base-4.3.0.0: GHC/Num.lhs
\begin{code}
{-# OPTIONS_GHC -XNoImplicitPrelude #-}
-- We believe we could deorphan this module, by moving lots of things
-- around, but we haven't got there yet:
{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_HADDOCK hide #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.Num
-- Copyright : (c) The University of Glasgow 1994-2002
-- License : see libraries/base/LICENSE
--
-- Maintainer : cvs-ghc@haskell.org
-- Stability : internal
-- Portability : non-portable (GHC Extensions)
--
-- The 'Num' class and the 'Integer' type.
--
-----------------------------------------------------------------------------
#include "MachDeps.h"
#if SIZEOF_HSWORD == 4
#define DIGITS 9
#define BASE 1000000000
#elif SIZEOF_HSWORD == 8
#define DIGITS 18
#define BASE 1000000000000000000
#else
#error Please define DIGITS and BASE
-- DIGITS should be the largest integer such that
-- 10^DIGITS < 2^(SIZEOF_HSWORD * 8 - 1)
-- BASE should be 10^DIGITS. Note that ^ is not available yet.
#endif
-- #hide
module GHC.Num (module GHC.Num, module GHC.Integer) where
import GHC.Base
import GHC.Enum
import GHC.Show
import GHC.Integer
infixl 7 *
infixl 6 +, -
default () -- Double isn't available yet,
-- and we shouldn't be using defaults anyway
\end{code}
%*********************************************************
%* *
\subsection{Standard numeric class}
%* *
%*********************************************************
\begin{code}
-- | Basic numeric class.
--
-- Minimal complete definition: all except 'negate' or @(-)@
class (Eq a, Show a) => Num a where
(+), (-), (*) :: a -> a -> a
-- | Unary negation.
negate :: a -> a
-- | Absolute value.
abs :: a -> a
-- | Sign of a number.
-- The functions 'abs' and 'signum' should satisfy the law:
--
-- > abs x * signum x == x
--
-- For real numbers, the 'signum' is either @-1@ (negative), @0@ (zero)
-- or @1@ (positive).
signum :: a -> a
-- | Conversion from an 'Integer'.
-- An integer literal represents the application of the function
-- 'fromInteger' to the appropriate value of type 'Integer',
-- so such literals have type @('Num' a) => a@.
fromInteger :: Integer -> a
{-# INLINE (-) #-}
{-# INLINE negate #-}
x - y = x + negate y
negate x = 0 - x
-- | the same as @'flip' ('-')@.
--
-- Because @-@ is treated specially in the Haskell grammar,
-- @(-@ /e/@)@ is not a section, but an application of prefix negation.
-- However, @('subtract'@ /exp/@)@ is equivalent to the disallowed section.
{-# INLINE subtract #-}
subtract :: (Num a) => a -> a -> a
subtract x y = y - x
\end{code}
%*********************************************************
%* *
\subsection{Instances for @Int@}
%* *
%*********************************************************
\begin{code}
instance Num Int where
(+) = plusInt
(-) = minusInt
negate = negateInt
(*) = timesInt
abs n = if n `geInt` 0 then n else negateInt n
signum n | n `ltInt` 0 = negateInt 1
| n `eqInt` 0 = 0
| otherwise = 1
fromInteger i = I# (toInt# i)
quotRemInt :: Int -> Int -> (Int, Int)
quotRemInt a@(I# _) b@(I# _) = (a `quotInt` b, a `remInt` b)
-- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
divModInt :: Int -> Int -> (Int, Int)
divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
-- Stricter. Sorry if you don't like it. (WDP 94/10)
\end{code}
%*********************************************************
%* *
\subsection{The @Integer@ instances for @Show@}
%* *
%*********************************************************
\begin{code}
instance Show Integer where
showsPrec p n r
| p > 6 && n < 0 = '(' : integerToString n (')' : r)
-- Minor point: testing p first gives better code
-- in the not-uncommon case where the p argument
-- is a constant
| otherwise = integerToString n r
showList = showList__ (showsPrec 0)
-- Divide an conquer implementation of string conversion
integerToString :: Integer -> String -> String
integerToString n0 cs0
| n0 < 0 = '-' : integerToString' (- n0) cs0
| otherwise = integerToString' n0 cs0
where
integerToString' :: Integer -> String -> String
integerToString' n cs
| n < BASE = jhead (fromInteger n) cs
| otherwise = jprinth (jsplitf (BASE*BASE) n) cs
-- Split n into digits in base p. We first split n into digits
-- in base p*p and then split each of these digits into two.
-- Note that the first 'digit' modulo p*p may have a leading zero
-- in base p that we need to drop - this is what jsplith takes care of.
