{-# LANGUAGE CPP, OverloadedStrings #-} #if __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} #endif -- | -- Module: Data.Text.Lazy.Builder.RealFloat -- Copyright: (c) The University of Glasgow 1994-2002 -- License: see libraries/base/LICENSE -- -- Write a floating point value to a 'Builder'. module Data.Text.Lazy.Builder.RealFloat ( FPFormat(..) , realFloat , formatRealFloat ) where import Data.Array.Base (unsafeAt) import Data.Array.IArray import Data.Text.Internal.Builder.Functions ((<>), i2d) import Data.Text.Lazy.Builder.Int (decimal) import Data.Text.Internal.Builder.RealFloat.Functions (roundTo) import Data.Text.Lazy.Builder import qualified Data.Text as T -- | Control the rendering of floating point numbers. data FPFormat = Exponent -- ^ Scientific notation (e.g. @2.3e123@). | Fixed -- ^ Standard decimal notation. | Generic -- ^ Use decimal notation for values between @0.1@ and -- @9,999,999@, and scientific notation otherwise. deriving (Enum, Read, Show) -- | Show a signed 'RealFloat' value to full precision, -- using standard decimal notation for arguments whose absolute value lies -- between @0.1@ and @9,999,999@, and scientific notation otherwise. realFloat :: (RealFloat a) => a -> Builder {-# SPECIALIZE realFloat :: Float -> Builder #-} {-# SPECIALIZE realFloat :: Double -> Builder #-} realFloat x = formatRealFloat Generic Nothing x formatRealFloat :: (RealFloat a) => FPFormat -> Maybe Int -- ^ Number of decimal places to render. -> a -> Builder {-# SPECIALIZE formatRealFloat :: FPFormat -> Maybe Int -> Float -> Builder #-} {-# SPECIALIZE formatRealFloat :: FPFormat -> Maybe Int -> Double -> Builder #-} formatRealFloat fmt decs x | isNaN x = "NaN" | isInfinite x = if x < 0 then "-Infinity" else "Infinity" | x < 0 || isNegativeZero x = singleton '-' <> doFmt fmt (floatToDigits (-x)) | otherwise = doFmt fmt (floatToDigits x) where doFmt format (is, e) = let ds = map i2d is in case format of Generic -> doFmt (if e < 0 || e > 7 then Exponent else Fixed) (is,e) Exponent -> case decs of Nothing -> let show_e' = decimal (e-1) in case ds of "0" -> "0.0e0" [d] -> singleton d <> ".0e" <> show_e' (d:ds') -> singleton d <> singleton '.' <> fromString ds' <> singleton 'e' <> show_e' [] -> error "formatRealFloat/doFmt/Exponent: []" Just dec -> let dec' = max dec 1 in case is of [0] -> "0." <> fromText (T.replicate dec' "0") <> "e0" _ -> let (ei,is') = roundTo (dec'+1) is (d:ds') = map i2d (if ei > 0 then init is' else is') in singleton d <> singleton '.' <> fromString ds' <> singleton 'e' <> decimal (e-1+ei) Fixed -> let mk0 ls = case ls of { "" -> "0" ; _ -> fromString ls} in case decs of Nothing | e <= 0 -> "0." <> fromText (T.replicate (-e) "0") <> fromString ds | otherwise -> let f 0 s rs = mk0 (reverse s) <> singleton '.' <> mk0 rs f n s "" = f (n-1) ('0':s) "" f n s (r:rs) = f (n-1) (r:s) rs in f e "" ds Just dec -> let dec' = max dec 0 in if e >= 0 then let (ei,is') = roundTo (dec' + e) is (ls,rs) = splitAt (e+ei) (map i2d is') in mk0 ls <> (if null rs then "" else singleton '.' <> fromString rs) else let (ei,is') = roundTo dec' (replicate (-e) 0 ++ is) d:ds' = map i2d (if ei > 0 then is' else 0:is') in singleton d <> (if null ds' then "" else singleton '.' <> fromString 