On 4/9/2018 7:11 PM, [email protected] wrote:
I'm very interested in using Racket for the purposes of numerical
analysis. Specifically, I am interested in using Racket as my test bed
for implementing simple numerical algorithms which operate on IEEE 754
single precision floats and compare those results against a ground
truth, ideally, the exact result. Racket appears to have great support
for double precision floats, but I haven't found any functions that
correspond to single precision floats.
Some questions:
1. Should I be implementing my own versions of the flonum arithmetic
functions that operate on single precision floats? (See these
functions:
https://docs.racket-lang.org/reference/flonums.html#%28part._.Flonum_.Arithmetic%29)
2. What about other support functions that require knowledge of the
bit patterns of the floats?
(See
https://docs.racket-lang.org/math/flonum.html#%28part._.Measuring_.Floating-.Point_.Error%29
or
https://docs.racket-lang.org/math/flonum.html#%28part._.Low-.Level_.Flonum_.Operations%29)
As Philip McGrath mentioned already, you can specify single precision at
least for input values ... but I think inexact (i.e. floating point)
math in Racket all is done at maximum hardware precision and the result
coerced back to the input precision if possible. For purposes of
numerical analysis, that is not the same as performing all operations at
the input precision.
Not kidding, if you REALLY need single precision your best bet might be
to build a custom version of Racket. But on most hardware today, single
precision is not any faster than double, so if your concern is about
speed it is mostly unfounded. If, OTOH, your concern is being able to
follow the bits using pencil and paper ... then I understand the desire
for smaller representation. 8-)
But your comment about exactness is a bit troubling. You need to
realize that, in general, floating point values can't be compared for
equality. Floating point - regardless of precision or base - is
problematic because any limited width representation will be unable to
exactly represent a significant fraction of the numbers within the
range. It doesn't matter how many bits are available. Not to mention
that IEEE 754 defines 2 zeros, 2 infinities, and multiple
unrepresentable values (NaNs) that you may or may not need to distinguish.
See: David Goldberg, "What every computer scientist should know about
floating-point arithmetic"
HTML: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
PDF: http://perso.ens-lyon.fr/jean-michel.muller/goldberg.pdf
Numerical analysis, in general, is not about getting exact answers -
rather it is about minimizing error when exact answers either are not
possible, or are not practical to compute.
I would /love/ to use Racket for this task and ideally, I need to have
access to all the functions on the pages linked above but for single
precision floats
(half precision floats would also be nice!).
Racket has no support for half precision numbers. Jay McCarthy has
made a binding library available for an old(er) version of OpenCL, but I
don't know its capabilities.
Have I missed something obvious?
-Dale Kim
Hope this helps,
George
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