Copyright	(c) Aleš Bizjak
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell98

Data.Number.MPFR

Contents

Assignment functions
Conversion functions
Basic arithmetic functions
Comparison functions
Special functions
Integer related functions
Miscellaneous functions

Description

This module exports a pure interface to the MPFR library functions. Functions return new MPFR structures instead of modifying existing ones and so all functions which produce a new MPFR structure take one more parameter than their original C counterparts. This parameter, Precision, is the precision of the resulting MPFR.

This is naturally slower than modifying in-place, especially when dealing with lower precisions, so a "mutable" interface is provided in Data.Number.MPFR.Mutable module.

Naming conventions

functions ending with _ (underscore) usually return a pair (MPFR, Int), where Int is a return value of a corresponding mpfr_ function. See the MPFR manual for a description of return values.
the same functions without the _ return just the MPFR.
mpfr_ prefix in functions is removed
_ui and ui_ in function becomes w (stands for Word). For example mpfr_sub_ui becomes subw and mpfr_ui_sub becomes wsub.
si_ and _si in functions becomes i (stands for Int). For example mpfr_sub_si becomes subi and mpfr_si_sub becomes isub.
comparison functions which have _p appended loose it. For example mpfr_less_p becomes less.

Instances

Eq

NaN /= NaN,
Infinity = Infinity,
-Infinity = -Infinity
otherwise normal comparison

Ord

compare NaN _ = GT
compare _ NaN = GT
infinity < _ = False
-infinity > _ = False
NaN [<,>,>=,<=] _ = False

This mimics the behaviour of built in Haskell Float and Double.

If you need instances of numeric typeclasses import one of the Data.Number.MPFR.Instances.* modules.

Synopsis

data RoundMode
- = Near
- | Zero
- | Up
- | Down
data MPFR
data Precision
type Exp = Int64
type MpSize = Int64
module Data.Number.MPFR.Assignment
module Data.Number.MPFR.Conversion
module Data.Number.MPFR.Arithmetic
module Data.Number.MPFR.Comparison
module Data.Number.MPFR.Special
module Data.Number.MPFR.Integer
module Data.Number.MPFR.Misc

Documentation

data RoundMode #

Constructors

Near
Zero
Up
Down

Instances

Enum RoundMode #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods succ :: RoundMode -> RoundMode # pred :: RoundMode -> RoundMode # toEnum :: Int -> RoundMode # fromEnum :: RoundMode -> Int # enumFrom :: RoundMode -> [RoundMode] # enumFromThen :: RoundMode -> RoundMode -> [RoundMode] # enumFromTo :: RoundMode -> RoundMode -> [RoundMode] # enumFromThenTo :: RoundMode -> RoundMode -> RoundMode -> [RoundMode] #
Read RoundMode #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods readsPrec :: Int -> ReadS RoundMode # readList :: ReadS [RoundMode] # readPrec :: ReadPrec RoundMode # readListPrec :: ReadPrec [RoundMode] #
Show RoundMode #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods showsPrec :: Int -> RoundMode -> ShowS # show :: RoundMode -> String # showList :: [RoundMode] -> ShowS #

