X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;ds=sidebyside;f=ghc%2Flib%2Fstd%2FNumeric.lhs;h=fa56105a824e94f43b234f51da5c3c91b76b9800;hb=dc8ebfaa71217b6f021e4c2d5a5a8145967b0e7c;hp=067c6728b1ae127d5826e0a3dc5d739813a6829b;hpb=28139aea50376444d56f43f0914291348a51a7e7;p=ghc-hetmet.git diff --git a/ghc/lib/std/Numeric.lhs b/ghc/lib/std/Numeric.lhs index 067c672..fa56105 100644 --- a/ghc/lib/std/Numeric.lhs +++ b/ghc/lib/std/Numeric.lhs @@ -1,5 +1,5 @@ % -% (c) The AQUA Project, Glasgow University, 1997-98 +% (c) The AQUA Project, Glasgow University, 1997-99 % \section[Numeric]{Numeric interface} @@ -10,76 +10,61 @@ Odds and ends, mostly functions for reading and showing \begin{code} {-# OPTIONS -fno-implicit-prelude #-} module Numeric - ( - fromRat, - showSigned, - readSigned, - showInt, - readInt, - - readDec, readOct, readHex, - - showEFloat, - showFFloat, - showGFloat, - showFloat, - readFloat, + + ( 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 + + , 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, - lexDigits + , floatToDigits -- :: (RealFloat a) => Integer -> a -> ([Int], Int) + , lexDigits -- :: ReadS String + -- Implementation checked wrt. Haskell 98 lib report, 1/99. ) where +#ifndef __HUGS__ import PrelBase import PrelMaybe +import PrelShow import PrelArr import PrelNum +import PrelNumExtra import PrelRead - +import PrelErr ( error ) +#else +import Char +import Array +#endif \end{code} -%********************************************************* -%* * -\subsection[Numeric-signatures]{Signatures} -%* * -%********************************************************* - -Interface on offer: - -\begin{pseudocode} -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 - -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 -\end{pseudocode} +#ifndef __HUGS__ \begin{code} showInt :: Integral a => a -> ShowS -showInt n r - = case quotRem n 10 of { (n', d) -> - case chr (ord_0 + fromIntegral d) of { C# c# -> -- stricter than necessary - let +showInt i rs + | i < 0 = error "Numeric.showInt: can't show negative numbers" + | otherwise = go i rs + where + go n r = + case quotRem n 10 of { (n', d) -> + case chr (ord_0 + fromIntegral d) of { C# c# -> -- stricter than necessary + let r' = C# c# : r - in - if n' == 0 then r' else showInt n' r' - }} + in + if n' == 0 then r' else go n' r' + }} \end{code} Controlling the format and precision of floats. The code that @@ -96,3 +81,233 @@ showFFloat d x = showString (formatRealFloat FFFixed d x) showGFloat d x = showString (formatRealFloat FFGeneric d x) \end{code} + +#else +\begin{code} +-- 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)) + + fromInt 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 toInt (reverse rds), k) +\end{code} +#endif