Calculation Methodology for Flexible Arithmetic Processing

Paper submitted to the IFIP International Conference on Very Large Scale Integration (VLSI-SOC), Darmstadt, Germany, 2003.A new operation model of flexible calculation that allows us to adjust the operation delay depending on the available time is presented. The operation method design uses look-up tables and progressive construction of the result. The increase in the operators’ granularity opens up new possibilities in calculation methods and microprocessor design. This methodology, together with the advances in technology, enables the functions of an arithmetic unit to be implemented on the basis of techniques based on stored data that provide quality results and systematization in the implementation. The proposed techniques are applied in the design of a multiplier operator. We report an evaluation of the architecture in area, delay and computation error, as well as a suitable implementation of an application example in FPGA to validate the design.This work is being backed by grant DPI2002-04434-C04-01 from the Ministerio de Ciencia y Tecnología of the Spanish Government

Floating-point exponential functions for DSP-enabled FPGAs

International audienceThis article presents a floating-point exponential operator generator targeting recent FPGAs with embedded memories and DSP blocks. A single-precision operator consumes just one DSP block, 18Kbits of dual-port memory, and 392 slices on Virtex-4. For larger precisions, a generic approach based on polynomial approximation is used and proves more resource-efficient than the literature. For instance a double-precision operator consumes 5 BlockRAM and 12 DSP48 blocks on Virtex-5, or 10 M9k and 22 18x18 multipliers on Stratix III. This approach is flexible, scales well beyond double-precision, and enables frequencies close to the FPGA's nominal frequency. All the proposed architectures are last-bit accurate for all the floating-point range.They are available in the open-source FloPoCo framework

Time-Precision Flexible Adder

Paper submitted to 10th IEEE International Conference on Electronics, Circuits and Systems (ICECS), Sharjah, Emiratos Árabes, 2003.A new conception of flexible calculation that allows us to adjust a sum depending on the available time computation is presented. More specifically, the objective is to obtain a calculation model that makes the processing time/precision more flexible. The addition method is based on carry-select scheme adder and the proposed design uses precalculated data stored in look-up tables, which provide, above all, quality results and systematization in the implementation of low level primitives that set parameters for the processing time. We report an evaluation of the architecture in area, delay and computation error, as well as a suitable implementation in FPGA to validate the design.This work is being backed by grant DPI2002-04434-C04-01 from the Ministerio de Ciencia y Tecnología of the Spanish Government

Hardware-Based Sobel Gradient Computations for Sharpness Enhancement

The majority of imaging systems are software based; they require some kind of microprocessor or microcontroller for the imaging algorithms to run. As the speed requirements of imaging and communications systems increase, the need for more hardware-based imaging systems arises. These fully hardware systems solve the fundamental problem inherent in software-based solutions, in which the speed of the algorithms depend on the instruction cycle speed of the processor. Once an algorithm is designed directly on hardware, the speed of the algorithm depends on the system clock frequency and the propagation delays of the logic cells (or standard cells) used in the design, usually measured in nanoseconds per cell. Therefore, such systems no longer depend on any instruction cycle delays, as there is no microprocessor involved. Most modern imaging and communications systems rely on digital signal processing (DSP) to compute complex mathematical operations. The emergence of powerful and low-cost field-programmable gate array (FPGA) devices with hundreds of arithmetic multipliers has enabled the development of many such DSP hardware applications, traditionally implemented only as software solutions

Computing floating-point logarithms with fixed-point operations

International audienceElementary functions from the mathematical library input and output floating-point numbers. However it is possible to implement them purely using integer/fixed-point arithmetic. This option was not attractive between 1985 and 2005, because mainstream processor hardware supported 64-bit floating-point, but only 32-bit integers. Besides, conversions between floating-point and integer were costly. This has changed in recent years, in particular with the generalization of native 64-bit integer support. The purpose of this article is therefore to reevaluate the relevance of computing floating-point functions in fixed-point. For this, several variants of the double-precision logarithm function are implemented and evaluated. Formulating the problem as a fixed-point one is easy after the range has been (classically) reduced. Then, 64-bit integers provide slightly more accuracy than 53-bit mantissa, which helps speed up the evaluation. Finally, multi-word arithmetic, critical for accurate implementations, is much faster in fixed-point, and natively supported by recent compilers. Novel techniques of argument reduction and rounding test are introduced in this context. Thanks to all this, a purely integer implementation of the correctly rounded double-precision logarithm outperforms the previous state of the art, with the worst-case execution time reduced by a factor 5. This work also introduces variants of the logarithm that input a floating-point number and output the result in fixed-point. These are shown to be both more accurate and more efficient than the traditional floating-point functions for some applications