full potential on code that is characterized by high data locality and high computational effort. A compiler for this architecture has to consider these design constraints. The compiler's primary objective is to concentrate computational expensive calculations to innermost loops and to make up as much data locality as possible for them.
- The compiler may contain usual analysis and optimizations. As interprocedural analysis, e.g., alias analysis, are especially useful, a global optimization driver may be necessary to ensure the propagation of global information to all optimizations. The way the PACT XPP may influence the compiler is discussed in the following sections.
FIG. 24provides a global view of the compiling procedure and shows main steps the compiler may follow to produce code for a system containing a RISC processor and a PACT XPP. The next sections focus on the XPP compiler itself, but first the other steps are briefly described.
- Code Preparation
- Code preparation may take the whole program as input and can be considered as a usual compiler front-end. It may prepare the code by applying code analysis and optimizations to enable the compiler to extract as many loop nests as possible to be executed by the PACT XPP. Important optimizations are idiom recognition, copy propagation, dead code elimination, and all usual analysis like dataflow and alias analysis.
- Partitioning
- Partitioning may decide which part of the program is executed by the host processor and which part is executed by the PACT XPP.
- A loop nest may be executed by the host in three cases:
- if the loop nest is not well-formed,
- if the number of operations to execute is not worth being executed on the PACT XPP, or
- if it is impossible to get a mapping of the loop nest on the PACT XPP.
- A loop nest is said to be well-formed if the loop bounds and the step of all loops are constant, the loop induction variables are known and if there is only one entry and one exit to the loop nest.
- Another problem may arise with loop nests where the loop bounds are constant but unknown at compile time. Loop tiling may allow for overcoming this problem, as will be described below. Nevertheless, it could be that it is not worth executing the loop nest on the PACT XPP if the loop bounds are too low. A conditional instruction testing if the loop bounds are large enough can be introduced, and two versions of the loop nest may be produced. One would be executed on the host processor, and the other on the PACT XPP when the loop bounds are suitable. This would also ease applications of loop transformations, as possible compensation code would be simpler due to the hypothesis on the loop bounds.
- RISC Code Generation and Scheduling
- After the XPP compiler has produced NML code for the loops chosen by the partitioning phase, the main compiling process may handle the code that will be executed by the host processor where instructions to manage the configurations have been inserted. This is an aim of the last two steps:
- RISC Code Generation and
- RISC Code Scheduling.
- The first one may produce code for the host processor and the second one may optimize it further by looking for a better scheduling using software pipelining for instance.
FIG. 25illustrates a detailed architecture and an internal processing of the XPP Compiler. It is a complex cooperation between program transformations, included in the XPP Loop optimizations, a temporal partitioning phase, NML code generation and the mapping of the configuration on the PACT XPP.
- First, loop optimizations targeted at the PACT XPP may be applied to try to produce innermost loop bodies that can be executed on the array of processors. If this is the case, the NML code generation phase may be called. If not, then temporal partitioning may be applied to get several configurations for the same loop. After NML code generation and the mapping phase, it can also happen that a configuration will not fit on tike PACT XPP. In this case, the loop optimizations may be applied again with respect to the reasons of failure of the NML code generation or of the mapping. If this new application of loop optimizations does not change the code, temporal partitioning may be applied. Furthermore, the number of attempts for the NML Code Generation and the mapping may be kept track of. If too many attempts are made and a solution is still not obtained, the process may be broken and the loop nest may be executed by the host processor.
- Temporal Partitioning
- Temporal partitioning may split the code generated for the PACT XPP into several configurations if the number of operations, i.e., the size of the configuration, to be executed in a loop nest exceeds the number of operations executable in a single configuration. This transformation is called loop dissevering. See, for example, João M. P. Cardoso & Markus Weinhardt, "XPP-VC: A C Compiler with Temporal Partitioning for the PACT-XPP Architecture," Proceedings of the 12th International Conference on Field-Programmable Logic and Applications, FPL '2002, 2438 LNCS, 864-874 (2002). These configurations may be then integrated in a loop of configurations whose number of execution corresponds to the iteration range of the original loop.
- Generation of NML Code
- Generation of NML code may take as input an intermediate form of the code produced by the XPP Loop optimizations step, together with a dataflow graph built upon it. NML code can then be produced by using tree or DAG-pattern matching techniques.
- Mapping Step
- A mapping step may take care of mapping the NML modules on the PACT XPP by placing the operations on the ALUs, FREGs, and BREGs, and routing the data through the buses.
- A goal of loop optimizations used for the PACT XPP is to extract as much parallelism as possible from the loop nests in order to execute them on the PACT XPP by exploiting the ALU-PAEs as effectively as possible and to avoid memory bottlenecks with the IRAMs. The following sections explain how they may be organized and how to take into account the architecture for applying the optimizations.
- Organization of the System
FIG. 26provides a detailed view of the XPP loop optimizations, including their organization. The transformations may be divided in six groups. Other standard optimizations and analysis may be applied in-between. Each group could be called several times. Loops over several groups can also occur if needed. The number of iterations for each driver loop can be of constant value or determined at compile time by the optimizations themselves, (e.g., repeat until a certain code quality is reached). In the first iteration of the loop, it can be checked if loop nests are usable for the PACT XPP. It is mainly directed to check the loop bounds etc. For instance, if the loop nest is well-formed and the data dependence graph does not prevent optimization, but the loop bounds are unknown, then, in the first iteration loop, tiling may be applied to get an innermost that is easier to handle and can be better optimized, and in the second iteration, loop normalization, if conversion, loop interchange and other optimizations can be applied to effectively optimize the inner-most loops for the PACT XPP. Nevertheless, this has not been necessary until now with the examples presented below.
- With reference to
FIG. 26, Group I may ensure that no procedure calls occur in the loop nest. Group II may prepare the loop bodies by removing loop-invariant instructions and conditional instruction to ease the analysis. Group III may generate loop nests suitable for the data dependence analysis. Group IV may contain optimizations to transform the loop nests to get data dependence graphs that are suitable for vectorization. Group V may contain optimizations that ensure that the innermost loops can be executed on the PACT XPP. Group VI may contain optimizations that further extract parallelism from the loop bodies. Group VII may contain optimizations more towards optimizing the usage of the hardware itself.
- In each group, the application of the optimizations may depend on the result of the analysis and the characteristics of the loop nest. For instance, it is clear that not all transformations in Group IV are applied. It depends on the data dependence graph computed before.
- Loop Preparation
- The optimizations of Groups I, II and III of the XPP compiler may generate loop bodies without procedure calls, conditional instructions and induction variables other than loop control variables. Thus, loop nests, where the innermost loops are suitable for execution on the PACT XPP, may be obtained. The iteration ranges may be normalized to ease data dependence analysis and the application of other code transformations.
- Transformation of the Data Dependence Graph
- The optimizations of Group IV may be performed to obtain innermost loops suitable for vectorization with respect to the data dependence graph. Nevertheless, a difference with usual vectorization is that a dependence cycle, which would normally prevent any vectorization of the code, does not prevent the optimization of a loop nest for the PACT XPP. If a cycle is due to an anti-dependence, then it could be that it will not prevent optimization of the code as stated in Markus Weinhardt & Wayne Luk, "Pipeline Vectorization," IEEE Transactions on Computer-Aided Design of integrated Circuits and Systems, 20(2):234-248 (February 2001). Furthermore, dependence cycles will not pre-vent vectorization for the PACT XPP when it consists only of a loop-carried true dependence on the same expression. If cycles with distance k occur in the data dependence graph, then this can be handled by holding k values in registers. This optimization is of the same class as cycle shrinking.
- Nevertheless, limitations due to the dependence graph exist. Loop nests cannot be handled if some dependence distances are not constant or unknown. If only a few dependencies prevent the optimization of the whole loop nest, this could be overcome by using the traditional vectorization algorithm that sorts topologically the strongly connected components of the data dependence graph (statement reordering), and then applying loop distribution. This way, loop nests, which can be handled by the PACT XPP and some by the host processor, can be obtained.
- Influence of the Architectural Parameters
- Some hardware specific parameters may influence the application of the loop transformations. The number of operations and memory accesses that a loop body performs may be estimated at each step. These parameters may influence loop unrolling, strip-mining, loop tiling and also loop interchange (iteration range).
- The table below lists the parameters that may influence the application of the optimizations. For each of them, two data are given: a starting value computed from the loop and a restriction value which is the value the parameter should reach or should not exceed after the application of the optimizations. Vector length depicts the range of the innermost loops, i.e., the number of elements of an array accessed in the loop body. Reused data set size represents the amount of data that must fit in the cache. I/O IRAMs, ALU, FREG, BREG stand for the number of IRAMs, ALUs, FREGs, and BREGs, respectively, of the PACT XPP. The dataflow graph width represents the number of operations that can be executed in parallel in the same pipeline stage. The dataflow graph height represents the length of the pipeline. Configuration cycles amounts to the length of the pipeline and to the number of cycles dedicated to the control. The application of each optimization may
- decrease a parameter's value (−),
- increase a parameter's value (+),
- not influence a parameter (id), or
- adapt a parameter's value to fit into the goal size (make fit).
- Furthermore, some resources must be kept for control in the configuration. This means that the optimizations should not make the needs exceed more than 70-80% each resource.
Parameter Goal Starting Value Vector length IRAM size (256 words) Loop count Reused data set size Approx. cache size Algorithm analysis/loop sizes I/O IRAMs PACT size (16) Algorithm inputs + outputs ALU PACT size (<64) ALU opcode estimate BREG PACT size (<80) BREG opcode estimate FREG PACT size (<80) FREG opcode estimate Data flow graph width High Algorithm data flow graph Data flow graph height Small Algorithm data flow graph Configuration cycles ≦ command line parameter Algorithm analysis
- Additional notations used in the following descriptions are as follows. n is the total number of processing elements available, r is the width of the dataflow graph, in is the maximum number of input values in a cycle, and out is the maximum number of output values possible in a cycle. On the PACT XPP, n is the number of ALUs, FREGs and BREGs available for a configuration, r is the number of ALUs, FREGs and BREGs that can be started in parallel in the same pipeline stage, and in and out amount to the number of available IRAMs. As IRAMs have 1 input port and 1 output port, the number of IRAMs yields directly the number of input and output data.
- The number of operations of a loop body may be computed by adding all logic and arithmetic operations occurring in the instructions. The number of input values is the number of operands of the instructions regardless of address operations. The number of output values is the number of output operands of the instructions regardless of address operations. To determine the number of parallel operations, input and output values, and the dataflow graph must be considered. The effects of each transformation on the architectural parameters are now presented in detail.
- Loop Interchange
- Loop interchange may applied when the innermost loop has a too narrow iteration range. In that case, loop interchange may allow for an innermost loop with a more profitable iteration range. It can also be influenced by the layout of the data in memory. It can be profitable to data locality to interchange two loops to get a more practical way to access arrays in the cache and therefore prevent cache misses. It is of course also influenced by data dependencies as explained above.
Parameter Effect Vector length + Reused data set size make fit I/O IRAMs id ALU id BREG id FREG id Data flow graph width id Data flow graph height id Configuration cycles −
- Loop Distribution
- Loop distribution may be applied if a loop body is too big to fit on the PACT XPP. A main effect of loop distribution is to reduce the processing elements needed by the configuration. Reducing the need for IRAMs can only be a side effect.
Parameter Effect Vector length id Reused data set size id I/O IRAMs make fit ALU make fit BREG make fit FREG make fit Data flow graph width − Data flow graph height − Configuration cycles −
- Loop Collapsing
- Loop collapsing can be used to make the loop body use more memory resources. As several dimensions are merged, the iteration range is increased and the memory needed is increased as well.
Parameter Effect Vector length + Reused data set size + I/O IRAMs + ALU id BREG id FREG id Data flow graph width + Data flow graph height + Configuration cycles +
- Loop Tiling
- Loop tiling, as multi-dimensional strip-mining, is influenced by all parameters. It may be especially useful when the iteration space is by far too big to fit in the IRAM, or to guarantee maximum execution time when the iteration space is unbounded. See the discussion below under the heading "Limiting the Execution Time of a Configuration." It can then make the loop body fit with respect to the resources of the PACT XPP, namely the IRAM and cache line sizes. The size of the tiles for strip-mining and loop tiling can be computed as:
tile size=resources available for the loop body/resources necessary for the loop body.
- The resources available for the loop body are the whole resources of the PACT XPP for this configuration. A tile size can be computed for the data and another one for the processing elements. The final tile size is then the minimum between these two. For instance, when the amount of data accessed is larger than the capacity of the cache, loop tiling may be applied according to the following example code for loop tiling for the PACT XPP.
for (i=0; i<=1048576; i++) for (i=0; i<=1048576; i+= CACHE_SIZE) <loop body> for (j=0; j<CACHE_SIZE; j+=IRAM_SIZE) for (k=0; k<IRAM_SIZE; k++) <tiled loop body>
Parameter Effect Vector length make fit Reused data set size make fit I/O IRAMs id. ALU id BREG id FREG id Data flow graph width + Data flow graph height + Configuration cycles +
- Strip-Mining
- Strip-mining may be used to make the amount of memory accesses of the innermost loop fit with the IRAMs capacity. The processing elements do not usually represent a problem as the PACT XPP has 64 ALU-PAEs which should be sufficient to execute any single loop body. Nevertheless, the number of operations can be also taken into account the same way as the data.
Parameter Effect Vector length- make fit Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles −
- Loop Fusion
- Loop fusion may be applied when a loop body does not use enough resources. In this case, several loop bodies can be merged to obtain a configuration using a larger part of the available resources.
Parameter Effect Vector length id Reused data set size id I/O IRAMs + ALU + BREG + FREG + Data flow graph width id Data flow graph height: + Configuration cycles +
- Scalar Replacement
- The amount of memory needed by the loop body should always fit in the IRAMs. Due to a scalar replacement optimization, some input or output data represented by array references that should be stored in IRAMs may be replaced by scalars that are either stored in FREGs or kept on buses.
Parameter Effect Vector length + Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles id
- Loop Unrolling
- Loop unrolling, loop collapsing, loop fusion and loop distribution may be influenced by the number of operations of the body of the loop nest and the number of data inputs and outputs of these operations, as they modify the size of the loop body. The number of operations should always be smaller than n, and the number of input and output data should always be smaller than in and out.
Parameter Effect Vector length id Reused data set size id I/O IRAMs + ALU + BREG + FREG + Data flow graph width id Data flow graph height + Configuration cycles +
- Unroll-and-Jam
- Unroll-and-Jam may include unrolling an outer loop and then merging the inner loops. It must compute the unrolling degree u with respect to the number of input memory accesses m and output memory accesses p in the inner loop. The following inequality must hold: u*m≦in ̂u* p≦out. Moreover, the number of operations of the new inner loop must also fit on the PACT XPP.
Parameter Effect Vector length id Reused data set size + I/O IRAMs + ALU + BREG + FREG + Data flow graph width id Data flow graph height + Configuration cycles +
- Optimizations Towards Hardware Improvements
- At this step other optimizations, specific to the PACT XPP, can be made. These optimizations deal mostly with memory problems and dataflow considerations. This is the case of shift register synthesis, input data duplication (similar to scalar privatization), or loop pipelining.