data MPFR #

Instances

Eq MPFR #
Instance details Defined in Data.Number.MPFR.Comparison Methods (==) :: MPFR -> MPFR -> Bool # (/=) :: MPFR -> MPFR -> Bool #
Floating MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods pi :: MPFR # exp :: MPFR -> MPFR # log :: MPFR -> MPFR # sqrt :: MPFR -> MPFR # (**) :: MPFR -> MPFR -> MPFR # logBase :: MPFR -> MPFR -> MPFR # sin :: MPFR -> MPFR # cos :: MPFR -> MPFR # tan :: MPFR -> MPFR # asin :: MPFR -> MPFR # acos :: MPFR -> MPFR # atan :: MPFR -> MPFR # sinh :: MPFR -> MPFR # cosh :: MPFR -> MPFR # tanh :: MPFR -> MPFR # asinh :: MPFR -> MPFR # acosh :: MPFR -> MPFR # atanh :: MPFR -> MPFR # log1p :: MPFR -> MPFR # expm1 :: MPFR -> MPFR # log1pexp :: MPFR -> MPFR # log1mexp :: MPFR -> MPFR #
Floating MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods pi :: MPFR # exp :: MPFR -> MPFR # log :: MPFR -> MPFR # sqrt :: MPFR -> MPFR # (**) :: MPFR -> MPFR -> MPFR # logBase :: MPFR -> MPFR -> MPFR # sin :: MPFR -> MPFR # cos :: MPFR -> MPFR # tan :: MPFR -> MPFR # asin :: MPFR -> MPFR # acos :: MPFR -> MPFR # atan :: MPFR -> MPFR # sinh :: MPFR -> MPFR # cosh :: MPFR -> MPFR # tanh :: MPFR -> MPFR # asinh :: MPFR -> MPFR # acosh :: MPFR -> MPFR # atanh :: MPFR -> MPFR # log1p :: MPFR -> MPFR # expm1 :: MPFR -> MPFR # log1pexp :: MPFR -> MPFR # log1mexp :: MPFR -> MPFR #
Floating MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods pi :: MPFR # exp :: MPFR -> MPFR # log :: MPFR -> MPFR # sqrt :: MPFR -> MPFR # (**) :: MPFR -> MPFR -> MPFR # logBase :: MPFR -> MPFR -> MPFR # sin :: MPFR -> MPFR # cos :: MPFR -> MPFR # tan :: MPFR -> MPFR # asin :: MPFR -> MPFR # acos :: MPFR -> MPFR # atan :: MPFR -> MPFR # sinh :: MPFR -> MPFR # cosh :: MPFR -> MPFR # tanh :: MPFR -> MPFR # asinh :: MPFR -> MPFR # acosh :: MPFR -> MPFR # atanh :: MPFR -> MPFR # log1p :: MPFR -> MPFR # expm1 :: MPFR -> MPFR # log1pexp :: MPFR -> MPFR # log1mexp :: MPFR -> MPFR #
Floating MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods pi :: MPFR # exp :: MPFR -> MPFR # log :: MPFR -> MPFR # sqrt :: MPFR -> MPFR # (**) :: MPFR -> MPFR -> MPFR # logBase :: MPFR -> MPFR -> MPFR # sin :: MPFR -> MPFR # cos :: MPFR -> MPFR # tan :: MPFR -> MPFR # asin :: MPFR -> MPFR # acos :: MPFR -> MPFR # atan :: MPFR -> MPFR # sinh :: MPFR -> MPFR # cosh :: MPFR -> MPFR # tanh :: MPFR -> MPFR # asinh :: MPFR -> MPFR # acosh :: MPFR -> MPFR # atanh :: MPFR -> MPFR # log1p :: MPFR -> MPFR # expm1 :: MPFR -> MPFR # log1pexp :: MPFR -> MPFR # log1mexp :: MPFR -> MPFR #
Fractional MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods (/) :: MPFR -> MPFR -> MPFR # recip :: MPFR -> MPFR # fromRational :: Rational -> MPFR #
Fractional MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods (/) :: MPFR -> MPFR -> MPFR # recip :: MPFR -> MPFR # fromRational :: Rational -> MPFR #
Fractional MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods (/) :: MPFR -> MPFR -> MPFR # recip :: MPFR -> MPFR # fromRational :: Rational -> MPFR #
Fractional MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods (/) :: MPFR -> MPFR -> MPFR # recip :: MPFR -> MPFR # fromRational :: Rational -> MPFR #
Num MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods (+) :: MPFR -> MPFR -> MPFR # (-) :: MPFR -> MPFR -> MPFR # (*) :: MPFR -> MPFR -> MPFR # negate :: MPFR -> MPFR # abs :: MPFR -> MPFR # signum :: MPFR -> MPFR # fromInteger :: Integer -> MPFR #
Num MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods (+) :: MPFR -> MPFR -> MPFR # (-) :: MPFR -> MPFR -> MPFR # (*) :: MPFR -> MPFR -> MPFR # negate :: MPFR -> MPFR # abs :: MPFR -> MPFR # signum :: MPFR -> MPFR # fromInteger :: Integer -> MPFR #
Num MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods (+) :: MPFR -> MPFR -> MPFR # (-) :: MPFR -> MPFR -> MPFR # (*) :: MPFR -> MPFR -> MPFR # negate :: MPFR -> MPFR # abs :: MPFR -> MPFR # signum :: MPFR -> MPFR # fromInteger :: Integer -> MPFR #
Num MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods (+) :: MPFR -> MPFR -> MPFR # (-) :: MPFR -> MPFR -> MPFR # (*) :: MPFR -> MPFR -> MPFR # negate :: MPFR -> MPFR # abs :: MPFR -> MPFR # signum :: MPFR -> MPFR # fromInteger :: Integer -> MPFR #
Ord MPFR #
Instance details Defined in Data.Number.MPFR.Comparison Methods compare :: MPFR -> MPFR -> Ordering # (<) :: MPFR -> MPFR -> Bool # (<=) :: MPFR -> MPFR -> Bool # (>) :: MPFR -> MPFR -> Bool # (>=) :: MPFR -> MPFR -> Bool # max :: MPFR -> MPFR -> MPFR # min :: MPFR -> MPFR -> MPFR #
Real MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods toRational :: MPFR -> Rational #
Real MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods toRational :: MPFR -> Rational #
