​

DA.Numeric

​

Module Snapshot

​

Data Types

​

data RoundingMode

Rounding modes. Constructors:

• RoundingUp

Round away from zero.

• RoundingDown

Round towards zero.

• RoundingCeiling

Round towards positive infinity.

• RoundingFloor

Round towards negative infinity.

• RoundingHalfUp

Round towards the nearest neighbor unless both neighbors are equidistant, in which case round away from zero.

• RoundingHalfDown

Round towards the nearest neighbor unless both neighbors are equidistant, in which case round towards zero.

• RoundingHalfEven

Round towards the nearest neighbor unless both neighbors are equidistant, in which case round towards the even neighbor.

• RoundingUnnecessary

Do not round. Raises an error if the result cannot be represented without rounding at the targeted scale.

​

Functions

​

mul

mul : NumericScale n3 => Numeric n1 -> Numeric n2 -> Numeric n3 Multiply two numerics. Both inputs and the output may have different scales, unlike (*) which forces all numeric scales to be the same. Raises an error on overflow, rounds to chosen scale otherwise.

​

div

div : NumericScale n3 => Numeric n1 -> Numeric n2 -> Numeric n3 Divide two numerics. Both inputs and the output may have different scales, unlike (/) which forces all numeric scales to be the same. Raises an error on overflow, rounds to chosen scale otherwise.

​

cast

cast : NumericScale n2 => Numeric n1 -> Numeric n2 Cast a Numeric. Raises an error on overflow or loss of precision.

​

castAndRound

castAndRound : NumericScale n2 => Numeric n1 -> Numeric n2 Cast a Numeric. Raises an error on overflow, rounds to chosen scale otherwise.

​

shift

shift : NumericScale n2 => Numeric n1 -> Numeric n2 Move the decimal point left or right by multiplying the numeric value by 10^(n1 - n2). Does not overflow or underflow.

​

pi

pi : NumericScale n => Numeric n The number pi.

​

epsilon

epsilon : NumericScale n => Numeric n The minimum strictly positive value that can be represented by a numeric of scale n.

​

roundNumeric

roundNumeric : NumericScale n => Int -> RoundingMode -> Numeric n -> Numeric n Round a Numeric number. The value of round n r a is the value of a rounded to n decimal places (i.e. scale), according to the rounding mode r. This will fail when using the RoundingUnnecessary mode for a number that cannot be represented exactly with at most n decimal places.

​

Orphan Typeclass Instances

• instance NumericScale n => Bounded (Numeric n)