Math.Extras.Double

Arithmetic on doubles. Some functions use more general types than Double.

Constant double values

positiveInfinity :: Double

A constant holding the positive infinity of type Double.

negativeInfinity :: Double

A constant holding the negative infinity of type Double.

nan :: Double

A constant holding a NaN value of type Double.

Fuzzy comparison

type Tolerance = Double

fuzzyEq :: Tolerance -> Double -> Double -> Bool

Returns True if the difference of the two numbers are no more than abs(tolerance).

• All NaNs are fuzzily equal.
• With finite tolerance, positiveInfinity and negativeInfinity are fuzzily equal only to themselves.
• With positiveInfinity or negativeInfinity tolerance, all non-NaN values are fuzzily equal.
• NaN tolerance behaves the same as zero tolerance.

fuzzyEq tolerance is reflexive and symmetric, but not transitive unless tolerance is zero, positiveInfinity, negativeInfinity, or NaN.

fuzzyCompare :: Tolerance -> Double -> Double -> Ordering

Compare two Doubles with a tolerance.

If fuzzyEq tolerance x y then fuzzyCompare tolerance x y == EQ; otherwise fuzzyCompare tolerance x y == compare x y.

(~=) :: Double -> Double -> Bool

(~=) is equivalent to fuzzyEq 1.0e-6.

(/~=) :: Double -> Double -> Bool

x /~= y is equivalent to not (x ~= y).

Rounding

data RoundingMode

Constructors

Up

Round away from 0

Down

Round towards 0

Ceiling

Round towards positive infinity

Floor

Round towards negative infinity

HalfUp

Round towards nearest integer; round Up in case of a tie

HalfDown

Round towards nearest integer; round Down in case of a tie

HalfEven

Round towards nearest integer; round towards the even neighbor in case of a tie

Instances

Eq RoundingMode

Defined in Math.Extras.Double

Methods

(==) :: RoundingMode -> RoundingMode -> Bool

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

Ord RoundingMode

Defined in Math.Extras.Double

Methods

compare :: RoundingMode -> RoundingMode -> Ordering

(<) :: RoundingMode -> RoundingMode -> Bool

(<=) :: RoundingMode -> RoundingMode -> Bool

(>) :: RoundingMode -> RoundingMode -> Bool

(>=) :: RoundingMode -> RoundingMode -> Bool

max :: RoundingMode -> RoundingMode -> RoundingMode

min :: RoundingMode -> RoundingMode -> RoundingMode

Show RoundingMode

Defined in Math.Extras.Double

Methods

showsPrec :: Int -> RoundingMode -> ShowS

show :: RoundingMode -> String

showList :: [RoundingMode] -> ShowS

roundToInteger :: RoundingMode -> Double -> Integer

Round a Double to an Integer using the specified RoundingMode.

saturatedRound :: forall a. (Bounded a, Integral a) => RoundingMode -> Double -> a

Round a Double to an integral number using the specified RoundingMode. Returns maxBound and minBound in case of overflow and underflow, respectively.

Predicates

isFinite :: RealFloat a => a -> Bool

Returns False for NaN and infinity, and True otherwise.

isInteger :: (Eq a, Num a, RealFloat a) => a -> Bool

Returns True if the input represents an integer.

Conversion

toInt64RawBits :: Double -> Int64

Returns an Int64 with the same bit representation as the given Double.

toWord64RawBits :: Double -> Word64

Returns a Word64 with the same bit representation as the given Double.

fromInt64RawBits :: Int64 -> Double

Returns a Double with the same bit representation as the given Int64.

fromWord64RawBits :: Word64 -> Double

Returns a Double with the same bit representation as the given Word64.