Decimal Floating-Point Square Root Using Newton-Raphson Iteration

2006 ◽  
Author(s):  
Liang-Kai Wang ◽  
M.J. Schulte
Keyword(s):  
Floating Point ◽  
Square Root ◽  
Newton Raphson ◽  
Raphson Iteration

scholarly journals Posit Arithmetic Hardware Implementations with The Minimum Cost Divider and SquareRoot

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1622
Author(s):  
Feibao Xiao ◽  
Feng Liang ◽  
Bin Wu ◽  
Junzhe Liang ◽  
Shuting Cheng ◽  
...  
Keyword(s):  
Hardware Implementation ◽  
Minimum Cost ◽  
Number System ◽  
Floating Point ◽  
Square Root ◽  
Subtraction Method ◽  
Embedded Devices ◽  
Hardware Implementations ◽  
Newton Raphson ◽  
Raphson Method

As a substitute for the IEEE 754-2008 floating-point standard, Posit, a new kind of number system for floating-point numbers, was put forward recently. Hitherto, some studies have proven that Posit is a better floating-point style than IEEE 754-2008 in some fields. However, most of these studies presented the advantages of Posit from the arithmetical aspect, but none of them suggested it had a better hardware implementation than that of IEEE 754-2008. In this paper, we propose several hardware implementations that contain the Posit adder/subtractor, multiplier, divider, and square root. Our goal is to achieve an arbitrary Posit format and exploit the minimum circuit area, which is required in embedded devices. To implement the minimum circuit area for the divider and square root, the alternating addition and subtraction method is used rather than the Newton–Raphson method. Compared with other works, the area of our divider is about 0.2×–0.7× (FPGA). Furthermore, this paper provides the synthesis results for each critical module with the Xilinx Virtex-7 FPGA VC709 platform.

scholarly journals A Modification of the Fast Inverse Square Root Algorithm

Computation ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 41 ◽  
Author(s):  
Cezary J. Walczyk ◽  
Leonid V. Moroz ◽  
Jan L. Cieśliński
Keyword(s):  
Analytical Approach ◽  
Floating Point ◽  
Square Root ◽  
Approximate Evaluation ◽  
Single Precision ◽  
Seed Solution ◽  
Numerical Tests ◽  
Newton Raphson ◽  
Relative Errors ◽  
Magic Constant

We present a new algorithm for the approximate evaluation of the inverse square root for single-precision floating-point numbers. This is a modification of the famous fast inverse square root code. We use the same “magic constant” to compute the seed solution, but then, we apply Newton–Raphson corrections with modified coefficients. As compared to the original fast inverse square root code, the new algorithm is two-times more accurate in the case of one Newton–Raphson correction and almost seven-times more accurate in the case of two corrections. We discuss relative errors within our analytical approach and perform numerical tests of our algorithm for all numbers of the type float.

scholarly journals A Modification of the Fast Inverse Square Root Algorithm

2019 ◽  
Author(s):  
Cezary J. Walczyk ◽  
Leonid V. Moroz ◽  
Jan L. Cieśliński
Keyword(s):  
Computational Cost ◽  
Floating Point ◽  
Square Root ◽  
Single Precision ◽  
Fast Calculation ◽  
Newton Raphson ◽  
Floating Point Numbers ◽  
Improved Algorithm

We present an improved algorithm for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithm is much more accurate than the famous fast inverse square root algorithm and has a similar computational cost. The presented modification concern Newton-Raphson corrections and can be applied when the distribution of these corrections is not symmetric (for instance, in our case they are always negative).

scholarly journals Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

2021 ◽  
Vol 2 (1) ◽  
pp. 37-45
Author(s):  
Riza Adrian Ibrahim ◽  
Sukono Sukono ◽  
Riaman Riaman
Keyword(s):  
Estimation Method ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Model ◽  
Economic Losses ◽  
Extreme Distribution ◽  
Newton Raphson ◽  
The Government ◽  
Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

Efficient Floating -Point Square Root and Reciprocal Square Root Algorithms

2021 ◽  
Author(s):  
Leonid Moroz ◽  
Volodymyr Samotyy ◽  
Mariusz Wegrzyn ◽  
Ulyana Dzelendzyak
Keyword(s):  
Floating Point ◽  
Square Root
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