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When (a+b)+c != a+(b+c)...

  • Artigo

In a discussion of C# this weekend, someone said (a+(b+c)) is the same as ((a+b)+c) when a,b,c are all primitive data types, like int, float, double, etc.

In pure math, sure.  In code, not necessarily. First consider System.Int32 and the following example test.cs:

using System;
class Program
{
    static void Main(string[] args)
    {
        int a = int.MaxValue;
        int b = 1;
        int c = -a;

        try { Console.WriteLine(a+(b+c)); }
        catch(Exception e) { Console.WriteLine(e.Message); }
  
        try { Console.WriteLine((a+b)+c); }
        catch(Exception e) { Console.WriteLine(e.Message); }
    }
}

Compile this with: csc.exe test.cs. Run test.exe, and you'll get the output:

1
1

Makes sense.  Now compile it with: csc.exe /checked test.cs. Run test.exe, and you'll get the output:

1
Arithmetic operation resulted in an overflow.

So order of operations does make a difference! Now consider an even more interesting example: floating-point numbers...

using System;
class Program
{
    static void Main(string[] args)
    {
        float a = float.MaxValue;
        float b = -a;
        float c = -1;

        Console.WriteLine(a+(b+c));
        Console.WriteLine((a+b)+c);
    }
}

Compile this with: csc.exe test.cs. Run test.exe, and you'll get the output:

0
-1

So, while addition is generally associative in code, you might not always get the same results.  Something to at least be aware of.

Comments

  • Anonymous
    February 28, 2005
    What about when a == a is false? :-)

    a = double.NaN

  • Anonymous
    February 28, 2005
    The comment has been removed

  • Anonymous
    February 28, 2005
    Good point, Dan. Thanks. I've clarified my comments.

  • Anonymous
    March 02, 2005
    The comment has been removed

  • Anonymous
    September 15, 2009
    a+(b+c) ist das gleiche wie a+b+c

  • Anonymous
    October 12, 2011
    Make non sense.