cocoa - Trouble with floats in Objective-C

Question

I've a small problem and I can't find a solution!

My code is (this is only a sample code, but my original code do something like this):

float x = [@"2.45" floatValue];


for(int i=0; i<100; i++)
    x += 0.22;

NSLog(@"%f", x);

the output is 52.450001 and not 52.450000 !

I don't know because this happens!

Thanks for any help!

~SOLVED~

Thanks to everybody! Yes, I've solved with the double type!

Answer 1

Floats are a number representation with a certain precision. Not every value can be represented in this format. See here as well.

You can easily think of why this would be the case: there is an unlimited number of number just in the intervall (1..1), but a float only has a limited number of bits to represent all numbers in (-MAXFLOAT..MAXFLOAT).

More aptly put: in a 32bit integer representation there is a countable number of integers to be represented, But there is an infinite innumerable number of real values that cannot be fully represented in a limited representation of 32 or 64bit. Therefore there not only is a limit to the highest and lowest representable real value, but also to the accuracy.

So why is a number that has little digits after the floating point affected? Because the representation is based on a binary system instead of a decimal, making other numbers easily represented then the decimal ones.