Haspara.Quantity

This module provides definitions and functions to encode and work on quantities with fixed decimal points.

Data Definition

data Quantity (s :: Nat)

Type encoding for common quantity values with given scaling (digits after the decimal point).

>>> 42 :: Quantity 0
42
>>> 42 :: Quantity 1
42.0
>>> 42 :: Quantity 2
42.00
>>> 41 + 1 :: Quantity 2
42.00
>>> 43 - 1 :: Quantity 2
42.00
>>> 2 * 3 * 7 :: Quantity 2
42.00
>>> negate (-42) :: Quantity 2
42.00
>>> abs (-42) :: Quantity 2
42.00
>>> signum (-42) :: Quantity 2
-1.00
>>> fromInteger 42 :: Quantity 2
42.00
>>> quantity 0.415 :: Quantity 2
0.42
>>> quantity 0.425 :: Quantity 2
0.42
>>> quantityLossless 0.42 :: Either String (Quantity 2)
Right 0.42
>>> quantityLossless 0.415 :: Either String (Quantity 2)
Left "Underflow while trying to create quantity: 0.415"

Instances

Lift (Quantity s :: Type)

Lift instance for Quantity.

Defined in Haspara.Internal.Quantity

Methods

lift :: Quantity s -> Q Exp

liftTyped :: Quantity s -> Q (TExp (Quantity s))

Eq (Quantity s)

Defined in Haspara.Internal.Quantity

Methods

(==) :: Quantity s -> Quantity s -> Bool

(/=) :: Quantity s -> Quantity s -> Bool

KnownNat s => Fractional (Arith (Quantity s))

Fractional arithmetic over Quantity values.

>>> import Numeric.Decimal
>>> arithM (fromRational 0.42) :: Either SomeException (Quantity 2)
Right 0.42
>>> arithM (fromRational 0.415) :: Either SomeException (Quantity 2)
Left PrecisionLoss (83 % 200) to 2 decimal spaces
>>> arithM $ (fromRational 0.84) / (fromRational 2) :: Either SomeException (Quantity 2)
Right 0.42
>>> arithM $ (fromRational 0.42) / (fromRational 0) :: Either SomeException (Quantity 2)
Left divide by zero
>>> let a = 84 :: Quantity 2
>>> let b =  2 :: Quantity 2
>>> let c =  0 :: Quantity 2
>>> arithM (Arith a / Arith b) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (Arith a / Arith b / Arith c) :: Either SomeException (Quantity 2)
Left divide by zero

Defined in Haspara.Internal.Quantity

Methods

(/) :: Arith (Quantity s) -> Arith (Quantity s) -> Arith (Quantity s)

recip :: Arith (Quantity s) -> Arith (Quantity s)

fromRational :: Rational -> Arith (Quantity s)

KnownNat s => Num (Arith (Quantity s))

Numeric arithmetic over Quantity values.

>>> import Numeric.Decimal
>>> let a = Arith (quantity 10) + Arith (quantity 32) :: Arith (Quantity 2)
>>> arithMaybe a
Just 42.00
>>> arithM (41 + 1) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (43 - 1) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (2 * 3 * 7) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (signum 42) :: Either SomeException (Quantity 2)
Right 1.00
>>> arithM (signum (-42)) :: Either SomeException (Quantity 2)
Right -1.00
>>> arithM (abs 42) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (abs (-42)) :: Either SomeException (Quantity 2)
Right 42.00
>>> arithM (fromInteger 42) :: Either SomeException (Quantity 2)
Right 42.00

Defined in Haspara.Internal.Quantity

Methods

(+) :: Arith (Quantity s) -> Arith (Quantity s) -> Arith (Quantity s)

(-) :: Arith (Quantity s) -> Arith (Quantity s) -> Arith (Quantity s)

