Data.Number.MPFR

Documentation

This module should always be imported qualified.

Naming

• functions ending with _ return a pair (value, rounding indicator). Rounding indicator indicates whether the result is rounded and in which directon as described in the MPFR manual.
• the same functions without the _ return just the value.
• functions with added "w" correspond to MPFR _ui functions
• functions with added "i" correspond to MPFR _si functions

Equality testing

Equality works as follows:

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

Ordering

Ordering works as follows:

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

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

Num instance

Operations defined in Num will be computed so that no precision is lost.

type Dyadic = MPFR_T

type Precision = Word

data RoundMode

Constructors

Near

Zero

Up

Down

Instances

Enum RoundMode

add :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

sub :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

mul :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

div :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

inverse :: Dyadic -> Dyadic

add_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

sub_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

mul_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

div_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

addw :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

addi :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

mulw :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

muli :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

divw :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

divi :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

wdiv :: RoundMode -> Precision -> Word -> Dyadic -> Dyadic

idiv :: RoundMode -> Precision -> Int -> Dyadic -> Dyadic

subw :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

subi :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

wsub :: RoundMode -> Precision -> Word -> Dyadic -> Dyadic

isub :: RoundMode -> Precision -> Int -> Dyadic -> Dyadic

addw_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

addi_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

mulw_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

muli_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

divw_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

divi_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

wdiv_ :: RoundMode -> Precision -> Word -> Dyadic -> (Dyadic, Int)

idiv_ :: RoundMode -> Precision -> Int -> Dyadic -> (Dyadic, Int)

subw_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

subi_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

wsub_ :: RoundMode -> Precision -> Word -> Dyadic -> (Dyadic, Int)

isub_ :: RoundMode -> Precision -> Int -> Dyadic -> (Dyadic, Int)

mul2w :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

mul2i :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

div2w :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

div2i :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

mul2w_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

mul2i_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

div2w_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

div2i_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

int2i :: RoundMode -> Precision -> Int -> Int -> Dyadic

int2w :: RoundMode -> Precision -> Word -> Int -> Dyadic

int2i_ :: RoundMode -> Precision -> Int -> Int -> (Dyadic, Int)

int2w_ :: RoundMode -> Precision -> Word -> Int -> (Dyadic, Int)

fma :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic -> Dyadic

fms :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic -> Dyadic

fma_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic -> (Dyadic, Int)

fms_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic -> (Dyadic, Int)

nextBelow :: Dyadic -> Dyadic

sqr :: RoundMode -> Precision -> Dyadic -> Dyadic

sqrt :: RoundMode -> Precision -> Dyadic -> Dyadic

root :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

pow :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

poww :: RoundMode -> Precision -> Dyadic -> Word -> Dyadic

powi :: RoundMode -> Precision -> Dyadic -> Int -> Dyadic

wpoww :: RoundMode -> Precision -> Word -> Word -> Dyadic

wpow :: RoundMode -> Precision -> Word -> Dyadic -> Dyadic

sqr_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

sqrt_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

root_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

pow_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

poww_ :: RoundMode -> Precision -> Dyadic -> Word -> (Dyadic, Int)

powi_ :: RoundMode -> Precision -> Dyadic -> Int -> (Dyadic, Int)

wpoww_ :: RoundMode -> Precision -> Word -> Word -> (Dyadic, Int)

wpow_ :: RoundMode -> Precision -> Word -> Dyadic -> (Dyadic, Int)

exp :: RoundMode -> Precision -> Dyadic -> Dyadic

exp2 :: RoundMode -> Precision -> Dyadic -> Dyadic

exp10 :: RoundMode -> Precision -> Dyadic -> Dyadic

log :: RoundMode -> Precision -> Dyadic -> Dyadic

log2 :: RoundMode -> Precision -> Dyadic -> Dyadic

log10 :: RoundMode -> Precision -> Dyadic -> Dyadic

sinh :: RoundMode -> Precision -> Dyadic -> Dyadic

cosh :: RoundMode -> Precision -> Dyadic -> Dyadic

tanh :: RoundMode -> Precision -> Dyadic -> Dyadic

exp_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

exp2_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

exp10_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

log_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

log2_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

log10_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

sinh_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

cosh_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

tanh_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

neg :: RoundMode -> Precision -> Dyadic -> Dyadic

absD :: RoundMode -> Precision -> Dyadic -> Dyadic

dim :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

neg_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

absD_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

dim_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

isNaN :: Dyadic -> Bool

isInfinite :: Dyadic -> Bool

isNumber :: Dyadic -> Bool

isZero :: Dyadic -> Bool

greater :: Dyadic -> Dyadic -> Bool

greatereq :: Dyadic -> Dyadic -> Bool

less :: Dyadic -> Dyadic -> Bool

lesseq :: Dyadic -> Dyadic -> Bool

equal :: Dyadic -> Dyadic -> Bool

maxD :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

minD :: RoundMode -> Precision -> Dyadic -> Dyadic -> Dyadic

maxD_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

minD_ :: RoundMode -> Precision -> Dyadic -> Dyadic -> (Dyadic, Int)

sgn :: Dyadic -> Int

dyadicToDouble :: RoundMode -> Dyadic -> Double

dyadicToWord :: RoundMode -> Dyadic -> Word

dyadicToInt :: RoundMode -> Dyadic -> Int

dyadicToString

Arguments

:: RoundMode

-> Word

number of significant digits

-> Word

base

-> Dyadic

-> (String, Int)

decompose :: Dyadic -> (Integer, Int)

toStringExp :: Word -> Dyadic -> String

toString :: Word -> Dyadic -> String

pi :: RoundMode -> Precision -> Dyadic

log2c :: RoundMode -> Precision -> Dyadic

euler :: RoundMode -> Precision -> Dyadic

catalan :: RoundMode -> Precision -> Dyadic

pi_ :: RoundMode -> Precision -> (Dyadic, Int)

log2c_ :: RoundMode -> Precision -> (Dyadic, Int)

euler_ :: RoundMode -> Precision -> (Dyadic, Int)

catalan_ :: RoundMode -> Precision -> (Dyadic, Int)

set :: RoundMode -> Precision -> Dyadic -> Dyadic

set_ :: RoundMode -> Precision -> Dyadic -> (Dyadic, Int)

fromDouble :: RoundMode -> Precision -> Double -> Dyadic

fromInt :: RoundMode -> Precision -> Int -> Dyadic

fromWord :: RoundMode -> Precision -> Word -> Dyadic

fromDouble_ :: RoundMode -> Precision -> Double -> (Dyadic, Int)

fromInt_ :: RoundMode -> Precision -> Int -> (Dyadic, Int)

fromWord_ :: RoundMode -> Precision -> Word -> (Dyadic, Int)

fromIntegerA :: RoundMode -> Precision -> Integer -> Dyadic

compose :: RoundMode -> Precision -> (Integer, Int) -> Dyadic

fromString :: String -> Precision -> Word -> Dyadic

getPrec :: Dyadic -> Precision

getMantissa :: Dyadic -> Integer

getMantissa and getExp return values such that

 d = getMantissa d * 2^(getExp d - ceiling ((getPrec d) / bitsPerMPLimb)* bitsPerMPLimb )

getExp :: Dyadic -> Int

minPrec :: Precision

one :: Dyadic

zero :: Dyadic

addPrec :: Dyadic -> Dyadic -> Precision