úÎ@ >²     HArbitrary precision decimal type. As a rule programs should do decimal C arithmetic with this type and only convert to other instances of   DecimalRaw* where required by an external interface. FUsing this type is also faster because it avoids repeated conversions  to and from Integer. IRaw decimal arithmetic type constructor. A decimal value consists of an M 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. EArithmetic and comparision operators convert their arguments to the I greater of the two precisions, and return a result of that precision. J Regardless of the type of the arguments, all mantissa arithmetic is done  using Integer= types, so application developers do not need to worry about K overflow in the internal algorithms. However the result of each operator G will be converted to the mantissa type without checking for overflow. CConvert a real fractional value into a Decimal of the appropriate  precision.  Convert a  DecimalRaw0 from one base representation to another. Does 3 not check for overflow in the new representation. Round a  DecimalRaw* to a specified number of decimal places.  Divide a  DecimalRaw0 value into one or more portions. The portions K will be approximately equal, and the sum of the portions is guaranteed to  be the original value. IThe portions are represented as a list of pairs. The first part of each K 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 a  DecimalRaw2 value proportionately with the values in a list. H The allocated portions are guaranteed to add up to the original value. JSome of the allocations may be zero or negative, but the sum of the list J must not be zero. The allocation is intended to be as close as possible  to the following:  let result = allocate d parts 6 in all (== d / sum parts) $ zipWith (/) result parts  Multiply a  DecimalRaw by a RealFrac value. read is the inverse of show.  read (show n) == n 'Read and show preserve decimal places. 2 decimalPlaces (read (show n)) == decimalPlaces n  fromInteger definition. ' decimalPlaces (fromInteger n) == 0 && & decimalMantissa (fromInteger n) == n .Increased precision does not affect equality. E decimalPlaces d < maxBound ==> roundTo (decimalPlaces d + 1) d == d IDecreased 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]   (x + y) - y == x %Multiplication is repeated addition. O forall d, NonNegative i : (sum $ replicate i d) == d * fromIntegral (max i 0) -Division produces the right number of parts. : forall d, Positive i : (sum $ map fst $ divide d i) == i Division doesn't drop any units. W forall d, Positive i : (sum $ map (\(n,d1) -> fromIntegral n * d1) $ divide d i) == d -Allocate produces the right number of parts. 7 sum ps /= 0 ==> length ps == length (allocate d ps) Allocate doesn't drop any units. 0 sum ps /= 0 ==> sum (allocate d ps) == d Absolute value definition ( decimalPlaces a == decimalPlaces d && . decimalMantissa a == abs (decimalMantissa d)  where a = abs d Sign number defintion 8 signum d == (fromInteger $ signum $ decimalMantissa d)           Decimal-0.2.2 Data.DecimalDecimal DecimalRaw decimalPlacesdecimalMantissarealFracToDecimaldecimalConvertroundTodivideallocate*. prop_readShowprop_readShowPrecisionprop_fromIntegerZeroprop_increaseDecimalsprop_decreaseDecimalsprop_inverseAddprop_repeatedAddprop_divisionPartsprop_divisionUnitsprop_allocatePartsprop_allocateUnitsprop_abs prop_signumdivRoundroundMax