Adaptive (empty) → 0.1

raw patch · 4 files changed

+515/−0 lines, 4 filesdep +basesetup-changed

Dependencies added: base

Files

• Adaptive.cabal +61/−0
• Data/Adaptive.hs +287/−0
• LICENSE +165/−0
• Setup.hs +2/−0

@@ -0,0 +1,61 @@+-- Adaptive.cabal auto-generated by cabal init. For additional+-- options, see+-- http://www.haskell.org/cabal/release/cabal-latest/doc/users-guide/authors.html#pkg-descr.+-- The name of the package.+Name:                Adaptive++-- The package version. See the Haskell package versioning policy+-- (http://www.haskell.org/haskellwiki/Package_versioning_policy) for+-- standards guiding when and how versions should be incremented.+Version:             0.1++-- A short (one-line) description of the package.+Synopsis:            Adaptive precision floating-point arithmetic++-- A longer description of the package.+Description:         Lazy arithmetic computed with as much precision as demanded ++-- URL for the project homepage or repository.+Homepage:            http://github.com/HackerFoo/Adaptive++-- The license under which the package is released.+License:             LGPL-3++-- The file containing the license text.+License-file:        LICENSE++-- The package author(s).+Author:              Dustin DeWeese++-- An email address to which users can send suggestions, bug reports,+-- and patches.+Maintainer:          dustin.deweese@gmail.com++-- A copyright notice.+-- Copyright:           ++Category:            Data++Build-type:          Simple++-- Extra files to be distributed with the package, such as examples or+-- a README.+-- Extra-source-files:  ++-- Constraint on the version of Cabal needed to build this package.+Cabal-version:       >=1.4+++Library+  -- Modules exported by the library.+  Exposed-modules:     Data.Adaptive+  +  -- Packages needed in order to build this package.+  Build-depends:       base >= 4 && < 5+  +  -- Modules not exported by this package.+  -- Other-modules:       +  +  -- Extra tools (e.g. alex, hsc2hs, ...) needed to build the source.+  -- Build-tools:         +  

