Hardware Architectures for the Inverse Square Root and the Inverse Functions using Harmonized Parabolic Synthesis
(2016) EITM01 20151Department of Electrical and Information Technology
 Abstract
 This thesis presents a comparison between implementations of the inverse square root function, using two approximation algorithms; Harmonized Parabolic Synthesis and the NewtonRaphson Method.
The input is a 15 bit fixedpoint number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floatingpoint numbers, and the designs are constrained by the error, which must be < 2^(15).
Multiple implementations of both algorithms have been investigated and simulated as ApplicationSpecific Integrated Circuits using STM 65.0nm Complementary MetalOxide Seminconductor technology libraries for Low Power and General Purpose, VDD levels of 1.00V and 1.10V, and for various... (More)  This thesis presents a comparison between implementations of the inverse square root function, using two approximation algorithms; Harmonized Parabolic Synthesis and the NewtonRaphson Method.
The input is a 15 bit fixedpoint number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floatingpoint numbers, and the designs are constrained by the error, which must be < 2^(15).
Multiple implementations of both algorithms have been investigated and simulated as ApplicationSpecific Integrated Circuits using STM 65.0nm Complementary MetalOxide Seminconductor technology libraries for Low Power and General Purpose, VDD levels of 1.00V and 1.10V, and for various clock speeds.
Error distribution, area, speed, power, and energy consumption are analyzed for variants of the implementations of the two algorithms.
Depending on how the properties rank in desirability, when choosing an implementation, the recommended choice will vary.
The thesis finds that if mean error, and error distribution are important, the implementations of Harmonized Parabolic Synthesis show superiority regarding implementable clock speed, area requirements, power and energy consumption.
If power and energy consumption is the most prioritised property, an implementation of the NewtonRaphson algorithm is promising, although at the cost of a worse error distribution. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8862555
 author
 Thuning, Niclas ^{LU} and Bärring, Tor Leo ^{LU}
 supervisor

 Peter Nilsson ^{LU}
 Erik Hertz ^{LU}
 Rakesh Gangarajaiah ^{LU}
 organization
 course
 EITM01 20151
 year
 2016
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 Approximation, Parabolic Synthesis, NewtonRaphson Metod, Inverse Square Root, Unary Functions, Elementary Functions, SecondDegree Interpolation, Arithmetic Computation, VLSI, ASIC
 report number
 LU/LTHEIT 2016491
 language
 English
 id
 8862555
 date added to LUP
 20160330 09:56:54
 date last changed
 20160511 14:36:57
@misc{8862555, abstract = {This thesis presents a comparison between implementations of the inverse square root function, using two approximation algorithms; Harmonized Parabolic Synthesis and the NewtonRaphson Method. The input is a 15 bit fixedpoint number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floatingpoint numbers, and the designs are constrained by the error, which must be < 2^(15). Multiple implementations of both algorithms have been investigated and simulated as ApplicationSpecific Integrated Circuits using STM 65.0nm Complementary MetalOxide Seminconductor technology libraries for Low Power and General Purpose, VDD levels of 1.00V and 1.10V, and for various clock speeds. Error distribution, area, speed, power, and energy consumption are analyzed for variants of the implementations of the two algorithms. Depending on how the properties rank in desirability, when choosing an implementation, the recommended choice will vary. The thesis finds that if mean error, and error distribution are important, the implementations of Harmonized Parabolic Synthesis show superiority regarding implementable clock speed, area requirements, power and energy consumption. If power and energy consumption is the most prioritised property, an implementation of the NewtonRaphson algorithm is promising, although at the cost of a worse error distribution.}, author = {Thuning, Niclas and Bärring, Tor Leo}, keyword = {Approximation,Parabolic Synthesis,NewtonRaphson Metod,Inverse Square Root,Unary Functions,Elementary Functions,SecondDegree Interpolation,Arithmetic Computation,VLSI,ASIC}, language = {eng}, note = {Student Paper}, title = {Hardware Architectures for the Inverse Square Root and the Inverse Functions using Harmonized Parabolic Synthesis}, year = {2016}, }