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

[Lars T. Kyllingstad]

On Wed, 20 Oct 2010 10:30:39 -0500, Andrei Alexandrescu wrote:

> On 10/20/10 5:32 CDT, Lars T. Kyllingstad wrote:
>> (This message was originally meant for the Phobos mailing list, but for
>> some reason I am currently unable to send messages to it*.  Anyway,
>> it's probably worth making others aware of this as well.)
>>
>> In my code, and in unittests in particular, I use
>> std.math.approxEqual() a lot to check the results of various
>> computations.  If I expect my result to be correct to within ten
>> significant digits, say, I'd write
>>
>>    assert (approxEqual(result, expected, 1e-10));
>>
>> Since results often span several orders of magnitude, I usually don't
>> care about the absolute error, so I just leave it unspecified.  So far,
>> so good, right?
>>
>> NO!
>>
>> I just discovered today that the default value for approxEqual's
>> default absolute tolerance is 1e-5, and not zero as one would expect. 
>> This means that the following, quite unexpectedly, succeeds:
>>
>>    assert (approxEqual(1e-10, 1e-20, 0.1));
>>
>> This seems completely illogical to me, and I think it should be fixed
>> ASAP.  Any objections?
> 
> I wonder what would be a sensible default. If the default for absolute
> error is zero, then you'd have an equally odd behavior for very small
> numbers (and most notably zero). Essentially nothing would be
> approximately zero.
> 
> Andrei


Well, seeing as we have now been made aware of Don's feqrel() function, 
would something like this work?

  bool approxEqual(T)(T lhs, T rhs, uint significantDigits)
  {
      enum r = log(10)/log(2);
      return feqrel(lhs, rhs) > significantDigits*r;
  }

-Lars