[Beowulf] Power calculations , double precision, ECC and power of APU's

Lux, Jim (337C) james.p.lux at jpl.nasa.gov
Mon Mar 18 17:09:49 PDT 2013

Another case where SP might be ok is in converting from fairly low precision gridded observations and doing some sort of model function retrieval, and perhaps regridding.

If your measurements of ocean backscatter are on 10km grids, and the uncertainty of the measurement after model function retrieval is 0.5 m/s out of a maximum value of 50 m/sec, SP is probably more than accurate enough, since the random noise in the input data set is enormous compared to any roundoff precision things.  

Likewise, if you're taking data that's unevenly spaced from an orbiting sensor (e.g. Seawinds on QuikScat) and regridding to a 10km mesh, I doubt that going to DP will make any difference in the interpolation.

SAR (synthetic aperture radar) data processing is another case where SP is probably good enough. If the radar is collecting data with a 12bit ADC, it's unlikely that you'd need more than 24 bits of mantissa even after all the range processing.  SAR is a notorious bandwidth hog, as well.  1 Gbit/s kinds of rates aren't unusual.  For on board processing, often they do some form of block floating point, so the math is really all integer.

But even in FP, the dynamic range of the signal isn't all that great.  Compare the 9.4 GHz radar cross section of an aphid head on is about 5E-6 cm^2 (from Riley, IEEE Proc, 1985), or 5E-10 m^2.  Let's consider something really big as a target, like the moon with a RCS of around 1E13 square meters (I just took the cross sectional area..the moon's round and rough, so its RCS is lower).   That's a range of 24 orders of magnitude, which would justify DP, but, on the other hand, it's unlikely we'll be looking for individual aphids on the moon.

If you were processing all the RF signals available in the HF band you might need DP.  The instantaneous dynamic range can be around 130dB within a small subband, and that's on the order of 21-22 bits, and if you look at the entire 2-30 MHz spectrum, you probably have more range than can be accommodated in the 24 bit mantissa of a SP floating point.

Jim Lux

-----Original Message-----
From: beowulf-bounces at beowulf.org [mailto:beowulf-bounces at beowulf.org] On Behalf Of Craig Tierney - NOAA Affiliate
Sent: Monday, March 18, 2013 12:50 PM
To: Mark Hahn
Cc: Beowulf List
Subject: Re: [Beowulf] Power calculations , double precision, ECC and power of APU's

On Mon, Mar 18, 2013 at 1:04 PM, Mark Hahn <hahn at mcmaster.ca> wrote:
>> flame-wars?  The people in HPC who care about SP gflops are those who 
>> understand the mathematics in their algorithms and don't want to 
>> waste very precious memory bandwidth by unnecessarily promoting their
> I'm not disagreeing, but wonder if you'd mind talking about 
> SP-friendly algorithms a bit.  I can see it in principle, but always 
> come up short when thinking about, eg simulation-type modeling with 
> such low-precision numbers.  does someone really comb through all the 
> calculations, looking for iffy stuff?  (iffy stuff can be pretty 
> subtle - ordering and theoretically equivalent substitutions.  maybe 
> there are compiler-based tools that perform this sort of analysis 
> automatically?)

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