Bug or is it me?

[Rogelio Nodal]

Mike Bird wrote:

>On Sat, 2005-10-29 at 19:28, Rogelio Nodal wrote:
>  
>
>>Hello List:
>>
>>    Is this a bug?Or is it me?
>>
>>    [code]
>>
>>    /* Created by Anjuta version 1.2.4 */
>>    /*    This file will not be overwritten */
>>
>>   #include <iostream>
>>   #include <fstream>
>>
>>   using namespace std;
>>
>>   int main()
>>   {
>>   
>>   
>>   
>>    double x = 0;
>>   
>>   
>>    x = -2.3;
>>    while(x <= 2.1)
>>    {
>>        cout << x << endl;
>>        x += 0.1;
>>    }
>>   
>>    return (0);
>>   }
>> 
>>    [code]
>>
>>
>>    When I run this little program I get the following output:
>>
>>
>>    -2.3
>>-2.2
>>-2.1
>>-2
>>-1.9
>>-1.8
>>-1.7
>>-1.6
>>-1.5
>>-1.4
>>-1.3
>>-1.2
>>-1.1
>>-1
>>-0.9
>>-0.8
>>-0.7
>>-0.6
>>-0.5
>>-0.4
>>-0.3
>>-0.2
>>-0.1
>>1.082e-15    ===> What the hell?
>>0.1
>>0.2
>>0.3
>>0.4
>>0.5
>>0.6
>>0.7
>>0.8
>>0.9
>>1
>>1.1
>>1.2
>>1.3
>>1.4
>>1.5
>>1.6
>>1.7
>>1.8
>>1.9
>>2       === Why did it stop here?It is supposed to stop at 2.1.
>>
>>
>>
>>Thanks a lot for your time.
>>
>>
>>    Rogelio.
>>    
>>
>
>Computers work in binary.  You can't represent 0.1 perfectly in
>a normal binary float or double.  (There are special techniques
>but they're beyond this discussion.)
>
>So none of the numbers you're working with are accurate.  They're
>all off by a microscopic amount.
>
>The errors are usually so small that the print program ignores
>them and just prints the nearest interesting number.  Instead of
>-2.3000000000001 or -2.2999999999 it prints -2.3.  However, once
>you counted down to zero, all that was left was the microscopic
>error part, so the print program printed that: 1.082e-15 which
>is 0.000000000000001082.
>
>When it got to the end of the loop it had 2.1 plus a microscopic
>amount.  Now 2.1 plus a microscopic amount is NOT <= 2.1, so it
>stopped without printing that value near 2.1.
>
>You really don't want to be using floats or doubles as loop
>counters.  There are nasty gotchas.  If you need to print those
>numbers, try something like this:
>
>    for (int x10 = -23; x10 <= 21; ++x10)
>	cout << (x10 * 0.1) << endl;	
>
>--Mike Bird
>
>
>  
>
Wow. Thanks a lot for your answer. That really explains a lot.  Thanks.

    -Rogelio.