Associativity math: (a + b) + c != a + (b + c)

Question

Recently I was going through an old blog post by Eric Lippert in which, while writing about associativity he mentions that in C#, (a + b) + c is not equivalent to a + (b + c) for certain values of a, b, c.

I am not able to figure out for what types and range of arithmetic values might that hold true and why.

Answer 1

On the range of the double type:

double dbl1 = (double.MinValue + double.MaxValue) + double.MaxValue; double dbl2 = double.MinValue + (double.MaxValue + double.MaxValue); 

The first one is double.MaxValue, the second one is double.Infinity

On the precision of the double type:

double dbl1 = (double.MinValue + double.MaxValue) + double.Epsilon; double dbl2 = double.MinValue + (double.MaxValue + double.Epsilon); 

Now dbl1 == double.Epsilon, while dbl2 == 0.

And on literally reading the question :-)

In checked mode:

checked {     int i1 = (int.MinValue + int.MaxValue) + int.MaxValue; } 

i1 is int.MaxValue

checked {     int temp = int.MaxValue;     int i2 = int.MinValue + (temp + temp); } 

(note the use of the temp variable, otherwise the compiler will give an error directly... Technically even this would be a different result :-) Compiles correctly vs doesn't compile)

this throws an OverflowException... The results are different :-) (int.MaxValue vs Exception)

Answer 2

one example

a = 1e-30 b = 1e+30 c = -1e+30