view release on metacpan or  search on metacpan

hugs98-Nov2003/libraries/Hugs/Numeric.hs  view on Meta::CPAN

        p0 = (integerLogBase b (numerator x) -
              integerLogBase b (denominator x) - p) `max` minExp
        f = if p0 < 0 then 1 % expt b (-p0) else expt b p0 % 1
        (x', p') = scaleRat (toRational b) minExp xMin xMax p0 (x / f)
        r = encodeFloat (round x') p'

-- Scale x until xMin <= x < xMax, or p (the exponent) <= minExp.
scaleRat :: Rational -> Int -> Rational -> Rational -> 
             Int -> Rational -> (Rational, Int)
scaleRat b minExp xMin xMax p x
 | p <= minExp = (x,p)
 | x >= xMax   = scaleRat b minExp xMin xMax (p+1) (x/b)
 | x <  xMin   = scaleRat b minExp xMin xMax (p-1) (x*b)
 | otherwise   = (x, p)

-- Exponentiation with a cache for the most common numbers.
minExpt = 0::Int
maxExpt = 1100::Int
expt :: Integer -> Int -> Integer
expt base n =
    if base == 2 && n >= minExpt && n <= maxExpt then
        expts!n
    else
        base^n

expts :: Array Int Integer
expts = array (minExpt,maxExpt) [(n,2^n) | n <- [minExpt .. maxExpt]]

-- Compute the (floor of the) log of i in base b.
-- Simplest way would be just divide i by b until it's smaller then b,
-- but that would be very slow!  We are just slightly more clever.
integerLogBase :: Integer -> Integer -> Int
integerLogBase b i =
     if i < b then
        0
     else
        -- Try squaring the base first to cut down the number of divisions.
        let l = 2 * integerLogBase (b*b) i
            doDiv :: Integer -> Int -> Int
            doDiv i l = if i < b then l else doDiv (i `div` b) (l+1)
        in  doDiv (i `div` (b^l)) l

-- Misc utilities to show integers and floats

showEFloat     :: (RealFloat a) => Maybe Int -> a -> ShowS
showFFloat     :: (RealFloat a) => Maybe Int -> a -> ShowS
showGFloat     :: (RealFloat a) => Maybe Int -> a -> ShowS
showFloat      :: (RealFloat a) => a -> ShowS

showEFloat d x =  showString (formatRealFloat FFExponent d x)
showFFloat d x =  showString (formatRealFloat FFFixed d x)
showGFloat d x =  showString (formatRealFloat FFGeneric d x)
showFloat      =  showGFloat Nothing 

-- These are the format types.  This type is not exported.

data FFFormat = FFExponent | FFFixed | FFGeneric

formatRealFloat :: (RealFloat a) => FFFormat -> Maybe Int -> a -> String
formatRealFloat fmt decs x 
  | isNaN      x = "NaN"
  | isInfinite x = if x < 0 then "-Infinity" else "Infinity"
  | x < 0 || isNegativeZero x = '-' : doFmt fmt (floatToDigits (toInteger base) (-x))
  | otherwise    = doFmt fmt (floatToDigits (toInteger base) x)
  where base = 10

        doFmt fmt (is, e) =
            let ds = map intToDigit is
            in  case fmt of
                FFGeneric -> 
                    doFmt (if e < 0 || e > 7 then FFExponent else FFFixed)
                          (is, e)
                FFExponent ->
                    case decs of
                    Nothing ->
                        case ds of
			 []    -> "0.0e0"
                         [d]   -> d : ".0e" ++ show (e-1)
                         d:ds  -> d : '.' : ds ++ 'e':show (e-1)
                    Just dec ->
                        let dec' = max dec 1 in
                        case is of
                         [] -> '0':'.':take dec' (repeat '0') ++ "e0"
                         _ ->
                          let (ei, is') = roundTo base (dec'+1) is
                              d:ds = map intToDigit
                                         (if ei > 0 then init is' else is')
                          in d:'.':ds  ++ "e" ++ show (e-1+ei)
                FFFixed ->
                  case decs of
                    Nothing 
		     | e > 0 -> take e (ds ++ repeat '0')
		     	        ++ '.' : mk0 (drop e ds)
		     | otherwise -> '0' : '.' : mk0 (replicate (-e) '0' ++ ds)
                    Just dec ->
                        let dec' = max dec 0 in
                        if e >= 0 then
                            let (ei, is') = roundTo base (dec' + e) is
                                (ls, rs) = splitAt (e+ei) (map intToDigit is')
                            in  mk0 ls ++ mkdot0 rs
                        else
                            let (ei, is') = roundTo base dec'
                                              (replicate (-e) 0 ++ is)
                                d : ds = map intToDigit
                                            (if ei > 0 then is' else 0:is')
                            in  d : mkdot0 ds
		  where
		    mk0 "" = "0"     -- Used to ensure we print 34.0, not 34.
	       	    mk0 s  = s       -- and 0.34 not .34
    
    		    mkdot0 "" = ""   -- Used to ensure we print 34, not 34.
		    mkdot0 s  = '.' : s

roundTo :: Int -> Int -> [Int] -> (Int, [Int])
roundTo base d is = case f d is of
                v@(0, is) -> v
                (1, is)   -> (1, 1 : is)
  where b2 = base `div` 2
        f n [] = (0, replicate n 0)
        f 0 (i:_) = (if i >= b2 then 1 else 0, [])
        f d (i:is) =