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. -- | 'floatToDigits' takes a base and a non-negative 'RealFloat' number, -- and returns a list of digits and an exponent. -- In particular, if @x>=0@, and -- -- > floatToDigits base x = ([d1,d2,...,dn], e) -- -- then -- -- (1) @n >= 1@ -- -- (2) @x = 0.d1d2...dn * (base**e)@ -- -- (3) @0 <= di <= base-1@ floatToDigits :: (RealFloat a) => a -> ([Int], Int) {-# SPECIALIZE floatToDigits :: Float -> ([Int], Int) #-} {-# SPECIALIZE floatToDigits :: Double -> ([Int], Int) #-} floatToDigits 0 = ([0], 0) floatToDigits 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 `quot` (expt b n), e0+n) else (f0, e0) (r, s, mUp, mDn) = if e >= 0 then let be = expt b e in if f == expt b (p-1) then (f*be*b*2, 2*b, be*b, be) -- according to Burger and Dybvig else (f*be*2, 2, be, be) else if e > minExp && f == expt b (p-1) then (f*b*2, expt b (-e+1)*2, b, 1) else (f*2, expt b (-e)*2, 1, 1) k :: Int k = let k0 :: Int k0 = if b == 2 then -- logBase 10 2 is very slightly larger than 8651/28738 -- (about 5.3558e-10), so if log x >= 0, the approximation -- k1 is too small, hence we add one and need one fixup step less. -- If log x < 0, the approximation errs rather on the high side. -- That is usually more than compensated for by ignoring the -- fractional part of logBase 2 x, but when x is a power of 1/2 -- or slightly larger and the exponent is a multiple of the -- denominator of the rational approximation to logBase 10 2, -- k1 is larger than logBase 10 x. If k1 > 1 + logBase 10 x, -- we get a leading zero-digit we don't want. -- With the approximation 3/10, this happened for -- 0.5^1030, 0.5^1040, ..., 0.5^1070 and values close above. -- The approximation 8651/28738 guarantees k1 < 1 + logBase 10 x -- for IEEE-ish floating point types with exponent fields -- <= 17 bits and mantissae of several thousand bits, earlier -- convergents to logBase 10 2 would fail for long double. -- Using quot instead of div is a little faster and requires -- fewer fixup steps for negative lx. let lx = p - 1 + e0 k1 = (lx * 8651) `quot` 28738 in if lx >= 0 then k1 + 1 else k1 else -- f :: Integer, log :: Float -> Float, -- ceiling :: Float -> Int ceiling ((log (fromInteger (f+1) :: Float) + fromIntegral e * log (fromInteger b)) / log 10) --WAS: fromInt e * log (fromInteger b)) fixup n = if n >= 0 then if r + mUp <= expt 10 n * s then n else fixup (n+1) else if expt 10 (-n) * (r + mUp) <= s then n else fixup (n+1) in fixup k0 gen ds rn sN mUpN mDnN = let (dn, rn') = (rn * 10) `quotRem` sN mUpN' = mUpN * 10 mDnN' = mDnN * 10 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 10 k) mUp mDn else let bk = expt 10 (-k) in gen [] (r * bk) s (mUp * bk) (mDn * bk) in (map fromIntegral (reverse rds), k) -- Exponentiation with a cache for the most common numbers. minExpt, maxExpt :: Int minExpt = 0 maxExpt = 1100 expt :: Integer -> Int -> Integer expt base n | base == 2 && n >= minExpt && n <= maxExpt = expts `unsafeAt` n | base == 10 && n <= maxExpt10 = expts10 `unsafeAt` n | otherwise = base^n expts :: Array Int Integer expts = array (minExpt,maxExpt) [(n,2^n) | n <- [minExpt .. maxExpt]] maxExpt10 :: Int maxExpt10 = 324 expts10 :: Array Int Integer expts10 = array (minExpt,maxExpt10) [(n,10^n) | n <- [minExpt .. maxExpt10]]