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

{-|
Module      :  Data.Number.MPFR.Down
Description :  top level

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

import Data.Number.MPFR.Base

import Data.Number.MPFR.Internal

import Data.Maybe

import Data.Ratio

import GHC.Integer.Internals
import GHC.Exts hiding (Down)
#else
import GHC.Exts
#endif

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