(MATLAB) The relative separation between two closest distinct nonzero computer floating numbers is called the machine precision, typically denoted as Emach. To un- derstand what this means, try the following MATLAB commands a = 1+0.5*eps; b= 1+0.5001*eps; c = 1-0.7499*eps; d 1-0.75*eps; disp([eps; a-1; b-1; c-1; d-1]); The result intuitively confirms that adding a tiny number to a large one (or subtract- ing from) may cause the former to disappear completely in computer arithmetic. To learn a bit more about the smallest and the largest real numbers that can be represented, try the command disp([realmin realmax]); disp([realmin*eps*0.5001 disp([realmax*(1+0.5*eps) realmin eps 0.5]); realmax*(1+0.5001 eps)]); Read our class slides to consolidate your understanding of the limit of relative ac- curacy in computer arithmetic. Explain in detail what you learn about machine precision from the above results (at least 50 words expected).

(MATLAB) The relative separation between two closest distinct nonzero computer floating numbers is called the machine precision, typically denoted as Emach. To un- derstand what this means, try the following MATLAB commands a = 1+0.5eps; b= 1+0.5001eps; c = 1-0.7499eps; d 1-0.75eps; disp([eps; a-1; b-1; c-1; d-1]); The result intuitively confirms that adding a tiny number to a large one (or subtract- ing from) may cause the former to disappear completely in computer arithmetic. To learn a bit more about the smallest and the largest real numbers that can be represented, try the command disp([realmin realmax]); disp([realmineps0.5001 disp([realmax(1+0.5eps) realmin eps 0.5]); realmax*(1+0.5001 eps)]); Read our class slides to consolidate your understanding of the limit of relative ac- curacy in computer arithmetic. Explain in detail what you learn about machine precision from the above results (at least 50 words expected).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

(MATLAB) The relative separation between two closest distinct nonzero computer
floating numbers is called the machine precision, typically denoted as Emach. To un-
derstand what this means, try the following MATLAB commands
a = 1+0.5*eps;
b= 1+0.5001*eps;
c=1-0.7499*eps;
d 1-0.75*eps;
disp([eps; a-1; b-1; c-1; d-1]);
The result intuitively confirms that adding a tiny number to a large one (or subtract-
ing from) may cause the former to disappear completely in computer arithmetic.
To learn a bit more about the smallest and the largest real numbers that can be
represented, try the command
disp([realmin realmax]);
disp([realmin eps*0.5001 realmin*eps*0.5]);
disp( [realmax*(1+0.5*eps)
realmax*(1+0.5001*eps)]);
Read our class slides to consolidate your understanding of the limit of relative ac-
curacy in computer arithmetic. Explain in detail what you learn about machine
precision from the above results (at least 50 words expected).

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