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. Binary arithmetic results have an exponent equal to the maximum of the exponents of the arguments.
Decimal numbers are defined as instances of Real
. This means that
conventional division is not defined. Instead the functions divide
and
allocate
will split a decimal amount into lists of results. These
results 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 recommended
that Decimal
be used, with other types being used only where necessary
(e.g. to conform to a network protocol).
 data Integral i => DecimalRaw i = Decimal {
 decimalPlaces :: !Word8
 decimalMantissa :: !i
 type Decimal = DecimalRaw Integer
 realFracToDecimal :: (Integral i, RealFrac r) => Word8 > r > DecimalRaw i
 decimalConvert :: (Integral a, Integral b) => DecimalRaw a > DecimalRaw b
 roundTo :: Integral i => Word8 > DecimalRaw i > DecimalRaw Integer
 (*.) :: (Integral i, RealFrac r) => DecimalRaw i > r > DecimalRaw i
 divide :: Integral i => DecimalRaw i > Int > [(Int, DecimalRaw i)]
 allocate :: Integral i => DecimalRaw i > [Integer] > [DecimalRaw i]
 prop_readShow :: Decimal > Bool
 prop_readShowPrecision :: Decimal > Bool
 prop_fromIntegerZero :: Integer > Bool
 prop_increaseDecimals :: Decimal > Property
 prop_decreaseDecimals :: Decimal > Decimal > Bool
 prop_inverseAdd :: Decimal > Decimal > Bool
 prop_repeatedAdd :: Decimal > Word8 > Bool
 prop_divisionParts :: Decimal > Positive Int > Property
 prop_divisionUnits :: Decimal > Positive Int > Bool
 prop_allocateParts :: Decimal > [Integer] > Property
 prop_allocateUnits :: Decimal > [Integer] > Property
 prop_abs :: Decimal > Bool
 prop_signum :: Decimal > Bool
Decimal Values
data Integral i => 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.
Arithmetic and comparision operators convert their arguments to the
greater of the two precisions, and return a result of that 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.
Decimal  

Integral i => Eq (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, Show i) => Show (DecimalRaw i)  
(Integral i, Arbitrary i) => Arbitrary (DecimalRaw i)  
(Integral i, Arbitrary i) => CoArbitrary (DecimalRaw i) 
type Decimal = DecimalRaw IntegerSource
Arbitrary precision decimal type. As a rule 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 iSource
Convert a real fractional value into a Decimal of the appropriate precision.
decimalConvert :: (Integral a, Integral b) => DecimalRaw a > DecimalRaw bSource
Convert a DecimalRaw
from one base representation to another. Does
not check for overflow in the new representation.
roundTo :: Integral i => Word8 > DecimalRaw i > DecimalRaw IntegerSource
Round a DecimalRaw
to a specified number of decimal places.
(*.) :: (Integral i, RealFrac r) => DecimalRaw i > r > DecimalRaw iSource
Multiply a DecimalRaw
by a RealFrac
value.
divide :: Integral i => DecimalRaw i > Int > [(Int, DecimalRaw i)]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 :: Integral i => DecimalRaw i > [Integer] > [DecimalRaw i]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
QuickCheck Properties
prop_readShowPrecision :: Decimal > BoolSource
Read and show preserve decimal places.
decimalPlaces (read (show n)) == decimalPlaces n
prop_fromIntegerZero :: Integer > BoolSource
fromInteger definition.
decimalPlaces (fromInteger n) == 0 && decimalMantissa (fromInteger n) == n
prop_increaseDecimals :: Decimal > PropertySource
Increased precision does not affect equality.
decimalPlaces d < maxBound ==> roundTo (decimalPlaces d + 1) d == d
prop_decreaseDecimals :: Decimal > Decimal > BoolSource
Decreased precision can make two decimals equal, but it can never change their order.
forAll d1, d2 :: Decimal > legal beforeRound afterRound where beforeRound = compare d1 d2 afterRound = compare (roundTo 0 d1) (roundTo 0 d2) legal GT x = x `elem` [GT, EQ] legal EQ x = x `elem` [EQ] legal LT x = x `elem` [LT, EQ]
prop_inverseAdd :: Decimal > Decimal > BoolSource
(x + y)  y == x
prop_repeatedAdd :: Decimal > Word8 > BoolSource
Multiplication is repeated addition.
forall d, NonNegative i : (sum $ replicate i d) == d * fromIntegral (max i 0)
prop_divisionParts :: Decimal > Positive Int > PropertySource
Division produces the right number of parts.
forall d, Positive i : (sum $ map fst $ divide d i) == i
prop_divisionUnits :: Decimal > Positive Int > BoolSource
Division doesn't drop any units.
forall d, Positive i : (sum $ map (\(n,d1) > fromIntegral n * d1) $ divide d i) == d
prop_allocateParts :: Decimal > [Integer] > PropertySource
Allocate produces the right number of parts.
sum ps /= 0 ==> length ps == length (allocate d ps)
prop_allocateUnits :: Decimal > [Integer] > PropertySource
Allocate doesn't drop any units.
sum ps /= 0 ==> sum (allocate d ps) == d
prop_abs :: Decimal > BoolSource
Absolute value definition
decimalPlaces a == decimalPlaces d && decimalMantissa a == abs (decimalMantissa d) where a = abs d
prop_signum :: Decimal > BoolSource
Sign number defintion
signum d == (fromInteger $ signum $ decimalMantissa d)