@@ -0,0 +1,287 @@+{-  +    This file is part of Adaptive.++    Adaptive is free software: you can redistribute it and/or modify+    it under the terms of the GNU Lesser General Public License as published by+    the Free Software Foundation, either version 3 of the License, or+    (at your option) any later version.++    Adaptive is distributed in the hope that it will be useful,+    but WITHOUT ANY WARRANTY; without even the implied warranty of+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the+    GNU Lesser General Public License for more details.++    You should have received a copy of the GNU Lesser General Public License+    along with Adaptive.  If not, see <http://www.gnu.org/licenses/>.+-}++{-# LANGUAGE FlexibleInstances, BangPatterns, UnboxedTuples #-}+{-# OPTIONS_GHC -fno-excess-precision -fno-spec-constr #-}+-- {-# OPTIONS_GHC -fglasgow-exts -fno-excess-precision -fno-spec-constr #-}+-- use SSE to avoid the excess precision of the 387 FPU+-- {-# OPTIONS_GHC -fvia-C -optc-O -optc-ffast-math -optc-mfpmath=sse -optc-msse #-}+-- {-# OPTIONS_GHC -fllvm -optlc-mattr=+sse4a -optlc--disable-excess-fp-precision #-}++-- | Based on Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, Jonathan Richard Shewchuk, 1997+module Data.Adaptive (Adaptive(..), fromFloatingPoint, approx, approx', approxFast, splitter, epsilon) where++import Data.List+import Data.Bits+import Data.Ratio++type FloatT = Double++--mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]+mergeBy _ xs [] = xs+mergeBy _ [] ys = ys+mergeBy cmp (x:xs) (y:ys) = case cmp x y of+                              GT -> y : mergeBy cmp (x:xs) ys+                              _ -> x : mergeBy cmp xs (y:ys)++newtype Adaptive a = Adaptive [a]++instance (Show a, RealFloat a) => Show (Adaptive a) where+  showsPrec n x = showParen (n > 6 && x < 0) $ showsPrec 0 (approx x) . ('~':)++------------------------- approximate instances -------------------------++liftAdaptive1 f = fromFloatingPoint . f . approxFast+liftAdaptive2 f x y = fromFloatingPoint $ approxFast x `f` approxFast y++instance (RealFloat a, Real a) => Real (Adaptive a) where+  toRational = toRational . approxFast++instance (RealFloat a, Floating a) => Floating (Adaptive a) where+  pi = fromFloatingPoint pi+  exp = liftAdaptive1 exp+  sqrt = sqrtA+  log = liftAdaptive1 log+  (**) = liftAdaptive2 (**)+  logBase = liftAdaptive2 logBase+  sin = liftAdaptive1 sin+  tan = liftAdaptive1 tan+  cos = liftAdaptive1 cos+  asin = liftAdaptive1 asin+  atan = liftAdaptive1 atan+  acos = liftAdaptive1 acos+  sinh = liftAdaptive1 sinh+  tanh = liftAdaptive1 tanh+  cosh = liftAdaptive1 cosh+  asinh = liftAdaptive1 asinh+  atanh = liftAdaptive1 atanh+  acosh = liftAdaptive1 acosh++instance (RealFloat a) => RealFloat (Adaptive a) where+  floatRadix = floatRadix . approxFast+  floatDigits = floatDigits . approxFast+  floatRange = floatRange . approxFast+  decodeFloat = decodeFloat . approxFast+  encodeFloat s r = fromFloatingPoint (encodeFloat s r)+  exponent = exponent . approxFast+  significand = liftAdaptive1 significand+  scaleFloat x = liftAdaptive1 (scaleFloat x)+  isNaN = isNaN . approxFast+  isInfinite = isInfinite . approxFast+  isDenormalized = isDenormalized . approxFast+  isNegativeZero = isNegativeZero . approxFast+  isIEEE = isIEEE . approxFast+  atan2 = liftAdaptive2 atan2++instance (RealFloat a, RealFrac a) => RealFrac (Adaptive a) where+  properFraction x = (y, fromFloatingPoint x')+    where (y, x') = properFraction (approxFast x)++-------------------------------------------------------------------------++instance (Num a, RealFloat a) => Eq (Adaptive a) where+  {-# SPECIALIZE instance Eq (Adaptive FloatT) #-}+  a == b | null x = True+         | otherwise = False+    where Adaptive x = a - b++instance (Num a, RealFloat a) => Ord (Adaptive a) where+  {-# SPECIALIZE instance Ord (Adaptive FloatT) #-}+  compare a b | null x = EQ+              | head x > 0 = GT+              | otherwise = LT+    where Adaptive x = a - b++instance (Num a, RealFloat a) => Num (Adaptive a) where+  {-# SPECIALIZE instance Num (Adaptive FloatT) #-}+  Adaptive x + Adaptive y = Adaptive . compress $ fastExpSum x y+  Adaptive x - Adaptive y = Adaptive x + Adaptive (map negate y)+  Adaptive x * Adaptive y = Adaptive $ expProd x y+  negate (Adaptive x) = Adaptive (map negate x)+  abs (Adaptive []) = Adaptive []+  abs (Adaptive x) | head x < 0 = Adaptive (map negate x)+                   | otherwise = Adaptive x+  signum (Adaptive []) = Adaptive []+  signum (Adaptive (x:_)) = Adaptive [signum x]+  fromInteger 0 = Adaptive []+  fromInteger x = Adaptive [fromInteger x]++instance (RealFloat a, Fractional a) => Fractional (Adaptive a) where+  {-# SPECIALIZE instance Fractional (Adaptive FloatT) #-}+  fromRational r = fromIntegral (numerator r) / fromIntegral (denominator r)+  a / b = Adaptive $ a `divA` b++{-# SPECIALIZE divA :: Adaptive FloatT -> Adaptive FloatT -> [FloatT] #-}+divA x y | d == 0 = []+         | e == 0 || abs e >= abs x = [d]+         | otherwise = d : divA e y+  where d = approxFast x / approxFast y+        e = x - fromFloatingPoint d * y++-- | Use Babylonian method to