Numeric.hs

{-# 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,
 showHFloat,

 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,
 Floating(..)

 ) where

import GHC.Base
import GHC.Read
import GHC.Real
import GHC.Float
import GHC.Num
import GHC.Show
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 "0644"
-- [(420,"")]
readOct :: (Eq a, Num a) => ReadS a
readOct = readP_to_S L.readOctP

-- | Read an unsigned number in decimal notation.
--
-- >>> readDec "0644"
-- [(644,"")]
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 "deadbeef"
-- [(3735928559,"")]
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 = errorWithoutStackTrace "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)

{- | Show a floating-point value in the hexadecimal format,
similar to the @%a@ specifier in C's printf.

 >>> showHFloat (212.21 :: Double) ""
 "0x1.a86b851eb851fp7"
 >>> showHFloat (-12.76 :: Float) ""
 "-0x1.9851ecp3"
 >>> showHFloat (-0 :: Double) ""
 "-0x0p+0"
-}
showHFloat :: RealFloat a => a -> ShowS
showHFloat = showString . fmt
 where
 fmt x
 | isNaN x = "NaN"
 | isInfinite x = (if x < 0 then "-" else "") ++ "Infinity"
 | x < 0 || isNegativeZero x = '-' : cvt (-x)
 | otherwise = cvt x

 cvt x
 | x == 0 = "0x0p+0"
 | otherwise =
 case floatToDigits 2 x of
 r@([], _) -> error $ "Impossible happened: showHFloat: " ++ show r
 (d:ds, e) -> "0x" ++ show d ++ frac ds ++ "p" ++ show (e-1)

 -- Given binary digits, convert them to hex in blocks of 4
 -- Special case: If all 0's, just drop it.
 frac digits
 | allZ digits = ""
 | otherwise = "." ++ hex digits
 where
 hex ds =
 case ds of
 [] -> ""
 [a] -> hexDigit a 0 0 0 ""
 [a,b] -> hexDigit a b 0 0 ""
 [a,b,c] -> hexDigit a b c 0 ""
 a : b : c : d : r -> hexDigit a b c d (hex r)

 hexDigit a b c d = showHex (8*a + 4*b + 2*c + d)

 allZ xs = case xs of
 x : more -> x == 0 && allZ more
 [] -> True

-- ---------------------------------------------------------------------------
-- 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 = errorWithoutStackTrace ("Numeric.showIntAtBase: applied to unsupported base " ++ show base)
 | n0 < 0 = errorWithoutStackTrace ("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