constructible 0.1 → 0.1.0.1

raw patch · 2 files changed

+31/−19 lines, 2 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• Data/Real/Constructible.hs +29/−17
• constructible.cabal +2/−2

@@ -211,24 +211,31 @@   LT | isZeroK k a -> negateS (mulSqrtS k (negateK k b) r) d      | otherwise -> (flip (showsPrecK k) a -! mulSqrtS k (negateK k b) r) d -fromConstructK :: Floating a => Field k -> Elt k -> a-fromConstructK Q = fromRational-fromConstructK kr@(Sqrt k r) = er where-  e = fromConstructK k-  s = sqrt (e r)-  er SqrtZero = 0-  er x@(SqrtElt a b) = case (sgnK k a, sgnK k b) of-    (_, EQ) -> e a-    (EQ, _) -> e b*s+fromRatioK :: Floating a => Field k -> Elt k -> Elt k -> a+fromRatioK Q = \a b -> fromRational (a/b)+fromRatioK (Sqrt k r) = er where+  e = fromRatioK k+  s = sqrt (e r (fromRationalK k 1))+  er SqrtZero _ = 0+  er _ SqrtZero = throw DivideByZero+  er (SqrtElt a0 b0) (SqrtElt a1 b1) = case (sgnK k a, sgnK k b) of+    (_, EQ) -> e a n1+    (EQ, _) -> e b n1*s     (GT, GT) -> x1     (LT, LT) -> x1     (GT, LT) -> x2     (LT, GT) -> x2     where-      x1 = e a + e b*s-      SqrtElt c d = recipK kr x-      x2 = recip $ e c + e d*s+      a = subK k (mulK k a0 a1) (mulK k r (mulK k b0 b1))+      b = subK k (mulK k b0 a1) (mulK k a0 b1)+      n0 = subK k (mulK k a0 a0) (mulK k r (mulK k b0 b0))+      n1 = subK k (mulK k a1 a1) (mulK k r (mulK k b1 b1))+      x1 = e a n1 + e b n1*s+      x2 = recip $ e a n0 - e b n0*s +fromConstructK :: Floating a => Field k -> Elt k -> a+fromConstructK k a = fromRatioK k a (fromRationalK k 1)+ -- |The type of constructible real numbers. data Construct where   C :: !(Field k) -> !(Elt k) -> Construct@@ -241,11 +248,13 @@   | otherwise = Right (C k a, C k b, C k r)  {- |-Deconstruct a constructible number as either a 'Rational', or a triple-@(a, b, r)@ of simpler constructible numbers representing @a + b*sqrt-r@ (with @b /= 0@ and @r > 0@).  Recursively calling 'deconstruct' on-all triples will yield a finite tree that terminates in 'Rational'-leaves.  Note that two constructible numbers that compare as equal may+Deconstruct a rational constructible number as a 'Rational', or an+irrational constructible number as a triple @(a, b, r)@ of simpler+constructible numbers representing @a + b*sqrt r@ (with @b /= 0@ and+@r > 0@).  Recursively calling 'deconstruct' on all triples will yield+a finite tree that terminates in 'Rational' leaves.++Note that two constructible numbers that compare as equal may deconstruct in different ways. -} deconstruct :: Construct -> Either Rational (Construct, Construct, Construct)@@ -400,6 +409,9 @@  To improve numerical stability, addition of numbers with different signs is avoided using quadratic conjugation.++>>> fromConstruct $ sum (map sqrt [7, 14, 39, 70, 72, 76, 85]) - sum (map sqrt [13, 16, 46, 55, 67, 73, 79])+1.8837969820815017e-19 -} fromConstruct :: Floating a => Construct -> a fromConstruct (C k a) = fromConstructK k a

@@ -1,5 +1,5 @@ name:                constructible-version:             0.1+version:             0.1.0.1 synopsis:            Exact computation with constructible real numbers description:   The constructible reals are the subset of the real numbers that can@@ -32,4 +32,4 @@ source-repository this   type:                git   location:            https://github.com/andersk/haskell-constructible-  tag:                 0.1+  tag:                 0.1.0.1