Phobos unit testing uncovers a CPU bug

[Walter Bright]

Kagamin wrote:
> Walter Bright Wrote:
> 
>>> Really? I think, the answer is neither correct nor wrong. It's
>>> approximate.
>> The rules for rounding the mathematical value to the representation are
>> precise, and so there is such a thing as the correctly rounded result and
>> the wrong result.
> 
> Well, maybe, but the result fits well in machine precision (which is equal to
> the last bit). And if this precision is not enough for the algorithm, then
> the algorithm is incorrect on any x87 FPU, and its output is garbage.

How do you decide how many bits should be enough for any algorithm?

The thing is, the FPU has 53 bits of precision and so ought to be correct to the 
last bit.