Implementations of high performance architecture for IEEE 754 compliant floating-point adders

This thesis presents a direct iteration and implementation on a high per-formance architecture for IEEE 754 floating-point addition. This thesis improves on the previous architecture's implementation in a variety of sub-operations required for IEEE 754 floating-point addition, which are focused on directly improving critical path delay performance. A key element of this paper is the introduction of a flagged-prefix adder within the main carry-propagation path of an end-around-carry adder. It also provides detailed documentation for the design of IEEE 754 compliant floating-point adders. This is particularly emphasized for uncommon operations and control logic used throughout floating-point addition, including denormalized numbers and multi-precision logic. The full design for this architecture has support for binary16, binary32, and binary64 operations. The full extended range provided by denormalized IEEE 754 values is supported. It also has conversion support between IEEE 754 and two's complement integer values in either binary16, binary32, or binary64 precision. The performance comparisons shown are synthesis results in cmos32soi 32nm GF technology and ARM-based standard cells

IEEE Compliant Double-Precision FPU and 64-bit ALU with Variable Latency Integer Divider

Together the arithmetic logic unit (ALU) and floating-point unit (FPU) perform all of the mathematical and logic operations of computer processors. Because they are used so prominently, they fall in the critical path of the central processing unit - often becoming the bottleneck, or limiting factor for performance. As such, the design of a high-speed ALU and FPU is vital to creating a processor capable of performing up to the demanding standards of today\u27s computer users. In this paper, both a 64-bit ALU and a 64-bit FPU are designed based on the reduced instruction set computer architecture. The ALU performs the four basic mathematical operations - addition, subtraction, multiplication and division - in both unsigned and two\u27s complement format, basic logic operations and shifting. The division algorithm is a novel approach, using a comparison multiples based SRT divider to create a variable latency integer divider. The floating-point unit performs the double-precision floating-point operations add, subtract, multiply and divide, in accordance with the IEEE 754 standard for number representation and rounding. The ALU and FPU were implemented in VHDL, simulated in ModelSim, and constrained and synthesized using Synopsys Design Compiler (2006.06). They were synthesized using TSMC 0.1 3nm CMOS technology. The timing, power and area synthesis results were recorded, and, where applicable, compared to those of the corresponding DesignWare components.The ALU synthesis reported an area of 122,215 gates, a power of 384 mW, and a delay of 2.89 ns - a frequency of 346 MHz. The FPU synthesis reported an area 84,440 gates, a delay of 2.82 ns and an operating frequency of 355 MHz. It has a maximum dynamic power of 153.9 mW

Measuring Improvement when Using HUB Formats to Implement Floating-Point Systems under Round-to-Nearest

MEC bajo TIN2013-42253-PThis paper analyzes the benefits of using HUB formats to implement floating-point arithmetic under round-tonearest mode from a quantitative point of view. Using HUB formats to represent numbers allows the removal of the rounding logic of arithmetic units, including sticky-bit computation. This is shown for floating-point adders, multipliers, and converters. Experimental analysis demonstrates that HUB formats and the corresponding arithmetic units maintain the same accuracy as conventional ones. On the other hand, the implementation of these units, based on basic architectures, shows that HUB formats simultaneously improve area, speed, and power consumption. Specifically, based on data obtained from the synthesis, a HUB single-precision adder is about 14% faster but consumes 38% less area and 26% less power than the conventional adder. Similarly, a HUB single-precision multiplier is 17% faster, uses 22% less area, and consumes slightly less power than conventional multiplier. At the same speed, the adder and multiplier achieve area and power reductions of up to 50% and 40%, respectively

ARITHMETIC LOGIC UNIT ARCHITECTURES WITH DYNAMICALLY DEFINED PRECISION

Modern central processing units (CPUs) employ arithmetic logic units (ALUs) that support statically defined precisions, often adhering to industry standards. Although CPU manufacturers highly optimize their ALUs, industry standard precisions embody accuracy and performance compromises for general purpose deployment. Hence, optimizing ALU precision holds great potential for improving speed and energy efficiency. Previous research on multiple precision ALUs focused on predefined, static precisions. Little previous work addressed ALU architectures with customized, dynamically defined precision. This dissertation presents approaches for developing dynamic precision ALU architectures for both fixed-point and floating-point to enable better performance, energy efficiency, and numeric accuracy. These new architectures enable dynamically defined precision, including support for vectorization. The new architectures also prevent performance and energy loss due to applying unnecessarily high precision on computations, which often happens with statically defined standard precisions. The new ALU architectures support different precisions through the use of configurable sub-blocks, with this dissertation including demonstration implementations for floating point adder, multiply, and fused multiply-add (FMA) circuits with 4-bit sub-blocks. For these circuits, the dynamic precision ALU speed is nearly the same as traditional ALU approaches, although the dynamic precision ALU is nearly twice as large

