Decimal-0.4.2: Decimal numbers with variable precision

Data.Decimal

Contents

Description

Decimal numbers are represented as `m*10^(-e)` where `m` and `e` are integers. The exponent `e` is an unsigned Word8. Hence the smallest value that can be represented is `10^-255`.

Unary arithmetic results have the exponent of the argument. Addition and subtraction results have an exponent equal to the maximum of the exponents of the arguments. Other operators have exponents sufficient to show the exact result, up to a limit of 255:

```0.15 * 0.15 :: Decimal    = 0.0225
(1/3) :: Decimal          = 0.33333333333333...
decimalPlaces (1/3)       = 255```

While `(/)` is defined, you don't normally want to use it. Instead The functions "divide" and "allocate" will split a decimal amount into lists of results which are guaranteed to sum to the original number. This is a useful property when doing financial arithmetic.

The arithmetic on mantissas is always done using `Integer`, regardless of the type of `DecimalRaw` being manipulated. In practice it is strongly recommended that `Decimal` be used, with other types being used only where necessary (e.g. to conform to a network protocol). For instance `(1/3) :: DecimalRaw Int` does not give the right answer.

Synopsis

## Decimal Values

data DecimalRaw i Source

Raw decimal arithmetic type constructor. A decimal value consists of an integer mantissa and a negative exponent which is interpreted as the number of decimal places. The value stored in a `Decimal d` is therefore equal to:

`decimalMantissa d / (10 ^ decimalPlaces d)`

The Show instance will add trailing zeros, so `show \$ Decimal 3 1500` will return "1.500". Conversely the Read instance will use the decimal places to determine the precision.

Regardless of the type of the arguments, all mantissa arithmetic is done using `Integer` types, so application developers do not need to worry about overflow in the internal algorithms. However the result of each operator will be converted to the mantissa type without checking for overflow.

Constructors

 Decimal FieldsdecimalPlaces :: !Word8 decimalMantissa :: !i

Instances

 Integral i => Enum (DecimalRaw i) Integral i => Eq (DecimalRaw i) Integral i => Fractional (DecimalRaw i) Integral i => Num (DecimalRaw i) Integral i => Ord (DecimalRaw i) (Integral i, Read i) => Read (DecimalRaw i) Integral i => Real (DecimalRaw i) Integral i => RealFrac (DecimalRaw i) (Integral i, Show i) => Show (DecimalRaw i) NFData i => NFData (DecimalRaw i) Typeable (* -> *) DecimalRaw

Arbitrary precision decimal type. Programs should do decimal arithmetic with this type and only convert to other instances of DecimalRaw where required by an external interface.

Using this type is also faster because it avoids repeated conversions to and from `Integer`.

realFracToDecimal :: (Integral i, RealFrac r) => Word8 -> r -> DecimalRaw i Source

Convert a real fractional value into a Decimal of the appropriate precision.

decimalConvert :: (Integral a, Integral b, Bounded b) => DecimalRaw a -> Maybe (DecimalRaw b) Source

Convert a `DecimalRaw` from one base to another. Returns `Nothing` if this would cause arithmetic overflow.

unsafeDecimalConvert :: (Integral a, Integral b) => DecimalRaw a -> DecimalRaw b Source

Convert a `DecimalRaw` from one base representation to another. Does not check for overflow in the new representation. Only use after using "roundTo" to put an upper value on the exponent, or to convert to a larger representation.

roundTo :: Integral i => Word8 -> DecimalRaw i -> DecimalRaw i Source

Round a `DecimalRaw` to a specified number of decimal places. If the value ends in `5` then it is rounded away from zero.

(*.) :: (Integral i, RealFrac r) => DecimalRaw i -> r -> DecimalRaw i Source

Multiply a `DecimalRaw` by a `RealFrac` value.

divide :: Decimal -> Int -> [(Int, Decimal)] Source

Divide a `DecimalRaw` value into one or more portions. The portions will be approximately equal, and the sum of the portions is guaranteed to be the original value.

The portions are represented as a list of pairs. The first part of each pair is the number of portions, and the second part is the portion value. Hence 10 dollars divided 3 ways will produce `[(2, 3.33), (1, 3.34)]`.

allocate :: Decimal -> [Integer] -> [Decimal] Source

Allocate a `DecimalRaw` value proportionately with the values in a list. The allocated portions are guaranteed to add up to the original value.

Some of the allocations may be zero or negative, but the sum of the list must not be zero. The allocation is intended to be as close as possible to the following:

```let result = allocate d parts
in all (== d / sum parts) \$ zipWith (/) result parts```

Try to convert Rational to Decimal with absolute precision return string with fail description if not converted

Reduce the exponent of the decimal number to the minimal possible value