Arbitrary precision reals?
Hi, Its been a while since I've been using Haskell seriously, so I might simply have overlooked the answer.. Is there an arbitrary precision real number library available for Haskell? IIRC, atleast GHC uses the GMP library, but only for integers? Thanks, niall ------------------------------ This e-mail is intended for the named addressee only. It may contain confidential and/or privileged information. If you have received this message in error, please let us know and then delete this message from your system. You should not copy the message, use it for any purpose or disclose its contents to anyone. ________________________________________________________________________ This e-mail has been scanned for all viruses by Star Internet. The service is powered by MessageLabs. For more information on a proactive anti-virus service working around the clock, around the globe, visit: http://www.star.net.uk ________________________________________________________________________
Niall Dalton writes: | Hi, | | Its been a while since I've been using Haskell seriously, so I might simply | have overlooked the answer.. | | Is there an arbitrary precision real number library available for Haskell? | IIRC, atleast GHC uses the GMP library, but only for integers? Hi. There's the Ratio library, which can be used to make arbitrary precision rationals from arbitrary precision integers. But it doesn't provide arbitrary *finite* precision implementations of imprecise functions such as exp, so I suspect it's not quite what you're after. I don't know whether arbitrary precision reals have been done in Haskell, but here's one of the issues... The floating point part of the GNU mp library looks difficult to fit into Haskell's numeric classes, because the type signatures in class Floating don't include a how-much-precision-do-you-want parameter. For example, Haskell's sqrt :: Floating a => a -> a may look like it matches GNU mp's void mpf_sqrt (mpf_t rop, mpf_t op) but the result pointer rop also provides the precision argument, which was prepared earlier by some impure stateful action such as void mpf_set_default_prec (unsigned long int prec) I can see three ways around this, but they're all rather fiddly. - Write a nonstandard version of Haskell's Floating class, introducing an explicit how-much-precision-do-you-want parameter. - Declare a separate Floating instance for each fixed precision level you want to use, e.g. instance Floating GNU_mpf_t_with_300bits. - Declare a data type which pairs a GNU mpf_t with a number of bits, and declare a Floating instance for this data type, inferring the required precision of the result from the precision of the arguments. This gets into trouble when there are no arguments: pi would presumably have to have fixed precision. Although you could always ignore it in favour of something like (4 `withBits` 300) * atan (1 `withBits` 300) Regards, Tom http://haskell.org/onlinereport/ratio.html http://www.swox.com/gmp/manual/Float-Arithmetic.html#Float%20Arithmetic http://www.swox.com/gmp/manual/Initializing-Floats.html#Initializing%20Float...
On 25-Mar-2003, Tom Pledger <Tom.Pledger@peace.com> wrote:
The floating point part of the GNU mp library looks difficult to fit into Haskell's numeric classes, because the type signatures in class Floating don't include a how-much-precision-do-you-want parameter.
How about using a function type which takes a precision and gives you back an answer to that many digits, and making this function type an instance of the numeric type classes? E.g. data MPF_T -- abstract, corresponds to GNU mp's mpf_t type PRECISION = Int type ARBITRARY_PRECISION_REAL = (PRECISION -> MPF_T) instance Floating ARBITRARY_PRECISION_REAL where sqrt x = (\prec -> mpf_sqrt_ui (x (prec + sqrt_lossage))) where sqrt_lossage = 1 -- amount of precision lost by sqrt ... Here mpf_sqrt_ui would be an interface to GMP's mpf_sqrt_ui() function, which takes as input an mpf_t and a precision and produces an mpf_t as output. -- Fergus Henderson <fjh@cs.mu.oz.au> | "I have always known that the pursuit The University of Melbourne | of excellence is a lethal habit" WWW: <http://www.cs.mu.oz.au/~fjh> | -- the last words of T. S. Garp.
Tom Pledger <Tom.Pledger@peace.com> wrote:
The floating point part of the GNU mp library looks difficult to fit into Haskell's numeric classes, because the type signatures in class Floating don't include a how-much-precision-do-you-want parameter.
Fergus Henderson <fjh@cs.mu.OZ.AU> writes:
How about using a function type which takes a precision and gives you back an answer to that many digits, and making this function type an instance of the numeric type classes?
That's pretty neat. But it seems that this will suffer from the same loss of sharing problem as we get with overloaded CAFs. That is, if I calculate: let a :: ARBITRARY_PRECISION_REAL a = 1 b = a+a c = b+b d = c+c e = d+d in e then, instead of doing just 4 additions, I will do 15. So I think we need to add in a memo table. More seriously though, can we make an Eq instance? Presumably the GNU MP equality test doesn't test for equality but equality over the first 'n' bits for some user-specified 'n'? -- Alastair Reid alastair@reid-consulting-uk.ltd.uk Reid Consulting (UK) Limited http://www.reid-consulting-uk.ltd.uk/alastair/
On Tue, 25 Mar 2003, Tom Pledger wrote:
I don't know whether arbitrary precision reals have been done in Haskell, but here's one of the issues...
There is a "Haskell implementation of exact real arithmetic using Linear Fractional Transformations", see http://www.doc.ic.ac.uk/~ae/exact-computation/ for implementations and a bunch of papers. (The web server does not seem to respond right now, but the pages are cached by Google.) /NAD
participants (5)
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Alastair Reid -
Fergus Henderson -
Niall Dalton -
Nils Anders Danielsson -
Tom Pledger