HEVC와 JPEG 하드웨어 부호화기를 위한 DCT의 Approximate Calculation

학위논문 (석사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 이혁재.Discrete Cosine Transform (DCT) is widely used for various image and video compression applications because of its excellent energy compaction property. DCT is computationally intensive and the calculations are parallelizable. Therefore it is often implemented in hardware for speeding up the calculation. However due to large size of DCT or multiple modules of DCT required for some applications, the hardware area taken up by DCT in image or video encoders become significant. The DCT required in most applications doesnt need to be exact. Taking advantage of this fact, here a novel approach is provided to reduce the hardware area cost of the DCT module. The DCT hardware module consists of combinational logic and memory. Both the components are reduced and the complete implementation is described. The application being aimed at is for HEVC and JPEG, however the idea is applicable to any DCT hardware implementation. Finally the degradation caused to encoded image and video in terms of BDBR is discussed and the gate count results from the synthesis is provided.Chapter 1 Introduction 1 1.1 2D DCT Hardware Module . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Pipelining the process . . . . . . . . . . . . . . . . . . . . 5 1.2 Approximate DCT . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2 Related Works 9 Chapter 3 The Moving Window Idea for Bit-Width Reduction 12 3.1 ML Recovery for Moving Window . . . . . . . . . . . . . . . . . 16 Chapter 4 Approximate DCT for HEVC 19 4.1 HEVC Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 HEVC Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 DCT in HEVC Encoder . . . . . . . . . . . . . . . . . . . . . . . 21 4.4 Approximate DCT in HEVC . . . . . . . . . . . . . . . . . . . . 23 4.4.1 The three components of the DCT module . . . . . . . . 27 4.4.2 Optimizing Partial Butterfly Adder/Subtractors . . . . . 29 4.4.3 Optimizing the multiplication module . . . . . . . . . . . 30 4.4.3.1 Multiple Constant Multiplication (MCM) . . . . 32 4.4.3.2 Approximate MCM . . . . . . . . . . . . . . . . 32 4.4.4 Optimizing the transpose memory . . . . . . . . . . . . . 36 Chapter 5 Approximate DCT for JPEG 39 5.1 JPEG Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.2 Approximate DCT . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.3 Application of Moving Window to DCT transpose memory . . . 42 5.3.1 Ideal implementation . . . . . . . . . . . . . . . . . . . . . 43 5.3.2 Window position based on first row . . . . . . . . . . . . . 43 5.3.2.1 Cases of failure . . . . . . . . . . . . . . . . . . . 46 5.3.3 Position based on first column . . . . . . . . . . . . . . . 48 5.3.3.1 Cases of failure . . . . . . . . . . . . . . . . . . . 49 5.4 Hybrid implementation . . . . . . . . . . . . . . . . . . . . . . . . 50 Chapter 6 Experimental Results 54 6.1 HEVC Experiments and Results . . . . . . . . . . . . . . . . . . 55 6.2 JPEG Experiments and Results . . . . . . . . . . . . . . . . . . . 55 Chapter 7 Conclusion 64Maste

VLSI Circuits for Approximate Computing

Approximate Computing has recently emerged as a promising solution to enhance circuits performance by relaxing the requisite on exact calculations. Multimedia and Machine Learning constitute a typical example of error resilient, albeit compute-intensive, applications. In this dissertation, the design and optimization of approximate fundamental VLSI digital blocks is investigated. In chapter one the theoretical motivations of Approximate Computing, from the VLSI perspective, are discussed. In chapter two my research activity about approximate adders is reported. In this chapter approximate adders for both traditional non-error tolerant applications and error resilient applications are discussed. In chapter three precision-scalable units are investigated. Real-time precision scalability allows adapting the precision level of the unit with the precision requirements of the applications. In this context my research activities regarding approximate Multiply-and-Accumulate and memory units are described. In chapter four a precision-scalable approximate convolver for computer vision applications is discussed. This is composed of both the approximate Multiply-and-Accumulate and memory units, presented in the chapter three

Timing-Error Tolerance Techniques for Low-Power DSP: Filters and Transforms

Low-power Digital Signal Processing (DSP) circuits are critical to commercial System-on-Chip design for battery powered devices. Dynamic Voltage Scaling (DVS) of digital circuits can reclaim worst-case supply voltage margins for delay variation, reducing power consumption. However, removing static margins without compromising robustness is tremendously challenging, especially in an era of escalating reliability concerns due to continued process scaling. The Razor DVS scheme addresses these concerns, by ensuring robustness using explicit timing-error detection and correction circuits. Nonetheless, the design of low-complexity and low-power error correction is often challenging. In this thesis, the Razor framework is applied to fixed-precision DSP filters and transforms. The inherent error tolerance of many DSP algorithms is exploited to achieve very low-overhead error correction. Novel error correction schemes for DSP datapaths are proposed, with very low-overhead circuit realisations. Two new approximate error correction approaches are proposed. The first is based on an adapted sum-of-products form that prevents errors in intermediate results reaching the output, while the second approach forces errors to occur only in less significant bits of each result by shaping the critical path distribution. A third approach is described that achieves exact error correction using time borrowing techniques on critical paths. Unlike previously published approaches, all three proposed are suitable for high clock frequency implementations, as demonstrated with fully placed and routed FIR, FFT and DCT implementations in 90nm and 32nm CMOS. Design issues and theoretical modelling are presented for each approach, along with SPICE simulation results demonstrating power savings of 21 – 29%. Finally, the design of a baseband transmitter in 32nm CMOS for the Spectrally Efficient FDM (SEFDM) system is presented. SEFDM systems offer bandwidth savings compared to Orthogonal FDM (OFDM), at the cost of increased complexity and power consumption, which is quantified with the first VLSI architecture

Low-cost duplication for separable error detection in computer arithmetic

Low-cost arithmetic error detection will be necessary in the future to ensure correct and safe system operation. However, current error detection mechanisms for arithmetic either have high area and energy overheads or are complex and offer incomplete protection against errors. Full duplication is simple, strong, and separable, but often is prohibitively costly. Alternative techniques such as arithmetic error coding require lower hardware and energy overheads than full duplication, but they do so at the expense of high design effort and error coverage holes. The goal of this research is to mitigate the deficiencies of duplication and arithmetic error coding to form an error detection scheme that may be readily employed in future systems. The techniques described by this work use a general duplication technique that employs an alternate number system in the duplicate arithmetic unit. These novel dual modular redundancy organizations are referred to as low-cost duplication, and they provide compelling efficiency and coverage advantages over prior arithmetic error detection mechanisms.Electrical and Computer Engineerin