calculate corrections to built in sqrt+{-# SPECIALIZE sqrtA :: Adaptive FloatT -> Adaptive FloatT #-}+sqrtA x = r + bab r+  where r = liftAdaptive1 sqrt x+        bab e | c == 0 = 0+              | otherwise = c + bab (e + c)+          where c = (x / e - e) / 2++{-# SPECIALIZE epsilon :: FloatT #-}+epsilon :: (RealFloat a) => a+epsilon = x+  where x = scaleFloat (- floatDigits x) 1++{-# SPECIALIZE splitter :: FloatT #-}+splitter :: (RealFloat a) => a+splitter = s+  where s = scaleFloat ((floatDigits s + 1) `shiftR` 1) 1 + 1++-- {-# INLINE fromFloatingPoint #-}+{-# SPECIALIZE fromFloatingPoint :: FloatT -> Adaptive FloatT #-}+fromFloatingPoint :: (RealFloat a) => a -> Adaptive a+fromFloatingPoint 0 = Adaptive []+fromFloatingPoint x = Adaptive [x]++{-# INLINE approx #-}+-- {-# SPECIALIZE approx :: Adaptive FloatT -> FloatT #-}+approx :: (RealFloat a, Ord a) => Adaptive a -> a+approx (Adaptive []) = 0+approx (Adaptive (x:xs)) = foldr (+) x . takeWhile ((> x*epsilon).abs) $ xs++{-# INLINE approx' #-}+-- {-# SPECIALIZE approx' :: Adaptive FloatT -> FloatT #-}+approx' :: (Real a, RealFloat b) => Adaptive a -> b+approx' (Adaptive []) = 0+approx' (Adaptive (x:xs)) = foldr (+) x' .+                            takeWhile ((> x' * epsilon) . abs) .+                            map realToFrac $ xs+  where x' = realToFrac x++-- {-# INLINE approxFast #-}+{-# SPECIALIZE approxFast :: Adaptive FloatT -> FloatT #-}+approxFast :: (Num a) => Adaptive a -> a+approxFast (Adaptive []) = 0+approxFast (Adaptive (x:_)) = x++-- |a| >= [b]+{-# INLINE fastTwoSum #-}+--{-# SPECIALIZE fastTwoSum :: FloatT -> FloatT -> (# FloatT, FloatT #) #-}+fastTwoSum :: (Num a) => a -> a -> (# a, a #)+fastTwoSum a b = (# x, y #)+  where x = a + b+        b' = x - a+        y = b - b'++{-# INLINE twoSum #-}+--{-# SPECIALIZE twoSum :: FloatT -> FloatT -> (# FloatT, FloatT #) #-}+twoSum :: (Num a) => a -> a -> (# a, a #)+twoSum !a !b = (# x, y #)+  where !x = a + b+        !b' = x - a+        !a' = x - b'+        !br = b - b'+        !ar = a - a'+        !y = ar + br++{-+{-# INLINE twoSum' #-}+--{-# SPECIALIZE twoSum' :: FloatT -> FloatT -> (FloatT, FloatT) #-}+twoSum' :: (Num a) => a -> a -> (a, a)+twoSum' a b = (x, y)+  where x = a + b+        b' = x - a+        a' = x - b'+        br = b - b'+        ar = a - a'+        y = ar + br++--{-# SPECIALIZE growExp :: FloatT -> [FloatT] -> [FloatT] #-}+growExp :: (Num a) => a -> [a] -> [a]+growExp b es = filter (/= 0) . uncurry (:) . mapAccumR twoSum' b $ es++--{-# SPECIALIZE expSum :: [FloatT] -> [FloatT] -> [FloatT] #-}+expSum :: (Num a) => [a] -> [a] -> [a]+expSum = foldr growExp+-}++{-# SPECIALIZE fastExpSum :: [FloatT] -> [FloatT] -> [FloatT] #-}+fastExpSum :: (RealFloat a) => [a] -> [a] -> [a]+fastExpSum [] x = x+fastExpSum x [] = x+fastExpSum e f = filter (/= 0) (q:hs)+  where g = mergeBy cmp e f+        cmp x y = compare (exponent y) (exponent x)+        (# q, hs #) = mapAccumR1 twoSum g++--mapAccumR1 :: (t -> t -> (# t, a #)) -> [t] -> (# t, [a] #)+mapAccumR1 f [x] = (# x, [] #)+mapAccumR1 f (x:xs) = (# a', y:xs' #)+  where (# a, xs' #) = mapAccumR1 f xs+        (# a', y #) = f a x++--{-# INLINE split #-}+--{-# SPECIALIZE split :: FloatT -> (# FloatT, FloatT #) #-}+--split :: (RealFloat a) => a -> (# a, a #)+split !a = (# ah, al #)+  where !c = splitter * a+        !ab = c - a+        !ah = c - ab+        !al = a - ah++--{-# INLINE twoProd #-}+--{-# SPECIALIZE twoProd :: FloatT -> FloatT -> (# FloatT, FloatT #) #-}+--twoProd :: (RealFloat a) => a -> a -> (# a, a #)+twoProd !a !b = (# x, y #)+  where !x = a * b+        (# !ah, !al #) = split a+        (# !bh, !bl #) = split b+        !err = x - ah * bh - al * bh - ah * bl+        !y = al * bl - err++--{-# INLINE scaleExp #-}+--{-# SPECIALIZE scaleExp :: FloatT -> [FloatT] -> [FloatT] #-}+--scaleExp :: (RealFloat a) => a -> [a] -> [a]+scaleExp _ [] = []+scaleExp b es = filter (/= 0) . (uncurry (:)) . foldr f (q0, [h0]) . init $ es+  where (# q0, h0 #) = twoProd (last es) b+        f e (q, h) = (q'', h2 : h1 : h)+          where (# th, tl #) = twoProd e b+                (# q', h1 #) = twoSum q tl+                (# q'', h2 #) = fastTwoSum th q'++--{-# INLINE expProd #-}+--{-# SPECIALIZE expProd :: [FloatT] -> [FloatT] -> [FloatT] #-}+--expProd :: (RealFloat a) => [a] -> [a] -> [a]+expProd [] _ = []+expProd _ [] = []+expProd x [y] = scaleExp y x+expProd [x] y = scaleExp x y+expProd (x:xs) ys = foldl' f (scaleExp x ys) xs+  where f h e = fastExpSum h . scaleExp e $ ys++--{-# SPECIALIZE compress :: [FloatT] -> [FloatT] #-}+--compress :: (Num a) => [a] -> [a]+compress e = comp up . comp down $ e+  where comp _ [] = []+        comp _ [x] = [x]+        comp f (x:xs) = uncurry (:) . foldl' f (x, []) $ xs+        down (q, h) e | ql /= 0 = (ql, qu:h)+                      | otherwise = (qu, h)+          where (# qu, ql #) = fastTwoSum q e+        up (q, h) e | ql /= 0 = (qu, ql:h) -- error on pg. 28, line 14: Q should be q+                    | otherwise = (qu, h)+          where (# qu, ql #) = fastTwoSum e q

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@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain