Speeding up the Division and Square Root of Power Series
نویسندگان
چکیده
We present new algorithms for the inverse, division, and square root of power series. The key trick is a new algorithm – MiddleProduct or, for short, MP – computing the n middle coefficients of a (2n− 1)× n full product in the same number of multiplications as a full n × n product. This improves previous work of Brent, Mulders, Karp and Markstein, Burnikel and Ziegler. These results apply both to series and polynomials.
منابع مشابه
Fast low-power shared division and square-root architecture
This paper addresses a fast low-power implementation of a shared division and square-root architecture. Two approaches are considered in this paper; these include the SRT (Sweeney, Robertson and Tocher) approach which does not require prescaling and the GST (generalized Svoboda and Tung) approach which requires prescaling of the operands. This paper makes two important contributions. Although S...
متن کاملDiode laser assisted endodontic treatments in periapical lesions repair: case series
Background and Aim: Bacterial disinfection is considered as the primary etiology of pulpal and periapical lesions and as the result, adequate elimination of such infections is one of the purposes of root canal treatment; But since this purpose is impossible to achieve, reducing the bacterial load seems to be as a rational goal. Diode lasers have made their way into endodontics for better disinf...
متن کاملLow-Power Radix-4 Combined Division and Square Root
Because of the similarities in the algorithm it is quite common to implement division and square root in the same unit. The purpose of this work is to implement a low-power combined radix-4 division and square root floating-point double precision unit and to compare its performance and energy consumption with a radix-4 division only unit. Previous work has been done on reducing the energy dissi...
متن کاملFloating Point Division and Square Root Algorithms and Implementation in the AMD-K7 Microprocessor
This paper presents the AMD-K7 IEEE 754 and x87 compliant floating point division and square root algorithms and implementation. The AMD-K7 processor employs an iterative implementation of a series expansion to converge quadratically to the quotient and square root. Highly accurate initial approximations and a high performance shared floating point multiplier assist in achieving low division an...
متن کاملComparison of Neural Network Models, Vector Auto Regression (VAR), Bayesian Vector-Autoregressive (BVAR), Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) Process and Time Series in Forecasting Inflation in Iran
This paper has two aims. The first is forecasting inflation in Iran using Macroeconomic variables data in Iran (Inflation rate, liquidity, GDP, prices of imported goods and exchange rates) , and the second is comparing the performance of forecasting vector auto regression (VAR), Bayesian Vector-Autoregressive (BVAR), GARCH, time series and neural network models by which Iran's inflation is for...
متن کامل