Module      :  Data.Number.MPFR.Near
    Description :  top level
    Copyright   :  (c) AleŇ° 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 Near and computed with max precision of two 
 operands or with the precision of the operand. Otherwise it is equivalent to 

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

module Data.Number.MPFR.Near (
       module Data.Number.MPFR.Base

import Data.Number.MPFR.Base

import Data.Number.MPFR.Internal

import Data.Maybe

import Data.Ratio

instance Num MPFR where
    d + d'        = add Near (maxPrec d d') d d'
    d - d'        = sub Near (maxPrec d d') d d'
    d * d'        = mul Near (maxPrec d d') d d'
    negate d      = neg Near (getPrec d) d
    abs d         = absD Near (getPrec d) d
    signum d      = fromInt Near minPrec (fromMaybe (-1) (sgn d))
    fromInteger i = fromIntegerA Zero (checkPrec $ binprec i) i
                    -- TODO works only partially

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'         = Data.Number.MPFR.Base.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           = Data.Number.MPFR.Base.pi Near 53
    exp d        = Data.Number.MPFR.Base.exp Near (getPrec d) d
    log d        = Data.Number.MPFR.Base.log Near (getPrec d) d
    sqrt d       = Data.Number.MPFR.Base.sqrt Near (getPrec d) d 
    (**) d d'    = Data.Number.MPFR.Base.pow Near (maxPrec d d') d d'
    logBase d d' = Prelude.log d' / Prelude.log d
    sin d        = Data.Number.MPFR.Base.sin Near (getPrec d) d
    cos d        = Data.Number.MPFR.Base.cos Near (getPrec d) d
    tan d        = Data.Number.MPFR.Base.tan Near (getPrec d) d
    asin d       = Data.Number.MPFR.Base.asin Near (getPrec d) d
    acos d       = Data.Number.MPFR.Base.acos Near (getPrec d) d
    atan d       = Data.Number.MPFR.Base.atan Near (getPrec d) d
    sinh d       = Data.Number.MPFR.Base.sinh Near (getPrec d) d
    cosh d       = Data.Number.MPFR.Base.cosh Near (getPrec d) d
    tanh d       = Data.Number.MPFR.Base.tanh Near (getPrec d) d
    asinh d      = Data.Number.MPFR.Base.asinh Near (getPrec d) d
    acosh d      = Data.Number.MPFR.Base.acosh Near (getPrec d) d
    atanh d      = Data.Number.MPFR.Base.atanh Near (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 Near (getPrec d) d