Numeric.Decimal

This module provides a general-purpose Number type supporting decimal arithmetic for both limited precision floating-point (IEEE 754-2008) and for arbitrary precision floating-point (following the same principles as IEEE 754 and IEEE 854-1987) as described in the General Decimal Arithmetic Specification by Mike Cowlishaw. In addition to floating-point arithmetic, integer and unrounded floating-point arithmetic are included as subsets.

Unlike the binary floating-point types Float and Double, the Number type can represent and perform arithmetic with decimal numbers exactly. Internally, a Number is represented with an integral coefficient and base-10 exponent.

The Number type supports lossless conversion to and from a string representation via the Show and Read instances. Note that there may be multiple representations of values that are numerically equal (e.g. 1 and 1.00) which are preserved by this conversion.

Usage

It is recommended that you create an alias for the type of numbers you wish to support in your application. For example:

 type Decimal = BasicDecimal

This is a basic number type with 9 decimal digits of precision that rounds half up.

 type Decimal = ExtendedDecimal P19

This is a number type with 19 decimal digits of precision that rounds half even.

 type Decimal = GeneralDecimal

This is a number type with infinite precision. (Note that not all operations support numbers with infinite precision.)

It is also possible to use a decimal number type in a default declaration, possibly replacing Double or Integer. For example:

 default (Integer, Decimal)

Arbitrary-precision decimal numbers

data Number p r

A decimal floating point number with selectable precision and rounding algorithm

Instances

(FinitePrecision p, Rounding r) => Enum (Number p r)

Methods

succ :: Number p r -> Number p r

pred :: Number p r -> Number p r

toEnum :: Int -> Number p r

fromEnum :: Number p r -> Int

enumFrom :: Number p r -> [Number p r]

enumFromThen :: Number p r -> Number p r -> [Number p r]

enumFromTo :: Number p r -> Number p r -> [Number p r]

enumFromThenTo :: Number p r -> Number p r -> Number p r -> [Number p r]

(Precision p, Rounding r) => Eq (Number p r)

Methods

(==) :: Number p r -> Number p r -> Bool

(/=) :: Number p r -> Number p r -> Bool

(FinitePrecision p, Rounding r) => Fractional (Number p r)

Methods

(/) :: Number p r -> Number p r -> Number p r

recip :: Number p r -> Number p r

fromRational :: Rational -> Number p r

(Precision p, Rounding r) => Num (Number p r)

Methods

(+) :: Number p r -> Number p r -> Number p r

(-) :: Number p r -> Number p r -> Number p r

(*) :: Number p r -> Number p r -> Number p r

negate :: Number p r -> Number p r

abs :: Number p r -> Number p r

signum :: Number p r -> Number p r

fromInteger :: Integer -> Number p r

(Precision p, Rounding r) => Ord (Number p r)

Methods

compare :: Number p r -> Number p r -> Ordering

(<) :: Number p r -> Number p r -> Bool

(<=) :: Number p r -> Number p r -> Bool

(>) :: Number p r -> Number p r -> Bool

(>=) :: Number p r -> Number p r -> Bool

max :: Number p r -> Number p r -> Number p r

min :: Number p r -> Number p r -> Number p r

(Precision p, Rounding r) => Read (Number p r)

Methods

readsPrec :: Int -> ReadS (Number p r)

readList :: ReadS [Number p r]

readPrec :: ReadPrec (Number p r)

readListPrec :: ReadPrec [Number p r]

(Precision p, Rounding r) => Real (Number p r)

Methods

toRational :: Number p r -> Rational

(FinitePrecision p, Rounding r) => RealFrac (Number p r)

Methods

properFraction :: Integral b => Number p r -> (b, Number p r)

truncate :: Integral b => Number p r -> b

round :: Integral b => Number p r -> b

ceiling :: Integral b => Number p r -> b

floor :: Integral b => Number p r -> b

Show (Number p r)

Methods

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

show :: Number p r -> String

showList :: [Number p r] -> ShowS

Precision p => Precision (Number p r)

Methods

precision :: Number p r -> Maybe Int

type BasicDecimal = Number P9 RoundHalfUp

A basic decimal floating point number with 9 digits of precision, rounding half up

type ExtendedDecimal p = Number p RoundHalfEven

A decimal floating point number with selectable precision, rounding half even

type GeneralDecimal = ExtendedDecimal PInfinite

A decimal floating point number with infinite precision

Precision types

class Precision p where

Precision indicates the maximum number of significant digits a number may have.

