Numeric.hs

{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE CPP, NoImplicitPrelude, MagicHash #-}

-----------------------------------------------------------------------------
-- |
-- Module : Numeric
-- Copyright : (c) The University of Glasgow 2002
-- License : BSD-style (see the file libraries/base/LICENSE)
-- 
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
-- Odds and ends, mostly functions for reading and showing
-- 'RealFloat'-like kind of values.
--
-----------------------------------------------------------------------------

module Numeric (

 -- * Showing

 showSigned, -- :: (Real a) => (a -> ShowS) -> Int -> a -> ShowS

 showIntAtBase, -- :: Integral a => a -> (a -> Char) -> a -> ShowS
 showInt, -- :: Integral a => a -> ShowS
 showHex, -- :: Integral a => a -> ShowS
 showOct, -- :: 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

 floatToDigits, -- :: (RealFloat a) => Integer -> a -> ([Int], Int)

 -- * Reading

 -- | /NB:/ 'readInt' is the \'dual\' of 'showIntAtBase',
 -- and 'readDec' is the \`dual\' of 'showInt'.
 -- The inconsistent naming is a historical accident.

 readSigned, -- :: (Real a) => ReadS a -> ReadS a

 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

 readFloat, -- :: (RealFloat a) => ReadS a

 lexDigits, -- :: ReadS String

 -- * Miscellaneous

 fromRat, -- :: (RealFloat a) => Rational -> a

 ) where

#ifdef __GLASGOW_HASKELL__
import GHC.Base
import GHC.Read
import GHC.Real
import GHC.Float
import GHC.Num
import GHC.Show
import Data.Maybe
import Text.ParserCombinators.ReadP( ReadP, readP_to_S, pfail )
import qualified Text.Read.Lex as L
#else
import Data.Char
#endif

#ifdef __HUGS__
import Hugs.Prelude
import Hugs.Numeric
#endif

#ifdef __GLASGOW_HASKELL__
-- -----------------------------------------------------------------------------
-- Reading

-- | Reads an /unsigned/ 'Integral' value in an arbitrary base.
readInt :: Num a
 => a -- ^ the base
 -> (Char -> Bool) -- ^ a predicate distinguishing valid digits in this base
 -> (Char -> Int) -- ^ a function converting a valid digit character to an 'Int'
 -> ReadS a
readInt base isDigit valDigit = readP_to_S (L.readIntP base isDigit valDigit)

-- | Read an unsigned number in octal notation.
readOct :: (Eq a, Num a) => ReadS a
readOct = readP_to_S L.readOctP

-- | Read an unsigned number in decimal notation.
readDec :: (Eq a, Num a) => ReadS a
readDec = readP_to_S L.readDecP

-- | Read an unsigned number in hexadecimal notation.
-- Both upper or lower case letters are allowed.
readHex :: (Eq a, Num a) => ReadS a
readHex = readP_to_S L.readHexP 

-- | Reads an /unsigned/ 'RealFrac' value,
-- expressed in decimal scientific notation.
readFloat :: RealFrac a => ReadS a
readFloat = readP_to_S readFloatP

readFloatP :: RealFrac a => ReadP a
readFloatP =
 do tok <- L.lex
 case tok of
 L.Number n -> return $ fromRational $ L.numberToRational n
 _ -> pfail

-- It's turgid to have readSigned work using list comprehensions,
-- but it's specified as a ReadS to ReadS transformer
-- With a bit of luck no one will use it.

-- | Reads a /signed/ 'Real' value, given a reader for an unsigned value.
readSigned :: (Real a) => ReadS a -> ReadS a
readSigned readPos = readParen False read'
 where read' r = read'' r ++
 (do
 ("-",s) <- lex r
 (x,t) <- read'' s
 return (-x,t))
 read'' r = do
 (str,s) <- lex r
 (n,"") <- readPos str
 return (n,s)

-- -----------------------------------------------------------------------------
-- Showing

-- | Show /non-negative/ 'Integral' numbers in base 10.
showInt :: Integral a => a -> ShowS
showInt n0 cs0
 | n0 < 0 = error "Numeric.showInt: can't show negative numbers"
 | otherwise = go n0 cs0
 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 #-}

-- | Show a signed 'RealFloat' value
-- using scientific (exponential) notation (e.g. @2.45e2@, @1.5e-3@).
--
-- In the call @'showEFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
showEFloat :: (RealFloat a) => Maybe Int -> a -> ShowS

-- | Show a signed 'RealFloat' value
-- using standard decimal notation (e.g. @245000@, @0.0015@).
--
-- In the call @'showFFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
showFFloat :: (RealFloat a) => Maybe Int -> a -> ShowS

-- | Show a signed 'RealFloat' value
-- using standard decimal notation for arguments whose absolute value lies 
-- between @0.1@ and @9,999,999@, and scientific notation otherwise.
--
-- In the call @'showGFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
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 /* __GLASGOW_HASKELL__ */

-- ---------------------------------------------------------------------------
-- Integer printing functions

-- | Shows a /non-negative/ 'Integral' number using the base specified by the
-- first argument, and the character representation specified by the second.
showIntAtBase :: (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS
showIntAtBase base toChr n0 r0
 | base <= 1 = error ("Numeric.showIntAtBase: applied to unsupported base " ++ show base)
 | n0 < 0 = error ("Numeric.showIntAtBase: applied to negative number " ++ show n0)
 | otherwise = showIt (quotRem n0 base) r0
 where
 showIt (n,d) r = seq c $ -- stricter than necessary
 case n of
 0 -> r'
 _ -> showIt (quotRem n base) r'
 where
 c = toChr (fromIntegral d)
 r' = c : r

-- | Show /non-negative/ 'Integral' numbers in base 16.
showHex :: (Integral a,Show a) => a -> ShowS
showHex = showIntAtBase 16 intToDigit

-- | Show /non-negative/ 'Integral' numbers in base 8.
showOct :: (Integral a, Show a) => a -> ShowS
showOct = showIntAtBase 8 intToDigit