[Haskell-cafe] implementing RealFloat decodeFloat
lemming at henning-thielemann.de
Fri Jan 7 00:09:30 CET 2011
Claude Heiland-Allen schrieb:
> I've been working on  Haskell bindings for  libqd for 
> double-double and quad-double arithmetic,
At the ICIAM conference in Zurich 2007 I heard about the sum algorithm
with two double precision floating point numbers in three talks. :-)
Nice to know that those ideas can be found in a library.
> The double-double and quad-double types do not have a fixed precision,
> though they do have a fixed minimum precision: this means that
> decodeFloat will (in general) lose some precision. This is because for
> example in:
> data DoubleDouble = DoubleDouble !CDouble !CDouble
> dd = DoubleDouble a b
> the semantics are that "dd = a + b", with |a|>>|b|; coupled with the
> IEEE implicit leading 1 bit, this means that there may be large gaps
> between exponents: for example: "1 + 0.5**100 :: DoubleDouble".
They are possible, but do they really occur? I thought the intention of
using two CDoubles is to double the precision, not more. I can hardly
imagine that its algorithms makes use of numbers like (1 + 0.5**100).
Does the library specify something about maximum precision?
I would just represent (1 + 0.5**100) as largeInteger*2^-largeExponent.
You can represent all such numbers without loss of precision, but with
loss of memory. :-)
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