numbers 2007.4.29 → 2007.9.23

raw patch · 3 files changed

+107/−6 lines, 3 files

Files

• Data/Number/BigFloat.hs +96/−0
• Data/Number/Fixed.hs +5/−2
• numbers.cabal +6/−4

@@ -0,0 +1,96 @@+module Data.Number.BigFloat(BigFloat) where+import Numeric(showSigned)++import Data.Number.Fixed+import qualified Data.Number.FixedFunctions as F++base :: (Num a) => a+base = 10++-- This representation is stupid, two Integers makes more sense,+-- but is more work.+data BigFloat e = BF (Fixed e) Integer+    deriving (Eq, Ord)++instance (Epsilon e) => Show (BigFloat e) where+    showsPrec = showSigned showBF+      -- Assumes base is 10+      where showBF (BF m e) = showsPrec 0 m . showString "e" . showsPrec 0 e++instance (Epsilon e) => Num (BigFloat e) where+    BF m1 e1 + BF m2 e2  =  bf (m1' + m2') e+      where (m1', m2') = if e == e1 then (m1, m2 / base^(e-e2))+      	    	       	      	    else (m1 / base^(e-e1), m2)+            e = e1 `max` e2+    -- Do - via negate+    BF m1 e1 * BF m2 e2  =  bf (m1 * m2) (e1 + e2)+    negate (BF m e) = BF (-m) e+    abs (BF m e) = BF (abs m) e+    signum (BF m _) = bf (signum m) 0+    fromInteger i = bf (fromInteger i) 0++instance (Epsilon e) => Real (BigFloat e) where+    toRational (BF e m) = toRational e * base^^m++instance (Epsilon e) => Fractional (BigFloat e) where+    recip (BF m e) = bf (base / m) (-(e + 1))+    -- Take care not to lose precision for small numbers+    fromRational x = if abs x < 1 then recip $ bf (fromRational (recip x)) 0+    		     	      	  else bf (fromRational x) 0++-- normalizing constructor+-- XXX The scaling is very inefficient+bf :: (Epsilon e) => Fixed e -> Integer -> BigFloat e+bf m e | m == 0     = BF 0 0+       | m < 0      = - bf (-m) e+       | m >= base  = bf (m / base) (e + 1)+       | m < 1      = bf (m * base) (e - 1)+       | otherwise  = BF m e++instance (Epsilon e) => RealFrac (BigFloat e) where+    properFraction x@(BF m e) =+        if e < 0 then (0, x)+	         else let (i, f) = properFraction (m * base^^e)+		      in  (i, bf f 0)++instance (Epsilon e) => Floating (BigFloat e) where+    pi = bf pi 0+    sqrt = toFloat1 F.sqrt+    exp = toFloat1 F.exp+    log = toFloat1 F.log+    sin = toFloat1 F.sin+    cos = toFloat1 F.cos+    tan = toFloat1 F.tan+    asin = toFloat1 F.asin+    acos = toFloat1 F.acos+    atan = toFloat1 F.atan+    sinh = toFloat1 F.sinh+    cosh = toFloat1 F.cosh+    tanh = toFloat1 F.tanh+    asinh = toFloat1 F.asinh+    acosh = toFloat1 F.acosh+    atanh = toFloat1 F.atanh++instance (Epsilon e) => RealFloat (BigFloat e) where+    floatRadix _ = base+    floatDigits (BF m _) =+        floor $ logBase base $ recip $ fromRational $ precision m+    floatRange _ = (minBound, maxBound)+    decodeFloat x@(BF m e) =+        let d = floatDigits x+	in  (round $ m * base^d, fromInteger e - d)+    encodeFloat m e = bf (fromInteger m) (toInteger e)+    exponent (BF _ e) = fromInteger e+    significand (BF m _) = BF m 0+    scaleFloat n (BF m e) = BF m (e + toInteger n)+    isNaN _ = False+    isInfinite _ = False+    isDenormalized _ = False+    isNegativeZero _ = False+    isIEEE _ = False++toFloat1 :: (Epsilon e) => (Rational -> Rational -> Rational) ->+	    BigFloat e -> BigFloat e+toFloat1 f x@(BF m e) =+    fromRational $ f (precision m * scl) (toRational m * scl)+      where scl = base^^e

@@ -1,6 +1,6 @@ {-# OPTIONS_GHC -fglasgow-exts -fscoped-type-variables #-} module Data.Number.Fixed(Fixed, Epsilon, Eps1, EpsDiv10, Prec10, Prec50, PrecPlus20,-			 convertFixed, dynamicEps) where+			 convertFixed, dynamicEps, precision) where import Numeric import Data.Char import Data.Ratio@@ -41,6 +41,9 @@  newtype Fixed e = F Rational deriving (Eq, Ord, Enum, Real, RealFrac) +precision :: (Epsilon e) => Fixed e -> Rational+precision = getEps+ instance (Epsilon e) => Num (Fixed e) where     (+) = lift2 (+)     (-) = lift2 (-)@@ -59,7 +62,7 @@ lift2 op fx@(F x) (F y) = F $ approx (x `op` y) (getEps fx)  approx :: Rational -> Rational -> Rational-approx x eps = approxRational (x + eps/2) eps+approx x eps = approxRational x (eps/2)  convertFixed :: (Epsilon e, Epsilon f) => Fixed e -> Fixed f convertFixed e@(F x) = f

@@ -1,15 +1,17 @@ Name:		numbers-Version:	2007.4.29+Version:	2007.9.23 License:	BSD3 Author:		Lennart Augustsson Maintainer:	Lennart Augustsson Category:	Data, Math Synopsis:	Various number types Description:	Instances of the numerical classes for a variety of-		different numbers: (computable) real numbers, arbitrary-		precion fixed numbers, differentiable numbers, symbolic numbers.+		different numbers: (computable) real numbers,+		arbitrary precision fixed numbers,+		arbitrary precision floating point numbers,+		differentiable numbers, symbolic numbers. Build-Depends:	base Exposed-modules:	Data.Number.Symbolic Data.Number.Dif 			Data.Number.CReal Data.Number.Fixed-			Data.Number.Interval+			Data.Number.Interval Data.Number.BigFloat Other-modules:	Data.Number.Vectorspace Data.Number.FixedFunctions