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

[Walter Bright]

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.