Safe Haskell | None |
---|---|
Language | Haskell2010 |
This module exports a bunch of utilities for working inside the CReal datatype. One should be careful to maintain the CReal invariant when using these functions
- newtype CReal n = CR (Int -> Integer)
- atPrecision :: CReal n -> Int -> Integer
- crealPrecision :: KnownNat n => CReal n -> Int
- expBounded :: CReal n -> CReal n
- logBounded :: CReal n -> CReal n
- atanBounded :: CReal n -> CReal n
- sinBounded :: CReal n -> CReal n
- cosBounded :: CReal n -> CReal n
- shiftL :: CReal n -> Int -> CReal n
- shiftR :: CReal n -> Int -> CReal n
- powerSeries :: [Rational] -> (Int -> Int) -> CReal n -> CReal n
- alternateSign :: Num a => [a] -> [a]
- (/.) :: Integer -> Integer -> Integer
- log2 :: Integer -> Int
- log10 :: Integer -> Int
- isqrt :: Integer -> Integer
- showAtPrecision :: Int -> CReal n -> String
- decimalDigitsAtPrecision :: Int -> Int
- rationalToDecimal :: Int -> Rational -> String
Documentation
The type CReal represents a fast binary Cauchy sequence. This is a Cauchy sequence with the invariant that the pth element will be within 2^-p of the true value. Internally this sequence is represented as a function from Ints to Integers.
KnownNat n => Eq (CReal n) Source | Values of type
|
Floating (CReal n) Source | |
Fractional (CReal n) Source | Taking the reciprocal of zero will not terminate |
Num (CReal n) Source |
This is a little bit of a fudge, but it's probably better than failing to terminate when trying to find the sign of zero. The class still respects the abs-signum law though.
|
KnownNat n => Ord (CReal n) Source | Like equality values of type |
KnownNat n => Read (CReal n) Source | |
KnownNat n => Real (CReal n) Source |
|
KnownNat n => RealFloat (CReal n) Source | Several of the functions in this class (
|
KnownNat n => RealFrac (CReal n) Source | |
KnownNat n => Show (CReal n) Source | A CReal with precision p is shown as a decimal number d such that d is within 2^-p of the true value.
|
atPrecision :: CReal n -> Int -> Integer Source
x `atPrecision` p
returns the numerator of the pth element in the
Cauchy sequence represented by x. The denominator is 2^p.
>>>
10 `atPrecision` 10
10240
crealPrecision :: KnownNat n => CReal n -> Int Source
crealPrecision x returns the type level parameter representing x's default precision.
>>>
crealPrecision (1 :: CReal 10)
10
expBounded :: CReal n -> CReal n Source
The input to expBounded must be in the range (-1..1)
logBounded :: CReal n -> CReal n Source
The input must be in [1..2]
atanBounded :: CReal n -> CReal n Source
The input to atanBounded must be in [-1..1]
sinBounded :: CReal n -> CReal n Source
The input to sinBounded must be in (-1..1)
cosBounded :: CReal n -> CReal n Source
The input to cosBounded must be in (-1..1)
shiftL :: CReal n -> Int -> CReal n Source
x `shiftL` n
is equal to x
multiplied by 2^n
n
can be negative or zero
This can be faster than doing the multiplication
shiftR :: CReal n -> Int -> CReal n Source
x `shiftR` n
is equal to x
divided by 2^n
n
can be negative or zero
This can be faster than doing the division
powerSeries :: [Rational] -> (Int -> Int) -> CReal n -> CReal n Source
powerSeries q f x
will evaluate the power series with
coefficients atPrecision
pq
at precision f p
at x
f
should be a function such that the CReal invariant is maintained
See any of the trig functions for an example
alternateSign :: Num a => [a] -> [a] Source
Apply negate
to every other element, starting with the second
>>>
alternateSign [1..5]
[1,-2,3,-4,5]
(/.) :: Integer -> Integer -> Integer infixl 7 Source
Division rounding to the nearest integer and rounding half integers to the nearest even integer.
showAtPrecision :: Int -> CReal n -> String Source
Return a string representing a decimal number within 2^-p of the value
represented by the given CReal p
.
decimalDigitsAtPrecision :: Int -> Int Source
How many decimal digits are required to represent a number to within 2^-p
rationalToDecimal :: Int -> Rational -> String Source
rationalToDecimal p x
returns a string representing x
at p
decimal
places.