- Shift Register Synthesis
- A shift register synthesis optimization deals with array accesses that occur during the execution of a loop body. When several values of an array are alive for different iterations, it can be convenient to store them in registers, rather than accessing memory each time they are needed. As the same value must be stored in different registers depending on the number of iterations it is alive, a value shares several registers and flows from a register to another at each iteration. It is similar to a vector register allocated to an array access with the same value for each element. This optimization is performed directly on the dataflow graph by inserting nodes representing registers when a value must be stored in a register. In the PACT XPP, it amounts to storing it in a data register. A detailed explanation can be found in Markus Weinhardt & Wayne Luk, "Memory Access Optimization for Reconfigurable Systems," IEEE Proceedings Computers and Digital Techniques, 48(3) (May 2001).
- Shift register synthesis may be mainly suitable for small to medium amounts of iterations where values are alive. Since the pipeline length increases with each iteration for which the value has to be buffered, the following method is better suited for medium to large distances between accesses in one input array.
- Nevertheless, this method may work very well for image processing algorithms which mostly alter a pixel by analyzing itself and its surrounding neighbors.
Parameter Effect Vector length + Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles id
- Input Data Duplication
- An input data duplication optimization is orthogonal to shift register synthesis. If different elements of the same array are needed concurrently, instead of storing the values in registers, the same values may be copied in different IRAMs. The advantage against shift register synthesis is the shorter pipeline length, and therefore the increased parallelism, and the unrestricted applicability. On the other hand, the cache-IRAMM bottle-neck can affect the performance of this solution, depending on the amounts of data to be moved. Nevertheless, it is assumed that cache IRAM transfers are negligible to transfers in the rest of the memory hierarchy.
Parameter Effect Vector length + Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles id
- Loop Pipelining
- A loop optimization pipelining optimization may include synchronizing operations by inserting delays in the dataflow graph. These delays may be registers. For the PACT XPP, it amounts to storing values in data registers to delay the operation using them. This is the same as pipeline balancing performed by xmap.
Parameter Effect Vector length + Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles +
- Tree Balancing
- A tree balancing optimization may include balancing the tree representing the loop body. It may reduce the depth of the pipeline, thus reducing the execution time of an iteration, and may increase parallelism.
Parameter Effect Vector length + Reused data set size id I/O IRAMs id ALU id BREG id FREG id Data flow graph width + Data flow graph height − Configuration cycles −
- Limiting the Execution Time of a Configuration
- The execution time of a configuration must be controlled. This is ensured in the compiler by strip-mining and loop tiling that take care that not more input data than the IRAM's capacity come in the PACT XPP in a cycle. This way the iteration-range of the innermost loop that is executed on the PACT XPP is limited, and therefore its execution time. Moreover, partitioning ensures that loops, whose execution count can be computed at run time, are going to be executed on the PACT XPP. This condition is trivial for-loops, but for while-loops, where the execution count cannot be determined statically, a transformation exemplified by the code below can be applied. As a result, the inner for-loop can be handled by the PACT XPP.
while (ok){ while (ok) <loop body> for (i=0; i<100 && ok; i++){ } <loop body> }
- Original Code
- The following is source code:
#define VERLEN 16 #define HORLEN 16 main( ){ int v, h, inp; int p1[VERLEN][HORLEN]; int p2[VERLEN][HORLEN]; int htmp, vtmp, sum; for(v=0; v<VERLEN; v++) //loop nest1 for(h=0; h<HORLEN; h++){ scanf("%d", &p1[v][h]); //read input pixels to p1 p2[v][h] = 0; //initialize p2 } for(v=0; v<=VERLEN−3; v++){ //loop nest 2 for(h=0; h<=HORLEN−3; h++) { htmp = (p1[v+2][h] − p1[v][h]) + (p1[v+2][h+2] − p1[v][h+2]) + 2 * (p1[v+2][h+1] − p1[v][h+1]); if(htmp < 0) htmp = −htmp; vtmp = (p1[v][h+2] − p1[v][h]) + (p1[v+2][h+2] − p1[v+2][h]) + 2 * (p1[v+1][h+2] − p1[v+1][h]); if (vtmp < 0) vtmp = −vtmp; sum = htmp + vtmp; if (sum > 255) sum = 255; p2[v+1][h+1] = sum; } } for(v=0; v<VERLEN; v++) //loop nest 3 for(h=0; h<HORLEN; h++) printf("%d\n", p2[v][h]); //print output pixels from p2 }
- Preliminary Transformations
- Interprocedural Optimizations
- The first step normally invokes interprocedural transformations like function dining and loop pushing. Since no procedure calls are within the loop body, these transformations are not applied to this example.
- Partitioning
- The partitioning algorithm chooses which code runs on the RISC processor and which code runs on the XPP. Since only inner loops are considered to run on the XPP, the basic blocks are annotated with the loop nest depth. Thus, basic blocks which are not in a loop are separated out. Furthermore, function calls within a loop body prevent a loop to be considered for running on the XPP.
- In our benchmark, the loop nests 1 and 3 are marked as to run on the RISC host because of the function call. In the following sections they are not considered any further.
- It is to say that at this compilation stage it is not predictable if the remaining loop nests can be synthesized for the XPP. Just the ones which definitely cannot run on it were separated. Others may follow, since running the code on the RISC CPU is always the reassurance in this strategy.
- Loop Analysis and Normalization
- The code upon has already normalized loops. Nevertheless, it is more likely that human written code would be approximately as follows:
for(v=1; v<VERLEN − 1; v++){ for(h=1; h<HORLEN − 1; h++){ htmp = (p1[v+1][h−1] − p1[v−1][h−1]) + (p1[v+1][h+1] − p1[v−1][h+1]) + 2 * (p1[v+1][h] − p1[v−1][h]); if(htmp < 0) htmp = −htmp; vtmp = (p1[v−1][h+1] − p1[v−1][h−1]) + (p1[v+1][h+1] − p1[v+1][h−1]) + 2 * (p1[v][h+1] − p1[v][h−1]); if(vtmp < 0) vtmp = −vtmp; sum = htmp + vtmp; if(sum > 255) sum = 255; p2[v+1][h+1] = sum; } }
- Although seen at first sight by a human reader, it is not obvious for the compiler that the loop is well formed. Therefore, normalizing of the loop is attempted.
- If the original loop induction variable is called i with the increment value s and lower and upper loop bounds/and u, respectively, then the normalized loop with the induction variable i′ and the upper bound u′ (the lower bound l′ is 0 by definition) is transformed as follows:
- The upper bound calculates to u′=(u−1)/s.
- All occurrences of i are replaced by 1+i′* s.
- Applied to the code above, the loop statement for (v=1; v<VERLEN −1; v++) with the lower bound v1=1, the upper bound vu=14 (<15 means <=14 in integer arithmetic) and the increment vs=1 transforms to
for(vn=0; vn<=(vu−v1)/vs; vn++)
or simplified
for(vn=0; vn<=13; vn++)
- The 'h-loop' is transformed equally, issuing the original code.
- Idiom Recognition
- In the second step, idiom recognition finds the abs( ) and min( ) structures in the loop body. Note that although the XPP has no abs opcode, it can easily be synthesized and should therefore be produced to simplify the internal representation. (Otherwise, if-conversion has to handle this case which increases the complexity.)
- Therefore, the code after idiom recognition is approximately as follows (abs( ) and min( ) are compiler known functions which are directly mapped to XPP opcodes or predefined NML modules):
for(v=0; v<=16−3; v++){ for(h=0; h<=16−−3; h++){ htmp = (p1[v+2][h] − p1[v][h]) + (p1[v+2][h+2] − p1[v][h+2]) + 2 * (p1[v+2][h+1] − p1[v][h+1]); htmp = abs(htmp); vtmp = (p1[v][h+2] − p1[v][h]) + (p1 [v+2] [h+2] − p1 [v+2] [h]) + 2 * (p1[v+1][h+2] − p1[v+1][h]); vtmp = abs(vtmp); sum = min(htmp + vtmp, 255); p2[v+1][h+1] = sum; } }
- Dependency Analysis
for(v=0; v<=16−3; v++){ for(h=0; h<=16−3; h++){ S1 htmp = (p1[v+2][h] − p1[v][h]) + (p1[v+2][h+2] − p1[v][h+2]) + 2 * (p1[v+2][h+1] − p1[v][h+1]); S2 htmp = abs(htmp); S3 vtmp = (p1[v][h+2] − p1[v][h]) + (p1[v+2][h+2] − p1[v+2][h]) + 2 * (p1[v+1][h+2] − p1 [v+1][h]); S4 vtmp = abs(vtmp); S5 sum = min(htmp + vtmp, 255); S6 p2[v+1][h+1] = sum; } }
- There are no loop carried dependencies which prevent pipeline vectorization. The loop independent scalar dependencies do not prevent pipeline vectorization since the transformation does not disturb the order of reads and writes. Furthermore, forward expression substitution/dead code elimination will remove the scalars completely.
- Pre Code Generation Transformations
- Forward Expression Substitution/Dead Code Elimination
- The lack of uses of htmp, vtmp and sum after the loop nest allows forward expression substitution along with dead code elimination to place the whole calculation into one statement.
p2[v+1][h+1] = min(abs((p1[v+2][h1] − p1[v][h]) + (p1[v+2][h+2] p1[v][h+2]) + 2 * (p1[v+2][h+1] − p1[v][h+1])) + abs((p1[v][h+2] − p1[v][h]) + (p1[v+2][h+2] − p1[v+2][h]) + 2 * (p1[v+1][h+2] − p1[v+1][h])), 255);
- The scalar accesses then disappear completely.
- Mapping to IRAMs
- The array accesses are mapped to IRAMs. At this stage the IRAM numbers are chosen arbitrarily. The actual mapping to XPP IRAMs is done later.
- Therefore, p1[v+x][h+y] and p2[v+X][h+y] are renamed to iramN[y], (e.g., p1[v+2][h] to iram2[0]). Accordingly, the code is
iram3[1] = min(abs (iram2[0] − iram0[0]) + (iram2[2] − iram0[2]) + 2 * (iram2[1] − iram0[1]) + abs (iram0[2] − iram0[0]) + (iram2[2] − iram2[0]) + 2 * (iram1[2] − iram1[0]), 255);
- Tree Balancing
FIG. 27shows an expression tree of an edge 3×3 inner loop body. The visualized expression tree of FIG. 27shows another valuable optimization before matching the tree. Since the depth of the tree determines the length of the synthesized pipeline, another simplification can decrease this depth. In both of the main sub trees, the operands of the commutative add expressions can be interchanged to reduce the overall tree depth. A resulting expression tree is shown in FIG. 28. In FIG. 28, one of the sub trees is shown before and after balancing. The numbers represent the annotated maximum tree depth from the node to its deepest child leaf node.
- XPP Code generation
- Pipeline Synthesis
- As already stated, the pipeline is synthesized by a dynamic programming tree matcher. In contrast to sequential processors, it does not generate instructions and register references, but PAE opcodes and port connections.
FIG. 29shows the main calculation network of the edge 3×3 configuration. The MULTI-SORT combination does the abs( ) calculation, while the SORT does the min( ) calculation. The input data preparation network is not shown in FIG. 29. FIG. 30shows the case of synthesized shift registers, while the variant with duplicated input data simply includes an IRAM for each input channel in FIG. 29. With respect to FIG. 30, there is one input after the shift register synthesis. The leftmost input contains p1[ ][h], the middle one contains p1[ ][h+1, and the rightmost one contains p1[ ][h+2].
- Although this is straight forward, there remains the question how to access the different offsets of the vector register accesses. Although the RAM-PAEs are dual ported, it is obvious that it is not possible to read different addresses concurrently.
- Since it is not efficient to synthesize a configuration which generates the different addresses sequentially and demultiplexes the read operands into different branches of the data flow, other arrangements have to be made.
- The two possibilities to access input data discussed above under the heading "Optimizations Towards Hardware Improvements" yield the following in RISC pseudo code and XPP utilization. The pseudo code running on the RISC core is approximately:
XPPPreload(config) for(v=0; v<=16−3; v++){ XPPPreload(0, &p1[v], 16) XPPPreload(1, &p1[v+1], 16) XPPPreload(2, &p1[v+2], 16) XPPPreloadClean(3, &p2[v+1], 16) XPPExecute(config, IRAM(0), IRAM(1), IRAM(2), IRAM(3)) }
for shift register synthesis and approximately:
XPPPreload(config) for(v=0; v<=16−3; v++){ XPPPreload(0, &p1[v], 16) XPPPreload(1, &p1[v], 16) XPPPreload(2, &p1[v], 16) XPPPreload(3, &p1[v+1], 16) XPPPreload(4, &p1[v+1], 16) XPPPreload(5, &p1[v+2], 16) XPPPreload(6, &p1[v+2], 16) XPPPreload(7, &p1[v+2], 16) XPPPreloadClean(3, &p2[v+1], 16) XPPExecute(config, IRAM(0), IRAM(1), IRAM(2), IRAM(3), IRAM(4), IRAM(5), IRAM(6), IRAM(7)) }
for data duplication.
- The values for place & route and simulation are compared in the following table. Note that a common RISC DSP with two MAC units and hardware loop support needs about 4000 cycles for the same code. This comparison does not account for cache misses. Furthermore, it is obvious that the number of input values is very small in this example and the DSP calculation time is proportional to that number. The XPP performance on the other hand will improve with the number of input values. Therefore, the XPP performance will be more impressive with bigger image sizes.
Parameter Value (shift register synthesis) Value (data duplication) Vector length 16 16 Reused data set size 256 256 I/O IRAMs 3 I + 1 O = 4 8 I + 1 O = 9 ALU 27 21 BREG 21 (1 defined + 20 route) 10 (1 defined + 9 route) FREg 22 (9 defined + 23 route) 19 (3 defined + 16 route) Data flow graph width 14 14 Data flow graph height 3 (shift registers) + 8 8 (calculation) (calculation) Configuration cycles configuration 2262 configuration 2145 (simulated) preloads 14 * 3 * 4 168 preloads 8 * 8 * 4 256 (assuming 4 words/cycle burst transfer) cycles 14 * 57 798 cycles 14 * 52 728 sum 3228 sum 3129
- Enhancing Parallelism
- After the synthesis, the configuration calculating the inner loop utilizes 27 ALUs and 4 IRAMs for shift register synthesis and 21 ALUs and 9 IRAMs for data duplication, respectively. Assuming an XPP64 core, this leaves plenty of room for further optimizations. Nevertheless, since all optimizations enhancing parallelism are performed before the synthesis takes place, it is crucial that they estimate the needed resources and the benefit of the transformation very carefully. Furthermore, they have to account for both input preparation strategies to estimate correct values.
- Loop Unrolling
- Fully unrolling the inner loop would not lead to satisfying results because the number of inputs and outputs increases dramatically. This means data duplication would not be applicable and shift register synthesis would exhaust most of the benefits of the parallelism by producing a very long pipeline for each data flow graph. Although partial unrolling of the inner loop would be applicable, it promises not much benefit for the area penalty introduced.
- Loop unrolling the outer loop is also not applicable since it produces a further configuration. Nevertheless, a related transformation could do a good job on this loop nest.
- Unroll-and-Jam
- The unroll-and-jam algorithm enhances parallelism and also improves IRAM usage. It brings pairs of iterations together ideally reusing IRAM outputs and calculation results. The algorithm partially unrolls the outer loop and fuses the originated inner loops. Before the unroll-and-jam is performed, the so-called unroll-and-jam factor must be determined, which denominates the unrolling factor of the outer loop. This is mainly influenced by the number of ALUs n(=64 assuming XPP64) and calculates to
- (integer division.