Real MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods toRational :: MPFR -> Rational #
Real MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods toRational :: MPFR -> Rational #
RealFloat MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods floatRadix :: MPFR -> Integer # floatDigits :: MPFR -> Int # floatRange :: MPFR -> (Int, Int) # decodeFloat :: MPFR -> (Integer, Int) # encodeFloat :: Integer -> Int -> MPFR # exponent :: MPFR -> Int # significand :: MPFR -> MPFR # scaleFloat :: Int -> MPFR -> MPFR # isNaN :: MPFR -> Bool # isInfinite :: MPFR -> Bool # isDenormalized :: MPFR -> Bool # isNegativeZero :: MPFR -> Bool # isIEEE :: MPFR -> Bool # atan2 :: MPFR -> MPFR -> MPFR #
RealFloat MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods floatRadix :: MPFR -> Integer # floatDigits :: MPFR -> Int # floatRange :: MPFR -> (Int, Int) # decodeFloat :: MPFR -> (Integer, Int) # encodeFloat :: Integer -> Int -> MPFR # exponent :: MPFR -> Int # significand :: MPFR -> MPFR # scaleFloat :: Int -> MPFR -> MPFR # isNaN :: MPFR -> Bool # isInfinite :: MPFR -> Bool # isDenormalized :: MPFR -> Bool # isNegativeZero :: MPFR -> Bool # isIEEE :: MPFR -> Bool # atan2 :: MPFR -> MPFR -> MPFR #
RealFloat MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods floatRadix :: MPFR -> Integer # floatDigits :: MPFR -> Int # floatRange :: MPFR -> (Int, Int) # decodeFloat :: MPFR -> (Integer, Int) # encodeFloat :: Integer -> Int -> MPFR # exponent :: MPFR -> Int # significand :: MPFR -> MPFR # scaleFloat :: Int -> MPFR -> MPFR # isNaN :: MPFR -> Bool # isInfinite :: MPFR -> Bool # isDenormalized :: MPFR -> Bool # isNegativeZero :: MPFR -> Bool # isIEEE :: MPFR -> Bool # atan2 :: MPFR -> MPFR -> MPFR #
RealFloat MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods floatRadix :: MPFR -> Integer # floatDigits :: MPFR -> Int # floatRange :: MPFR -> (Int, Int) # decodeFloat :: MPFR -> (Integer, Int) # encodeFloat :: Integer -> Int -> MPFR # exponent :: MPFR -> Int # significand :: MPFR -> MPFR # scaleFloat :: Int -> MPFR -> MPFR # isNaN :: MPFR -> Bool # isInfinite :: MPFR -> Bool # isDenormalized :: MPFR -> Bool # isNegativeZero :: MPFR -> Bool # isIEEE :: MPFR -> Bool # atan2 :: MPFR -> MPFR -> MPFR #
RealFrac MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Zero Methods properFraction :: Integral b => MPFR -> (b, MPFR) # truncate :: Integral b => MPFR -> b # round :: Integral b => MPFR -> b # ceiling :: Integral b => MPFR -> b # floor :: Integral b => MPFR -> b #
RealFrac MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Up Methods properFraction :: Integral b => MPFR -> (b, MPFR) # truncate :: Integral b => MPFR -> b # round :: Integral b => MPFR -> b # ceiling :: Integral b => MPFR -> b # floor :: Integral b => MPFR -> b #
RealFrac MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Near Methods properFraction :: Integral b => MPFR -> (b, MPFR) # truncate :: Integral b => MPFR -> b # round :: Integral b => MPFR -> b # ceiling :: Integral b => MPFR -> b # floor :: Integral b => MPFR -> b #
RealFrac MPFR #
Instance details Defined in Data.Number.MPFR.Instances.Down Methods properFraction :: Integral b => MPFR -> (b, MPFR) # truncate :: Integral b => MPFR -> b # round :: Integral b => MPFR -> b # ceiling :: Integral b => MPFR -> b # floor :: Integral b => MPFR -> b #
Show MPFR #
Instance details Defined in Data.Number.MPFR.Conversion Methods showsPrec :: Int -> MPFR -> ShowS # show :: MPFR -> String # showList :: [MPFR] -> ShowS #
Generic MPFR #
Instance details Defined in Data.Number.MPFR.FFIhelper Associated Types type Rep MPFR :: * -> * # Methods from :: MPFR -> Rep MPFR x # to :: Rep MPFR x -> MPFR #
Storable MPFR #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods sizeOf :: MPFR -> Int # alignment :: MPFR -> Int # peekElemOff :: Ptr MPFR -> Int -> IO MPFR # pokeElemOff :: Ptr MPFR -> Int -> MPFR -> IO () # peekByteOff :: Ptr b -> Int -> IO MPFR # pokeByteOff :: Ptr b -> Int -> MPFR -> IO () # peek :: Ptr MPFR -> IO MPFR # poke :: Ptr MPFR -> MPFR -> IO () #
type Rep MPFR #
Instance details Defined in Data.Number.MPFR.FFIhelper type Rep MPFR = D1 (MetaData "MPFR" "Data.Number.MPFR.FFIhelper" "hmpfr-0.4.4-KfmVnLltHtMIge4kApZiX2" False) (C1 (MetaCons "MP" PrefixI True) ((S1 (MetaSel (Just "precision") SourceUnpack SourceStrict DecidedStrict) (Rec0 CPrecision) :: S1 (MetaSel (Just "sign") SourceUnpack SourceStrict DecidedStrict) (Rec0 Sign)) :: (S1 (MetaSel (Just "exponent") SourceUnpack SourceStrict DecidedStrict) (Rec0 Exp) :*: S1 (MetaSel (Just "limbs") SourceUnpack SourceStrict DecidedStrict) (Rec0 (ForeignPtr Limb)))))

