I wrote:
I added a new page for the Numeric Quest library...
http://www.haskell.org/haskellwiki/Numeric_Quest
I also updated the references to Numeric Quest
on the Mathematics and Physics page.
http://www.haskell.org/haskellwiki/Libraries_and_tools/Mathematics
Henning Thielemann wrote
I wou
On Mon, Jan 22, 2007 at 03:26:38PM +0200, Yitzchak Gale wrote:
>
> Can someone with access to darcs.haskell.org
> please fix this library? darcs get currently does not
> seem to work for it.
>
> http://darcs.haskell.org/numeric-quest/
I've fixed the permissions, although applying patches in the
On Mon, 22 Jan 2007, Yitzchak Gale wrote:
> Henning Thielemann wrote:
> > > > there is already an implementation of continued
> > > > fractions for approximation of roots and transcendent functions by Jan
> > > > Skibinski:
> > > > http://darcs.haskell.org/numeric-quest/Fraction.hs
>
> I wrote:
Henning Thielemann wrote:
there is already an implementation of continued
fractions for approximation of roots and transcendent functions by Jan
Skibinski:
http://darcs.haskell.org/numeric-quest/Fraction.hs
I wrote:
Wow, nice. Now - how was I supposed to have found that?
http://www.haskell.
Henning Thielemann wrote:
Certainly no surprise - there is already an implementation of continued
fractions for approximation of roots and transcendent functions by Jan
Skibinski:
http://darcs.haskell.org/numeric-quest/Fraction.hs
Wow, nice. Now - how was I supposed to have found that?
It has
On Sun, 21 Jan 2007, Yitzchak Gale wrote:
> You always get the best approximation for a Rational
> using continued fractions. For most calculations that
> is easier said than done, but for square root we are
> very lucky.
Certainly no surprise - there is already an implementation of continued
fr
Sorry folks, it is just wrong to use Newton's method
for Rational.
Andrew Bromage wrote:
First off, note that for fractions, sqrt(p/q) = sqrt p / sqrt q.
Don't do that for Rational - you lose precious precision.
The whole idea for calculations in Rational is to find
a lucky denominator that i
G'day all.
I said:
> I've also extended the range for approxSmallSqrt here from (0,255) to
> (0,271). It is left as an exercise as to why this might be a good idea.
>
> (Hint: 272 is approximately 16.5*16.5.)
The correct answer, for those playing at home, is it's because it WAS a
good idea when
Hello,
On Friday 19 January 2007 16:48, [EMAIL PROTECTED] wrote:
> ...
> sqrtApprox' :: Integer -> Rational
> sqrtApprox' n
> | n < 0 = error "sqrtApprox'"
> | otherwise = approx n 1
> where
> approx n acc
> | n < 256 = (acc%1) * approxSmallSqrt (fromIntegral
G'day all.
Quoting Henning Thielemann <[EMAIL PROTECTED]>:
> Newton method for sqrt is very fast. It converges quadratically, that is
> in each iteration the number of correct digits doubles. The problem is to
> find a good starting approximation.
Yup. So how might we go about doing this?
Firs
If it's arbitrary precision floating point that you want then sqrt
should where it already is, as a member of Floating. (I find
"arbitrary precision real" to be an oxymoron, the real numbers are
the real numbers, they already have arbitrary precision.)
For a real number module, you can use,
Hi Zoltán,
I only need sqrt, so probably I will... use... just
the simple Newton alg.
It is still not clear to me what type you want
to work in. Is it Rational? In that case, you don't
need the Newton algorithm.
realToFrac . sqrt . realToFrac
works fine, as you originally suggested. If that
Hi,
Thanks for the answers. The best solution would be a general purpose
arbitrary precision math library for Haskell. I found two:
http://medialab.freaknet.org/bignum/
http://r6.ca/FewDigits/
I think both uses power series and have trigonometric functions too. (I only
need sqrt, so probably I
On Thu, 18 Jan 2007, Novák Zoltán wrote:
> I have to admit that I do not fully understand the Haskell numerical tower...
> Now I'm using the Newton method:
>
> mysqrt :: (Fractional a) => a -> a
> mysqrt x = (iterate (\y -> (x / y + y) / 2.0 ) 1.0) !!2000
>
> But I want a faster solution. (Not
Lennart Augustsson wrote:
I don't see a much better way than using something like Newton-
Raphson and testing for some kind of convergence. The Fractional
class can contain many things; for instance it contains rational
numbers. So your mysqrt function would have to be able to cope with
returni
I don't see a much better way than using something like Newton-
Raphson and testing for some kind of convergence. The Fractional
class can contain many things; for instance it contains rational
numbers. So your mysqrt function would have to be able to cope with
returning arbitrary precisio
Hello,
I would like to use the sqrt function on Fractional numbers.
(mysqrt :: (Fractional a) => a->a)
Half of the problem is solved by:
Prelude> :t (realToFrac.sqrt)
(realToFrac.sqrt) :: (Fractional b, Real a, Floating a) => a -> b
For the other half I tried:
Prelude> :t (realToFrac.sqrt.real
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