- Thus the source code would be transformed to:
for(v=0; v<=VERLEN−3; v+=2){ for(h=0; h<=HORLEN−3; h++){ p2[v+1][h+1] = min(abs((p1[v+2][h] − p1[v][h]) + (p1[v+2][h+2] − p1[v][h+2]) + 2 * (p1[v+2][h+1] − p1[v][h+1])) + abs((p1[v][h+2] − p1[v][h]) + (p1[v+2][h+2] − p1[v+2][h]) + 2 * (p1[v+1][h+2] − p1[v+1][h])), 255); p2[v+2][h+1] = min(abs((p1[v+3][h] − p1[v+1][h]) + (p1[v+3][h+2] − p1[v+1][h+2]) + 2 * (p1[v+3][h+1] − p1[v+1][h+1])) + abs((p1[v+1][h+2] − p1[v+1][h]) + (p1[v+3][h+2] − p1[v+3][h]) + 2 * (p1[v+2][h+2] − p1[v+2][h])), 255); } }
- The transformation introduces additional accesses to p1[v+3][h], p1[v+3][h+2], p1[v+3][h+1], and p1[v+1][h+1] (the former hole in the access pattern) as well as a write access to p2[v+2][h+1]. This means 2 IRAMs more for shift register synthesis (one input, one output) and 5 IRAMs more for data duplication (4 input, 1 output), while performance is doubled.
Value (shift register Value (data duplication - Value (data duplications - with Parameter synthesis) no IRAM placement) IRAM placement) Vector length 16 16 16 Reused data set size 256 256 256 I/O, IRAMs 4 I + 2 O = 6 12 I + 2 O = 14 12 I + 2 O = 14 ALU 45 37 37 BREG 31 (12 defined + 19 route) 42 (4 defined + 38 route) 36 (4 defined + 32 route) FREG 29 (1 defined + 28 route) 18 (1 defined + 17 route) 24 (1 defined + 23 route) Data flow graph width 14 14 14 Data flow graph height 3 (shift registers) + 8 8 (calculation) 3 (shift registers) + (calculation) 8 (calculation) Configuration cycles configuration 2753 configuration 2754 configuration 2768 (simulated) preloads 7 * 4 * 4 112 preloads 7 * 12 * 4 336 preloads 7 * 12 * 4 336 cycles 7 * 53 371 cycles 7 * 69 483 cycles 7 * 51 357 sum 3236 sum 3573 sum 3461
- The simulated results are shown in the table above. Note the differences of the two columns labeled with "data duplication." The first used xmap to place the IRAMs, while in the second, the IRAMs were placed by hand using a greedy algorithm which places IRAMs that are operands of the same operator in one line (as long as this is possible). The second solution improved the iteration cycles by 18. This shows that IRAM placement has a great impact to the final performance.
- The traditional unroll-and-jam algorithm uses loop peeling to split the outer loop in a preloop and an unroll-able main loop to handle odd loop counts. When, for instance, n=128 is assumed, the unroll-and-jam factor would calculate to
- Since the outer loop count (14) is not a multiple of 4, the algorithm virtually peels off the first two iterations and fuses the two loops at the end adding guards to the inner loop body. Then the code looks approximately as follows (guards emphasized):
for(v=0; v<=VERLEN−5; v+=4){ for(h=0; h<=HORLEN−3; h++){ p2 [v+1] [h+1] = min(abs((p1 [v+2] [h] − p1 [v] [h]) + (p1 [v+2] [h+2] − p1 [v] [h+2]) + 2 * (p1 [v+2] [h+1] − p1 [v] [h+1])) + abs((p1 [v] [h+2] − p1 [v] [h]) + (p1 [v+2] [h+2] − p1 [v+2] [h]) + 2 * (p1 [v+1] [h+2] − p1 [v+1] [h])), 255); p2 [v+2] [h+1] = min(abs((p1 [v+3] [h] − p1 [v+1] [h]) + (p1 [v+3] [h+2] − p1 [v+1] [h+2]) + 2 * (p1 [v+3] [h+1] − p1 [v+1] [h+1])) + abs((p1 [v+1] [h+2] − p1 [v+1] [h]) + (p1(v [+3] [h+2] − p1 [v+3] [h]) + 2 * (p1 [v+2] [h+2] − p1 [v+2] [h])), 255); if (v>0) p2 [v+3] [h+1] = min(abs((p1 [v+4] [h] − p1 [v+2] [h]) + (p1 [v+4] [h+2] − p1 [v+2] [h+2]) + 2 * (p1 [v+4] [h+1] − p1 [v+2] [h+1])) + abs((p1 [v+2] [h+2] − p1 [v+2] [h]) + (p1 [v+4] [h+2] − p1 [v+4] [h]) + 2 * (p1 [v+3] [h+2] − p1 [v+3] [h])), 255); if (v>1) p2 [v+4] [h+1] = min(abs((p1 [v+5] [h] − p1 [v+3] [h]) + (p1 [v+5] [h+2] − p1 [v+3] [h+2]) + 2 * (p1 [v+5] [h+1] − p1 [v+3] [h+1])) + abs((p1 [v+3] [h+2] − p1 [v+3] [h]) + (p1 [v+5] [h+2] − p1 [v+5] [h]) + 2 * (p1 [v+4] [h+2] − p1 [v+4] [h])), 255); } }
- Parameterized Function
- Source Code
- The benchmark source code is not very likely to be written in that form in real world applications. Normally, it would be encapsulated in a function with parameters for input and output arrays along with the sizes of the picture to work on.
- Therefore the source code would look similar to the following:
void edge3x3(int *p1, int *p2, int HORLEN, int VERLEN) { for(v=0; v<=VERLEN−3; v++){ for(h=0; h<=HORLEN−3; h++){ htmp = (**(p1 + (v+2) * HORLEN + h) − **(p1 + v * HORLEN + h)) + (**(p1 + (v+2) * HORLEN + h+2) − **(p1 + v * HORLEN + h+2)) + 2 * (**(p1 + (v+2) * HORLEN + h+1) − **(p1 + v * HORLEN + h+1)); if (htmp < 0) htmp = htmp; vtmp = (**(p1 + v * HORLEN + h+2) − **(p1 + v * HORLEN + h)) + (**(p1 + (v+2) * HORLEN + h+2) −**(p1 + (v+2) * HORLEN + h) )+ 2 * (**(p1 + (v+1) * HORLEN + h+2) −**(p1 + (v+1) * HORLEN + h)); if (vtmp < 0) vtmp = vtmp; sum = htmp + vtmp; if (sum > 255) sum = 255; ** (p2 + (v+1) * HORLEN + h+1) = sum; } } }
- This requires some additional features from the compiler.
- interprocedural optimizations and analysis
- hints by the Programmer, (e.g., a compiler known assert(VERLEN % 2=0) makes unroll-and-jam actually possible without peeling off iterations and running them conditionally).
- Fitting the Algorithm Optimally to the Array
- Since HORLEN and VERLEN are not known at compile time these unknown parameters introduce some constraints which prevent pipeline vectorization. The compiler must assume that the IRAMs cannot hold all HORLEN input values in a row, so pipeline vectorization would not be possible.
- Strip Mining Inner Loop
- Strip mining partitions the inner loop into a loop that runs over a strip, which is chosen to be of the same size as the IRAMs can hold and a by strip loop iterating over the strips. The strip loops upper bound must be adjusted for the possible incomplete last strip. After the strip mining, the original code would be approximately as follows (outer v-loop neglected):
for(h=0; h<=HORLEN−3; h+=stripsize) for(hh=h; h<=min(h+stripsize−1, HORLEN−3); hh++){ htmp = (**(p1 + (v+2) * HORLEN + hh) − **(p1 + v * HORLEN + hh)) + . . . } }
- Assuming an IRAM size strip size of 256, the following simulated results cart be obtained for one strip. The values must be multiplied with the number of strips to be calculated.
Value (shift register Value (data duplication - with Parameter synthesis) IRAM placement) Vector length 16 16 Reused data set size 256 256 I/O IRAMs 4 I + 2 O = 6 12 I + 2 O = 14 ALU 45 37 BREG 31 (12 defined + 19 route) 42 (4 defined + 38 route) FREG 29 (1 defined + 28 route) 18 (1 defined + 17 route) Data flow graph width 14 14 Data flow graph height 3 (shift registers) + 8 8 (calculation) (calculation) Configuration cycles configuration 2753 configuration 2754 (simulated) preloads 7 * 4 * 64 1792 preloads 7 * 12 * 64 5376 cycles 128 * 530 67840 cycles 128 * 553 70784 sum 72385 sum 78914
- The RISC DSP needs about 1.47 million cycles for this amount of data. As mentioned above, these values do not include cache miss penalties and truly underestimate the real values. Furthermore, it can be seen that data duplication does not improve the performance. The reason for this seems to be a worse placement and routing.
- Original Code
- Source code:
#define N 256 #define M 8 for (i = 0; i < N−M+1; i++) { S: y[i] = 0; for (j = 0; j < M; j++) S′: y[i] += c[j] * x[i+M−j−1); }
- The constants N and M are replaced by their values by the pre-processor. The data dependency graph is shown in
for (i = 0; i < 269; i++) { S: y[i] = 0; for (j = 0; j < 8; j++) S′: y[i] += c[j] * x[i+7−j]; }
- The following is a corresponding table:
Parameter Value Vector length 269 Reused data set size — I/O IRAMs 3 ALU 2 BREG 0 FREG 0 Data flow graph width 1 Data flow graph height 2 Configuration cycles 2 + 8 = 10
- First Solution
- In a case in which it is desired to save memory, a straightforward solution is to unroll the inner loop and to use shift register synthesis to delay the values of array x in the pipeline. No other optimization is applied before as either they do not have an effect on the loop or they increase the need for IRAMs. After loop unrolling, the following code is obtained:
for (i = 0; i < 269; i++){ Y[i] = 0; Y[i] += c[0] * x[i+7]; Y[i] += c[1] * x[i+6]; Y[i] += c[2] * x[i+5]; Y[i] += c[3] * x[i+4]; Y[i] += c[4] * x[i+3]; Y[i] += c[5] * x[i+2]; Y[i] += c[6] * x[i+1]; Y[i] += c[7] * x[i]; }
- The following is a corresponding table:
Parameter Value Vector length 269 Reused data set size — I/O IRAMs 9 ALU 16 BREG 0 FREG 0 Data flow graph width 2 Data flow graph height 9 Configuration cycles 9 + 269 = 278
- Dataflow analysis reveals that y[0]=f(x[0], . . . , x[7], y[1]−f(x. [1], . . . , x[8]), . . . , y[i]=f(x[i], . . . , x[i+7]). Successive values of y depend on almost the same successive values of x. To prevent unnecessary accesses to the IRAMs, the values of x needed for the computation of the next values of y are kept in registers. In this case, this shift register synthesis needs 7 registers. This will be achieved on the PACT XPP by keeping them in FREGs. Then the dataflow graph of
FIG. 32is obtained. An IRAM is used for the input values and an IRAM for the output values. The first 8 cycles are used to fill the pipeline and then the throughput is of one output value/cycle. The code may be represented as follows:
r0 = x[0]; r1 = x[1]; r2 = x[2]; r3 = x[3]; r4 = x[4]; r5 = x[5]; r6 = x[6]; r7 = x[7]; for (i = 0; i < 269; i++) { y[i] = c7*r0 + c6*r1 + c5*r2 + c4*r3 + c3*r4 + c2*r5 + cl*r6 + c0*r7; r0 = r1; r1 = r2; r2 = r3; r3 = r4; r4 = r5; r5 = r6; r6 = r7; r7 = x[i+7]; }
- A final table is shown below, and the expected speedup with respect to a standard superscalar processor with 2 instructions issued per cycle is 13.6.
Parameter Value Vector length 269 Reused data set size — I/O IRAMs 2 ALU 16 BREG 0 FREG 7 Data flow graph width 3 Data flow graph height 9 Configuration cycles 8 + 269 = 277 Ops Number LD/ST (2 cycles) 2 ADDRCOMP (1 cycle) 0 ADD/SUB (1 cycle) 8 MUL (2 cycles) 8 SHIFT (1 cycle) 0 Cycles per iteration 28 Cycles needed for the (28 * 269)/2 = 3766 loop (2-way)
- Variant with Larger Loop Bounds
- Taking larger loop bounds and setting the values of N and M to 1024 and 64:
for (i = 0; i < 961; i++){ y[i] = 0; for (j = 0; j < 64; j++) y[i] += c[j] * x[i+63−j]; }
- Following the loop optimizations driver given before, loop tiling is applied to reduce the iteration range of the inner loop. The following loop nest is obtained:
for (i = 0; i < 961; i++) { y[i] = 0; for (jj = 0; jj < 8; jj++) for (j = 0; j < 8; j++) y[i] ++ c[8*jj+j] * x[i+63−8*jj−j]; }
- A subsequent application of loop unrolling on the inner loop yields:
for (i = 0; i < 961; i++) { y[i] = 0; for (jj = 0; jj < 8; jj++) { y[i] += c[8*jj] * x[i+63−8*jj]; y[i] += c[8*jj+1] * x[i+62−8*jj]; y[i] += c[8*jj+2] * x[i+61−8*jj]; y[i] += c[8*jj+3] * x[i+60−8*jj]; y[i] += c[8*jj+4] * x[i+59−8*jj]; y[i] += c[8*jj+5] * x[i+58−8*jj]; y[i] += c[8*jj+6] * x[i+57−8*jj]; y[i] += c[8*jj+7] * x[i+56−8*jj]; }
- Finally, the same dataflow graph as above is obtained, except that the coefficients must be read from another IRAM rather than being-directly handled like constants by the multiplications. After shift register synthesis, the code may be the following:
for (i = 0; i < 961; i++) { r0 = x[i+56]; r1 = x[i+57]; r2 = x[i+58]; r3 = x[i+59]; r4 = x[i+60]; r5 = x[i+61]; r6 = x[i+62]; r7 = x[i+63]; for (jj = 0; jj < 8; j j++) Y[i] = c[8*jj]*r0 + c[8*jj+1]*r1 + c[8*jj+2]*r2 + c[8*jj+3]*r3 + c[8*jj+4]*r4 + c[8*jj+5]*r5 + c[8*jj+6]*r6 + c[8*jj+7]*r7; r0 = r1; r1 = r2; r2 = r3; r3 = r4; r4 = r5; r5 = r6; r6 = r7; r7 = x[i+63−8*jj]; } }
- The following table is the same as above except for the vector length and the expected speedup with respect to a standard superscalar processor with 2 instructions issued per cycle is 17.5.
Parameter Value Vector length 8 Reused data set size — I/O IRAMs 2 ALU 16 BREG 0 FREG 7 Data flow graph width 3 Data flow graph height 9 Configuration cycles 8 + 8 = 16 Ops Number LD/ST (2 cycles) 10 ADDRCOMP (1 cycle) 0 ADD/SUB (1 cycle) 16 MUL (2 cycles) 17 SHIFT (1 cycle) 0 Cycles per iteration 70 Cycles needed for (70 * 8)/2 = 280 the loop (2-way)
- More Parallel Solution
- The solution presented above does not expose a lot of parallelism in the loop. To explicitly parallelize the loop before generating the dataflow graph can be tried. Exposing more parallelism may mean more pressure on the memory hierarchy.
