diff --git a/continued-fractions.cabal b/continued-fractions.cabal --- a/continued-fractions.cabal +++ b/continued-fractions.cabal @@ -1,5 +1,5 @@ name: continued-fractions -version: 0.9.1.0 +version: 0.9.1.1 stability: provisional cabal-version: >= 1.6 @@ -17,13 +17,18 @@ tested-with: GHC == 6.8.3, GHC == 6.10.4, - GHC == 6.12.1, GHC == 6.12.3 + GHC == 6.12.1, GHC == 6.12.3, + GHC == 7.0.4, + GHC == 7.2.1, + GHC == 7.4.1-rc1 source-repository head - type: darcs - location: http://code.haskell.org/~mokus/continued-fractions + type: git + location: https://github.com/mokus0/continued-fractions.git Library hs-source-dirs: src exposed-modules: Math.ContinuedFraction build-depends: base >= 3 && <5 + if impl(ghc >= 7.2) + ghc-options: -trust base diff --git a/src/Math/ContinuedFraction.hs b/src/Math/ContinuedFraction.hs --- a/src/Math/ContinuedFraction.hs +++ b/src/Math/ContinuedFraction.hs @@ -1,4 +1,8 @@ {-# LANGUAGE ParallelListComp #-} +{-# LANGUAGE CPP #-} +#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 +{-# LANGUAGE Safe #-} +#endif module Math.ContinuedFraction ( CF , cf, gcf @@ -34,6 +38,13 @@ -- > = CFZero -- eval CFZero = 0 -- > | CFAdd a (CF a) -- eval (CFAdd b x) = b + eval x -- > | CFCont a a (CF a) -- eval (CFCont a b x) = a / (b + eval x) +-- +-- Or perhaps Bill Gosper's "∞-centered" representation: +-- +-- > data CF a +-- > = CFInfinity -- eval CFInfinity = ∞ +-- > | CFCont a a (CF a) -- eval (CFCont p q x) = p + q / eval x +-- -- |A continued fraction. Constructed by 'cf' or 'gcf'. data CF a @@ -88,7 +99,7 @@ cs = recip a : [recip (a*c) | c <- cs | a <- as] -- |Extract all the partial numerators and partial denominators of a 'CF'. -asGCF :: Num a => CF a -> (a,[(a,a)]) +asGCF :: (Num a, Eq a) => CF a -> (a,[(a,a)]) asGCF (CF b0 cf) = (b0, [(1, b) | b <- cf]) asGCF (GCF b0 gcf) = (b0, takeWhile ((/=0).fst) gcf) @@ -101,7 +112,7 @@ -- with the corresponding element of the supplied list and transforming -- subsequent partial numerators and denominators as necessary. If the list -- is too short, the rest of the 'CF' will be unscaled. -equiv :: Num a => [a] -> CF a -> CF a +equiv :: (Num a, Eq a) => [a] -> CF a -> CF a equiv cs orig = gcf b0 (zip as' bs') where @@ -115,7 +126,7 @@ -- |Apply an equivalence transformation that sets the partial denominators -- of a 'CF' to the specfied values. If the input list is too short, the -- rest of the 'CF' will be unscaled. -setDenominators :: Fractional a => [a] -> CF a -> CF a +setDenominators :: (Fractional a, Eq a) => [a] -> CF a -> CF a setDenominators denoms orig = gcf b0 (zip as' bs') where @@ -129,7 +140,7 @@ -- |Apply an equivalence transformation that sets the partial numerators -- of a 'CF' to the specfied values. If the input list is too short, the -- rest of the 'CF' will be unscaled. -setNumerators :: Fractional a => [a] -> CF a -> CF a +setNumerators :: (Fractional a, Eq a) => [a] -> CF a -> CF a setNumerators numers orig = gcf b0 (zip as' bs') where @@ -143,7 +154,7 @@ -- |Computes the even and odd parts, respectively, of a 'CF'. These are new -- 'CF's that have the even-indexed and odd-indexed convergents of the -- original, respectively. -partitionCF :: Fractional a => CF a -> (CF a, CF a) +partitionCF :: (Fractional a, Eq a) => CF a -> (CF a, CF a) partitionCF orig = case terms of [] -> (orig, orig) [(a1,b1)] -> @@ -172,12 +183,12 @@ -- |Computes the even part of a 'CF' (that is, a new 'CF' whose convergents are -- the even-indexed convergents of the original). -evenCF :: Fractional a => CF a -> CF a +evenCF :: (Fractional