```{-# LANGUAGE MagicHash, CPP #-}

{-|
Module      :  Data.Number.MPFR.Up
Description :  top level
Copyright   :  (c) Aleš Bizjak

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 Up and computed with max precision of two
operands or with the precision of the operand. Otherwise it is equivalent to
Data.Number.MPFR
-}

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

module Data.Number.MPFR.Up (
module Data.Number.MPFR.Base
)
where

import Data.Number.MPFR.Base

import Data.Number.MPFR.Internal

import Data.Maybe

import Data.Ratio

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

instance Num MPFR where
d + d'        = add Up (maxPrec d d') d d'
d - d'        = sub Up (maxPrec d d') d d'
d * d'        = mul Up (maxPrec d d') d d'
negate d      = neg Up (getPrec d) d
abs d         = absD Up (getPrec d) d
signum d      = fromInt Up minPrec (fromMaybe (-1) (sgn d))
fromInteger (S# i) = fromInt Up minPrec (I# i)
fromInteger i@(J# n _) = fromIntegerA Zero (fromIntegral \$ 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'         = 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 Up 53
exp d        = Data.Number.MPFR.Base.exp Up (getPrec d) d
log d        = Data.Number.MPFR.Base.log Up (getPrec d) d
sqrt d       = Data.Number.MPFR.Base.sqrt Up (getPrec d) d
(**) d d'    = Data.Number.MPFR.Base.pow Up (maxPrec d d') d d'
logBase d d' = Prelude.log d' / Prelude.log d
sin d        = Data.Number.MPFR.Base.sin Up (getPrec d) d
cos d        = Data.Number.MPFR.Base.cos Up (getPrec d) d
tan d        = Data.Number.MPFR.Base.tan Up (getPrec d) d
asin d       = Data.Number.MPFR.Base.asin Up (getPrec d) d
acos d       = Data.Number.MPFR.Base.acos Up (getPrec d) d
atan d       = Data.Number.MPFR.Base.atan Up (getPrec d) d
sinh d       = Data.Number.MPFR.Base.sinh Up (getPrec d) d
cosh d       = Data.Number.MPFR.Base.cosh Up (getPrec d) d
tanh d       = Data.Number.MPFR.Base.tanh Up (getPrec d) d
asinh d      = Data.Number.MPFR.Base.asinh Up (getPrec d) d
acosh d      = Data.Number.MPFR.Base.acosh Up (getPrec d) d
atanh d      = Data.Number.MPFR.Base.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
```