Numeric.Decimal.Arithmetic

It is not usually necessary to import this module unless you want to use the arithmetic operations from Numeric.Decimal.Operation or you need precise control over the handling of exceptional conditions in an arithmetic computation.

Decimal arithmetic

Decimal arithmetic is performed within a context that maintains state to handle exceptional conditions such as underflow, rounding, or division by zero (cf. Signal). The Arith monad provides a means to evaluate an arithmetic computation and manipulate its Context.

Context

data Context p r

A context for decimal arithmetic, carrying signal flags, trap enabler state, and a trap handler, parameterized by precision p and rounding mode r

Instances

MonadState (Context p r) (Arith p r)

The Context of an arithmetic computation may be manipulated using get and put, et al. For example, the current signal flags can be observed with gets flags.

Defined in Numeric.Decimal.Arithmetic

Methods

get :: Arith p r (Context p r)

put :: Context p r -> Arith p r ()

state :: (Context p r -> (a, Context p r)) -> Arith p r a

newContext :: Context p r

Return a new context with all signal flags cleared and all traps disabled.

flags :: Context p r -> Signals

The current signal flags of the context

getPrecision :: Precision p => Arith p r (Maybe Int)

Return the precision of the arithmetic context (or Nothing if the precision is infinite).

getRounding :: Rounding r => Arith p r RoundingAlgorithm

Return the rounding mode of the arithmetic context.

data RoundingAlgorithm

A value representation of a rounding algorithm (cf. Rounding).

Constructors

RoundDown

RoundHalfUp

RoundHalfEven

RoundCeiling

RoundFloor

RoundHalfDown

RoundUp

Round05Up

Instances

Eq RoundingAlgorithm

Defined in Numeric.Decimal.Rounding

Methods

(==) :: RoundingAlgorithm -> RoundingAlgorithm -> Bool

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

Default contexts

The General Decimal Arithmetic specification defines optional default contexts, which define suitable settings for basic arithmetic and for the extended arithmetic defined by IEEE 854 and IEEE 754.

basicDefaultContext :: Context P9 RoundHalfUp

Return a new context with all signal flags cleared, all traps enabled except for Inexact, Rounded, and Subnormal, using a precision of 9 significant decimal digits, and rounding half up. Trapped signals simply call throwError with the corresponding Exception, and can be caught using catchError.

extendedDefaultContext :: Context p RoundHalfEven

Return a new context with all signal flags cleared, all traps disabled (IEEE 854 §7), using selectable precision, and rounding half even (IEEE 754 §4.3.3).

The Arith monad

data Arith p r a

A decimal arithmetic monad parameterized by the precision p and rounding mode r

Instances

Monad (Arith p r)

Defined in Numeric.Decimal.Arithmetic

Methods

(>>=) :: Arith p r a -> (a -> Arith p r b) -> Arith p r b

(>>) :: Arith p r a -> Arith p r b -> Arith p r b

return :: a -> Arith p r a

fail :: String -> Arith p r a

Functor (Arith p r)

Defined in Numeric.Decimal.Arithmetic

Methods

fmap :: (a -> b) -> Arith p r a -> Arith p r b

(<$) :: a -> Arith p r b -> Arith p r a

Applicative (Arith p r)

Defined in Numeric.Decimal.Arithmetic

Methods

pure :: a -> Arith p r a

(<*>) :: Arith p r (a -> b) -> Arith p r a -> Arith p r b

liftA2 :: (a -> b -> c) -> Arith p r a -> Arith p r b -> Arith p r c

(*>) :: Arith p r a -> Arith p r b -> Arith p r b

(<*) :: Arith p r a -> Arith p r b -> Arith p r a

MonadState (Context p r) (Arith p r)

The Context of an arithmetic computation may be manipulated using get and put, et al. For example, the current signal flags can be observed with gets flags.

Defined in Numeric.Decimal.Arithmetic

Methods

get :: Arith p r (Context p r)

put :: Context p r -> Arith p r ()

state :: (Context p r -> (a, Context p r)) -> Arith p r a

MonadError (Exception p r) (Arith p r)

Traps (vis-à-vis TrapHandler) may call throwError to abort the arithmetic computation (or be caught using catchError).

Defined in Numeric.Decimal.Arithmetic

Methods

throwError :: Exception p r -> Arith p r a

catchError :: Arith p r a -> (Exception p r -> Arith p r a) -> Arith p r a

runArith :: Arith p r a -> Context p r -> (Either (Exception p r) a, Context p r)

Evaluate an arithmetic computation in the given context and return the final value (or exception) and resulting context.

evalArith :: Arith p r a -> Context p r -> Either (Exception p r) a

Evaluate an arithmetic computation in the given context and return the final value or exception, discarding the resulting context.

subArith :: Arith a b (Decimal a b) -> Arith p r (Decimal a b)

Perform a subcomputation using a different precision and/or rounding mode. The subcomputation is evaluated within a new context with all flags cleared and all traps disabled. Any flags set in the context of the subcomputation are ignored, but if an exception is returned it will be re-raised within the current context.

