Unbiased Rounding for HUB Floating-Point Addition

Villalba-Moreno, Julio; Hormigo, Javier; González-Navarro, Sonia

doi:10.1109/tc.2018.2807429

Cited by 7 publications

(3 citation statements)

References 13 publications

(26 reference statements)

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“…To obtain both of these metrics, we compared the results of all the arithmetics under study to the same algorithm computed using the GNU MPFR multiple-precision library with 128 fraction bits, which we use as our golden solution. We chose the MSE as a general accuracy metric and the MaxAbsE to also take into account the maximum error, which can be a critical value in certain applications [44], [45].…”

Section: Polybenchmentioning

confidence: 99%

Big-PERCIVAL: Exploring the Native Use of 64-Bit Posit Arithmetic in Scientific Computing

Mallasén,

Del Barrio,

Prieto-Matias

2024

IEEE Trans. Comput.

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The accuracy requirements in many scientific computing workloads result in the use of double-precision floating-point arithmetic in the execution kernels. Nevertheless, emerging real-number representations, such as posit arithmetic, show promise in delivering even higher accuracy in such computations. In this work, we explore the native use of 64-bit posits in a series of numerical benchmarks and compare their timing performance, accuracy and hardware cost to IEEE 754 doubles. In addition, we also study the conjugate gradient method for numerically solving systems of linear equations in real-world applications. For this, we extend the PERCIVAL RISC-V core and the Xposit custom RISC-V extension with posit64 and quire operations. Results show that posit64 can obtain up to 4 orders of magnitude lower mean square error than doubles. This leads to a reduction in the number of iterations required for convergence in some iterative solvers. However, leveraging the quire accumulator register can limit the order of some operations such as matrix multiplications. Furthermore, detailed FPGA and ASIC synthesis results highlight the significant hardware cost of 64-bit posit arithmetic and quire. Despite this, the large accuracy improvements achieved with the same memory bandwidth suggest that posit arithmetic may provide a potential alternative representation for scientific computing.

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Section: Polybenchmentioning

confidence: 99%

Big-PERCIVAL: Exploring the Native Use of 64-Bit Posit Arithmetic in Scientific Computing

Mallasén,

Del Barrio,

Prieto-Matias

2024

IEEE Trans. Comput.

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“…SDF interacts with calcium and phosphate ions and creates fluorohydroxyapatite [18][19][20]. On a parallel level, the use of diode laser (DL) seems to be an attractive fluoride replacement, since many studies reported that when laser is used alone or with fluoride, it may enhance the dental resistance to caries attack [21,22,23]. Diode laser enhances the resistance of enamel to acidic attack [14,15].…”

Section: Egyptianmentioning

confidence: 99%

Effect Of White Spot Lesion Pretreatment With Silver Diamine Fluoride Compared To Diode Laser On The Shear Bond Strength Of Orthodontic Brackets. An In-Vitro Study

Saifeldin,

Samaha,

Sanafawy

2023

Egyptian Orthodontic Journal

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Objective: The aim of this study is to determine the impact of silver diamine fluoride and diode laser on the shear bond strength of orthodontic brackets invitro. Materials and methods: Fifty natural humanpremolars were used in this study. The sample was randomly divided into five groups (10 teeth in each group) as follows: Group 1: control group with no intervention, group 2: SDF application before enamel etching, group 3: SDF application after enamel etching, group 4: DL application before enamel etching, group 5: DL application after enamel etching. Then the bonding procedure followed. Each specimen was tested to failure in shear mode. After debonding, the adhesive remnant index (ARI) was calculated.Results: The mean shear bond strength of the orthodontic brackets when DL was applied after enamel etching was significantly higher than the other intervention groups but lower than that of the control group. SDF groups and DL group applied before enamel etching had the least mean shear bond strength with no statistically significant difference among them. ARI scores for the different groups indicated no significant differences in their distribution frequencies.Conclusions: SDF and DL maintained high shear bond strength to orthodontic brackets. ARI score showed no statistically significant difference in failure site between all groups.

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“…Nonetheless, the value is still very low and enough for many applications. Unbiased rounding could also be implemented [21], but its study is out of scope.…”

Section: A Error Analysismentioning

confidence: 99%

HUB Meets Posit: Arithmetic Units Implementation

Murillo,

Hormigo,

Barrio

et al. 2023

IEEE Trans. Circuits Syst. II

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The posit™ format was introduced in 2017 as an alternative to replacing the widespread IEEE 754. Posit arithmetic provides reproducible results across platforms and possesses tapered accuracy, among other improvements. Nevertheless, despite the advantages provided by such a format, their functional units are not as competitive as the IEEE 754 ones yet. The HUB approach was presented in 2016 to reduce the hardware cost of floating-point units. In this brief, we present HUB posit, a new format to mitigate the hardware overhead of posit units. Results show that it is possible to reach up to 15% and 12% in terms of area-delay product for adders and multipliers, respectively, while maintaining a similar level of accuracy. In addition, synthesis results show that HUB posit units are able to reach higher frequencies than conventional ones.

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Unbiased Rounding for HUB Floating-Point Addition

Cited by 7 publications

References 13 publications

Big-PERCIVAL: Exploring the Native Use of 64-Bit Posit Arithmetic in Scientific Computing

Big-PERCIVAL: Exploring the Native Use of 64-Bit Posit Arithmetic in Scientific Computing

Effect Of White Spot Lesion Pretreatment With Silver Diamine Fluoride Compared To Diode Laser On The Shear Bond Strength Of Orthodontic Brackets. An In-Vitro Study

HUB Meets Posit: Arithmetic Units Implementation

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