approxEqual() has fooled me for a long time...

[Lars T. Kyllingstad]

On Wed, 20 Oct 2010 23:33:54 +0200, Don wrote:

> Walter Bright wrote:
>> Andrei Alexandrescu wrote:
>>> On 10/20/10 13:42 CDT, Walter Bright wrote:
>>>> Don wrote:
>>>>> I'm personally pretty upset about the existence of that function at
>>>>> all.
>>>>> My very first contribution to D was a function for floating point
>>>>> approximate equality, which I called approxEqual. It gives equality
>>>>> in terms of number of bits. It gives correct results in all the
>>>>> tricky special cases. Unlike a naive relative equality test
>>>>> involving divisions, it doesn't fail for values near zero. (I
>>>>> _think_ that's the reason why people think you need an absolute
>>>>> equality test as well).
>>>>> And it's fast. No divisions, no poorly predictable branches.
>>>>
>>>> I totally agree that a precision based on the number of bits, not the
>>>> magnitude, is the right approach.
>>>
>>> I wonder, could that be also generalized for zero? I.e., if a number
>>> is zero except for k bits in the mantissa.
>> 
>> Zero is a special case I'm not sure how to deal with.
> 
> It does generalize to zero.
> Denormals have the first k bits in the mantissa set to zero. feqrel
> automatically treats them as 'close to zero'. It just falls out of the
> maths.
> 
> BTW if the processor has a "flush denormals to zero" mode, denormals
> will compare exactly equal to zero.


writeln(feqrel(0.0, double.min_normal/100));  // -688 ???

-Lars