(*) :: Arith (Quantity s) -> Arith (Quantity s) -> Arith (Quantity s)

negate :: Arith (Quantity s) -> Arith (Quantity s)

abs :: Arith (Quantity s) -> Arith (Quantity s)

signum :: Arith (Quantity s) -> Arith (Quantity s)

fromInteger :: Integer -> Arith (Quantity s)

KnownNat s => Num (Quantity s)

Defined in Haspara.Internal.Quantity

Methods

(+) :: Quantity s -> Quantity s -> Quantity s

(-) :: Quantity s -> Quantity s -> Quantity s

(*) :: Quantity s -> Quantity s -> Quantity s

negate :: Quantity s -> Quantity s

abs :: Quantity s -> Quantity s

signum :: Quantity s -> Quantity s

fromInteger :: Integer -> Quantity s

Ord (Quantity s)

Defined in Haspara.Internal.Quantity

Methods

compare :: Quantity s -> Quantity s -> Ordering

(<) :: Quantity s -> Quantity s -> Bool

(<=) :: Quantity s -> Quantity s -> Bool

(>) :: Quantity s -> Quantity s -> Bool

(>=) :: Quantity s -> Quantity s -> Bool

max :: Quantity s -> Quantity s -> Quantity s

min :: Quantity s -> Quantity s -> Quantity s

KnownNat s => Show (Quantity s)

Show instance for Quantity.

>>> show (42 :: Quantity 2)
"42.00"
>>> 42 :: Quantity 2
42.00

Defined in Haspara.Internal.Quantity

Methods

showsPrec :: Int -> Quantity s -> ShowS

show :: Quantity s -> String

showList :: [Quantity s] -> ShowS

Generic (Quantity s)

Defined in Haspara.Internal.Quantity

Associated Types

type Rep (Quantity s) :: Type -> Type

Methods

from :: Quantity s -> Rep (Quantity s) x

to :: Rep (Quantity s) x -> Quantity s

KnownNat s => ToJSON (Quantity s)

ToJSON instance for Quantity.

>>> Aeson.encode (quantity 0.42 :: Quantity 2)
"0.42"

Defined in Haspara.Internal.Quantity

Methods

toJSON :: Quantity s -> Value

toEncoding :: Quantity s -> Encoding

toJSONList :: [Quantity s] -> Value

toEncodingList :: [Quantity s] -> Encoding

KnownNat s => FromJSON (Quantity s)

FromJSON instance for Quantity.

>>> Aeson.decode "0.42" :: Maybe (Quantity 2)
Just 0.42
>>> Aeson.decode "0.415" :: Maybe (Quantity 2)
Just 0.42
>>> Aeson.decode "0.425" :: Maybe (Quantity 2)
Just 0.42

Defined in Haspara.Internal.Quantity

Methods

parseJSON :: Value -> Parser (Quantity s)

parseJSONList :: Value -> Parser [Quantity s]

type Rep (Quantity s)

Defined in Haspara.Internal.Quantity

type Rep (Quantity s) = D1 ('MetaData "Quantity" "Haspara.Internal.Quantity" "haspara-0.0.0.1-GIZpgp6So3jGG6B29GnUaf" 'True) (C1 ('MetaCons "MkQuantity" 'PrefixI 'True) (S1 ('MetaSel ('Just "unQuantity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Decimal RoundHalfEven s Integer))))

unQuantity :: Quantity s -> Decimal RoundHalfEven s Integer

Constructors

quantity :: KnownNat s => Scientific -> Quantity s

Constructs Quantity values from Scientific values in a lossy way.

This function uses quantityAux in case that the lossless attempt fails. We could have used quantityAux directly. However, quantityAux is doing too much (see roundScientific). Therefore, we are first attempting a lossless construction (see quantityLossless) and we fallback to quantityAux in case the lossless construction fails.

