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Hardware Implementation of Number Inversion Function

Chen, Jiajun LU and Shi, Jianan (2016) EITM02 20152
Department of Electrical and Information Technology
Abstract
Nowadays, number inversion is of great significance and a complex arithmetical operator, especially the implementation in hardware. It provides a higher speed performance and lower power consumption.
Initially, the conversion of the inputs to floating-point numbers contains sign, exponent, and mantissa parts. The scope of the project is to perform an approximation of the number inversion function. In this paper, the number inversion function carried out by two methods: one based on Harmonized Parabolic Synthesis and the other one on an unrolled Newton-Raphson algorithm. It is worth mentioning that the implementation of these two methods performed as an Application Specific Integrated Circuit using a 65nm Complementary Metal Oxide... (More)
Nowadays, number inversion is of great significance and a complex arithmetical operator, especially the implementation in hardware. It provides a higher speed performance and lower power consumption.
Initially, the conversion of the inputs to floating-point numbers contains sign, exponent, and mantissa parts. The scope of the project is to perform an approximation of the number inversion function. In this paper, the number inversion function carried out by two methods: one based on Harmonized Parabolic Synthesis and the other one on an unrolled Newton-Raphson algorithm. It is worth mentioning that the implementation of these two methods performed as an Application Specific Integrated Circuit using a 65nm Complementary Metal Oxide Semiconductor technology with Low Power High Threshold Voltage transistors. Furthermore, the investigation and comparison for various aspects such as accuracy, error behavior, chip area, power consumption, and performance for both methods are realizable. (Less)
Popular Abstract
How to Calculate Number Inversion
Jiajun Chen and Jianan Shi
Mar. 2016

Number inversion is of great significance and a complex arithmetical operator, especially the implementation in hardware. How to implement it in hardware? How to reduce chip area and power consumption? How is its speed performance?
Non-linear operations such as sine, logarithmic, exponential and number inversion functions have been widely applied. If you were asked to calculate the inversion of a number, you would say, “What a piece of cake! Give me a pen!” It is simple in software implementation as well. But what about precision and speed? For some high precision and high-speed applications, software implementation are insufficient. Therefore, hardware... (More)
How to Calculate Number Inversion
Jiajun Chen and Jianan Shi
Mar. 2016

Number inversion is of great significance and a complex arithmetical operator, especially the implementation in hardware. How to implement it in hardware? How to reduce chip area and power consumption? How is its speed performance?
Non-linear operations such as sine, logarithmic, exponential and number inversion functions have been widely applied. If you were asked to calculate the inversion of a number, you would say, “What a piece of cake! Give me a pen!” It is simple in software implementation as well. But what about precision and speed? For some high precision and high-speed applications, software implementation are insufficient. Therefore, hardware implementations are worth considering.
In this study, Harmonized Parabolic Synthesis (HPS) method is one method to be taken into consideration. This method is put forward by Erik Hertz and Peter Nilsson based on Parabolic Synthesis. Parabolic Synthesis, is to apply an approximation to the required function to avoid complex operations such as divisions in hardware. It is a new method with high speed performance and promising short delay. It contains three steps, pre-processing, processing and post-processing. By combining with a synthesis of parabolic functions, the target function can be approximated. The improved method based on parabolic synthesis, HPS, required only two sub-functions, which results in better performance and shorter delay. The most interesting part is in the second sub-function. There is a LUT in the second sub-function. If we increase the size of the LUT and implement it in hardware, it will result in smaller area and higher speed. Surprised? That is because the design with larger LUT has smaller multipliers and smaller adders to meet the same accuracy requirement.
The other method used in this study is Newton-Raphson (NR) method. It is a method named after Isaac Newton and Joseph Raphson to find approximations to the roots of a real-valued function. This method is hardware-friendly. A LUT is often required to select a start value. It is important for the start value to be as close as possible to the true result. Several iterations would be needed to meet the precision requirement. More iterations yield smaller sizes of the LUTs. This is a trade-off between the number of iterations and size of LUTs.
In this study, we implement HPS and NR method for number inversion both in software and in hardware. Furthermore, various factors such as accuracy, error behavior, chip area, power consumption, and performance are investigated and compared. Interested? Hardware Implementation of Number Inversion Function, with author Jiajun Chen and Jianan Shi focusing on this field and described these in detail.
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author
Chen, Jiajun LU and Shi, Jianan
supervisor
organization
course
EITM02 20152
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Harmonized Parabolic Synthesis, unrolled Newton-Raphson, power consumption.
report number
LU/LTH-EIT 2016-487
language
English
id
8869123
date added to LUP
2016-03-29 14:45:27
date last changed
2018-01-01 04:09:12
@misc{8869123,
  abstract     = {Nowadays, number inversion is of great significance and a complex arithmetical operator, especially the implementation in hardware. It provides a higher speed performance and lower power consumption.
Initially, the conversion of the inputs to floating-point numbers contains sign, exponent, and mantissa parts. The scope of the project is to perform an approximation of the number inversion function. In this paper, the number inversion function carried out by two methods: one based on Harmonized Parabolic Synthesis and the other one on an unrolled Newton-Raphson algorithm. It is worth mentioning that the implementation of these two methods performed as an Application Specific Integrated Circuit using a 65nm Complementary Metal Oxide Semiconductor technology with Low Power High Threshold Voltage transistors. Furthermore, the investigation and comparison for various aspects such as accuracy, error behavior, chip area, power consumption, and performance for both methods are realizable.},
  author       = {Chen, Jiajun and Shi, Jianan},
  keyword      = {Harmonized Parabolic Synthesis,unrolled Newton-Raphson,power consumption.},
  language     = {eng},
  note         = {Student Paper},
  title        = {Hardware Implementation of Number Inversion Function},
  year         = {2016},
}