Safe Haskell	None
Language	Haskell2010

Data.CDAR.Dyadic

Description

The Dyadic module provides dyadic numbers. Syntax for dyadic number 'a * 2 ^ s' is 'a :^ s'. The exponent s is an Int, but the a is an arbitrary Integer.

Synopsis

data Dyadic = Integer :^ Int
shiftD :: Int -> Dyadic -> Dyadic
sqrtD :: Int -> Dyadic -> Dyadic
sqrtD' :: Int -> Dyadic -> Dyadic -> Dyadic
sqrtRecD :: Int -> Dyadic -> Dyadic
sqrtRecD' :: Int -> Dyadic -> Dyadic -> Dyadic
initSqrtRecD :: Dyadic -> Dyadic
initSqrtRecDoubleD :: Dyadic -> Dyadic
piMachinD :: Int -> Dyadic
piBorweinD :: Int -> Dyadic
ln2D :: Int -> Dyadic
logD :: Int -> Dyadic -> Dyadic
atanhD :: Int -> Dyadic -> Dyadic
divD :: Dyadic -> Dyadic -> Dyadic
divD' :: Int -> Dyadic -> Dyadic -> Dyadic

Documentation

data Dyadic Source #

The Dyadic data type.

Constructors

Integer :^ Int infix 8

Instances

Instances details

Eq Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods (==) :: Dyadic -> Dyadic -> Bool # (/=) :: Dyadic -> Dyadic -> Bool #
Num Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods (+) :: Dyadic -> Dyadic -> Dyadic # (-) :: Dyadic -> Dyadic -> Dyadic # (*) :: Dyadic -> Dyadic -> Dyadic # negate :: Dyadic -> Dyadic # abs :: Dyadic -> Dyadic # signum :: Dyadic -> Dyadic # fromInteger :: Integer -> Dyadic #
Ord Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods compare :: Dyadic -> Dyadic -> Ordering # (<) :: Dyadic -> Dyadic -> Bool # (<=) :: Dyadic -> Dyadic -> Bool # (>) :: Dyadic -> Dyadic -> Bool # (>=) :: Dyadic -> Dyadic -> Bool # max :: Dyadic -> Dyadic -> Dyadic # min :: Dyadic -> Dyadic -> Dyadic #
Read Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods readsPrec :: Int -> ReadS Dyadic # readList :: ReadS [Dyadic] # readPrec :: ReadPrec Dyadic # readListPrec :: ReadPrec [Dyadic] #
Real Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods toRational :: Dyadic -> Rational #
Show Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods showsPrec :: Int -> Dyadic -> ShowS # show :: Dyadic -> String # showList :: [Dyadic] -> ShowS #
Scalable Dyadic Source #
Instance details Defined in Data.CDAR.Dyadic Methods scale :: Dyadic -> Int -> Dyadic Source #

shiftD :: Int -> Dyadic -> Dyadic Source #

Shift a dyadic number to a given base and round in case of right shifts.

sqrtD :: Int -> Dyadic -> Dyadic Source #

Computes the square root of a Dyadic number to the specified base. The Newton-Raphson method may overestimates the square root, but the overestimate is bounded by 1 ulp. For example, sqrtD 0 2 will give 2, whereas the closest integer to the square root is 1. Need double precision to guarantee correct rounding, which was not considered worthwhile.

This is actually Heron's method and is no longer used in Approx as it is faster to use sqrtRecD.

sqrtD' :: Int -> Dyadic -> Dyadic -> Dyadic Source #

Square root with initial approximation as third argument.

sqrtRecD :: Int -> Dyadic -> Dyadic Source #

Reciprocal of square root using Newton's iteration.

sqrtRecD' :: Int -> Dyadic -> Dyadic -> Dyadic Source #

Reciprocal of square root using Newton's iteration with inital value as third argument.

initSqrtRecD :: Dyadic -> Dyadic Source #

Gives initial values for the iteration. Based on the three most significant bits of the argument. Should consider to use machine floating point to give initial value.

initSqrtRecDoubleD :: Dyadic -> Dyadic Source #

piMachinD :: Int -> Dyadic Source #

Compute dyadic values close to pi by Machin's formula.

piBorweinD :: Int -> Dyadic Source #

Compute dyadic values close to pi by Borwein's formula.

ln2D :: Int -> Dyadic Source #

Compute dyadic values close to ln 2.

logD :: Int -> Dyadic -> Dyadic Source #

atanhD :: Int -> Dyadic -> Dyadic Source #

divD :: Dyadic -> Dyadic -> Dyadic Source #

divD' :: Int -> Dyadic -> Dyadic -> Dyadic Source #