- In the data dependence graph presented above, the only loop-carried dependence is the dependence on S′ and it is only caused by the reference to y[i]. Hence, node splitting is applied to get a more suitable data dependence graph. Accordingly, the following may be obtained:
for (i = 0; i < 249; i++) { y[i] = 0; for (j = 0; j < 8; j++) { tmp = c[j] * x[i+7−j]; y[i] += tmp; } }
- Then scalar expansion may be performed on tmp to remove the anti loop-carried dependence caused by it, and the following code may be obtained:
for (i = 0; i < 249; i++) { y[i] = 0; for (j = 0; j < 8; j++) { tmp[j] = c[j] * x[i+7−j]; Y[i] += tmp[j]; } }
- The parameter table is the following:
Parameter Value Vector length 249 Reused data set size — I/O IRAMs 3 ALU 2 BREG 0 FREG 1 Data flow graph width 2 Data flow graph height 2 Configuration cycles 2 + 8 = 10
- Loop distribution may then be applied to get a vectorizable and a not vectorizable loop.
for (i = 0; i < 249; i++) { y[i] = 0; for (j = 0; j < 8; j++) tmp[j] = c[j] * x[i+7−j]; for (j = 0; j < 8; j++) y[i] += tmp [j]; } }
- The following parameter table corresponds to the two inner loops in order to be compared with the preceding table.
Parameter Value Vector length 249 Reused data set size — I/O IRAMs 5 ALU 2 BREG 0 FREG 1 Data flow graph width 1 Data flow graph height 3 Configuration cycles 1 * 8 + 1 * 8 = 16
- The architecture may be taken into account. The first loop is fully parallel, which means that we would need 2*8=16 input values at a time. This is all right, as it corresponds to the number of IRAMS of the PACT XPP. Hence, to strip-mine the first inner loop is not required. To strip-mine the second loop is also not required. The second loop is a reduction. It computes the sum of a vector. This may be easily found by the reduction recognition optimization and the following code may be obtained.
for (i = 0; i < 249; i++) { y[i] = 0; for (j = 0; j < 8; j++) tmp[j] = c[j] * x[i+7−j]; /* load the partial sums from memory using a shorter vector length */ for (j = 0; j < 4; j++) aux[j] = tmp[2*j] + tmp[2*j+1]; /* accumulate the short vector */ for (j = 0; j < 1; j++) aux[2*j] = aux[2*j] + aux[2*j+1]; /* sequence of scalar instructions to add up the partial sums */ y[i] = aux[0] + aux(2]; }
- Like above, only one table is given below for all innermost loops and the last instruction computing y[i].
Parameter Value Vector length 249 Reused data set size — I/O IRAMs 12 ALU 4 BREG 0 FREG 0 Data flow graph width 1 Data flow graph height 4 Configuration cycles 1 * 8 + 1 * 4 + 1 * 1 = 13
- Finally, loop unrolling may be applied on the inner loops. The number of operations is always less than the number of processing elements of the PACT XPP.
for (i = 0; i < 961; i++) { tmp[0] = c[0] * x[i+7]; tmp[1] = c[1] * x[i+6]; tmp[2] = c[2] * x[i+5]; tmp[3] = c[3] * x[i+4]; tmp[4] = c[4] * x[i+3]; tmp[5) = c[5] * x[i+2]; tmp[6] = c[6] * x[i+1]; tmp[7] = c[7] * x[i]; aux[0] = tmp[0] + tmp[1]; aux[1] = tmp[2] + tmp[3]; aux[2] = tmp[4] + tmp[5]; aux[3] = tmp[6] + tmp[7]; aux[0] = aux[0] + aux[1]; aux[2] = aux[2] + aux[3]; y[i] = aux[0] + aux[2]; }
- The dataflow graph illustrated in
FIG. 33, representing the inner loop, may be obtained.
- It could be mapped on the PACT XPP with each layer executed in parallel, thus requiring 4 cycles/iteration and 15 ALU-PAEs, 8 of which are needed in parallel. As the graph is already synchronized, the throughput reaches one iteration/cycle after 4 cycles to fill the pipeline. The coefficients are taken as constant inputs by the ALUs performing the multiplications.
- A drawback of this solution may be that it uses 16 IRAMs, and that the input data must be stored in a special order. The number of needed IRAMs can be reduced if the coefficients are handled like constant for each ALU. But due to data locality of the program, it can be assumed that the data already reside in the cache. As the transfer of data from the cache to the IRAMs can be achieved efficiently, the configuration can be executed on the PACT XPP without waiting for the data to be ready in the IRAMs. Accordingly, the parameter table may be the following:
Parameter Value Vector length 249 Reused data set size — I/O IRAMs 16 ALU 15 BREG 0 FREG 0 Data flow graph width 8 Data flow graph height 4 Configuration cycles 4 + 961
- Variant with Larger Bounds
- To make the things a bit more interesting, in one case, the values of N and M were set to 1024 and 64.
for (i = 0; i < 961; i++) { y[i] = 0; for (j = 0; j < 64; j++) y[i] += c[j] * x[i+63−j]; }
- The data dependence graph is the same as above. Node splitting may then be applied to get a more convenient data dependence graph.
for (i = 0; i < 961; i++) { y[i] = 0; for (j = 0; j < 64; j++) { tmp = c[j] * x[i+63−j]; y[i] += tmp; } }
- After scalar expansion:
for (i = 0; i < 961; i++) { y[i] = 0, for (j = 0; j < 64; j++) { tmp[j] = c[j] * x[i+63−j]; y[i] += tmp [j]; } }
- After loop distribution:
for (i = 0; i < 961; i++) { y[i] = 0; for (j = 0; j < 64; j++) tmp[j] = c[j] * x[i+63−j]; for (j = 0; j < 64; j++) y[i] += tmp[j]; }}
- After going through the compiling process, the set of optimizations that depends upon architectural parameters may be arrived at. It might be desired to split the iteration space, as too many operations would have to be performed in parallel, if it is kept as such. Hence, strip-mining may be performed on the 2 loops. Only 16 data can be accessed at a time, so, because of the first loop, the factor will be 64*2/16=8 for the 2 loops (as it is desired to execute both at the same time on the PACT XPP).
for (i = 0; i < 961; i++) { y[i] = 0 for (jj = 0; jj < 8; jj++) for (j = 0; j < 8; j++) tmp[8*jj+j] = c[8*jj+j] * x[i+63−8*jj−j]; for (jj = 0; jj < 8; jj++) for (j= 0; j < 8; j++) y[i] += tmp[8*jj+j]; }
- Then, loop fusion on the jj loops may be performed.
for (i = 0; i < 961; i++) { y[i] = 0; for (jj = 0; jj < 8; jj++) { for (j = 0; j < 8;j++) tmp[8*jj+j] = c[8*jj+j] * x[i+63−8*jj−j]; for (j = 0; j < 8; j++) y[i] += tmp[8*jj+j]; } }
- Reduction recognition may then be applied on the second innermost loop.
for (i = 0; i < 961; i++) { tmp = 0; for (jj = 0; jj < 8; jj++) { for (j = 0; j < 8; j++) tmp[8*jj+j] = c[8*jj+j] * x[i+63−8*jj−j]; /* load the partial sums from memory using a shorter vector length */ for (j = 0; j < 4; j++) aux[j] = tmp[8*jj+2*j] + tmp[8*jj+2*j+1]; /* accumulate the short vector */ for (j = 0; j < 1; j++) aux[2*j] = aux[2*j] + aux[2*j+1]; /* sequence of scalar instructions to add up the partial sums */ y[i] = aux[0] + aux[2];
- Loop unrolling may then be performed:
for (i = 0; i < 961; i++) for (jj = 0; jj < 8; jj++) { tmp[8*jj] = c[8*jj] * x[i+63−8*jj]; tmp[8*jj+1] = c[8*jj+1] * x[i+62−8*jj]; tmp[8*jj+2] = c[8*jj+2] * x[i+61−8*jj]; tmp[8*jj+3] = c[8*jj+3] * x[i+59−8*jj]; tmp[8*jj+4] = c[8*jj+4] * x[i+58−8*jj]; tmp[8*jj+5] = c[8*jj+5] * x[i+57−8*jj]; tmp[8*jj+6] = c[8*jj+6] * x[i+56−8*jj]; tmp[8*jj+7] = c[8*jj+7] * x[i+55−8*jj]; aux[0] = tmp[8*jj] + tmp[8*jj+1]; aux[1] = tmp[8*jj+2] + tmp[8*jj+3]; aux[2] = tmp[8*jj+4] + tmp[8*jj+5]; aux[3] = tmp[8*jj+6] + tmp[8*jj+7]; aux[0] = aux[0] + aux[1]; aux[2] = aux[2] + aux[3]; y[i] = aux[0] + aux[2]; }
- The innermost loop may be implemented on the PACT XPP directly with a counter. The IRAMs may be used in FIFO mode, and filled according to the addresses of the arrays in the loop. IRAM0, IRAM2, IRAM4, IRAM6 and IRAM8 contain array 'c'. IRAM1, IRAM3, IRAM5 and IRAM7 contain array 'x'. Array 'c' contains 64 elements, i.e., each IRAM contains 8 elements. Array 'x' contains 1024 elements, i.e., 128 elements for each IRAM. Array 'y' is directly written to memory, as it is a global array and its address is constant. This constant is used to initialize the address counter of the configuration. A final parameter table is the following:
Parameter Value Vector length 8 Reused data set size — I/O IRAMs 16 ALU 15 BREG 0 FREG 0 Data flow graph width 8 Data flow graph height 4 Configuration cycles 4 + 8 = 12
- Nevertheless, it should be noted that this version should be less efficient than the previous one. As the same data must be loaded in the different IRAMs from the cache, there are a lot of transfers to be achieved before the configuration can begin the computations. This overhead must be taken into account by the compiler when choosing the code generation strategy. This means also that the first solution is the solution that will be chosen by the compiler.
- Other Variant
Source Code for (i = 0; i < N−M+1; i++) { tmp = 0; for (j = 0; j < M; j++) tmp += c[j] * x[i+M−j−1]; x[i] = tmp; }
- In this case, the data dependence graph is cyclic due to dependences on tmp. Therefore, scalar expansion is applied on the loop, and, in fact, the same code as the first version of the FIR filter is obtained as shown below.
for (i = 0; i < N−M+1; i++) { tmp[i] = 0; for (j = 0; j < M; j++) tmp[i] += c[j] * x[i+M−j−1]; x[i] = tmp[i]; }
- Original Code
Source code: #define L 10 #define M 15 #define N 20 int A[L][M]; int B[M][N]; int R[L][N]; main( ) { int i, j, k, tmp, aux; /* input A (L*M values) */ for (i=0; i<L; i++) for (j=0; j<M; j++) scanf("%d", &A[i][j]); /* input B (M*N values) */ for (i=0; i<M; i++) for (j=0; j<N; j++) scanf("%d", &B[i][j]); /* multiply */ for (i=0; i<L; i++) for (j=0; j<N; j++) { aux = 0;. for (k=0; k<M; k++) aux += A[i][k] * B[k][j]; R[i][j] = aux; } /* write data stream */ for (i=0; i<L; i++) for (j=0; j<N; j++) printf("%d\n", R [i][j]); }
- Preliminary Transformations
- Since no inline-able function calls are present, no interprocedural code movement is done.
- Of the four loop nests, the one with the "/*multiply*/" comment is the only candidate for running partly on the XPP. All others have function calls in the loop body and are therefore discarded as candidates very early in the compiler.
Dependency Analysis for (i=0; i<L; i++) for (j=0; j<N; j++) { S1 aux = 0; for (k=0; k<M; k++) S2 aux += A[i][k] * B[k][j]; S3 R[i][j] = aux; }
FIG. 34shows a data dependency graph for matrix multiplication. The data dependency graph shows no dependencies that prevent pipeline vectorization. The loop carried true dependence from S2 to itself can be handled by a feedback of aux as described in Markus Weinhardt et al., "Memory Access Optimization for Reconfigurable Systems," supra.
- Reverse Loop-Invariant Code Motion
- To get a perfect loop nest, S1 and S3 may be moved inside the k-loop. Therefore, appropriate guards may be generated to protect the assignments. The code after this transformation is as follows:
for (i=0; i<L; i++) for(j=0; j<N; j++) for (k=0; k<M; k++) { if (k == 0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; if (k == M−1) R[i][j] = aux[j]; }
- Scalar Expansion
- A goal may be to interchange the loop nests to improve the array accesses to utilize the cache best. However, the guarded statements involving 'aux' may cause backward loop carried anti-dependencies carried by the j loop. Scalar expansion may break these dependencies, allowing loop interchange.
for (i=0; i<L; i++) for (j=0; j<N; j++) for (k=0; k<M; k++) { if (k == 0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; if (k == M−1) R[i][j] = aux[j]; }
- Loop Interchange for Cache Reuse
- Visualizing the main loop shows the iteration spaces for the array accesses.
FIG. 35is a visualization of array access sequences. Since C arrays are placed in row major order, the cache lines are placed in the array rows. At first sight, there seems to be no need for optimization because the algorithm requires at least one array access to stride over a column. Nevertheless, this assumption misses the fact that the access rate is of interest, too. Closer examination shows that array R is accessed in every j iteration, while B is accessed every k iteration, always producing a cache miss. ("aux" is not currently discussed since it is not expected that it would be written to or read from memory, as there are no defs or uses outside the loop nest.) This leaves a possibility for loop interchange to improve cache access as proposed by Kennedy and Allen in Markus Weinhardt et al., "Pipeline Vectorization," supra.
- To find the best loop nest, the algorithm may interchange each loop of the nests into the innermost position and annotate it with the so-called innermost memory cost term. This cost term is a constant for known loop bounds or a function of the loop bound for unknown loop bounds. The term may be calculated in three steps.
- First, the cost of each reference in the innermost loop body may be calculated to:
- 1, if the reference does not depend on the loop induction variable of the (current) innermost loop;
- the loop count, if the reference depends on the loop induction variable and strides over a non-contiguous area with respect of the cache layout;
- First, the cost of each reference in the innermost loop body may be calculated to:
- if the reference depends on the loop induction variable and strides over a contiguous dimension. In this case, N is the loop count, s is the step size and b is the cache line size, respectively.
- In this case, a "reference" is an access to an array. Since the transformation attempts to optimize cache access, it must address references to the same array within small distances as one. This may prohibit over-estimation of the actual costs.
- Second, each reference cost may be weighted with a factor for each other loop, which is:
- 1, if the reference does not depend on the loop index;
- the loop count, if the reference depends on the loop index.
- Third, the overall loop nest cost may be calculated by summing the costs of all reference costs.
- Second, each reference cost may be weighted with a factor for each other loop, which is:
- After invoking this algorithm for each loop as the innermost, the one with the lowest cost may be chosen as the innermost, the next as the next outermost, and so on.
