Claude Heiland-Allen schrieb:
I've been working on [0] Haskell bindings for [1] libqd for [2] 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. :-)