#endif
#ifdef __HUGS__
-import Array
+import Hugs.Numeric
#endif
-
+#ifdef __GLASGOW_HASKELL__
-- -----------------------------------------------------------------------------
-- Reading
(n,"") <- readPos str
return (n,s)
-
-- -----------------------------------------------------------------------------
-- Showing
-#ifdef __GLASGOW_HASKELL__
showInt :: Integral a => a -> ShowS
showInt n cs
| n < 0 = error "Numeric.showInt: can't show negative numbers"
showEFloat d x = showString (formatRealFloat FFExponent d x)
showFFloat d x = showString (formatRealFloat FFFixed d x)
showGFloat d x = showString (formatRealFloat FFGeneric d x)
-#endif
-
-#ifdef __HUGS__
--- This converts a rational to a floating. This should be used in the
--- Fractional instances of Float and Double.
-
-fromRat :: (RealFloat a) => Rational -> a
-fromRat x =
- if x == 0 then encodeFloat 0 0 -- Handle exceptional cases
- else if x < 0 then - fromRat' (-x) -- first.
- else fromRat' x
-
--- Conversion process:
--- Scale the rational number by the RealFloat base until
--- it lies in the range of the mantissa (as used by decodeFloat/encodeFloat).
--- Then round the rational to an Integer and encode it with the exponent
--- that we got from the scaling.
--- To speed up the scaling process we compute the log2 of the number to get
--- a first guess of the exponent.
-fromRat' :: (RealFloat a) => Rational -> a
-fromRat' x = r
- where b = floatRadix r
- p = floatDigits r
- (minExp0, _) = floatRange r
- minExp = minExp0 - p -- the real minimum exponent
- xMin = toRational (expt b (p-1))
- xMax = toRational (expt b p)
- 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 =
- if p <= minExp then
- (x, p)
- else if x >= xMax then
- scaleRat b minExp xMin xMax (p+1) (x/b)
- else if x < xMin then
- scaleRat b minExp xMin xMax (p-1) (x*b)
- else
- (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 = s
- where base = 10
- s = if isNaN x then
- "NaN"
- else if isInfinite x then
- if x < 0 then "-Infinity" else "Infinity"
- else if x < 0 || isNegativeZero x then
- '-' : doFmt fmt (floatToDigits (toInteger base) (-x))
- else
- doFmt fmt (floatToDigits (toInteger base) x)
- 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'] -> "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] -> '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 ->
- let f 0 s ds = mk0 s ++ "." ++ mk0 ds
- f n s "" = f (n-1) (s++"0") ""
- f n s (d:ds) = f (n-1) (s++[d]) ds
- mk0 "" = "0"
- mk0 s = s
- in f e "" 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 (if null ls then "0" else ls) ++
- (if null rs then "" else '.' : 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 : '.' : ds
-
-roundTo :: Int -> Int -> [Int] -> (Int, [Int])
-roundTo base d is = case f d is of
- (0, is) -> (0, is)
- (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) =
- let (c, ds) = f (d-1) is
- i' = c + i
- in if i' == base then (1, 0:ds) else (0, i':ds)
-
---
--- Based on "Printing Floating-Point Numbers Quickly and Accurately"
--- by R.G. Burger and R. K. Dybvig, in PLDI 96.
--- This version uses a much slower logarithm estimator. It should be improved.
-
--- This function returns a list of digits (Ints in [0..base-1]) and an
--- exponent.
-
-floatToDigits :: (RealFloat a) => Integer -> a -> ([Int], Int)
-
-floatToDigits _ 0 = ([0], 0)
-floatToDigits base x =
- let (f0, e0) = decodeFloat x
- (minExp0, _) = floatRange x
- p = floatDigits x
- b = floatRadix x
- minExp = minExp0 - p -- the real minimum exponent
- -- Haskell requires that f be adjusted so denormalized numbers
- -- will have an impossibly low exponent. Adjust for this.
- (f, e) = let n = minExp - e0
- in if n > 0 then (f0 `div` (b^n), e0+n) else (f0, e0)
-
- (r, s, mUp, mDn) =
- if e >= 0 then
- let be = b^e in
- if f == b^(p-1) then
- (f*be*b*2, 2*b, be*b, b)
- else
- (f*be*2, 2, be, be)
- else
- if e > minExp && f == b^(p-1) then
- (f*b*2, b^(-e+1)*2, b, 1)
- else
- (f*2, b^(-e)*2, 1, 1)
- k =
- let k0 =
- if b==2 && base==10 then
- -- logBase 10 2 is slightly bigger than 3/10 so
- -- the following will err on the low side. Ignoring
- -- the fraction will make it err even more.
- -- Haskell promises that p-1 <= logBase b f < p.
- (p - 1 + e0) * 3 `div` 10
- else
- ceiling ((log (fromInteger (f+1)) +
- fromIntegral e * log (fromInteger b)) /
- log (fromInteger base))
- fixup n =
- if n >= 0 then
- if r + mUp <= expt base n * s then n else fixup (n+1)
- else
- if expt base (-n) * (r + mUp) <= s then n
- else fixup (n+1)
- in fixup k0
-
- gen ds rn sN mUpN mDnN =
- let (dn, rn') = (rn * base) `divMod` sN
- mUpN' = mUpN * base
- mDnN' = mDnN * base
- in case (rn' < mDnN', rn' + mUpN' > sN) of
- (True, False) -> dn : ds
- (False, True) -> dn+1 : ds
- (True, True) -> if rn' * 2 < sN then dn : ds else dn+1 : ds
- (False, False) -> gen (dn:ds) rn' sN mUpN' mDnN'
- rds =
- if k >= 0 then
- gen [] r (s * expt base k) mUp mDn
- else
- let bk = expt base (-k)
- in gen [] (r * bk) s (mUp * bk) (mDn * bk)
- in (map fromIntegral (reverse rds), k)
-#endif
+#endif /* __GLASGOW_HASKELL__ */
-- ---------------------------------------------------------------------------
-- Integer printing functions
projects / ghc-base.git / blobdiff