Innermost loop R[i][j] A[i][k] B[k][j] Memory access cost k 1 · L · N M · N i 1 · L · N 1 · L · M 1 · M · N L · N + L · M + M · N j L · M
- The preceding table shows the values for the matrix multiplication. Since the j term is the smallest (assuming b>1), the j-loop is chosen to be the innermost. The next outer loop then is k, and the outermost is i. Thus, the resulting code after loop interchange may be:
for (i=0; i<L; i++) for (k=0; k<M; k++) , for (j=0; j<N; j++) { if (k == 0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; if (k == M−1) R[i][j] = aux[j]; }
FIG. 36shows the improved iteration spaces. It shows array access sequences after optimization. The improvement is visible to the naked eye since array B is now read following the cache lines. This optimization does not optimize primarily for the XPP; but mainly optimizes the cache-hit rate, thus improving the overall performance.
- Unroll and Jam
- After improving the cache access behavior, the possibility for reduction recognition has been destroyed. This is a typical example for transformations where one excludes the other. Nevertheless, more parallelism may be obtained by doing unroll-and-jam. Therefore, the outer loop may be partially unrolled with the unroll factor. This factor is mainly chosen by the minimum of two calculations:
- # available IRAMs/# used IRAMs in the inner loop body
- # available ALU resources/# used ALU resources in the inner loop.
- In this example embodiment, the accesses to "A" and "B" depend on k (the loop which will be unrolled). Therefore, they are considered in the calculation. The accesses to "aux" and "R" do not depend on k. Thus, they can be subtracted from the available IRAMs, but do not need to be added to the denominator. Therefore, (assuming an XPP64) 14/2=7 is calculated for the unroll factor obtained by the IRAM resources.
- On the other hand, the loop body involves two ALU operations (1 add, 1 mult), which may yield an unrolling factor of approximately 64/2=32. (This is an inaccurate estimation since it neither estimates the resources spent by the controlling network, which may decrease the unroll factor, nor takes into account that, e.g., the BREG-PAEs also have an adder, which may increase the unroll factor. Although it does not influence this example, the unroll factor calculation should account for this in a production compiler.) The constraint generated by the IRAMs therefore dominates by far.
- Having chosen the unroll factor, the loop trip count is trimmed to be a multiple of that factor. Since the k loop has a loop count of 15, the first iteration may be peeled off and the remaining loop may be unrolled.
for (i=0; i<L; i++) { for (k=0; k<1; k++) { for (j=0; j<N; j++) { if (k==0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; if (k==M−1) R[i][j] = aux[j]; } } for (k=1; k<M; k+=7) { for (j=0; j<N; j++) { if (k==0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; if (k==M−1) R[i][j] = aux[j]; } for (j=0; j<N; j++) { if (k+1==0) aux[j] = 0; aux[j] += A[i][k+1] * B[k+1][j]; if (k+1==M−1) R[i][j] = aux[j]; } for (j=0; j<N; j++) { if (k+2==0) aux[j] = 0; aux[j] += A[i][k+2] * B[k+2][j]; if (k+2==M−1) R[i][j] = aux[j]; } for (j=0; j<N; j++) { if (k+3==0) aux[j] = 0; aux[j] += A[i][k+3] * B[k+3][j]; if (k+3==M−1) R[i][j] = aux[j]; } for (j=0; j<N; j++) { if (k+4==0) aux[j] = 0; aux[j] += A[i][k+4] * B[k+4][j]; if (k+4==M−1) R[i][j] = aux[j]; } for (j=0; j<N; j++) { if (k+5==0) aux[j] = 0; aux[j] += A[i][k+5] * B[k+5][j]; if (k+5==M−1) R[i][j] = aux[j]; } for(j=0; j<N; j++) { if (k+6==0) aux[j] = 0; aux[j] += A[i][k+6] * B[k+6][j]; if (k+6==M−1) R[i][j] = aux[j]; } } }
- Due to placement by the reverse loop invariant code motion of the loop invariant code into the inner loop, which is duplicated seven times, it is very likely that dead code elimination can get rid of some of these duplicates. Thus, the code may be shortened to:
for (i=0; i<L; i++) { for (k=0; k<1; k++) { for(j=0; j<N; j++) { if (k==0) aux[j] = 0; aux[j] += A[i][k] * B[k][j]; } } for (k=1; k<M; k+=7) { for (j=0; j<N; j++) { aux[j] += A[i][k] * B[k][j]; } for (j=0; j<N; j++) { aux[j] += A[i][k+1] * B[k+1][j]; } for(j=0; j<N; j++) { aux[j] += A[i][k+2] * B[k+2][j]; } for (j=0; j<N; j++) { aux[j] += A[i][k+3] * B[k+3][j]; } for (j=0; j<N; j++) { aux[j] += A[i][k+4] * B[k+4][j]; } for (j=0; j<N; j++) { aux[j] += A[i][k+5] * B[k+5][j]; } for (j=0; j<N; j++) { aux[j] += A[i][k+6] * B[k+6][j]; if (k+6==M−1) R[i][j] } } }
- Before jamming of the inner loops, it may be taken into account that the first iteration of the k loop was peeled of which would produce an own configuration. Since the unroll-and-jam factor is calculated to fit into one configuration, this side effect should be prevented. Because it should be no problem to run the k loop with variable step sizes, the k loops may be fused again, the step size may be adjusted, and the statements may be guarded. This may yield:
for (i=0; i<L; i++) { for (k=0; k<M; k+= k<1 ? 1 : 7) { for (j=0; j<N; j++) { if (k==0) aux[j] = 0; if (k==0) aux[j] += A[i][k] * B[k][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k] * B[k][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+1] * B[k+1][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+2] * B[k+2][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+3] * B[k+3][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+4] * B[k+4][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+5] * B[k+5][j]; } for(j=0; j<N; j++) { if (k>0) aux[j] += A[i][k+6] * B[k+6][j]; if (k+6==M−1) R[i][j] = aux[j]; } } }
- Now, the inner loops may be jammed, and the following may be obtained.
for (i=0; i<L; i++) { for (k=0; k<M; k+= k<1 ? 1 : 7) { for (j=0; j<N; j++) { if (k==0) aux[j] = 0; if (k==0) aux[j] += A[i][k] * B[k][j]; if (k>0) { aux[j] += A[i][k] * B[k][j]; aux[j] += A[i][k+1] * B[k+1 ][j]; aux[j] += A[i][k+2] * B[k+2][j]; aux[j] += A[i][k+3] * B[k+3][j]; aux[j] += A[i][k+4] * B[k+4][j]; aux[j] += A[i][k+5] * B[k+5][j]; aux[j] += A[i][k+6] * B[k+6][j]; if (k+6==M−1) R[i][j] = aux[j]; } } } }
- XPP Code Generation
- The innermost loop can be synthesized in a configuration which uses 14 IRAMs for the input data, one IRAM to temporary store aux, and one IRAM for the output may R. Furthermore, it may be necessary to pass the value of k to the XPP to direct the dataflow. This may be done by a streaming input.
FIG. 37shows the dataflow graph of the synthesized configuration and shows matrix multiplication after unroll and jam. The rightmost 3 branches are omitted from the graph and event connections are highlighted.
- The following code shows the pseudo code that may be executed on the RISC processor.
XPPPreload(config) for (i=0; i<L; i++) { XPPPreload(0, &A[i][0], M) XPPPreload(1, &A[i][0], M) XPPPreload(2, &A[i][0], M) XPPPreload(3, &A[i][0], M) XPPPreload(4, &A[i][0], M) XPPPreload(5, &A[i][0], M) XPPPreload(6, &A[i][0], M) XPPPreloadClean(15, &R[i][0], M) for (k=0; k<M; k+= k<1 ? 1 : 7) { XPPPreload(7, &B[k][0], N) XPPPreload(8, &B[k+1][0],N) XPPPreload(9, &B[k+2][0],N) XPPPreload(10, &B[k+3][0],N) XPPPreload(11, &B[k+4][0],N) XPPPreload(12, &B[k+5][0],N) XPPPreload(13, &B[k+6][0],N) XPPExecute(config, IRAM(0), IRAM(1), IRAM(2), IRAM(3), IRAM(4), IRAM(5), IRAM(6), IRAM(7), IRAM(8), IRAM(9), IRAM(10), IRAM(11), IRAM(12), IRAM(13), IRAM(15), k) } }
- The following table shows the simulated configuration. The complete multiplication needs about 3120 cycles without the preloading and configuration. A typical RISC-DSP core with two MAC units and hardware loop support needs over 26000 cycles (when data is in zero-latency internal memory). Although the time for preloads and cache misses is neglected here, the values according to an embodiment of the present invention may result in improvements of 200-300 percent compared to a standalone RISC core.
- The following is a corresponding parameter table.
Parameter Value Vector length 20 Reused data set size 20 I/O IRAMs 14 I + 1 O + 1 internal ALU 20 BREG 26 (8 defined + 18 route) FREG 28 (4 defined + 24 route) Data flow graph width 14 Data flow graph height 6 (without routing and balancing) Configuration cycles (simulated) configuration 2633 preloads 10 * 3 * 7 * 5 1050 cycles 10 * 7 * 15 1050 sum (k == 0) 112 + 3120 (k == 1) 100 + (k == 7) 100 * 10 = 7853
- Original Code
Source Code: /* C-language butterfly */ #define BFLY(i) {\ unsigned char metric, m0, m1, decision; \ metric = ((Branchtab29_1[i] {circumflex over ( )} sym1) + (Branchtab29_2[i] {circumflex over ( )} sym2) + 1)/2; \ m0 = vp->old_metrics[i] + metric; \ m1 = vp->old_metrics[i+128] + (15 − metric); \ decision = (m0−m1) >= 0; \ vp->new_metrics[2*i] = decision ? m1 : m0; \ vp->dp->w[i/16] |= decision << ((2*i)&31); \ m0 −= (metric+metric−15); \ m1 += (metric+metric−15); \ decision = (m0−m1) >= 0; \ vp->new_metrics[2*i+1] = decision ? m1 : m0; \ vp->dp->w[i/16] |= decision << ((2*i+1)&31); \ } int update_viterbi29(void *p,unsigned char sym1,unsigned char sym2) { int i; struct v29 *vp = p; unsigned char *tmp; int normalize = 0; for (i=0; i<8; i++) vp->dp->w[i] = 0; for (i=0; i<128; i++) BFLY(i); /* Renormalize metrics */ if (vp->new_metrics[0] > 150) { int i; unsigned char minmetric = 255; for (i=0; i<64; i++) if (vp->new_metrics[i] < minmetric) minmetric = vp->new_metrics[i]; for (i=0; i<64; i++) vp->new_metrics[i] −= minmetric; normalize = minmetric; } vp->dp++; tmp = vp->old_metrics; vp->old_metrics = vp->new_metrics; vp->new_metrics = tmp; return normalize; }
- Interprocedural Optimizations and Scalar Transformations
- Since no inline-able function calls are present, in an embodiment of the present invention, no interprocedural code movement is done.
- After expression simplification, strength reduction, SSA renaming, copy coalescing and idiom recognition, the code may be approximately as presented below (statements are reordered for convenience). Note that idiom recognition may find the combination of min( ) and use the comparison result for decision and _decision. However, the resulting computation cannot be expressed in C, so it is described below as a comment.
int update_viterbi29 (void *p,unsigned char sym1,unsigned char sym2) { int i; struct v29 *vp = p; unsigned char *tmp; int normalize = 0; char *_vpdpw = vp->dp->w; for (i=0; i<8; i++) *_vpdpw_++ = 0; char *_bt29_1= Branchtab29_1; char *_bt29_2= Branchtab29_2; char *_vpom0= vp->old_metrics; char *_vpom128= vp->old_metrics+128; char * vpnm= vp->new_metrics; char *_vpdpw= vp->dp->w; for (i=0; i<128; i++) { unsigned char metric, _tmp, m0, m1, _m0, _m1, decision, _decision; metric = ((*_bt29_1++ {circumflex over ( )} sym1) + (*_bt29_2++ {circumflex over ( )} sym2) + 1)/2; _tmp= (metric+metric−15); m0 = *_vpom++ + metric; m1 = *_vpom128++ + (15 − metric); _m0 = m0 − _tmp; _m1 = m1 + _tmp; // decision = m0 >= m1; // _decision = _m0 >= m1; *_vpnm++ = min(m0,m1); // = decision ? m1 : m0 *_vpnm++ = min(_m0,_m1); // = _decision ? _m1 : _m0 _vpdpw[i >> 4] |= ( m0 >= m1) /* decision*/ << ((2*i) & 31) | (_mO >= _m1) /*_decision*/ << ((2*i+1)&31); } /* Renormalize metrics */ if(vp->new_metrics[0] > 150) { int i; unsigned char minmetric = 255; char *_vpnm= vp->new_metrics; for (i=0; i<64; i++) minmetric = min(minmetric, *vpnm++); char *_vpnm= vp->new_metrics; for (i=0; i<64; i++) *vpnm++ −= minmetric; normalize = minmetric; } vp->dp++; tmp = vp->old_metrics; vp->old_metrics = vp->new_metrics; vp->new_metrics = tmp; return normalize; }
- Initialization
- The first loop (setting vp->dp->w[0.7] to zero) may be most efficiently executed on the RISC.
- Butterfly Loop
- The second loop (with the BFLY( ) macro expanded) is of interest for the XPP compiler and needs further examination:
char*iram0= Branchtab29_1; // XPPPreload(0, Branchtab29_1, 128/4); char*iram2= Branchtab29_2; // XPPPreload(2, Branchtab29_2, 128/4); char*iram4= vp->old_metrics; // XPPPreload(4, vp->old metrics, 128/4); char*iram5= vp->old_metrics+128; // XPPPreload(5, vp->old_metrics+128,128/4); short *iram6= vp->new_metrics; // XPPPreload(6, vp->new_metrics, 128/2); unsigned long *iram7= vp->dp->w; // XPPPreload(7, vp->dp->w, 8); // sym1 & sym2 are in IRAM 1 & 3 for (i=0; i<128; i++) { unsigned char metric, _tmp, m0, m1, _m0, _m1 metric = ((*iram0++ {circumflex over ( )} sym1) + (*iram1++ {circumflex over ( )} sym2) + 1)/2; _tmp= (metric << 1) −15; m0 = *iram2++ + metric; m1 = *iram3++ + (15 − metric); _m0 = m0 − _tmp; _m1 = m1 + _tmp; // assuming big endian; little endian has the shift on the latter min( ) *iram6++ = (min(m0,m1) << 8) | min(_m0,_m1); *iram7[i >> 4] |= (m0 >= m1) << ((2*i) & 31) | (_m0 >= _m1) << ((2*i+1)&31); }
- The corresponding data flow graph is shown in
FIG. 38(for now ignoring that the IRAM accesses are mostly char accesses). The solid lines represent data flow, while the dashed lines represent event flow.
- The following is a corresponding parameter table.
Parameter Value Vector length 128 Reused data set size — I/O IRAMs 6 I + 2 O ALU 25 BREG few FREG few Data flow graph width 4 Data flow graph height 11 Configuration cycles 11 + 128
- Some problems are immediately noticed: IRAM7 is fully busy reading and rewriting the same address sixteen times. Loop tiling to a tile size of sixteen gives the redundant load store elimination a chance to read the value once and accumulate the bits temporarily, writing the value to the IRAM at the end of this inner loop. Loop Fusion with the initialization loop then may allow propagation of the zero values set in the first loop to the reads of vp->dp->w[i] (IRAM7), eliminating the first loop altogether. Loop tiling with a tile size of 16 may also eliminate the & 31 expressions for the shift values. Since the new inner loop only runs from 0 to 16, the value range analysis now finds that the & 31 expression is not limiting the value range any further.
