Why does the modulo function seem to break for large numbers?

For part of a function I am writing that tests whether an input number is an integer.

The answer should be zero, because for any integer n, (n*10)/10 = n , Therefore, mod(n*10,10) = 0

But in this case of very large numbers (like the one in the screenshot above), it does not work. I would appreciate any explanations as to why this is and/or how to solve this problem?

Answer 1

[Stephen23]

You used a binary floating point number whose precision is limited to around 15-16 significant decimal digits.

The output of MOD is "correct" (even if those end digits are effectively noise):

format bank
x = 290384798012501645096234 % check the value stored in memory:

x = 
 290384798012501642969088.00

y = x*10 % and also the value stored after that multiplication:

y = 
 2903847980125016228364288.00

mod(y,10)

ans = 
          8.00

You could use the symbolic toolbox, which supports arbitrary integer lengths:

x = sym('290384798012501645096234')

x = 

290384798012501645096234

y = x*10

y = 

2903847980125016450962340

mod(y,10)

ans = 

0

Another approach is to download this toolbox:

https://www.mathworks.com/matlabcentral/fileexchange/22725-variable-precision-integer-arithmetic

[Kiran KC]

Makes sense, thank you for the detailed answer!

Answer 2

[Steven Lord]

For sufficiently large numbers, not all numbers in that vicinity are representable in IEEE double precision. What's the distance between your number and the next largest number?

x = 290384798012501645096234;
eps(x)

ans = 33554432

So if I were to add a million to x, I still haven't gotten to the next largest number.

y = x + 1e6;
y == x % true

ans = logical
   1

The same were to hold if I added a number that you would expect changes the last digit of x. In fact it's negligible enough relative to x that it doesn't change x at all.

y = x + 1234567;
y == x

ans = logical
   1

If you want to work with numbers that large and represent each number in that vicinity, you're going to need to work symbolically.

s = sym('290384798012501645096234');
t = s + 1e6;
isAlways(s == t) % false

ans = logical
   0

t = s + 1234567;
isAlways(s == t) % false

ans = logical
   0

mod(s, 10)

ans = 

4

[Kiran KC]

Thank you very much, I am a newbie here, is there a way to accept both your and Stephen's answers because they are both quite good and detailed?

[Steven Lord]

There is not, each Answers post allows at most one accepted answer. If they both helped you vote for one (or both) and accept one of them of your choice.

[Rik]

That is not intended to be possible (it can happen in some rare cases where servers are slow to update, creating a sort of race condition, I don't know if this is still possible).

You can click the vote button and write a comment with a thank you.