High performance and energy efficient single‐precision and double‐precision merged floating‐point adder on FPGA

2017 ◽  
Vol 12 (1) ◽  
pp. 20-29 ◽  
Author(s):  
Hao Zhang ◽  
Dongdong Chen ◽  
Seok‐Bum Ko
Keyword(s):  
Energy Efficient ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Single Precision

scholarly journals DGX-A100 Face to Face DGX-2—Performance, Power and Thermal Behavior Evaluation

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 376
Author(s):  
Matej Špeťko ◽  
Ondřej Vysocký ◽  
Branislav Jansík ◽  
Lubomír Říha
Keyword(s):  
Artificial Intelligence ◽  
Thermal Behavior ◽  
Energy Efficient ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Face To Face ◽  
Scientific Simulations ◽  
Performance Computing ◽  
Dynamic Frequency

Nvidia is a leading producer of GPUs for high-performance computing and artificial intelligence, bringing top performance and energy-efficiency. We present performance, power consumption, and thermal behavior analysis of the new Nvidia DGX-A100 server equipped with eight A100 Ampere microarchitecture GPUs. The results are compared against the previous generation of the server, Nvidia DGX-2, based on Tesla V100 GPUs. We developed a synthetic benchmark to measure the raw performance of floating-point computing units including Tensor Cores. Furthermore, thermal stability was investigated. In addition, Dynamic Frequency and Voltage Scaling (DVFS) analysis was performed to determine the best energy-efficient configuration of the GPUs executing workloads of various arithmetical intensities. Under the energy-optimal configuration the A100 GPU reaches efficiency of 51 GFLOPS/W for double-precision workload and 91 GFLOPS/W for tensor core double precision workload, which makes the A100 the most energy-efficient server accelerator for scientific simulations in the market.

scholarly journals Design and Implementation of FPU for Optimised Speed

2020 ◽  
Vol 9 (3) ◽  
pp. 3922-3933
Keyword(s):  
Energy Efficient ◽  
High Speed ◽  
Software Tool ◽  
Digital Signal ◽  
Floating Point ◽  
Double Precision ◽  
Arithmetic Unit ◽  
Single Precision ◽  
Point Multiplication ◽  
Floating Point Unit

Currently, each CPU has one or additional Floating Point Units (FPUs) integrated inside it. It is usually utilized in math wide-ranging applications, such as digital signal processing. It is found in places be established in engineering, medical and military fields in adding along to in different fields requiring audio, image or video handling. A high-speed and energy-efficient floating point unit is naturally needed in the electronics diligence as an arithmetic unit in microprocessors. The most operations accounting 95% of conformist FPU are multiplication and addition. Many applications need the speedy execution of arithmetic operations. In the existing system, the FPM(Floating Point Multiplication) and FPA(Floating Point Addition) have more delay and fewer speed and fewer throughput. The demand for high speed and throughput intended to design the multiplier and adder blocks within the FPM (Floating point multiplication)and FPA(Floating Point Addition) in a format of single precision floating point and double-precision floating point operation is internally pipelined to achieve high throughput and these are supported by the IEEE 754 standard floating point representations. This is designed with the Verilog code using Xilinx ISE 14.5 software tool is employed to code and verify the ensuing waveforms of the designed code

scholarly journals Research on IEEE 754 Standard Single Precision Floating Point Multipliers Designed using Urdhva Triyagbhyam Sutra of Vedic Mathematics

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2990-2993
Keyword(s):  
Floating Point ◽  
Double Precision ◽  
Single Precision ◽  
Vedic Mathematics ◽  
Quadruple Precision

Duplication of the coasting element numbers is the big activity in automated signal handling. So the exhibition of drifting problem multipliers count on a primary undertaking in any computerized plan. Coasting factor numbers are spoken to utilizing IEEE 754 modern day in single precision(32-bits), Double precision(sixty four-bits) and Quadruple precision(128-bits) organizations. Augmentation of those coasting component numbers can be completed via using Vedic generation. Vedic arithmetic encompass sixteen wonderful calculations or Sutras. Urdhva Triyagbhyam Sutra is most usually applied for growth of twofold numbers. This paper indicates the compare of tough work finished via exceptional specialists in the direction of the plan of IEEE 754 ultra-modern-day unmarried accuracy skimming thing multiplier the usage of Vedic technological statistics.

