A VLSI implementation of logarithmic and exponential functions using a novel parabolic synthesis methodology compared to the CORDIC algorithm

Pouyan, Peyman; Hertz, Erik; Nilsson, Peter

doi:10.1109/ecctd.2011.6043642

Cited by 18 publications

(10 citation statements)

References 10 publications

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“…The results of the implementation carried out with the Parabolic Synthesis are based on [11] after a redesign without bonding pads. The results for chip area, path delay, and energy consumption per sample are shown in the upper entry of Table 5.…”

Section: Comparing Methodologiesmentioning

confidence: 99%

“…The results for chip area, path delay, and energy consumption per sample are shown in the upper entry of Table 5. In [11], four sub-functions were used in the architecture. Unfortunately, in the implementation performed with Parabolic Synthesis in [11], no fully performed optimization of the word lengths in the look-up tables containing the coefficients was performed; therefore slightly longer word lengths than needed were used in this part of the design.…”

Section: Comparing Methodologiesmentioning

confidence: 99%

“…As shown in (3), only the coefficient c 1 has to be determined when developing the first sub-function. To perform the calculation of the absolute error, f error (x), the second sub-function, s 2 (x), has therefore to be made dependent on the coefficient c 1 in the first sub-function, s 1 (x), as shown in (3) to (5) and (8) to (11). The calculation is interesting only as an indication of how the absolute error, f error (x), depends on the coefficient c 1 .…”

Section: Simultaneous Development Of the Two Sub-functionsmentioning

confidence: 99%

“…After the multiplication, the start value of the interval l 2,i is added. The third branch of the second sub-function consists of a look-up table containing the coefficients c 2,i from (11) …”

Section: Hardware Architecturementioning

confidence: 99%

“…The Parabolic Synthesis methodology [8][9][10][11] is founded on a multiplicative synthesis of factors, each of them a secondorder function. The more factors that are used, the higher the accuracy of the approximation is.…”

Section: Introductionmentioning

confidence: 99%

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The Harmonized Parabolic Synthesis Methodology for Hardware Efficient Function Generation with Full Error Control

Hertz

Lai

Svensson

et al. 2017

J Sign Process Syst

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The Harmonized Parabolic Synthesis methodology is a further development of the Parabolic Synthesis methodology for approximation of unary functions such as trigonometric functions, logarithms and the square root with moderate accuracy for ASIC implementation. These functions are extensively used in computer graphics, communication systems and many other application areas. For these high-speed applications, software solutions are not sufficient, and a hardware implementation is therefore needed. The Harmonized Parabolic Synthesis methodology has two outstanding advantages: it is parallel, thus reducing the execution time, and it is based on low complexity operations, thus being simple to implement in hardware. A difference compared to other approximation methodologies is that it is a multiplicative, and not additive, methodology. Compared to the Parabolic Synthesis methodologies it is possible to significantly enhance the performance in terms of reducing chip area, computation delay and power consumption. Furthermore, it increases the possibility to tailor the characteristics of the error, improving conditions for subsequent calculations. To evaluate the methodology, the fractional part of the logarithm is implemented and its performance is compared to the Parabolic Synthesis methodology. The comparison is made with 15-bit resolution. The design implemented using the proposed methodology performs 3× better than the Parabolic Synthesis implementation in terms of throughput, while consuming 90% less energy. The chip area is 70% smaller than for the Parabolic Synthesis methodology. In summary, the new technology further increases the advantages of Parabolic Synthesis.

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Section: Comparing Methodologiesmentioning

confidence: 99%

Section: Comparing Methodologiesmentioning

confidence: 99%

Section: Simultaneous Development Of the Two Sub-functionsmentioning

confidence: 99%

Section: Hardware Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Harmonized Parabolic Synthesis Methodology for Hardware Efficient Function Generation with Full Error Control

Hertz

Lai

Svensson

et al. 2017

J Sign Process Syst

Self Cite

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The laser control of the muon g−2 experiment at Fermilab

et al. 2018

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The Muon g−2 Experiment at Fermilab is expected to start data taking in 2017. It will measure the muon anomalous magnetic moment, aμ=(gμ−2)/2 to an unprecedented precision: the goal is 0.14 parts per million (ppm). The new experiment will require upgrades of detectors, electronics and data acquisition equipment to handle the much higher data volumes and slightly higher instantaneous rates. In particular, it will require a continuous monitoring and state-of-art calibration of the detectors, whose response may vary on both the millisecond and hour long timescale. The calibration system is composed of six laser sources and a light distribution system will provide short light pulses directly into each crystal (54) of the 24 calorimeters which measure energy and arrival time of the decay positrons. A Laser Control board will manage the interface between the experiment and the laser source, allowing the generation of light pulses according to specific needs including detector calibration, study of detector performance in running conditions, evaluation of DAQ performance. Here we present and discuss the main features of the Laser Control board.

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An Efficient and Fast Softmax Hardware Architecture (EFSHA) for Deep Neural Networks

Hussain

Tsai

2021

2021 IEEE 3rd International Conference on Artificial Intelligence Circuits and Systems (AICAS)

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A VLSI implementation of logarithmic and exponential functions using a novel parabolic synthesis methodology compared to the CORDIC algorithm

Cited by 18 publications

References 10 publications

The Harmonized Parabolic Synthesis Methodology for Hardware Efficient Function Generation with Full Error Control

The Harmonized Parabolic Synthesis Methodology for Hardware Efficient Function Generation with Full Error Control

The laser control of the muon g−2 experiment at Fermilab

An Efficient and Fast Softmax Hardware Architecture (EFSHA) for Deep Neural Networks

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