Up.hs

{-# LANGUAGE MagicHash, CPP #-}

{-|
    Module      :  Data.Number.MPFR.Instances.Up
    Description :  Instance declarations
    Copyright   :  (c) Aleš Bizjak
    License     :  BSD3

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

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

module Data.Number.MPFR.Instances.Up ()
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

-- #ifdef INTEGER_SIMPLE
-- --import GHC.Integer.Simple.Internals
-- #endif
-- #ifdef INTEGER_GMP
-- import GHC.Integer.GMP.Internals
-- import qualified GHC.Exts as E
-- #endif


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

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

instance RealFloat MPFR where
    floatRadix _ = 2
    floatDigits = fromInteger . toInteger . getPrec
    floatRange _ = error "floatRange is not defined for MPFR numbers"
    decodeFloat x = (d,e)
      where
      (d,eE) = decompose x
      e = fromInteger (toInteger eE)
    encodeFloat d e =
      (fromInteger d) / ((fromInteger 2)^e) -- TODO: construct it directly
    isNaN (MP _ _ e _) = (e == expNaN)
    isInfinite (MP _ _ e _) = (e == expInf)
    isDenormalized _ = False
    isNegativeZero d@(MP _ _ e _) = (e == expZero && signbit d)
    isIEEE _ = False
    atan2 d1 d2 = S.atan2 Near (maxPrec d1 d2) d1 d2