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

{-|
Module      :  Data.Number.MPFR.Zero
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 Zero 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.Zero (
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
#endif
import GHC.Exts

instance Num MPFR where
d + d'        = add Zero (maxPrec d d') d d'
d - d'        = sub Zero (maxPrec d d') d d'
d * d'        = mul Zero (maxPrec d d') d d'
negate d      = neg Zero (getPrec d) d
abs d         = 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 \$ 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 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           = Data.Number.MPFR.Base.pi Zero 53
exp d        = Data.Number.MPFR.Base.exp Zero (getPrec d) d
log d        = Data.Number.MPFR.Base.log Zero (getPrec d) d
sqrt d       = Data.Number.MPFR.Base.sqrt Zero (getPrec d) d
(**) d d'    = Data.Number.MPFR.Base.pow Zero (maxPrec d d') d d'
logBase d d' = Prelude.log d' / Prelude.log d
sin d        = Data.Number.MPFR.Base.sin Zero (getPrec d) d
cos d        = Data.Number.MPFR.Base.cos Zero (getPrec d) d
tan d        = Data.Number.MPFR.Base.tan Zero (getPrec d) d
asin d       = Data.Number.MPFR.Base.asin Zero (getPrec d) d
acos d       = Data.Number.MPFR.Base.acos Zero (getPrec d) d
atan d       = Data.Number.MPFR.Base.atan Zero (getPrec d) d
sinh d       = Data.Number.MPFR.Base.sinh Zero (getPrec d) d
cosh d       = Data.Number.MPFR.Base.cosh Zero (getPrec d) d
tanh d       = Data.Number.MPFR.Base.tanh Zero (getPrec d) d
asinh d      = Data.Number.MPFR.Base.asinh Zero (getPrec d) d
acosh d      = Data.Number.MPFR.Base.acosh Zero (getPrec d) d
atanh d      = Data.Number.MPFR.Base.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
```