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computational science basics 271.5.4 Determine Your Machine PrecisionWrite a program to determine the machine precision ɛ m of your computer system(within a factor of 2 or better). A sample pseudocode is✞✝eps = 1.begin do N timeseps = eps/2. / / Make smallerone = 1. + eps / / Write loop number, one , epsend doA Java implementation is given in Listing 1.5, while a more precise one isByteLimit.java on the instructor’s CD.✞// Limits . java : Determines machine precisionpublic class Limits {public static void main ( String [] args ) {final int N = 60;int i;double eps = 1. , onePlusEps ;for ( i = 0; i < N; i=i + 1) {eps = eps/2.;onePlusEps = 1. + eps ;System . out . println ("onePlusEps = " +onePlusEps+" , eps = "+eps ) ;}✝} }☎☎Listing 1.5 The code Limits.java determines machine precision within a factor of 2. Notehow we skip a line at the beginning of each class or method and how we align the closingbrace vertically with its appropriate key word (in italics).1. Determine experimentally the precision of single-precision floats.2. Determine experimentally the precision of double-precision floats.To print out a number in decimal format, the computer must make a conversionfrom its internal binary format. This not only takes time, but unless the number isa power of 2, there is a concordant loss of precision. So if you want a truly preciseindication of the stored numbers, you should avoid conversion to decimals andinstead print them out in octal or hexadecimal format (printf with \0NNN).1.6 Problem: Summing SeriesA classic numerical problem is the summation of a series to evaluate a function. Asan example, consider the infinite series for sin x:sin x = x − x33! + x55! − x7+ ··· (exact).7!−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 27