How to tell if a value is an integer?

I have a for loop and this is an example of an iteration within the loop:

x=725*(77/29)

if x==floor(x)

a=1

else

a=0

end

where i am trying to see if x is an integer. a=1 is true which should apply to this since x=1925 however when I run the code it does a=0. How can i fix this?

Answer 1

[Stephen23]

"...which should apply to this since x=1925 ..."

Nope. Its actual value is:

>> x = 725*(77/29);
>> fprintf('%.40f\n',x)
1925.0000000000002273736754432320594787597656

The difference is:

>> 1925-x
ans =   -2.27373675443232e-13

Clearly your operations accumulate some floating point error. The answer to your question is: change your algorithm so that you are not checking for exact equality between two binary floating point numbers. For example, check the absolute difference against some suitable tolerance value:

abs(A-B)<tol

Read more about binary floating point numbers:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

Answer 2

[James Tursa]

Welcome to the world of floating point arithmetic. (77/29) cannot be represented exactly in IEEE double precision arithmetic, so any calculations that use this will be subject to small round-off errors.

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

>> num2strexact(725*(77/29))
ans =
1.925000000000000227373675443232059478759765625e3
>> num2strexact((725*77)/29)
ans =
1.925e3

You will need to rearrange the calculation and/or do the comparison within some tolerance.

Answer 3

[David Hill]

if abs(x-floor(x))<1e-10