>>> quantity 0 :: Quantity 0
0
>>> quantity 0 :: Quantity 1
0.0
>>> quantity 0 :: Quantity 2
0.00
>>> quantity 0.04 :: Quantity 1
0.0
>>> quantity 0.05 :: Quantity 1
0.0
>>> quantity 0.06 :: Quantity 1
0.1
>>> quantity 0.14 :: Quantity 1
0.1
>>> quantity 0.15 :: Quantity 1
0.2
>>> quantity 0.16 :: Quantity 1
0.2
>>> quantity 0.04 :: Quantity 2
0.04
>>> quantity 0.05 :: Quantity 2
0.05
>>> quantity 0.06 :: Quantity 2
0.06
>>> quantity 0.14 :: Quantity 2
0.14
>>> quantity 0.15 :: Quantity 2
0.15
>>> quantity 0.16 :: Quantity 2
0.16
>>> quantity 0.04 :: Quantity 3
0.040
>>> quantity 0.05 :: Quantity 3
0.050
>>> quantity 0.06 :: Quantity 3
0.060
>>> quantity 0.14 :: Quantity 3
0.140
>>> quantity 0.15 :: Quantity 3
0.150
>>> quantity 0.16 :: Quantity 3
0.160

quantityLossless :: (KnownNat s, MonadError String m) => Scientific -> m (Quantity s)

Constructs Quantity values from Scientific values in a lossy way.

>>> quantityLossless 0 :: Either String (Quantity 0)
Right 0
>>> quantityLossless 0 :: Either String (Quantity 1)
Right 0.0
>>> quantityLossless 0 :: Either String (Quantity 2)
Right 0.00
>>> quantityLossless 0.04 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 4.0e-2"
>>> quantityLossless 0.05 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 5.0e-2"
>>> quantityLossless 0.06 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 6.0e-2"
>>> quantityLossless 0.14 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 0.14"
>>> quantityLossless 0.15 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 0.15"
>>> quantityLossless 0.16 :: Either String (Quantity 1)
Left "Underflow while trying to create quantity: 0.16"
>>> quantityLossless 0.04 :: Either String (Quantity 2)
Right 0.04
>>> quantityLossless 0.05 :: Either String (Quantity 2)
Right 0.05
>>> quantityLossless 0.06 :: Either String (Quantity 2)
Right 0.06
>>> quantityLossless 0.14 :: Either String (Quantity 2)
Right 0.14
>>> quantityLossless 0.15 :: Either String (Quantity 2)
Right 0.15
>>> quantityLossless 0.16 :: Either String (Quantity 2)
Right 0.16
>>> quantityLossless 0.04 :: Either String (Quantity 3)
Right 0.040
>>> quantityLossless 0.05 :: Either String (Quantity 3)
Right 0.050
>>> quantityLossless 0.06 :: Either String (Quantity 3)
Right 0.060
>>> quantityLossless 0.14 :: Either String (Quantity 3)
Right 0.140
>>> quantityLossless 0.15 :: Either String (Quantity 3)
Right 0.150
>>> quantityLossless 0.16 :: Either String (Quantity 3)
Right 0.160

Operations

roundQuantity :: KnownNat k => Quantity (n + k) -> Quantity n

Rounds given quantity by k digits.

>>> roundQuantity (quantity 0.415 :: Quantity 3) :: Quantity 2
0.42
>>> roundQuantity (quantity 0.425 :: Quantity 3) :: Quantity 2
0.42

times :: (KnownNat s, KnownNat k) => Quantity s -> Quantity k -> Quantity s

Multiplies two quantities with different scales and rounds back to the scale of the frst operand.

>>> times (quantity 0.42 :: Quantity 2) (quantity 0.42 :: Quantity 2)
0.18

timesLossless :: (KnownNat s, KnownNat k) => Quantity s -> Quantity k -> Quantity (s + k)

Multiplies two quantities with different scales.

>>> timesLossless (quantity 0.42 :: Quantity 2) (quantity 0.42 :: Quantity 2)
0.1764