{-# LANGUAGE MagicHash, CPP #-} {-| Module : Data.Number.MPFR.Instances.Down 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' 'Down' and computed with maximum precision of two operands or with the precision of the operand. -} module Data.Number.MPFR.Instances.Down () 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 Down (maxPrec d d') d d' d - d' = A.sub Down (maxPrec d d') d d' d * d' = A.mul Down (maxPrec d d') d d' negate d = A.neg Down (getPrec d) d abs d = A.absD Down (getPrec d) d signum = fromInt Down minPrec . fromMaybe (-1) .sgn fromInteger i = fromIntegerA Down (max minPrec $ 1 + bitsInInteger i) i -- #ifdef INTEGER_SIMPLE -- fromInteger i = -- fromIntegerA Down (max minPrec $ 1 + bitsInInteger i) i -- #endif -- #ifdef INTEGER_GMP -- fromInteger (S# i) = fromInt Down 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 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 = S.pi Down 53 exp d = S.exp Down (getPrec d) d log d = S.log Down (getPrec d) d sqrt d = A.sqrt Down (getPrec d) d (**) d d' = A.pow Down (maxPrec d d') d d' logBase d d' = Prelude.log d' / Prelude.log d sin d = S.sin Down (getPrec d) d cos d = S.cos Down (getPrec d) d tan d = S.tan Down (getPrec d) d asin d = S.asin Down (getPrec d) d acos d = S.acos Down (getPrec d) d atan d = S.atan Down (getPrec d) d sinh d = S.sinh Down (getPrec d) d cosh d = S.cosh Down (getPrec d) d tanh d = S.tanh Down (getPrec d) d asinh d = S.asinh Down (getPrec d) d acosh d = S.acosh Down (getPrec d) d atanh d = S.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 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