- All remaining input IRAMs are character (8 bit) based. So it may be required for split networks to split the 32-bit stream into four 8-bit streams which are then merged. This adds 3 shifts, 3 ands, and 3 merges for every character IRAM. The merges could be eliminated when unrolling the loop body. However, unrolling may be limited to unrolling twice due to ALU availability as well as due to that IRAM6 is already 16 bit based. Unrolling once requires a shift by 16 and an or to write 32 bits in every cycle. Unrolling further cannot increase pipeline throughput any more. So the body is only unrolled once, eliminating one layer of merges. This may yield two separate pipelines that each handle two eight bit slices of the 32-bit value from the IRAM, serialized by merges.
- The modified code may be approximately as follows (unrolling and splitting omitted for simplicity):
char*iram0= Branchtab29_1; // XPPPreload(0, Branchtab29_1, 128/4); char*iram2= Branchtab29_2; // XPPPreload(2, Branchtab29_2, 128/4); char*iram4= vp->old_metrics; // XPPPreload(4, vp->old metrics, 128/4); char*iram5= vp->old_metrics+128; // XPPPreload(5, vp->old_metrics+128,128/4); short *iram6= vp->new_metrics; // XPPPreload(6, vp->new_metrics, 128/2); unsigned long *iram7= vp->dp->w; // XPPPreload(7, vp->dp->w, 8); // sym1 & sym2 are in IRAM 1 & 3 for (_i=0;_i<8;_i++) { rlse= 0; for (i2=0; i2<32; i2+=2) { unsigned char metric, _tmp, m0, m1, _m0, _m1; metric = ((*iram0++ {circumflex over ( )} sym1) + (*iram1++ {circumflex over ( )} sym2) + 1)/2; _tmp= (metric << 1) −15; m0 = *iram2++ + metric; m1 = *iram3++ + (15 − metric); _m0 = m0 − _tmp; _m1 = m1 + _tmp; *iram6++ = (min(m0,m1) << 8) | min(_m0,_m1); rlse = rlse | ( m0 >= m1) << i2 | (_m0 >= _m1) << (i2+1); } *iram7++ = rlse; }
- The modified data flow graph (unrolling and splitting omitted for simplicity) is shown in
FIG. 39. The splitting network is shown in FIG. 40. The bottom most level merge is omitted for each level of unrolling.
- The following is a corresponding parameter table.
Parameter Value Vector length 128 Reused data set size — I/O IRAMs 6 I + 2 O ALU 2 * 24 + 4 * 3 (split) + 2 (join) = 62 BREG few FREG few Data flow graph width 4 Data flow graph height 11 + 3 (split) Configuration cycles 14 + 64
- Re-Normalization
- The Normalization consists of a loop scanning the input for the minimum and a second loop that subtracts the minimum from all elements. There is a data dependency between all iterations of the first loop and all iterations of the second loop. Therefore, the two loops cannot be merged or pipelined. They may be handled individually.
- Minimum Search
- The third loop is a minimum search on a byte array.
char *iram0 = vp->new_metrics; //XPPPzeload(0, vp->new_metrics, 64/4); for (i=0; i<64; i++) minmetric = min(minmetric, *iram0++);
- The following is a corresponding parameter table.
Parameter Value Vector length 64 Reused data set size — I/O IRAMs 1 + 1 ALU 1 BREG 0 FREG 0 Data flow graph width 1 Data flow graph height 1 Configuration cycles 64
- Reduction recognition may eliminate the dependence for minmetric, enabling a four-times unroll to utilize the IRAM width of 32 bits. A split network has to be added to separate the 8 bit streams using 3 SHIFT and 3 AND operations. Tree balancing may re-distribute the min( ) operations to minimize the tree height.
char *iram0 = vp->new metrics; // XPPPreload(0, vp->new_metrics, 16); for (i=0; i<16; i++) minmetric = min(minmetric, min(min(*iram0++, *iram0++), min(*iram0++, *iram0++)));
- The following is a corresponding parameter table.
Parameter Value Vector length 16 Reused data set size — I/0 IRAMs 1 I + 1 O ALU 4 * min BREG 3 * shln + 3 * shrn FREG 0 Data flow graph width 4 Data flow graph height 5 Configuration cycles 5 + 16
- Reduction recognition again may eliminate the loop carried dependence for minmetric, enabling loop tiling and then unroll and jam to increase parallelism. The maximum for the tiling size is 16 IRAMs/2 IRAMS=8. Constant propagation and tree rebalancing may reduce the dependence height of the final merging expression:
char *iram0= vp->new_metrics; // XPPPreload(0, vp->new_metrics, 2); char *iram1= vp->new_metrics+8; // XPPPreload(1, vp->new_metrics+8, 2); char *iram2= vp->new_metrics+16; // XPPPreload(2, vp->new_metrics+16, 2); char *iram3= vp->new_metrics+24; // XPPPreload(3, vp->new_metrics+24, 2); char *iram4= vp->new_metrics+32; // XPPPreload(4, vp->new_metrics+32, 2); char *iram5= vp->new_metrics+40; // XPPPreload(5, vp->new_metrics+40, 2); char *iram6= vp->new_metrics+48; // XPPPreload(6, vp->new_metrics+48, 2); char *iram7= vp->new_metrics+56; // XPPPreload(7, vp->new_metrics+56, 2); for (i=0;_i<2; i++) { minmetric0 = min (minmetric0, min( min(*iram0++, *iram0++), min(*iram0++, *iram0++))); minmetric1 = min (minmetric1, min( min(*iram1++, *iram1++), min(*iram1++, *iram1++))); minmetric2 = min (minmetric2, min( min(*iram2++, *iram2++), min(*iram2++, *iram2++))); minmetric3 = min (minmetric3, min( min(*iram3++, *iram3++), min(*iram3++, *iram3++))); minmetric4 = min (minmetric4, min( min(*iram4++, *iram4++), min(*iram4++, *iram4++))); minmetric5 = min (minmetric5, min( min(*iram5++, *iram5++), min(*iram5++, *iram5++))); minmetric6 = min (minmetric6, min( min(*iram6++, *iram6++), min(*iram6++, *iram6++))); minmetric7 = min (minmetric7, min( min(*iram7++, *iram7++), min(*iram7++, *iram7++))); } minmetric = min(min(( min(minmetric_0, minmetric_1), min(minmetric_2, minmetric_3)), min(( min(minmetric_4, minmetric_5), min(minmetric_6, minmetric_7));
- The following is a corresponding parameter table.
Parameter Value Vector length 2 Reused data set size — I/O IRAMs 8 I + 1 O ALU 8 * 4 * min = 32 BREG 8 * (3 * shln + 3 * shrn) = 48 FREG 0 Data flow graph width 8 * 4 = 32 Data flow graph height 5 Configuration cycles 8 + 2
- Re-Normalization
- The fourth loop subtracts the minimum of the third loop from each element in the array. The read-modify-write operation has to be broken up into two IRAMs. Otherwise, the IRAM ports will limit throughput.
char *iram0= vp->new_metrics; // XPPPreload (0, vp->new_metrics, 64/4) char *iram1= vp->new_metrics; // XPPPreloadClean(1, vp->new_metrics, 64/4) for (i=0; i<64; i++) *iram1++ = *iram0++ − minmetric;
- The following is a corresponding parameter table.
Parameter Value Vector length 64 Reused data set size — I/O IRAMs 2 I + 1 O ALU 1 BREG 0 FREG 0 Data flow graph width 1 Data flow graph height 1 Configuration cycles 64
- There are no loop carried dependencies. Since the data size is bytes, the inner loop can be unrolled four times without exceeding the IRAM bandwidth requirements. Networks splitting the 32-bit stream into 4 8-bit streams and rejoining the individual results to a common 32-bit result stream are inserted.
char *iram0= vp->new_metrics; // XPPPreload (0, vp->new_metrics, 16) char *iram1= vp->new_metrics; // XPPPreloadClean (1, vp->new metrics, 16) for (i=0; i<16; i++) { *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; }
- The following is a corresponding parameter table.
Parameter Value Vector length 16 Reused data set size — 110 IRAMs 2 I + 1 O ALU 4 * 4(sub) = 16 BREG 6 * shln + 6 * shrn = 12 FREG 0 Data flow graph width 4 Data flow graph height 5 Configuration cycles 2(split) + 4 * 1(sub) + 2(join) = 8
- Unroll and jam can be applied after loop tiling, in analogy to the third loop, but loop tiling is now limited by the BREGs used by the split and join networks. The computed tiling size (unroll factor) is 64 BREGs/12 BREGs=5, which is replaced by 4, since the same throughput is achieved with less over-head.
char *iram0= vp->new_metrics; // XPPPreload (0, vp->new_metrics, 4) char *iram1= vp->new_metrics; // XPPPreloadClean (1, vp->new_metrics, 4) char *iram2= vp->new_metrics+16; // XPPPreload (2, vp->new_metrics+16, 4) char *iram3= vp->new_metrics+16; // XPPPreloadClean (3, vp->new_metrics+16, 4) char *iram4= vp->new_metrics+32; // XPPPreload (4, vp->new_metrics+32, 4) char *iram5= vp->new_metrics+32; // XPPPreloadClean (5, vp->new_metrics+32, 4) char *iram6= vp->new_metrics+48; // XPPPreload (6, vp->new_metrics+48, 4) char *iram7= vp->new_metrics+48; // XPPPreloadClean (7, vp->new_metrics+48, 4) for (i=0; i<4; i++) { *iram1++ = *iram0++ − minmetric; // first pipeline *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram3++ = *iram2++ − minmetric; // second pipeline *iram3++ = *iram2++ − minmetric; *iram3++ = *iram2++ − minmetric; *iram3++ = *iram2++ − minmetric; *iram5++ = *iram4++ − minmetric; // third pipeline *iram5++ = *iram4++ − minmetric; *iram5++ = *iram4++ − minmetric; *iram5++ = *iram4++ − minmetric; *iram7++ = *iram6++ − minmetric; // fourth pipeline *iram7++ = *iram6++ − minmetric; *iram7++ = *iram6++ − minmetric; *iram7++ = *iram6++ − minmetric; }
- The following is a corresponding parameter table.
Parameter Value Vector length 4 Reused data set size — I/O IRAMs 51 + 40 ALU 4 * (6(split) + 4(sub) + 6(join)) = 64 BREG 4 * (6 * shln + 6 * shrn) = 48 FREG 0 Data flow graph width 16 Data flow graph height 1 Configuration cycles 2(split) + 4 * 1(sub) + 2(join) = 8
- Final Code
- Finally the following code may be obtained:
int update_viterbi29 (void *p, unsigned char sym1, unsigned char sym2) { int i; struct v29 *vp = p; unsigned char *tmp; int normalize = 0; // initialization loop eliminated // for (i=0; i<8; i++) // vp->dp->w[i] = 0; // Configuration for butterfly loop char*iram0= Branchtab29_1; // XPPPreload(0, Branchtab29_1, 128/4); char*iram2= Branchtab29_2; // XPPPreload(2, Branchtab29_2, 128/4); char*iram4= vp->old_metrics; // XPPPreload(4, vp->old metrics, 128/4); char*iram5= vp->old_metrics+128; // XPPPreload(5, vp->old_metrics+128,128/4); short*iram6= vp->new_metrics; // XPPPreload(6, vp->new_metrics, 128/2); unsigned long *iram7= vp->dp->w; // XPPPreload(7, vp->dp->w, 8); // sym1 & sym2 are in IRAM 1 & 3 for (_i=0;_i<8;_i++) { rlse= 0; for (i2=0; i<32; i2+=2) { // unrolled once unsigned char metric, _tmp, m0, m1, _m0, _m1 metric = ((*iram0++ {circumflex over ( )} sym1) + (*iram1++ {circumflex over ( )} sym2) + 1)/2; _tmp= (metric << 1) −15; m0 = *iram2++ + metric; m1 = *iram3++ + (15 − metric); _m0 = m0 − _tmp; _m1 = m1 + _tmp; *iram6++ = (min(m0,m1) << 8) | min(_m0,_m1); rlse = rlse | ( m0 >= m1) << i2 | (_m0 >= _m1) << (i2+1); } *iram7++ = rlse; } /* Renormalize metrics */ if (vp->new_metrics[0] > 150) { int 1; // Configuration for loop 3 char *iram0= vp->new_metrics; // XPPPreload(0, vp->new_metrics, 8); char *iram1= vp->new_metrics+8; // XPPPreload(1, vp->new_metrics+8, 8); char *iram2= vp->new_metrics+16; // XPPPreload(2, vp->new_metrics+16, 8); char *iram3= vp->new_metrics+24; // XPPPreload(3, vp->new_metrics+24, 8); char *iram4= vp->new_metrics+32; // XPPPreload(4, vp->new_metrics+32, 8); char *iram5= vp->new_metrics+40; // XPPPreload(5, vp->new_metrics+40, 8); char *iram6= vp->new_metrics+48; // XPPPreload(6, vp->new_metrics+48, 8); char *iram7= vp->new_metrics+56; // XPPPreload(7, vp->new_metrics+56, 8); for (i=0;_i<2; i++) { minmetric0 = min (minmetric0, min( min(*iram0++, *iram0++), min(*iram0++, *iram0++))); minmetric1 = min (minmetric1, min( min(*iram1++, *iram1++), min(*iram1++, *iram1++))); minmetric2 = min (minmetric2, min( min(*iram2++, *iram2++), min(*iram2++, *iram2++))); minmetric3 = min (minmetric3, min( min(*iram3++, *iram3++), min(*iram3++, *iram3++))); minmetric4 = min (minmetric4, min( min(*iram4++, *iram4++), min(*iram4++, *iram4++))); minmetric5 = min (minmetric5, min( min(*iram5++, *iram5++), min(*iram5++, *iram5++))); minmetric6 = min (minmetric6, min( min(*iram6++, *iram6++), min(*iram6++, *iram6++))); minmetric7 = min (minmetric7, min( min(*iram7++, *iram7++), min(*iram7++, *iram7++))); } minmetric = min(min(( min(minmetric_0, minmetric_1), min(minmetric_2, minmetric_3)), min(( min(minmetric_4, minmetric_5), min(minmetric_6, minmetric_7)); // minmetric is written to the output IRAM // Configuration for loop 4, minmetric is in an input IRAM char *iram0= vp->new_metrics; // XPPPreload (0, vp->new_metrics, 4) char *iram1= vp->new_metrics; // XPPPreloadClean (1, vp->new_metrics, 4) char *iram2= vp->new_metrics+16; // XPPPreload (2, vp->new_metrics+16, 4) char *iram3= vp->new_metrics+16; // XPPPreloadClean (3, vp->new_metrics+16, 4) char *iram4= vp->new_metrics+32; // XPPPreload (4, vp->new_metrics+32, 4) char *iram5= vp->new_metrics+32; // XPPPreloadClean (5, vp->new_metrics+32, 4) char *iram6= vp->new_metrics+48; // XPPPreload (6, vp->new_metrics+48, 4) char *iram7= vp->new_metrics+48; // XPPPreloadClean (7, vp->new_metrics+48, 4) for (i=0; i<4; i++) { *iram1++ = *iram0++ − minmetric; // first pipeline *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram1++ = *iram0++ − minmetric; *iram3++ = *iram2++ − minmetric; // second pipeline *iram3++ = *iram2++ − minmetric; *iram3++ = *iram2++ − minmetric; *iram3++ = *iram2++ − minmetric; *iram5++ = *iram4++ − minmetric; // third pipeline *iram5++ = *iram4++ − minmetric; *iram5++ = *iram4++ − minmetric; *iram5++ = *iram4++ − minmetric; *iram7++ = *iram6++ − minmetric; // fourth pipeline *iram7++ = *iram6++ − minmetric; *iram7++ = *iram6++ − minmetric; *iram7++ = *iram6++ − minmetric; } normalize = minmetric; } vp->dp++; tmp = vp->old_metrics; vp->old_metrics = vp->new_metrics; vp->new_metrics = tmp; return normalize; }
- Performance Considerations
- In this example there is not a high data locality. Every input data item is read exactly once. Only in the case of re-normalization, the new metric array is re-read and re-written. To fully utilize the PAE array, loop tiling was used in conjunction with reduction recognition to break dependencies using algebraic identities. In some cases (minimum search) this may lead to extremely short vector lengths. This is not a problem as it still does reduce the running time of the configuration and the transfer time from the top of the memory hierarchy to the IRAMs stays the same. The vector length can be increased if the outer loop that calls the function is known. The additional data can be used to increase the fill grade of the IRAMs by unrolling the outer loop, keeping the vector length longer. This would further increase configuration performance by reducing overall pipeline setup times.