Operational Single-Precision Earth-System Modelling at ECMWF

2021 ◽  
Author(s):  
Sam Hatfield ◽  
Kristian Mogensen ◽  
Peter Dueben ◽  
Nils Wedi ◽  
Michail Diamantakis
Keyword(s):  
Atmospheric Model ◽  
Floating Point ◽  
System Modelling ◽  
Double Precision ◽  
Earth System ◽  
Single Precision ◽  
System Models ◽  
Floating Point Arithmetic ◽  
Point Arithmetic ◽  
Earth System Models

<p>Earth-System models traditionally use double-precision, 64 bit floating-point numbers to perform arithmetic. According to orthodoxy, we must use such a relatively high level of precision in order to minimise the potential impact of rounding errors on the physical fidelity of the model. However, given the inherently imperfect formulation of our models, and the computational benefits of lower precision arithmetic, we must question this orthodoxy. At ECMWF, a single-precision, 32 bit variant of the atmospheric model IFS has been undergoing rigorous testing in preparation for operations for around 5 years. The single-precision simulations have been found to have effectively the same forecast skill as the double-precision simulations while finishing in 40% less time, thanks to the memory and cache benefits of single-precision numbers. Following these positive results, other modelling groups are now also considering single-precision as a way to accelerate their simulations.</p><p>In this presentation I will present the rationale behind the move to lower-precision floating-point arithmetic and up-to-date results from the single-precision atmospheric model at ECMWF, which will be operational imminently. I will then provide an update on the development of the single-precision ocean component at ECMWF, based on the NEMO ocean model, including a verification of quarter-degree simulations. I will also present new results from running ECMWF's coupled atmosphere-ocean-sea-ice-wave forecasting system entirely with single-precision. Finally I will discuss the feasibility of even lower levels of precision, like half-precision, which are now becoming available through GPU- and ARM-based systems such as Summit and Fugaku, respectively. The use of reduced-precision floating-point arithmetic will be an essential consideration for developing high-resolution, storm-resolving Earth-System models.</p>

Implementation of Embedded Floating Point Arithmetic Units on FPGA

2014 ◽  
Vol 550 ◽  
pp. 126-136
Author(s):  
N. Ramya Rani
Keyword(s):  
High Speed ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Embedded Computing ◽  
Floating Point Arithmetic ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Arithmetic Units ◽  
Point Arithmetic

:Floating point arithmetic plays a major role in scientific and embedded computing applications. But the performance of field programmable gate arrays (FPGAs) used for floating point applications is poor due to the complexity of floating point arithmetic. The implementation of floating point units on FPGAs consumes a large amount of resources and that leads to the development of embedded floating point units in FPGAs. Embedded applications like multimedia, communication and DSP algorithms use floating point arithmetic in processing graphics, Fourier transformation, coding, etc. In this paper, methodologies are presented for the implementation of embedded floating point units on FPGA. The work is focused with the aim of achieving high speed of computations and to reduce the power for evaluating expressions. An application that demands high performance floating point computation can achieve better speed and density by incorporating embedded floating point units. Additionally this paper describes a comparative study of the design of single precision and double precision pipelined floating point arithmetic units for evaluating expressions. The modules are designed using VHDL simulation in Xilinx software and implemented on VIRTEX and SPARTAN FPGAs.

