PreciseFloat

data PreciseFloat

The PreciseFloat data type is a non-fractional representation of rational numbers, ie. it is an infinit precision floating point number. Rational numbers can have recurring, and thus, infinit, non-fractional represenations. The finit, ie. not recurring, and infinit , ie. recurring, part are seperated. infinitLength specifies the length of the infinit part. This is necessarry to encode the difference between infinit parts which are lead by zeros and infinit parts which are not, eg. "0.[1]" and "0.[001]" have both infinit = 1, but different infinitLengths. shift specifies by how many digits the radix points has to be shifted to the left, so that, finit and infinit become whole numbers. Thus, in contrast to traditional floating point types, shift is only positive, and always interpreted as negative exponent, eg. "1000" is coded as {f: 1000, i: 0, il: 0, s: 0}, but "0.001" as {f: 1, i: 0, il: 0, s: 3}

Constructors

• PreciseFloat { finit :: BigInt, infinit :: BigInt, infinitLength :: BigInt, shift :: BigInt }

Instances

• Show PreciseFloat
• Eq PreciseFloat

fromRatio :: PreciseRational -> PreciseFloat

Convert a PreciseRational to a PreciseFloat, ie. convert a fractional representation of a rational to a non-fractoinal one.

fromInts :: Int -> Int -> Int -> Int -> PreciseFloat

Construct PreciseFloat from four Ints describiing finit, infinit, infinitLength and shift

fromStrings :: String -> String -> String -> String -> Maybe PreciseFloat

Try to construct PreciseFloat from four Stringss describiing finit, infinit, infinitLength and shift

toRatio :: PreciseFloat -> PreciseRational

Convert a PreciseFloat to a PreciseRational ie. convert a non-fractional representation of a rational to a fractional one.

isRecurring :: PreciseFloat -> Boolean

Check if the PreciseFloat has a recurring part

isZero :: PreciseFloat -> Boolean

Check if the PreciseFloat is zero

scale :: PreciseFloat -> BigInt -> PreciseFloat

Scale the PreciseFloat by a BigInt factor

appendNZerosOnTheRight :: BigInt -> BigInt -> BigInt

Eg. 123 appendNZerosOnTheRight 2 -> 12300

stripNDigitsOnTheRight :: BigInt -> BigInt -> BigInt

eg. 12345 stripNDigitsOnTheRight 2 -> 123

toMixedRatio :: PreciseRational -> { propper :: PreciseRational, whole :: BigInt }

Seperate the whole from the propper part of an (possibly) impropper fraction