Minimal complete definition

precision

Methods

precision :: p -> Maybe Int

Return the precision of the argument, or Nothing if the precision is infinite.

Instances

Precision P1

Methods

precision :: P1 -> Maybe Int

Precision PInfinite

Methods

precision :: PInfinite -> Maybe Int

Precision p => Precision (PTimes2 p)

Methods

precision :: PTimes2 p -> Maybe Int

Precision p => Precision (PPlus1 p)

Methods

precision :: PPlus1 p -> Maybe Int

Precision p => Precision (Number p r)

Methods

precision :: Number p r -> Maybe Int

class Precision p => FinitePrecision p

A subclass of precisions which are finite

Instances

FinitePrecision P1

FinitePrecision p => FinitePrecision (PTimes2 p)

FinitePrecision p => FinitePrecision (PPlus1 p)

data P1

A precision of 1 significant digit

Instances

FinitePrecision P1

Precision P1

Methods

precision :: P1 -> Maybe Int

type P2 = PTimes2 P1

A precision of 2 significant digits

type P3 = PPlus1 P2

A precision of 3 significant digits

type P4 = PTimes2 P2

Et cetera

type P5 = PPlus1 P4

type P6 = PTimes2 P3

type P7 = PPlus1 P6

type P8 = PTimes2 P4

type P9 = PPlus1 P8

type P10 = PTimes2 P5

type P11 = PPlus1 P10

type P12 = PTimes2 P6

type P13 = PPlus1 P12

type P14 = PTimes2 P7

type P15 = PPlus1 P14

type P16 = PTimes2 P8

type P17 = PPlus1 P16

type P18 = PTimes2 P9

type P19 = PPlus1 P18

type P20 = PTimes2 P10

type P21 = PPlus1 P20

type P22 = PTimes2 P11

type P23 = PPlus1 P22

type P24 = PTimes2 P12

type P25 = PPlus1 P24

type P26 = PTimes2 P13

type P27 = PPlus1 P26

type P28 = PTimes2 P14

type P29 = PPlus1 P28

type P30 = PTimes2 P15

type P31 = PPlus1 P30

type P32 = PTimes2 P16

type P33 = PPlus1 P32

type P34 = PTimes2 P17

type P35 = PPlus1 P34

type P36 = PTimes2 P18

type P37 = PPlus1 P36

type P38 = PTimes2 P19

type P39 = PPlus1 P38

type P40 = PTimes2 P20

type P41 = PPlus1 P40

type P42 = PTimes2 P21

type P43 = PPlus1 P42

type P44 = PTimes2 P22

type P45 = PPlus1 P44

type P46 = PTimes2 P23

type P47 = PPlus1 P46

type P48 = PTimes2 P24

type P49 = PPlus1 P48

type P50 = PTimes2 P25

type P75 = PPlus1 P74

type P100 = PTimes2 P50

type P150 = PTimes2 P75

type P200 = PTimes2 P100

type P250 = PTimes2 P125

type P300 = PTimes2 P150

type P400 = PTimes2 P200

type P500 = PTimes2 P250

type P1000 = PTimes2 P500

type P2000 = PTimes2 P1000

data PPlus1 p

A precision of (p + 1) significant digits

Instances

FinitePrecision p => FinitePrecision (PPlus1 p)

Precision p => Precision (PPlus1 p)

Methods

precision :: PPlus1 p -> Maybe Int

data PTimes2 p

A precision of (p × 2) significant digits

Instances

FinitePrecision p => FinitePrecision (PTimes2 p)

Precision p => Precision (PTimes2 p)

