CustomFloat

[Don]

Bill Baxter wrote:
> On Fri, Oct 17, 2008 at 1:56 PM, Andrei Alexandrescu
> <SeeWebsiteForEmail at erdani.org> wrote:
>> Bill Baxter wrote:
>>> On Fri, Oct 17, 2008 at 1:30 PM, Andrei Alexandrescu
>>> <SeeWebsiteForEmail at erdani.org> wrote:
>>>> I found myself in need for smaller and specialized floating point types,
>>>> where I configure the exact configuration (sign, mantissa, exponent,
>>>> bias).
>>>> See http://en.wikipedia.org/wiki/Half_precision for a half precision
>>>> number
>>>> slated for inclusion in IEEE 754r.

754r became official two months ago. It's now IEEE 754-2008, and it 
includes 16 bit floats.

>>>>
>>>> Would it be interesting to add a CustomFloat template to phobos? I'm
>>>> thinking along the lines of:
>>>>
>>>> template CustomFloat!(bool sign, uint mantissa,
>>>>       uint exponent, uint bias)
>>>> {
>>>>   ...
>>>> }
>>>>
>>>> So half-precision numbers are:
>>>>
>>>> alias CustomFloat!(true, 5, 10, 15) HalfFloat;
>>>>
>>>> There are quite a few details to kink out but this is definitely doable.
>>>> Numbers like 24-bit floating point and even 8-bit floating point would be
>>>> easy to support too. For now CustomFloat would be intended exclusively as
>>>> a
>>>> compact storage mechanism; only conversion to the standard floating
>>>> points
>>>> would be implemented. Later, maybe we can get to implement some
>>>> operations
>>>> natively at least on machines that support them in hardware. I wanted to
>>>> gauge interest in the topic.
>>>>
>>>
>>> In theory it would be great to have this in Phobos.  I say in theory
>>> because I haven't actually been in need of such a thing recently, but
>>> it is definitely handy to have if you're working with high dynamic
>>> range images (like from openEXR), or doing other GPU-related things.
>>> Is that the kind of thing you need them for too?  I've heard of using
>>> anything beyond 16-bit and 24-bit floats in the GPU/HDR world, though.
>>>  A full generic solution is probably overkill for that.
>> Yah, graphics is a big target for such types (and a big pusher for
>> standardizing them). I need such numbers for different purposes, i.e.
>> storing large arrays of probability distribution. In that case the range is
>> [0, 1] and I need to cram those numbers in as little space as possible. I
>> could definitely use a customized floating point layout.

Wouldn't it be better to use fixed point for that application? Or are 
the numbers distributed uniformly in IEEE space (ie, as many between 
0.0025 and 0.005, as between 0.5 and 0.1)?

>>
>> Note that a fully generic implementation is not overkill; if there are two
>> layouts to support, you might as well support any.
> 
> Yeh, mostly thinking about ASM tweaks to make them fast.
> 
> That and handling of denormal numbers.  Not sure how regular denormals
> are across different precisions of floating point numbers.   Been a
> while since I looked at how denormals are defined, though.  Maybe it's
> easy.

Yeah. If it's in the denormal range you can't treat the mantissa and 
exponent independently. NaNs are a pain, too.
Actually I think most GPUs don't support denormals, infinity, or NaN.

> 
> But writing optimized ASM for math ops is probably not as easy to do
> in a generic way.  Don's probably going to prove me wrong though.  :-)

It's very hairy if you're going to support all the rounding modes.

On processors with SSE2, you can do a load/shift/or sequence to shuffle 
the bits of a halffloat[4] into a float[4], so the performance shouldn't 
be too terrible for array operations, for example. Need to check for 
denormals, though, so it gets ugly.
The amount to shift and the bitmasks should be the only things which 
change. Perfect application for mixin asm!

There's no SSE shift instructions, so it would be very slow on earlier 
x86 machines.