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Hardware Architectures for the Inverse Square Root and the Inverse Functions using Harmonized Parabolic Synthesis

Thuning, Niclas LU and Bärring, Tor Leo LU (2016) EITM01 20151
Department 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 Newton-Raphson Method.
The input is a 15 bit fixed-point number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floating-point 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 Application-Specific Integrated Circuits using STM 65.0nm Complementary Metal-Oxide 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 Newton-Raphson Method.
The input is a 15 bit fixed-point number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floating-point 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 Application-Specific Integrated Circuits using STM 65.0nm Complementary Metal-Oxide 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 Newton-Raphson algorithm is promising, although at the cost of a worse error distribution. (Less)
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author
Thuning, Niclas LU and Bärring, Tor Leo LU
supervisor
organization
course
EITM01 20151
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Approximation, Parabolic Synthesis, Newton-Raphson Metod, Inverse Square Root, Unary Functions, Elementary Functions, Second-Degree Interpolation, Arithmetic Computation, VLSI, ASIC
report number
LU/LTH-EIT 2016-491
language
English
id
8862555
date added to LUP
2016-03-30 09:56:54
date last changed
2016-05-11 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 Newton-Raphson Method.
The input is a 15 bit fixed-point number, the range of which is selected so that the implementation is suitable for use as a block implementing the inverse square root for floating-point 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 Application-Specific Integrated Circuits using STM 65.0nm Complementary Metal-Oxide 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 Newton-Raphson algorithm is promising, although at the cost of a worse error distribution.},
  author       = {Thuning, Niclas and Bärring, Tor Leo},
  keyword      = {Approximation,Parabolic Synthesis,Newton-Raphson Metod,Inverse Square Root,Unary Functions,Elementary Functions,Second-Degree 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},
}