-- jsplitb the handles the remaining digits.
jsplitf :: Integer -> Integer -> [Integer]
jsplitf p n
| p > n = [n]
| otherwise = jsplith p (jsplitf (p*p) n)
jsplith :: Integer -> [Integer] -> [Integer]
jsplith p (n:ns) =
case n `quotRemInteger` p of
(# q, r #) ->
if q > 0 then q : r : jsplitb p ns
else r : jsplitb p ns
jsplith _ [] = error "jsplith: []"
jsplitb :: Integer -> [Integer] -> [Integer]
jsplitb _ [] = []
jsplitb p (n:ns) = case n `quotRemInteger` p of
(# q, r #) ->
q : r : jsplitb p ns
-- Convert a number that has been split into digits in base BASE^2
-- this includes a last splitting step and then conversion of digits
-- that all fit into a machine word.
jprinth :: [Integer] -> String -> String
jprinth (n:ns) cs =
case n `quotRemInteger` BASE of
(# q', r' #) ->
let q = fromInteger q'
r = fromInteger r'
in if q > 0 then jhead q $ jblock r $ jprintb ns cs
else jhead r $ jprintb ns cs
jprinth [] _ = error "jprinth []"
jprintb :: [Integer] -> String -> String
jprintb [] cs = cs
jprintb (n:ns) cs = case n `quotRemInteger` BASE of
(# q', r' #) ->
let q = fromInteger q'
r = fromInteger r'
in jblock q $ jblock r $ jprintb ns cs
-- Convert an integer that fits into a machine word. Again, we have two
-- functions, one that drops leading zeros (jhead) and one that doesn't
-- (jblock)
jhead :: Int -> String -> String
jhead n cs
| n < 10 = case unsafeChr (ord '0' + n) of
c@(C# _) -> c : cs
| otherwise = case unsafeChr (ord '0' + r) of
c@(C# _) -> jhead q (c : cs)
where
(q, r) = n `quotRemInt` 10
jblock = jblock' {- ' -} DIGITS
jblock' :: Int -> Int -> String -> String
jblock' d n cs
| d == 1 = case unsafeChr (ord '0' + n) of
c@(C# _) -> c : cs
| otherwise = case unsafeChr (ord '0' + r) of
c@(C# _) -> jblock' (d - 1) q (c : cs)
where
(q, r) = n `quotRemInt` 10
\end{code}
%*********************************************************
%* *
\subsection{The @Integer@ instances for @Num@}
%* *
%*********************************************************
\begin{code}
instance Num Integer where
(+) = plusInteger
(-) = minusInteger
(*) = timesInteger
negate = negateInteger
fromInteger x = x
abs = absInteger
signum = signumInteger
\end{code}
%*********************************************************
%* *
\subsection{The @Integer@ instance for @Enum@}
%* *
%*********************************************************
\begin{code}
instance Enum Integer where
succ x = x + 1
pred x = x - 1
toEnum (I# n) = smallInteger n
fromEnum n = I# (toInt# n)
{-# INLINE enumFrom #-}
{-# INLINE enumFromThen #-}
{-# INLINE enumFromTo #-}
{-# INLINE enumFromThenTo #-}
enumFrom x = enumDeltaInteger x 1
enumFromThen x y = enumDeltaInteger x (y-x)
enumFromTo x lim = enumDeltaToInteger x 1 lim
enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
{-# RULES
"enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
"efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
"enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
"enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
#-}
enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
enumDeltaIntegerFB c x d = x `seq` (x `c` enumDeltaIntegerFB c (x+d) d)
enumDeltaInteger :: Integer -> Integer -> [Integer]
enumDeltaInteger x d = x `seq` (x : enumDeltaInteger (x+d) d)
-- strict accumulator, so
-- head (drop 1000000 [1 .. ]
-- works
{-# NOINLINE [0] enumDeltaToIntegerFB #-}
-- Don't inline this until RULE "enumDeltaToInteger" has had a chance to fire
enumDeltaToIntegerFB :: (Integer -> a -> a) -> a
-> Integer -> Integer -> Integer -> a
enumDeltaToIntegerFB c n x delta lim
| delta >= 0 = up_fb c n x delta lim
| otherwise = dn_fb c n x delta lim
enumDeltaToInteger :: Integer -> Integer -> Integer -> [Integer]
enumDeltaToInteger x delta lim
| delta >= 0 = up_list x delta lim
| otherwise = dn_list x delta lim
up_fb :: (Integer -> a -> a) -> a -> Integer -> Integer -> Integer -> a
up_fb c n x0 delta lim = go (x0 :: Integer)
where
go x | x > lim = n
| otherwise = x `c` go (x+delta)
dn_fb :: (Integer -> a -> a) -> a -> Integer -> Integer -> Integer -> a
dn_fb c n x0 delta lim = go (x0 :: Integer)
where
go x | x < lim = n
| otherwise = x `c` go (x+delta)
up_list :: Integer -> Integer -> Integer -> [Integer]
up_list x0 delta lim = go (x0 :: Integer)
where
go x | x > lim = []
| otherwise = x : go (x+delta)
dn_list :: Integer -> Integer -> Integer -> [Integer]
dn_list x0 delta lim = go (x0 :: Integer)
where
go x | x < lim = []
| otherwise = x : go (x+delta)
\end{code}