Multiple-precision arithmetic

With respect to the use of Hankel determinants, the memory function PD algorithm is very convenient because it needs only two arrays of 2n storage locations, instead of = storage locations, to construct n steps of the continued fraction. It is thus possible to use multiple-precision arithmetic, when necessary, and to overcome round-ofif errors and numerical instabilities. 

A direct measure of the trajectory error is provided by the use of so-called multiple-precision arithmetic. Here one considers a set of P trajectories Xp (0 p = 1,2,..., P. Suppose, for simplicity, that the initial phase Xp (0) is precisely represented in the computer by the m-digit registers of the machine. 

An efficient architecture was synthesised by using multiple precision arithmetic, local controllers and an optimised routing network [Pau90]. In the next paragraphs, the synthesis tasks of the Cathbdral-2nd script (Figure 7), that were most relevant for this application, are briefly discussed. At the end, the final results are summarised. 

High-level data-path mapping In order to allocate operators in the data path, all operations of the DSFG were analysed. Besides the type of operation also the dimensions of operands and results are important. Prom this the required operator types, as well as their minimal dimensions can be deducted. The operator dimensions determine whether single or multiple precision arithmetic should be used. 

Precision determines the reproducibility or repeatability of the analytical data. It measures how closely multiple analysis of a given sample agree with each other. If a sample is repeatedly analyzed under identical conditions, the results of each measurement, x, may vary from each other due to experimental error or causes beyond control. These results will be distributed randomly about a mean value which is the arithmetic average of all measurements. If the frequency is plotted against the results of each measurement, a bell-shaped curve known as normal distribution curve or gaussian curve, as shown below, will be obtained (Figure 1.2.1). (In many highly dirty environmental samples, the results of multiple analysis may show skewed distribution and not normal distribution.)... 

Precision, which quantifies the variation between replicated measurements on test portions from the same sample material, is also an important consideration in determining when a residue in a sample should be considered to exceed a MRL or other regulatory action limit. Precision of a method is usually expressed in terms of the within-laboratory variation (repeatability) and the between-laboratory variability (reproducibility) when the method has been subjected to a multi-laboratory trial. For a single-laboratory method validation, precision should be determined from experiments conducted on different days, using a minimum of six different tissue pools, different reagent batches, preferably different equipment, and so on, and preferably by different analysts Repeatability of results when determined within a single laboratory but based on results from multiple analysts is termed intermediate precision Precision of a method is usually expressed as the standard deviation. Another useful term is relative standard deviation, or coefficient of variation (the standard deviation divided by the absolute value of the arithmetic mean result, multiplied by 100 and expressed as a percentage). 

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