[Haskell-cafe] 16 bit floating point data in Haskell?

[minh thu]

2009/9/28 Casey Hawthorne <caseyh at istar.ca>:
> On Mon, 28 Sep 2009 12:06:47 +1300, you wrote:
>
>>
>>On Sep 28, 2009, at 9:40 AM, Olex P wrote:
>>
>>> Hi,
>>>
>>> Yes, I mean "sizeOf 2". It's useful not only on GPUs but also in
>>> "normal" software. Think of huge data sets in computer graphics
>>> (particle clouds, volumetric data, images etc.) Some data (normals,
>>> density, temperature and so on) can be easily represented as float
>>> 16 making files 200 GB instead of 300 GB. Good benefits.
>>
>> From the OpenEXR technical introduction:
>>
>>       half numbers have 1 sign bit, 5 exponent bits,
>>       and 10 mantissa bits.  The interpretation of
>>       the sign, exponent and mantissa is analogous
>>       to IEEE-754 floating-point numbers.  half
>>       supports normalized and denormalized numbers,
>>       infinities and NANs (Not A Number).  The range
>>       of representable numbers is roughly 6.0E-8 to 6.5E4;
>>       numbers smaller than 6.1E-5 are denormalized.
>>
>>Single-precision floats are already dangerously short for
>>many computations.  (Oh the dear old B6700 with 39 bits of
>>precision in single-precision floats...)  Half-precision
>>floats actually have less than half the precision of singles
>>(11 bits instead of 23).  It's probably best to think of
>>binary 16 as a form of compression for Float, and to write
>>stuff that will read half-precision from a binary stream as
>>single-precision, and conversely stuff that will accept
>>single-precision values and write them to a binary stream in
>>half-precision form.
>>
>
> I agree with the above.
>
> I hadn't realized how dangerously short for many computations
> single-precision is.
>
> So, as he says, for computing, you do want to convert half-precision
> to single-precision, if not double-precision.
>
> If you want to save storage space, then some sort of compression
> scheme might be better on secondary storage.
>
> As for the video card, some sort of fast decompression scheme would be
> necessary for the half-precision numbers coming in.

'Half', as they are called, are supported in GPU. The half-precision
floating point is a core feature in OpenGL 3.0.

As said above, they are merely a data storage format, which should be
translated to floats or doubles before any computation.

Cheers,
Thu