Comparison issue

[Don Clugston]

On 19/03/12 15:45, H. S. Teoh wrote:
> On Mon, Mar 19, 2012 at 08:50:02AM -0400, bearophile wrote:
>> James Miller:
>>
>>>          writeln(v1 == 1); //false
>>>          writeln(v1 == 1.0); //false
>>>          writeln(v1 == 1.0f); //false
>>>          writeln(v1+1 == 2.0f); //true
>
>
>
>> Maybe I'd like to deprecate and then statically forbid the use of ==
>> among floating point values, and replace it with a library-defined
>> function.
> [...]
>
> I agree. Using == for any floating point values is pretty much never
> right. Either we should change the definition of == for floats to use
> abs(y-x)<epsilon for some given epsilon value, or we should prohibit it
> altogether, and force people to always write abs(y-x)<epsilon.

No, no, no. That's nonsense.

For starters, note that ANY integer expression which is exact, is also 
exact in floating point.
Another important case is that
if (f == 0)
is nearly always correct.


 > Using == to compare floating point values is wrong. Due to the nature of
 > floating point computation, there's always a possibility of roundoff
 > error. Therefore, the correct way to compare floats is:
 >
 > 	immutable real epsilon = 1.0e-12; // adjustable accuracy here
 > 	if (abs(y-x)<  epsilon) {
 > 		// approximately equal
 > 	} else {
 > 		// not equal
 > 	}

And this is wrong, if y and x are both small, or both large. Your 
epsilon value is arbitrary.
Absolute tolerance works for few functions like sin(), but not in general.

See std.math.feqrel for a method which gives tolerance in terms of 
roundoff error, which is nearly always what you want.

To summarize:

For scientific/mathematical programming:
* Usually you want relative tolerance
* Sometimes you want exact equality.
* Occasionally you want absolute tolerance

But it depends on your application. For graphics programming you 
probably want absolute tolerance in most cases.