Data.Number.MPFR

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.

Documentation

data RoundMode

Constructors

Near

Zero

Up

Down

Instances

Enum RoundMode

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

Methods

readsPrec :: Int -> ReadS RoundMode

readList :: ReadS [RoundMode]

readPrec :: ReadPrec RoundMode

readListPrec :: ReadPrec [RoundMode]

Show RoundMode

Methods

showsPrec :: Int -> RoundMode -> ShowS

show :: RoundMode -> String

showList :: [RoundMode] -> ShowS

data MPFR

Instances

Generic MPFR

Associated Types

type Rep MPFR :: * -> *

Methods

from :: MPFR -> Rep MPFR x

to :: Rep MPFR x -> MPFR

Storable MPFR

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

type Rep MPFR = D1 * (MetaData "MPFR" "Data.Number.MPFR.FFIhelper" "hmpfr-0.4.4-CVSKNSw033MEWP1hktuXpF" False) (C1 * (MetaCons "MP" PrefixI True) ((:*:) * ((:*:) * (S1 * (MetaSel (Just Symbol "precision") SourceUnpack SourceStrict DecidedStrict) (Rec0 * CPrecision)) (S1 * (MetaSel (Just Symbol "sign") SourceUnpack SourceStrict DecidedStrict) (Rec0 * Sign))) ((:*:) * (S1 * (MetaSel (Just Symbol "exponent") SourceUnpack SourceStrict DecidedStrict) (Rec0 * Exp)) (S1 * (MetaSel (Just Symbol "limbs") SourceUnpack SourceStrict DecidedStrict) (Rec0 * (ForeignPtr Limb))))))

data Precision

Instances

Enum Precision

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

Methods

(==) :: Precision -> Precision -> Bool

(/=) :: Precision -> Precision -> Bool

Integral Precision

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

Methods

(+) :: Precision -> Precision -> Precision

(-) :: Precision -> Precision -> Precision

(*) :: Precision -> Precision -> Precision

negate :: Precision -> Precision

abs :: Precision -> Precision

signum :: Precision -> Precision

fromInteger :: Integer -> Precision

Ord Precision

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

Methods

toRational :: Precision -> Rational

Show Precision

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