- Performance of XPP for this example is compared to a hypothetical superscalar RISC-architecture. An average issue width of two is assumed, which means that the RISC on average executes two operations in parallel. The estimate is achieved by counting instructions for the source code presented under the heading "Interprocedural Optimizations and Scalar Transformations." See the table below.
Operation Cycles Bfly Setup Butterfly Min Setup Min Search Norm Setup Normalize ADRCOMP 1 6 7 1 LD/ST 2 5 8 2 1 2 LDI 1 3 4 1 1 MOVE 1 4 1 BITOP 1 10 ADD/SUB 1 20 3 1 3 MULT 2 2 CJMP 3 3 2 1 Cycles 23 70 5 11 4 10 Count 1 126 1 64 1 64 Issue Width 2 Est. RISC cycles Total Cycles 12 4480 3 352 2 320 5168 RISC Cycles
- Quantization/Inverse Quantization (quant.c)
- The quantization file may include routines for quantization and inverse quantization of 8×8 macro blocks. These functions may differ for intra and non-intra blocks. Furthermore, the encoder may distinguish between MPEG1 and MPEG2 inverse quantization.
- This may give a total of 6 functions, which are all candidates for function inlining, since they do not use the XPP capacity by far.
- Since all functions may have the same layout (some checks, one main loop running over the macro block quantizing with a quantization matrix), focus is placed on "iquant_intra," the inverse quantization of intra-blocks, since it may include all elements found in the other procedures. (The non_intra quantization loop bodies are more complicated, but add no compiler complexity). In the source code the mpeg part is already inlined, which is straightforward since the function is statically defined and includes no function calls itself. Therefore, the compiler may inline it and dead function elimination may remove the whole definition.
Original Code void iquant_intra(src,dst,dc_prec,quant_mat,mquant) short *src, *dst; int dc_prec; unsigned char *quant_mat; int mquant; { int i, val, sum; if (mpeg1) { dst[0] = src[0] << (3-dc_prec); for (i=1; i<64; i++) { val = (int)(src[i]*quant_mat[i]*mquant)/16; /* mismatch control */ if ((val&1)==0 && val!=0) val+= (val>0) ? −1 : 1; /* saturation */ dst[i] = (val>2047) ? 2047 : ((val<−2048) ? −2048 : val); } } else { sum = dst[0] = src[0] << (3-dc_prec); for (i=1; i<64; i++) { val = (int) (src[i]*quant_mat[i]*mquant)/16; sum+= dst[i] = (val>2047) ? 2047 : ((val<−2048) ? −2048 : val); } /* mismatch control */ if ((sum&1)==0) dst[63] {circumflex over ( )}=1; } }
- Interprocedural Optimizations
- Analyzing the loop bodies, it can be seen that they may easily fit to the XPP and do not use the maximum of resources by far. The function is called three times from module putseq.c. With inter-module function inlining, the code for the function call may disappear and may be replaced with the function. Therefore, it may be as follows:
for (k=0; k<mb_height*mb_width; k++) { if (mbinfo[k].mb_type & MB_INTRA) for (j=0; j<block_count; j++) if (mpeg1) { blocks[k*block_count+j][0] = blocks[k*block_count+j][0] << (3-dc_prec); for (i=1; i<64; i++) { val = (int)(blocks[k*block_count+j][i] * intra_q[i]*mquant)/16; . . . } }else { sum = blocks[k*block_count+j][0] = blocks[k*block_count+j][0] << (3-dc_prec); for (i=1; i<64; i++) { val = (int)(blocks[k*block_count+j][i] * intra_q[i]*mquant) /16; . . . } }else { . . . }
- Basic Transformations
- Since global mpeg1 does not change within the loop, unswitching may move the control statement outside the j loop and may produce two loop nests.
for (k=0; k<mb_height*mb_width; k++) { if (mbinfo[k].mb_type & MB_INTRA) if (mpeg1) for (j=0; j<block_count; j++) { blocks[k*block_count+j][0] = blocks[k*block_count+j][0]<< (3-dc_prec); for (i=1; i<64; i++) { val = (int)(blocks[k*block_count+j][i] * intra_q[i]*mquant)/16; . . . } } else for (j=0; j<block_count; j++) { sum = blocks[k*block_count+j][0] = blocks[k*block_count+j][0] << (3-dc_prec); for (i=1; i<64; i++) { val = (int)(blocks[k*block_count+j][i] * intra_q[i]*mquant) /16; . . . } } }
- Furthermore, the following transformations may be performed:
- A peephole optimization may reduce the divide by 16 to a right shift 4. This may be essential since loop bodies including division for the XPP are not considered.
- Idiom recognition may reduce the statement after the "saturation" comment to dst[i]=min(max(val, −2048), 2047).
- Increasing Parallelism
- It may be desired to increase parallelism. The j-i loop nest is a candidate for unroll-and-jam when the interprocedural value range analysis finds that block_count can only get the values 6, 8, or 12. Therefore, it has a value range [6,12] with the additional attribute to be dividable by 2. Thus, an unroll-and-jam with the factor 2 is applicable (the resource constraints would choose a greater value). Since no loop carried dependencies exist, this transformation is safe.
- This is to say that the source code contains a manually peeled first iteration. This peeling has been done because the value calculated for the first block value is completely different from the other iterations, and the control statement in the loop would cause a major performance decrease on traditional processors. Although this does not prevent unroll-and-jam (because there are no dependencies between the peeled off first iteration and the rest of the loop), the transformation must be prepared to handle such cases.
- After unroll-and-jam, the source code may be approximately as follows (only one of the nests shown and the peeled first iterations moved in front):
for (j=0; j<block_count; j+=2) { blocks[k*count+j][0] = blocks[k*count+j][0] << (3-dc prec); blocks[k*count+j+1][0] = blocks[k*count+j+1][0] << (3-dc prec); for (i=1; i<64; i++) { val = (int)(blocks[k*count+j][i]*intra_q[i]*mbinfo[k].mquant) >>4; /* mismatch control */ if ((val&1)==0 && val!=0) val+= (val>0) ? −1 : 1; /* saturation */ blocks[k*count+j][i] = min(max(val, −2048), 2047); val = (int) (blocks[k*count+j+1][i]*intra_q[i]*mbinfo[k].mquant) >>4; /* mismatch control */ if ((val&1)==0 && val!=0) val+= (val>0) ? −1 : 1; /* saturation */ blocks[k*count+j+1][i] = min(max(val, −2048), 2047); } }
- Further parallelism can be obtained by index set splitting. Normally used to break dependence cycles in the DDG, it can here be used to split the i-loop in two and let two sub-configurations (sub-configuration is chosen as a working title for configurations that include independent networks that do not interfere) work on distinct blocks of data. Thus, the i loop is split into 2 or more loops which work on different subsets of the data at the same time.
- Handling the Data Types
- In contrast to the FIR-Filter, edge detector and matrix multiplication benchmarks, which all use data types fitting perfectly to the XPP (it is assumed that the size of int is chosen to be the XPP architecture data bit width, as everything else would not lead to any feasible result), the MPEG2 codec uses all data types commonly used on a processor for desktop applications. Written for the Intel x86 and comparable architectures, it may be assumed that the sizes of char, short, and int are 8, 16, and 32 respectively. Assuming that the XPP has a bit width of 32 precautions should be taken for the smaller data types.
- Therefore, the stream of data packets with each packet including 2 or 4 values of the shorter data type may be split into 2 or 4 streams. If enough resources are left, this will cause no performance penalty. Each of the divided streams may be sent to its own calculation network. Therefore, in every cycle, two short or four char values may be handled. Nevertheless, this may cause an area penalty because, besides the split-merge elements, the whole data flow graph has to be duplicated as often as needed.
FIG. 41shows how short values are handled. It shows the splitting of short values into two streams and the merging of the streams after the calculation. The packet is split into its hi and lo part by shift operations and merged behind the calculation branches. The legality of this transformation is the same as with loop unrolling, with an unrolling factor as big as the data type being smaller as the architecture data type.
- This, however, is not the end of the pole. It may be further required for the compiler to ensure that every intermediate result which produces an over/under-flow for the shorter data type does the same with the bigger data type. Therefore, it has to insert clipping operations which ensure that the network calculates with real 16 or 8 bit values, respectively.
- If the configuration size does not allow the whole loop body to be duplicated or dependencies prevent this, there is still a possibility of merging the split values again. This causes a performance penalty to the previous solution, because the throughput is only one (short) value/cycle.
FIG. 42shows how the merge is done. Instead of streaming parallel through two networks, the values are serialized and de-serialized again after the network. The split values are merged before the network. An event generator drives the merge and Demux PAEs. FIG. 42replaces the two boxes labeled "network" in FIG. 41.
- Inverse Discrete Cosine Transformation (idct.c)
- The idct-algorithm may be used for the MPEG2 video decompression algorithm. It operates on 8×8 blocks of video images in their frequency representation and transforms them back into their original signal form. The MPEG2 decoder contains a transform-function that calls idct for all blocks of a frequency-transformed picture to restore the original image.
- The idct function may include two for-loops. The first loop calls idctrow, and the second calls idctcol. Function inlining is able to eliminate the function calls within the entire loop nest structure so that the numeric code is not interrupted by function calls anymore. In another embodiment, a way to get rid of function calls between the loop nest is loop embedding that pushes loops from the caller into the callee.
Original Code (idct.c) /* two dimensional inverse discrete cosine transform */ void idct (block) short *block; { int i; for (i=0; i<8; i++) idctrow(block+8*i); for (i=0; i<8; i++) idctcol(block+i); }
- The first loop may change the values of the block row by row. Afterwards, the changed block is further transformed column by column. In this embodiment, all rows have to be finished before any column processing can be started. The function is illustrated in
- Dependency analysis may detect true data dependencies between row processing and column processing. Therefore, it may be required for the processing of the columns to be delayed until all rows are done. The innermost loop bodies idctrow and idctcol are nearly identical. They process numeric calculations on eight input values (column values in case of idctcol and row values in case of idctcol). Eight output values are calculated and written back (as column/row). Idctcol additionally applies clipping before the values are written back. Accordingly, idctcol is presented herein. The code may be as follows:
/* column (vertical) IDCT * * * * * * where: c[0] = 1/1024 * c[1 . . . 7] = (1/1024) *sqrt(2) */ static void idctcol (blk) short *blk; { int x0, x1, x2, x3, x4, x5, x6, x7, x8; /* shortcut */ if (! (x1 = (blk[8*4]<<8))) | (x2 = blk[8*6]) | (x3 = blk[8*2]) | (x4 = blk[8*1]) | (x5 = blk[8*7]) | (x6 = blk[8*5]) | (x7 = blk[8*3]))) { blk[8*0] = blk[8*1] = blk[8*2] = blk[8*3] = blk[8*4] = blk[8*5] = blk[8*6] = blk[8*7] = iclp[(blk[8*0] +32) >>6]; return; } x0 = (blk[8*0] <<8) + 8192; /* first stage */ x8 = W7* (x4+x5) + 4; x4 = (x8+ (W1−W7) *x4) >>3; x5 = (x8− (W1+W7) *x5) >>3; x8 = W3* (x6+x7) + 4; x6 = (x8− (W3−W5) *x6) >>3; x7 = (x8− (W3+W5) *x7) >>3; /* second stage */ x8 = x0 + x1; x0 −= x1; x1 = W6* (x3+x2) + 4; x2 = (x1− (W2+W6) *x2) >>3 x3 = (x1+ (W2−W6) *x3) >>3; x1 = x4 + x6; x4 −= x6; x6 = x5 + x7; x5 −= x7; /* third stage */ x7 = x8 + x3; x8 −= x3; x3 = x0 + x2; x0 −= x2; x2 = (181* (x4+x5) + 128) >>8; x4 = (181* (x4−x5) + 128) >>8; /* fourth stage */ blk[8*0] = iclp[(x7+x1) >>14]; blk[8*1] = iclp[(x3+x2) >>14]; blk[8*2] = iclp[(x0+x4) >>14]; blk[8*3] = iclp[(x8+x6) >>14]; blk[8*4] = iclp[(x8−x6) >>14]; blk[8*5] = iclp[(x0−x4) >>14]; blk[8*6] = iclp[(x3−x2) >>14]; blk[8*7] = iclp[(x7−x1) >>14]; }
- W1-W7 are macros for numeric constants that are substituted by the preprocessor. The iclp array is used for clipping the results to 8-bit values. It is fully defined by the init_jdct function before idct is called the first time:
void init_idct( ) { int i; iclp = iclip+512; for (i= −512; i<512; i++) iclp[i] = (i<−256) ? −256 : ((i>255) ? 255 : i); }
- A special kind of idiom recognition (function recognition) is able to replace the calculation of each array element by a compiler known function that can be realized efficiently on the XPP. If the compiler features whole program memory aliasing analysis, it is able to replace all uses of the iclp array with the call of the compiler known function. Alternatively, a developer can replace the iclp array accesses manually by the compiler known saturation function calls.
FIG. 44shows a possible implementation for saturate (val,n) as an NML schematic using two ALUs. In this case, it is necessary to replace array accesses like iclp[i] with saturate (i,256).
- The /*shortcut*/ code in idctcol may speed column processing up if x1 to x7 is zero. This breaks the well-formed structure of the loop nest. The if-condition is not loop invariant and loop unswitching cannot be applied. Nonetheless, the code after shortcut handling is well suited for the XPP. It is possible to synthesize if-conditions for the XPP (speculative processing of both blocks plus selection based on condition) but this would just waste PAEs without any performance benefit. Therefore, the /*shortcut*/ code in idctrow and idctcol has to be removed manually. The code snippet below shows the inlined version of the idctrow-loop with additional cache instructions for XPP control:
void idct(block) short *block; { int i; XPPPreload(IDCTROW_CONFIG); // Loop Invariant for (i=0; i<8; i++) { short *blk; int x0, x1, x2, x3, x4, x5, x6, x7, x8; blk = block+8*i; XPPPreload (0, blk, 8); XPPPreloadClean(1,blk,8); //IRAM1 is erased and assigned to blk XPPExcute(IDCTROW_CONFIG, IRAM(0); IRAM(1)); } for (i=0; i<8; i++) { . . . } }
- As the configuration of the XPP does not change during the loop execution, invariant code motion has moved out XPPPreload(IDCTROW_CONFIG) from the loop.