a, Eq a) => CF a -> CF a evenCF = fst . partitionCF -- |Computes the odd part of a 'CF' (that is, a new 'CF' whose convergents are -- the odd-indexed convergents of the original). -oddCF :: Fractional a => CF a -> CF a +oddCF :: (Fractional a, Eq a) => CF a -> CF a oddCF = snd . partitionCF @@ -195,7 +206,7 @@ -- B{n+1} = b{n+1}Bn + a{n+1}B{n-1} -- -- The convergents are then Xn = An/Bn -convergents :: Fractional a => CF a -> [a] +convergents :: (Fractional a, Eq a) => CF a -> [a] convergents orig = drop 1 (zipWith (/) nums denoms) where (b0, terms) = asGCF orig @@ -219,7 +230,7 @@ -- x{i} = x{i-1} + dx{i} -- -- The convergents are given by @scanl (+) b0 dxs@ -steed :: Fractional a => CF a -> [a] +steed :: (Fractional a, Eq a) => CF a -> [a] steed (CF b0 []) = [b0] steed (GCF b0 []) = [b0] steed (CF 0 ( a :rest)) = map (1 /) (steed (CF a rest)) @@ -245,7 +256,7 @@ -- D{n} = 1 / (b{n} + a{n} * D{n-1}) -- -- The convergents are given by @scanl (*) b0 (zipWith (*) cs ds)@ -lentz :: Fractional a => CF a -> [a] +lentz :: (Fractional a, Eq a) => CF a -> [a] lentz = lentzWith id (*) recip -- |Evaluate the convergents of a continued fraction using Lentz's method, @@ -274,9 +285,9 @@ -- -- > signLog x = (signum x, log (abs x)) -- > addSignLog (xS,xL) (yS,yL) = (xS*yS, xL+yL) --- > negateSignLog (s,l) = (negate s, l) +-- > negateSignLog (s,l) = (s, negate l) {-# INLINE lentzWith #-} -lentzWith :: Fractional a => (a -> b) -> (b -> b -> b) -> (b -> b) -> CF a -> [b] +lentzWith :: (Fractional a, Eq a) => (a -> b) -> (b -> b -> b) -> (b -> b) -> CF a -> [b] lentzWith f op inv (CF 0 ( a :rest)) = map inv (lentzWith f op inv (CF a rest)) lentzWith f op inv (GCF 0 ((a,b):rest)) = map (op (f a) . inv) (lentzWith f op inv (GCF b rest)) lentzWith f op inv c = scanl opF (f b0) (zipWith (*) cs ds) @@ -285,7 +296,8 @@ (b0, cs, ds) = lentzRecurrence c -lentzRecurrence :: Fractional a => CF a -> (a,[a],[a]) +-- precondition: b0 /= 0 +lentzRecurrence :: (Fractional a, Eq a) => CF a -> (a,[a],[a]) lentzRecurrence orig | null terms = (b0,[],[]) | otherwise = (b0, cs, ds) @@ -304,7 +316,7 @@ -- -- Additionally splits the resulting list of convergents into sublists, -- starting a new list every time the \'modification\' is invoked. -modifiedLentz :: Fractional a => a -> CF a -> [[a]] +modifiedLentz :: (Fractional a, Eq a) => a -> CF a -> [[a]] modifiedLentz = modifiedLentzWith id (*) recip -- |'modifiedLentz' with a group homomorphism (see 'lentzWith', it bears the @@ -312,7 +324,7 @@ -- and solves the same problems). Alternatively, 'lentzWith' with the same -- modification to the recurrence as 'modifiedLentz'. {-# INLINE modifiedLentzWith #-} -modifiedLentzWith :: Fractional a => (a -> b) -> (b -> b -> b) -> (b -> b) -> a -> CF a -> [[b]] +modifiedLentzWith :: (Fractional a, Eq a) => (a -> b) -> (b -> b -> b) -> (b -> b) -> a -> CF a -> [[b]] modifiedLentzWith f op inv z (CF 0 ( a :rest)) = map (map inv ) (modifiedLentzWith f op inv z (CF a rest)) modifiedLentzWith f op inv z (GCF 0 ((a,b):rest)) = map (map (op (f a) . inv)) (modifiedLentzWith f op inv z (GCF b rest)) modifiedLentzWith f op inv z orig = separate (scanl opF (False, f b0) cds) @@ -329,7 +341,8 @@ separate ((_,x):xs) = case break fst xs of (xs, ys) -> (x:map snd xs) : separate ys -modifiedLentzRecurrence :: Fractional a => a -> CF a -> (a,[(Bool, a)],[(Bool, a)]) +-- precondition: b0 /= 0 +modifiedLentzRecurrence :: (Fractional a, Eq a) => a -> CF a -> (a,[(Bool, a)],[(Bool, a)]) modifiedLentzRecurrence z orig | null terms = (b0, [], []) | otherwise = (b0, cs, ds)