module Data.Number.MPFR.Near (
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 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 = fromInt Near minPrec . fromMaybe (1) . sgn
fromInteger (S# i) = fromInt Near 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 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