- NML Code Generation
- Data Flow Graph
- As idctcol is more complex due to clipping at the end of the calculations, idctcol is well suited as a representative loop body for a presentation of the data flow graph.
FIG. 45shows the data flow graph for the IDCTCOLUMN_CONFIG. A heuristic has to be applied to the graph to estimate the resource needs on the XPP. In this example, the heuristic produces the following results:
ADD, SUB MUL <<X, >>X Saturate (x, n) Ops needed 35 11 18 8 ALUs FREGs BREGs Res. left 19 80 45 Res. avail. 64 80 80
- The data flow graph fits into an XPP64 and this example may proceed without loop dissevering (splitting the loop body into suitable chunks). See João M. P. Cardoso et al., supra.
- Address Generation
- To fully synthesize the loop body the problem of address generation for accessing the data must be addressed.
- For IDCTCOLUMN_CONFIG, the nth element of every row must be selected, which means an address serial of (0, 8, 16 . . . 1, 9, 17 . . . 7, 15, 23 . . . ). Two counter macros may be used for address generation as shown in
FIG. 46. The upper counter increments by eight and the lower counter increments by one. The IRAM output is passed to the data flow graph of IDCTCOLUMN. If all (eight) row elements of a column are available, SWAP is switched through to the data flow graph input and the calculation for a new column begins.
- For the IDCTROW_CONFIG, the address generation is very simple as the IRAM already has the block in the appropriate order (row after row as it has to be accessed). Again, by using SIUP (stepped iterative up)-counter macros as described in the XPP tutorial, it is possible to map linear address expressions to NML-code in a generic way. As IDCTROW_CONFIG accesses a two-dimensional array, two SIUP-counters may be needed in the corresponding NML code. The column-elements have to be accessed row after row so the upper counter's increment is one and the lower counter's increment is eight. However, the NML code for this access pattern (0 . . . 5, 6, 7, 8, 9 . . . 63) can be reduced to one single counter (or to FIFO-mode IRAM access).
- Address generation for write access may be implemented in the same manner. The resources have to be updated to take this additional code into account. It takes 2*(8+8+2*1) FREGs and 2*(2+1) more BREGs in the worst case, which is still available on the XPP.
- If IRAM use is not critical, it is also possible to distribute the data on several IRAMs to improve the memory throughput into the XPP-array. This task may be done by the RISC-core or by a more sophisticated XPP-cache controller.
- Further Enhancing XPP Utilization
- As mentioned above, idct is called for all data blocks of a video image (loop in transform.c). This circumstance may allow for improvement of the XPP utilization.
- When looking at the data flow graph of idctcol in detail, it can be seen that it forms a very deep pipeline. Considering that the IDCTROW_CONFIG runs only eight times on the XPP, which means that only 64 (8 times 8 elements of a column) elements are processed through this pipeline, and that change from the XPP configuration to the IDCTCOLUMN_CONFIG configuration to go on with column processing must wait until all data has left the pipeline, this example is suboptimal.
- Problem (Pipeline Depth)
- The pipeline is just too deep for processing only eight times eight rows. Filling and flushing a deep pipeline is expensive if only little data is processed with it. First the units at the end of the pipeline are idle and then the units at the beginning are unused, as shown in
- Solution (Loop Tiling)
- It is profitable to use loop interchange for moving the dependencies between row and column processing to an outer level of the loop nest. The loop that calls the idct-function (in transform.c) on several blocks of the image has no loop interchange preventing dependencies. Therefore, this loop can be moved inside the loops of column and row processing, as shown in
- Now the processing of rows and columns can be applied on more data (by applying loop tiling). Therefore, filling and flushing the pipeline can be neglected.
- Constraints (Cache Sensitive Loop Tiling)
- The caching hierarchy has to be taken into account when defining the number of blocks that will be processed by the IDCTROW_CONFIG. As discussed above, the same blocks are needed in the subsequent IDCTCOLUMN_CONFIG configuration. It should be ensured that all blocks that are processed during IDCTROW_CONFIG fit into the cache. Loop tiling has to be applied with respect to the cache size so that the processed data fits into the cache.
- IRAM Reuse Between Different Configurations
- This example implies another bandwidth optimization that is just another version of loop tiling. Instead of transferring data from row processing to column processing via the memory hierarchy (cache sensitive loop tiling takes care that only the cache memory is accessed), the memory interface can be completely bypassed by using the output IRAM of Config A as input IRAM of Config B, as shown in
- Putting all Together
- If we apply cache sensitive loop tiling, IRAM reuse, and function in-lining, the example can be further optimized.
- Finally, the idct-function becomes completely inlined in transform.c. If block_count is, e.g., 6 and it is assumed that 64*6 words do not exceed the cache size, then the example may be transformed to:
// transform.c .. block = blocks [k* 6]; XPPPreload(IDCTROW_CONFIG); XPPPreload(0,block,64*6); //IRAM0 gets 64 words from 6 blocks XPPPreloadClean(1,block,64*6); //erase IRAM1 and assign to the 6 blocks XPPExecute(IDCTROW_CONFIG, IRAM(0), IRAM(1)); XPPPreload(IDCOLUMN_CONFIG); XPPPreload(1,block,64 *6 ); //redundant -> will be eliminated XPPExecute(IDCOLUMN_CONFIG, IRAM(1), IRAM(2)); ..
- The address generation in IDCTROW_CONFIG and IDCOLUMN_CONFIG has to be modified for reflecting the different data block size—caused by loop tiling—that has to be processed. This can be implemented by an additional SUM counter that generates the block offsets inside the tiles, as shown in
- The following table provides architectural parameters for IDCTROW_CONFIG and IDCOLUMN_CONFIG of the final result. It relies on a cache that is able to store block_count blocks. As two configurations are executed in this example, the configuration cycles have to be taken twice. Therefore, the total configuration cycles are 2×(block_count×64+(12+2×8)×2).
Parameter Value Vector length 8 words Reused data set size block_count × 64 words I/O IRAMs 3 (one shared) ALU 45 FUs DREG 41 FUs FREG 36 FUs Data flow graph width 8 Data flow graph height 12 Configuration cycles block_count × 64 + (12 + 2 * 8) × 2
- Performance Considerations
- In this example, it is possible to exploit high data locality, which means that many operations are performed on a limited memory range. The performance of the XPP solution of this embodiment is compared to a hypothetical superscalar RISC-architecture. An issue width of two is assumed, which means that the RISC executes on average two operations in parallel.
Ops for Row/Column Est. RISC cycles LD/ST 16 2 32 ADRCOMP 16 1 16 ADD/SUB 35 1 35 MULT 11 2 22 SHIFT 18 1 18 SAT 8 4 32 Issue Width 2 155 Cyc/Row(Col) 78 Proc. Rows 8 620 Proc. Cols 8 620 RISC Cyc/Blk 1240 XPP Cyc/Blk 128 with data duplication + reordering 24 Speedup 10 with data duplication + reordering 52
- Even though speedup is reasonable, fetching the input data from a single IRAM (which means that it is required to feed the eight inputs in eight cycles before processing is started) reduces the potential speedup significantly. In other words, there is a pipeline that is able to process eight input values per cycle, but the pipeline is loaded only every eighth cycle. This causes that only every eighth pipeline stage is filled.
FIG. 51illustrates this.
- Full utilization can be achieved only by loading the eight input values of the pipeline in one cycle. A solution to improve the memory throughput to the pipeline is data duplication as described under the heading "Hardware."
- Instead of loading the six 8×8 blocks to a single IRAM, in an embodiment of the present invention, the XPPPreloadMultiple command may be used to load the eight IRAMs with the same contents:
XPPPreload(0,block,64*6); //IRAM0 gets 64 words from 6 blocks is changed to: XPPPreloadMultiple(0xFF,block,64×6) //load RAM0 up to IRAM7 with blocks
- Now the pipeline gets fully utilized and eight results per cycle must be stored. This can be achieved by writing every output value to another IRAM, which additionally takes eight more IRAMs. (Using data duplication in this example requires all 16 IRAMs of the XPP64.) For storing the data that is generated with IDCTROW_CONFIG we have to change:
XPPPreloadClean(1,block,64*6); //erase IRAM1 and assign to the 6 blocks to: tmpsize = 64*6/8; XPPPreloadClean(8, block+0*tmpsize, tmpsize); //IRAM8 for interm. Rslt 1 XPPPreloadClean(9, block+1*tmpsize, tmpsize); //IRAM9 for interm. Rslt 1 XPPPreloadClean(10, block+2*tmpsize, tmpsize); //IRAM10 for interm. Rslt 1 XPPPreloadClean(11, block+3*tmpsize, tmpsize); //IRAM11 for interm. Rslt 1 XPPPreloadClean(12, block+4*tmpsize, tmpsize); //IRAM12 for interm. Rslt 1 XPPPreloadClean(13, block+5*tmpsize, tmpsize); //IRAM13 for interm. Rslt 1 XPPPreloadClean(14, block+6*tmpsize, tmpsize); //IRAM14 for interm. Rslt 1 XPPPreloadClean(15, block+7*tmpsize, tmpsize); //IRAM15 for interm. Rslt 1
- This causes different data layouts for the intermediate results. An additional configuration (REORDER_CONFIG), as shown in
FIG. 52, may be needed to restore the original data layout.
- Again, address generation has to be modified to fetch eight input values per cycle. This, on the one hand, requires seven additional adders, but, on the other hand, avoids swaps and latches for keeping the data eight cycles.
- Data duplication and data reordering may finally transforms the example code to:
// transform c . . block = blocks[k*6]; XPPPreload (IDCTROW_CONFIG); XPPPreloadMultiple (0xFF, block, 64×6) //load IRAM0 up to IRAM7 with blocks tmpsize = 64 * 6/8; //result gets seperated into 8 IRAMs XPPPreloadClean(8, block+0*tmpsize, tmpsize); // IRAM 8 tmpsize); for interm. Rslt 1 XPPPreloadClean(9, block+1*tmpsize, tmpsize); // IRAM 9 tmpsize); for interm. Rslt 1 XPPPreloadClean(10, block+2*tmpsize, tmpsize); // IRAM 10 tmpsize); for interm. Rslt 1 XPPPreloadClean(11, block+3*tmpsize, tmpsize); // IRAM 11 tmpsize); for interm. Rslt 1 XPPPreloadClean(12, block+4*tmpsize, tmpsize); // IRAM 12 tmpsize); for interm. Rslt 1 XPPPreloadClean(13, block+5*tmpsize, tmpsize); // IRAM 13 tmpsize); for interm. Rslt 1 XPPPreloadClean(14, block+6*tmpsize, tmpsize); // IRAM 14 tmpsize); for interm. Rslt 1 XPPPreloadClean(15, block+7*tmpsize, tmpsize); // IRAM 15 tmpsize); for interm. Rslt 1 XPPExecute(IDCTROW_CONFIG, IRAM(0-7), IRAM(8-15)); XPPPreload(IDCOLUMN_CONFIG); XPPPreloadMultiple (0xFF, block, 64×6) / / ld IRAM0-IRAM7 with interm. Rslt 1 XPPPreloadClean(8, block+0 *tmpsize, tmpsize); // IRAM8 for interm. Rslt 2 XPPPreloadClean(9, block+1 *tmpsize, tmpsize); // IRAM9 for interm. Rslt 2 XPPPreloadClean(10, block+2 *tmpsize, tmpsize); // IRAM10 for interm. Rslt 2 XPPPreloadClean(11, block+3 *tmpsize, tmpsize); // IRAM11 for interm. Rslt 2 XPPPreloadClean(12, block+4 *tmpsize, tmpsize); // IRAM12 for interm. Rslt 2 XPPPreloadClean(13, block+5 *tmpsize, tmpsize); // IRAM13 for interm. Rslt 2 XPPPreloadClean(14, block+6 *tmpsize, tmpsize); // IRAM14 for interm. Rslt 2 XPPPreloadClean(15, block+7 *tmpsize, tmpsize); // IRAM15 for interm. Rslt 2 XPPExecute (IDCOLUMN_CONFIG, IRAM(0-7), IRAM(8-15)); XPPPreload(REORDER_CONFIG); XPPPreloadMultiple(0xFF, block, 64×6) / /ld IRAM0-IRAM7 with interm. Rslt 2 rsltsize = 64; // 64*6/6; XPPPreloadClean(8, block+0 *rsltsize, rsltsize); // IRAM8 for final Rslt XPPPreloadClean(9, block+1 *rsltsize, rsltsize); // IRAM9 for final Rslt XPPPreloadClean(10, block+2 *rsltsize, rsltsize); // IRAM10 for final Rslt XPPPreloadClean(11, block+3 *rsltsize, rsltsize); // IRAM11 for final Rslt XPPPreloadClean(12, block+4 *rsltsize, rsltsize); // IRAM12 for final Rslt XPPPreloadClean(13, block+4 *rsltsize, rsltsize); // IRAM13 for final Rslt XPPExecute(IDCOLUMN_CONFIG, IRAM(0-7), IRAM(8-13));
- Original Code
void forward_wavelet( ) { int i, nt, *dmid; int *sp, *dp, d_tmp0, d_tmp1, d_tmpi, s_tmp0, s_tmp1; int mid, ii; int *x; int s[256], d[256]; for (nt=COL; nt>=BLOCK_SIZE; nt>>=1) { for (i=0; i<nt*COL/*tmp_nt*/; i+=COL) { x = &int_data[i]; mid=(nt>>1)−1; s[0] = x[0]; d[0] = x[ROW]; s[1] = x[2]; s[mid] = x[2*mid]; d[mid] = x[2*mid+ROW]; d[0] = (d[0]<<1)−s[0]−s[1]; s[0] = s[0]+(d[0]>>2); d_tmp0 = d[0]; s_tmp0 = s[1]; for (ii=1; ii<mid; ii++) { s_tmp1 = x[2*ii+2]; d_tmp1 = ((x[2*ii+ROW])<<1) − s_tmp0 − s_tmp1; d[ii] = dtmp1; s[ii] = s_tmp0+((d_tmp0+d_tmp1)>>3); d_tmp0 = d_tmp1; s_tmp0 = s_tmp1; } d[mid] = (d[mid]−s[mid])<<1; s[mid] = s[mid]+((d[mid−1]+d[mid])>>3); for (ii=0; ii<=mid; ii==) { x[ii] = s [ii]; x[ii+mid+1] = d[ii]; } } for (i=0; i<nt; i++) { x = &int_data[i]; mid = (nt>>1)−1; s[0] = x[0]; d[0] = x[COL]; s[1] = x[COL<<1]; s[mid] = x[(COL<<1)*mid]; d[mid] = x[(COL<<1)*mid +COL]; d[0] = (d[0]<<1)−s[0]−s[1]; s[0] = s[0]+(d[0]>>2); d_tmp0 = d[0]; s_tmp0 = s[1]; for (ii=1; ii<mid; ii++) {