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{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE 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,
showIntAtBase,
showInt,
showHex,
showOct,
showEFloat,
showFFloat,
showGFloat,
showFFloatAlt,
showGFloatAlt,
showFloat,
floatToDigits,
-- * Reading
-- | /NB:/ 'readInt' is the \'dual\' of 'showIntAtBase',
-- and 'readDec' is the \`dual\' of 'showInt'.
-- The inconsistent naming is a historical accident.
readSigned,
readInt,
readDec,
readOct,
readHex,
readFloat,
lexDigits,
-- * Miscellaneous
fromRat,
) where
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
-- -----------------------------------------------------------------------------
-- 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)
-- | Show a signed 'RealFloat' value
-- using standard decimal notation (e.g. @245000@, @0.0015@).
--
-- This behaves as 'showFFloat', except that a decimal point
-- is always guaranteed, even if not needed.
--
-- /Since: 4.7.0.0/
showFFloatAlt :: (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.
--
-- This behaves as 'showFFloat', except that a decimal point
-- is always guaranteed, even if not needed.
--
-- /Since: 4.7.0.0/
showGFloatAlt :: (RealFloat a) => Maybe Int -> a -> ShowS
showFFloatAlt d x = showString (formatRealFloatAlt FFFixed d True x)
showGFloatAlt d x = showString (formatRealFloatAlt FFGeneric d True x)
-- ---------------------------------------------------------------------------
-- 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