Methods

precision :: PTimes2 p -> Maybe Int

data PInfinite

A precision of unlimited significant digits

Instances

Precision PInfinite

Methods

precision :: PInfinite -> Maybe Int

Rounding types

class Rounding r

A rounding algorithm to use when the result of an arithmetic operation exceeds the precision of the result type

Minimal complete definition

round

Instances

Rounding Round05Up

Methods

round :: Precision p => Number p Round05Up -> Number p Round05Up

isRoundFloor :: Number p Round05Up -> Bool

Rounding RoundUp

Methods

round :: Precision p => Number p RoundUp -> Number p RoundUp

isRoundFloor :: Number p RoundUp -> Bool

Rounding RoundHalfDown

Methods

round :: Precision p => Number p RoundHalfDown -> Number p RoundHalfDown

isRoundFloor :: Number p RoundHalfDown -> Bool

Rounding RoundFloor

Methods

round :: Precision p => Number p RoundFloor -> Number p RoundFloor

isRoundFloor :: Number p RoundFloor -> Bool

Rounding RoundCeiling

Methods

round :: Precision p => Number p RoundCeiling -> Number p RoundCeiling

isRoundFloor :: Number p RoundCeiling -> Bool

Rounding RoundHalfEven

Methods

round :: Precision p => Number p RoundHalfEven -> Number p RoundHalfEven

isRoundFloor :: Number p RoundHalfEven -> Bool

Rounding RoundHalfUp

Methods

round :: Precision p => Number p RoundHalfUp -> Number p RoundHalfUp

isRoundFloor :: Number p RoundHalfUp -> Bool

Rounding RoundDown

Methods

round :: Precision p => Number p RoundDown -> Number p RoundDown

isRoundFloor :: Number p RoundDown -> Bool

data RoundHalfUp

If the discarded digits represent greater than or equal to half (0.5) of the value of a one in the next left position then the value is rounded up. If they represent less than half, the value is rounded down.

Instances

Rounding RoundHalfUp

Methods

round :: Precision p => Number p RoundHalfUp -> Number p RoundHalfUp

isRoundFloor :: Number p RoundHalfUp -> Bool

data RoundHalfEven

If the discarded digits represent greater than half (0.5) of the value of a one in the next left position then the value is rounded up. If they represent less than half, the value is rounded down. If they represent exactly half, the value is rounded to make its rightmost digit even.

Instances

Rounding RoundHalfEven

Methods

round :: Precision p => Number p RoundHalfEven -> Number p RoundHalfEven

isRoundFloor :: Number p RoundHalfEven -> Bool

data RoundHalfDown

If the discarded digits represent greater than half (0.5) of the value of a one in the next left position then the value is rounded up. If they represent less than half or exactly half, the value is rounded down.

Instances

Rounding RoundHalfDown

Methods

round :: Precision p => Number p RoundHalfDown -> Number p RoundHalfDown

isRoundFloor :: Number p RoundHalfDown -> Bool

data RoundCeiling

Round toward +∞

Instances

Rounding RoundCeiling

Methods

round :: Precision p => Number p RoundCeiling -> Number p RoundCeiling

isRoundFloor :: Number p RoundCeiling -> Bool

data RoundFloor

Round toward −∞

Instances

Rounding RoundFloor

Methods

round :: Precision p => Number p RoundFloor -> Number p RoundFloor

isRoundFloor :: Number p RoundFloor -> Bool

data RoundUp

Round away from 0

Instances

Rounding RoundUp

Methods

round :: Precision p => Number p RoundUp -> Number p RoundUp

isRoundFloor :: Number p RoundUp -> Bool

data Round05Up

Round zero or five away from 0

Instances

Rounding Round05Up

Methods

round :: Precision p => Number p Round05Up -> Number p Round05Up

isRoundFloor :: Number p Round05Up -> Bool

data RoundDown

Round toward 0 (truncate)

Instances

Rounding RoundDown

Methods

round :: Precision p => Number p RoundDown -> Number p RoundDown

isRoundFloor :: Number p RoundDown -> Bool

Functions

cast :: (Precision p, Rounding r) => Number a b -> Number p r

Cast a Number to another precision and/or rounding algorithm, immediately rounding if necessary to the new precision using the new algorithm.