[project @ 2001-07-04 12:07:27 by simonmar]

Add Numeric library here for the time being.  This is a combination of
the H98 Numeric library and a few functions from GHC's NumExts.

1 files changed, 367 insertions, 0 deletions

diff --git a/libraries/base/Numeric.hs b/libraries/base/Numeric.hs
new file mode 100644
index 0000000000..4a4ecf4577
--- /dev/null
+++ b/libraries/base/Numeric.hs
@@ -0,0 +1,367 @@
+-----------------------------------------------------------------------------
+-- 
+-- Module      :  Numeric
+-- Copyright   :  (c) The University of Glasgow 2001
+-- License     :  BSD-style (see the file libraries/core/LICENSE)
+-- 
+-- Maintainer  :  libraries@haskell.org
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-- $Id: Numeric.hs,v 1.1 2001/07/04 12:07:27 simonmar Exp $
+--
+-- Odds and ends, mostly functions for reading and showing
+-- RealFloat-like kind of values.
+--
+-----------------------------------------------------------------------------
+
+module Numeric (
+
+        fromRat,          -- :: (RealFloat a) => Rational -> a
+	showSigned,       -- :: (Real a) => (a -> ShowS) -> Int -> a -> ShowS
+	readSigned,       -- :: (Real a) => ReadS a -> ReadS a
+	showInt,          -- :: Integral a => a -> ShowS
+	readInt,          -- :: (Integral a) => a -> (Char -> Bool)
+			  --         -> (Char -> Int) -> ReadS a
+	
+	readDec,          -- :: (Integral a) => ReadS a
+	readOct,          -- :: (Integral a) => ReadS a
+	readHex,          -- :: (Integral a) => ReadS a
+
+        showHex,          -- :: Integral a => a -> ShowS
+        showOct,          -- :: Integral a => a -> ShowS
+        showBin,          -- :: Integral a => a -> ShowS
+        
+	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
+	readFloat,        -- :: (RealFloat a) => ReadS a
+	
+	 
+	floatToDigits,    -- :: (RealFloat a) => Integer -> a -> ([Int], Int)
+	lexDigits,        -- :: ReadS String
+
+          -- general purpose number->string converter.
+        showIntAtBase,    -- :: Integral a 
+			  -- => a		-- base
+			  -- -> (a -> Char)      -- digit to char
+			  -- -> a                -- number to show.
+			  -- -> ShowS
+	) where
+
+import Prelude		-- For dependencies
+import Data.Char
+
+#ifdef __GLASGOW_HASKELL__
+import GHC.Base		( Char(..), unsafeChr )
+import GHC.Read
+import GHC.Real		( showSigned )
+import GHC.Float
+#endif
+
+#ifdef __HUGS__
+import Array
+#endif
+
+#ifdef __GLASGOW_HASKELL__
+showInt :: Integral a => a -> ShowS
+showInt n cs
+    | n < 0     = error "Numeric.showInt: can't show negative numbers"
+    | otherwise = go n cs
+    where
+    go n cs
+        | n < 10    = case unsafeChr (ord '0' + fromIntegral n) of
+            c@(C# _) -> c:cs
+        | otherwise = case unsafeChr (ord '0' + fromIntegral r) of
+            c@(C# _) -> go q (c:cs)
+        where
+        (q,r) = n `quotRem` 10
+
+-- Controlling the format and precision of floats. The code that
+-- implements the formatting itself is in @PrelNum@ to avoid
+-- mutual module deps.
+
+{-# SPECIALIZE showEFloat ::
+	Maybe Int -> Float  -> ShowS,
+	Maybe Int -> Double -> ShowS #-}
+{-# SPECIALIZE showFFloat ::
+	Maybe Int -> Float  -> ShowS,
+	Maybe Int -> Double -> ShowS #-}
+{-# SPECIALIZE showGFloat ::
+	Maybe Int -> Float  -> ShowS,
+	Maybe Int -> Double -> ShowS #-}
+
+showEFloat    :: (RealFloat a) => Maybe Int -> a -> ShowS
+showFFloat    :: (RealFloat a) => Maybe Int -> a -> ShowS
+showGFloat    :: (RealFloat a) => Maybe Int -> 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)
+#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
+
+-- ---------------------------------------------------------------------------
+-- Integer printing functions
+
+showIntAtBase :: Integral a => a -> (a -> Char) -> a -> ShowS
+showIntAtBase base toChr n r
+  | n < 0  = error ("Numeric.showIntAtBase: applied to negative number " ++ show n)
+  | otherwise = 
+    case quotRem n base of { (n', d) ->
+    let c = toChr d in
+    seq c $ -- stricter than necessary
+    let
+	r' = c : r
+    in
+    if n' == 0 then r' else showIntAtBase base toChr n' r'
+    }
+
+showHex :: Integral a => a -> ShowS
+showHex n r = 
+ showString "0x" $
+ showIntAtBase 16 (toChrHex) n r
+ where  
+  toChrHex d
+    | d < 10    = chr (ord '0' + fromIntegral d)
+    | otherwise = chr (ord 'a' + fromIntegral (d - 10))
+
+showOct :: Integral a => a -> ShowS
+showOct n r = 
+ showString "0o" $
+ showIntAtBase 8 (toChrOct) n r
+ where toChrOct d = chr (ord '0' + fromIntegral d)
+
+showBin :: Integral a => a -> ShowS
+showBin n r = 
+ showString "0b" $
+ showIntAtBase 2 (toChrOct) n r
+ where toChrOct d = chr (ord '0' + fromIntegral d)