Design of a Reconfigurable Coprocessor for Double Precision Floating Point Matrix Algorithms

2011 ◽  
Vol 58-60 ◽  
pp. 1037-1042
Author(s):  
Sheng Long Li ◽  
Zhao Lin Li ◽  
Qing Wei Zheng
Keyword(s):  
High Performance ◽  
Cmos Technology ◽  
General Purpose ◽  
Floating Point ◽  
Double Precision ◽  
Synthesis Time ◽  
Matrix Algorithms ◽  
Matrix Operations ◽  
On Chip ◽  
Software Execution

Double precision floating point matrix operations are wildly used in a variety of engineering and scientific computing applications. However, it’s inefficient to achieve these operations using software approaches on general purpose processors. In order to reduce the processing time and satisfy the real-time demand, a reconfigurable coprocessor for double precision floating point matrix algorithms is proposed in this paper. The coprocessor is embedded in a Multi-Processor System on Chip (MPSoC), cooperates with an ARM core and a DSP core for high-performance control and calculation. One algorithm in GPS applications is taken for example to illustrate the efficiency of the coprocessor proposed in this paper. The experiment result shows that the coprocessor can achieve speedup a factor of 50 for the quaternion algorithm of attitude solution in inertial navigation application compare with software execution time of a TI C6713 DSP. The coprocessor is implemented in SMIC 0.13μm CMOS technology, the synthesis time delay is 9.75ns, and the power consumption is 63.69 mW when it works at 100MHz.

scholarly journals Bit Grooming: Statistically accurate precision-preserving quantization with compression, evaluated in the netCDF Operators (NCO, v4.4.8+)

2016 ◽  
Author(s):  
Charles S. Zender
Keyword(s):  
Data Storage ◽  
Lossy Compression ◽  
Floating Point ◽  
Decimal Digit ◽  
Double Precision ◽  
Storage Space ◽  
Climate Data ◽  
Single Precision ◽  
Precision Data ◽  
Point Data

Abstract. Lossy compression schemes can help reduce the space required to store the false precision (i.e, scientifically meaningless data bits) that geoscientific models and measurements generate. We introduce, implement, and characterize a new lossy compression scheme suitable for IEEE floating-point data. Our new Bit Grooming algorithm alternately shaves (to zero) and sets (to one) the least significant bits of consecutive values to preserve a desired precision. This is a symmetric, two-sided variant of an algorithm sometimes called Bit Shaving which quantizes values solely by zeroing bits. Our variation eliminates the artificial low-bias produced by always zeroing bits, and makes Bit Grooming more suitable for arrays and multi-dimensional fields whose mean statistics are important. Bit Grooming relies on standard lossless compression schemes to achieve the actual reduction in storage space, so we tested Bit Grooming by applying the DEFLATE compression algorithm to bit-groomed and full-precision climate data stored in netCDF3, netCDF4, HDF4, and HDF5 formats. Bit Grooming reduces the storage space required by uncompressed and compressed climate data by up to 50 % and 20 %, respectively, for single-precision data (the most common case for climate data). When used aggressively (i.e., preserving only 1–3 decimal digits of precision), Bit Grooming produces storage reductions comparable to other quantization techniques such as linear packing. Unlike linear packing, Bit Grooming works on the full representable range of floating-point data. Bit Grooming reduces the volume of single-precision compressed data by roughly 10 % per decimal digit quantized (or "groomed") after the third such digit, up to a maximum reduction of about 50 %. The potential reduction is greater for double-precision datasets. Data quantization by Bit Grooming is irreversible (i.e., lossy) yet transparent, meaning that no extra processing is required by data users/readers. Hence Bit Grooming can easily reduce data storage volume without sacrificing scientific precision or imposing extra burdens on users.

scholarly journals Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190052 ◽  
Author(s):  
Michael Hopkins ◽  
Mantas Mikaitis ◽  
Dave R. Lester ◽  
Steve Furber
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Least Significant Bit ◽  
Fixed Point Arithmetic ◽  
Solution Algorithms ◽  
Point Arithmetic

Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of ordinary differential equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single-precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by partial differential equations. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

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