Zero.hs

{-# LANGUAGE MagicHash, CPP #-}
{-|
    Module      :  Data.Number.MPFR.Instances.Zero
    Description :  Instance declarations
    Copyright   :  (c) Aleš Bizjak
    License     :  BSD3

    Maintainer  :  ales.bizjak0@gmail.com
    Stability   :  experimental
    Portability :  non-portable

  This module defines instances 'Num', 'Real', 'Fractional', 'Floating' and 'RealFrac' of 'MPFR'.
  Operations are rounded with 'RoundMode' 'Zero' and computed with maximum precision of two 
  operands or with the precision of the operand.
-}

{-# INCLUDE <mpfr.h> #-}
{-# INCLUDE <chsmpfr.h> #-}


module Data.Number.MPFR.Instances.Zero ()
where

import qualified Data.Number.MPFR.Arithmetic as A
import qualified Data.Number.MPFR.Special as S
import Data.Number.MPFR.Misc
import Data.Number.MPFR.Assignment
import Data.Number.MPFR.Comparison
import Data.Number.MPFR.Internal
import Data.Number.MPFR.Conversion
import Data.Number.MPFR.Integer

import Data.Maybe

import Data.Ratio

#if __GLASGOW_HASKELL__ >= 610
import GHC.Integer.Internals
#endif
import GHC.Exts

instance Num MPFR where
    d + d'        = A.add Zero (maxPrec d d') d d'
    d - d'        = A.sub Zero (maxPrec d d') d d'
    d * d'        = A.mul Zero (maxPrec d d') d d'
    negate d      = A.neg Zero (getPrec d) d
    abs d         = A.absD Zero (getPrec d) d
    signum        = fromInt Zero minPrec . fromMaybe (-1) . sgn
    fromInteger (S# i) = fromInt Zero minPrec (I# i)
    fromInteger i@(J# n _) = fromIntegerA Zero (fromIntegral . abs $ I# n * bitsPerIntegerLimb) i 

instance Real MPFR where
    toRational d = n % 2 ^ e
        where (n', e') = decompose d
              (n, e) = if e' >= 0 then ((n' * 2 ^ e'), 0)
                         else (n', - e')

instance Fractional MPFR where
    d / d'         = A.div Zero (maxPrec d d') d d'
    fromRational r = fromInteger n / fromInteger d
        where n = numerator r
              d = denominator r
    recip d        = one / d

instance Floating MPFR where
    pi           = S.pi Zero 53
    exp d        = S.exp Zero (getPrec d) d
    log d        = S.log Zero (getPrec d) d
    sqrt d       = A.sqrt Zero (getPrec d) d 
    (**) d d'    = A.pow Zero (maxPrec d d') d d'
    logBase d d' = Prelude.log d' / Prelude.log d
    sin d        = S.sin Zero (getPrec d) d
    cos d        = S.cos Zero (getPrec d) d
    tan d        = S.tan Zero (getPrec d) d
    asin d       = S.asin Zero (getPrec d) d
    acos d       = S.acos Zero (getPrec d) d
    atan d       = S.atan Zero (getPrec d) d
    sinh d       = S.sinh Zero (getPrec d) d
    cosh d       = S.cosh Zero (getPrec d) d
    tanh d       = S.tanh Zero (getPrec d) d
    asinh d      = S.asinh Zero (getPrec d) d
    acosh d      = S.acosh Zero (getPrec d) d
    atanh d      = S.atanh Zero (getPrec d) d

instance RealFrac MPFR where
    properFraction d = (fromIntegral n, f)
        where r = toRational d
              m = numerator r
              e = denominator r
              n = quot m e
              f = frac Zero (getPrec d) d