data Precision #

Instances

Enum Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods succ :: Precision -> Precision # pred :: Precision -> Precision # toEnum :: Int -> Precision # fromEnum :: Precision -> Int # enumFrom :: Precision -> [Precision] # enumFromThen :: Precision -> Precision -> [Precision] # enumFromTo :: Precision -> Precision -> [Precision] # enumFromThenTo :: Precision -> Precision -> Precision -> [Precision] #
Eq Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods (==) :: Precision -> Precision -> Bool # (/=) :: Precision -> Precision -> Bool #
Integral Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods quot :: Precision -> Precision -> Precision # rem :: Precision -> Precision -> Precision # div :: Precision -> Precision -> Precision # mod :: Precision -> Precision -> Precision # quotRem :: Precision -> Precision -> (Precision, Precision) # divMod :: Precision -> Precision -> (Precision, Precision) # toInteger :: Precision -> Integer #
Num Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods (+) :: Precision -> Precision -> Precision # (-) :: Precision -> Precision -> Precision # (*) :: Precision -> Precision -> Precision # negate :: Precision -> Precision # abs :: Precision -> Precision # signum :: Precision -> Precision # fromInteger :: Integer -> Precision #
Ord Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods compare :: Precision -> Precision -> Ordering # (<) :: Precision -> Precision -> Bool # (<=) :: Precision -> Precision -> Bool # (>) :: Precision -> Precision -> Bool # (>=) :: Precision -> Precision -> Bool # max :: Precision -> Precision -> Precision # min :: Precision -> Precision -> Precision #
Real Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods toRational :: Precision -> Rational #
Show Precision #
Instance details Defined in Data.Number.MPFR.FFIhelper Methods showsPrec :: Int -> Precision -> ShowS # show :: Precision -> String # showList :: [Precision] -> ShowS #

type Exp = Int64 #

type MpSize = Int64 #

Assignment functions

See http://www.mpfr.org/mpfr-current/mpfr.html#Assignment-Functions documentation on particular functions.

module Data.Number.MPFR.Assignment

Conversion functions

See http://www.mpfr.org/mpfr-current/mpfr.html#Conversion-Functions documentation on particular functions.

module Data.Number.MPFR.Conversion

Basic arithmetic functions

For documentation on particular functions see http://www.mpfr.org/mpfr-current/mpfr.html#Basic-Arithmetic-Functions.

module Data.Number.MPFR.Arithmetic

Comparison functions

For documentation on particular functions see http://www.mpfr.org/mpfr-current/mpfr.html#Comparison-Functions

module Data.Number.MPFR.Comparison

Special functions

For documentation on particular functions see http://www.mpfr.org/mpfr-current/mpfr.html#Special-Functions.

module Data.Number.MPFR.Special

Integer related functions

For documentation on particular functions see http://www.mpfr.org/mpfr-chttp://www.mpfr.org/mpfr-current/mpfr.html#Integer-Related-Functions

module Data.Number.MPFR.Integer

Miscellaneous functions

For documentation on particular functions see http://www.mpfr.org/mpfr-current/mpfr.html#Miscellaneous-Functions.

module Data.Number.MPFR.Misc