[Haskell-cafe] 16 bit floating point data in Haskell?
noteed at gmail.com
Mon Sep 28 03:04:24 EDT 2009
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:
>>> 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
> 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.
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