Re: floating point

Bruce Dawson <comments@cygnus-software.com> writes:


>I'll have to
>partially retract my statement about nobody being happy with the x87 -
>it doesn't implement double precision as badly as I had feared, since
>the only unavoidable problem if you set the rounding to double is the
>exponent range - which will rarely matter.


Stick to your guns! The basic problem with x86 and strict `double' is
that, even in 64-bit mode, the x86 doesn't round denormalized numbers
properly. It simply rounds the mantissa at 53 bits, resulting in a
double-rounding error. The proper behavior is to round at fewer bits.


I've seen claims of efficient workarounds, but whenever I see details,
it's clear that the methods are either incorrect or inefficient. I'm
not saying it's impossible, but I've never seen it done, and I believe
it's infeasible to implement strict IEEE `double' arithmetic
efficiently on the x86 architecture.


Most people don't care about the errors, though, which is why the Java
spec is being relaxed to allow x86-like behavior (and PowerPC
multiply-add, too). For the vast majority of floating point
applications, performance is more important than bit-for-bit
compatibility, so it's easy to see why bit-for-bit compatibility is
falling by the wayside.

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