CODEWITHSUNDEEP
matlabrounding
Legendre
Legendre

Reputation: 3156

How to stop Matlab rounding up doubles?

e = realmin;
x = 1 - e;

fprintf('x is %g',x);

Produces x is 1. However, I am trying to set x to 1 minus a small epsilon, which is equal to realmin.

How do I stop the rounding up?

Upvotes: 1

Views: 1805

Answers (1)

High Performance Mark
High Performance Mark

Reputation: 78316

Consider the difference between the exponents of realmin and of 1 -- the difference is about 308. This means that Matlab would need about 308 digits (all of them 9 apart from the last one perhaps) to represent 1-realmin but Matlab, of course, works natively with double precision floating point numbers which provide only 15 or 16 decimal digits.

The 'problem' is one of failing to understand one of the subtleties of floating-point arithemtic. The nearest representable double precision number to 1 - realmin is 1.

The function you want is Matlab's eps. While 1 - eps(1) is represented (with format long set) as 1.000000000000000 evaluation of 1 - eps(1) == 1 returns 0 or false if you prefer. Here it is the representation that is a bit confusing.

Upvotes: 5

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