Exceptional conditions

Exceptional conditions are grouped into signals, which can be controlled individually. A Context contains a flag and a trap enabler (i.e. enabled or disabled) for each Signal.

data Exception p r

A representation of an exceptional condition

Instances

Show (Exception p r)

Defined in Numeric.Decimal.Arithmetic

Methods

showsPrec :: Int -> Exception p r -> ShowS

show :: Exception p r -> String

showList :: [Exception p r] -> ShowS

MonadError (Exception p r) (Arith p r)

Traps (vis-à-vis TrapHandler) may call throwError to abort the arithmetic computation (or be caught using catchError).

Defined in Numeric.Decimal.Arithmetic

Methods

throwError :: Exception p r -> Arith p r a

catchError :: Arith p r a -> (Exception p r -> Arith p r a) -> Arith p r a

exceptionSignal :: Exception p r -> Signal

The signal raised by the exceptional condition

exceptionResult :: Exception p r -> Decimal p r

The defined result for the exceptional condition

Signals

data Signal

Constructors

Clamped

Raised when the exponent of a result has been altered or constrained in order to fit the constraints of a specific concrete representation

DivisionByZero

Raised when a non-zero dividend is divided by zero

Inexact

Raised when a result is not exact (one or more non-zero coefficient digits were discarded during rounding)

InvalidOperation

Raised when a result would be undefined or impossible

Overflow

Raised when the exponent of a result is too large to be represented

Rounded

Raised when a result has been rounded (that is, some zero or non-zero coefficient digits were discarded)

Subnormal

Raised when a result is subnormal (its adjusted exponent is less than Emin), before any rounding

Underflow

Raised when a result is both subnormal and inexact

Instances

Bounded Signal

Defined in Numeric.Decimal.Arithmetic

Methods

minBound :: Signal

maxBound :: Signal

Enum Signal

Defined in Numeric.Decimal.Arithmetic

Methods

succ :: Signal -> Signal

pred :: Signal -> Signal

toEnum :: Int -> Signal

fromEnum :: Signal -> Int

enumFrom :: Signal -> [Signal]

enumFromThen :: Signal -> Signal -> [Signal]

enumFromTo :: Signal -> Signal -> [Signal]

enumFromThenTo :: Signal -> Signal -> Signal -> [Signal]

Eq Signal

Defined in Numeric.Decimal.Arithmetic

Methods

(==) :: Signal -> Signal -> Bool

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

Show Signal

Defined in Numeric.Decimal.Arithmetic

Methods

showsPrec :: Int -> Signal -> ShowS

show :: Signal -> String

showList :: [Signal] -> ShowS

data Signals

A group of signals can be manipulated as a set.

Instances

Eq Signals

Defined in Numeric.Decimal.Arithmetic

Methods

(==) :: Signals -> Signals -> Bool

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

Show Signals

Defined in Numeric.Decimal.Arithmetic

Methods

showsPrec :: Int -> Signals -> ShowS

show :: Signals -> String

showList :: [Signals] -> ShowS

Semigroup Signals

Defined in Numeric.Decimal.Arithmetic

Methods

(<>) :: Signals -> Signals -> Signals

sconcat :: NonEmpty Signals -> Signals

stimes :: Integral b => b -> Signals -> Signals

Monoid Signals

Defined in Numeric.Decimal.Arithmetic

Methods

mempty :: Signals

mappend :: Signals -> Signals -> Signals

mconcat :: [Signals] -> Signals

signal :: Signal -> Signals

Create a set of signals from a singleton.

signals :: [Signal] -> Signals

Create a set of signals from a list.

allSignals :: Signals

A set containing every signal

signalMember :: Signal -> Signals -> Bool

Determine whether a signal is a member of a set.

raiseSignal :: Signal -> Decimal p r -> Arith p r (Decimal p r)

Set the given signal flag in the context of the current arithmetic computation, and call the trap handler if the trap for this signal is currently enabled.

clearFlags :: Signals -> Arith p r ()

Clear the given signal flags from the context of the current arithmetic computation.

Traps

type TrapHandler p r = Exception p r -> Arith p r (Decimal p r)

A trap handler function may return a substitute result for the operation that caused the exceptional condition, or it may call throwError to pass control to an enclosing catchError handler (or abort the arithmetic computation).

trap :: Signals -> TrapHandler p r -> Arith p r a -> Arith p r a

Evaluate an arithmetic computation within a modified context that enables the given signals to be trapped by the given handler. The previous trap handler (and enabler state) will be restored during any trap, as well as upon completion. Any existing trap handlers for signals not mentioned remain in effect.