Data.Number.FixedPrec

A reasonably efficient implementation of arbitrary-but-fixed precision real numbers. This is inspired by, and partly based on, Data.Number.Fixed and Data.Number.CReal, but more efficient.

Type-level integers for precision

class Precision e

A type class for type-level integers, capturing a precision parameter. Precision is measured in decimal digits.

Minimal complete definition

digits

Instances

Precision P2000

Precision P1000

Precision P100

Precision P10

Precision P1

Precision P0

Precision e => Precision (PPlus1000 e)

Precision e => Precision (PPlus100 e)

Precision e => Precision (PPlus10 e)

Precision e => Precision (PPlus3 e)

Precision e => Precision (PPlus1 e)

data P0

Precision of 0 digits.

Instances

Precision P0

data P1

Precision of 1 digit.

Instances

Precision P1

data P10

Precision of 10 digits.

Instances

Precision P10

data P100

Precision of 100 digits.

Instances

Precision P100

data P1000

Precision of 1000 digits.

Instances

Precision P1000

data P2000

Precision of 2000 digits.

Instances

Precision P2000

data PPlus1 e

Add 1 digit to the given precision.

Instances

Precision e => Precision (PPlus1 e)

data PPlus3 e

Add 3 digits to the given precision.

Instances

Precision e => Precision (PPlus3 e)

data PPlus10 e

Add 10 digits to the given precision.

Instances

Precision e => Precision (PPlus10 e)

data PPlus100 e

Add 100 digits to the given precision.

Instances

Precision e => Precision (PPlus100 e)

data PPlus1000 e

Add 1000 digits to the given precision.

Instances

Precision e => Precision (PPlus1000 e)

Fixed-precision numbers

data FixedPrec e

The type of fixed-precision numbers.

Instances

Eq (FixedPrec e)

Precision e => Floating (FixedPrec e)

Precision e => Fractional (FixedPrec e)

Precision e => Num (FixedPrec e)

Ord (FixedPrec e)

Precision e => Real (FixedPrec e)

Precision e => RealFrac (FixedPrec e)

Precision e => Show (FixedPrec e)

Precision e => Random (FixedPrec e)

getprec :: Precision e => FixedPrec e -> Int

Get the precision of a fixed-precision number, in decimal digits.

Static and dynamic casts

cast :: (Precision e, Precision f) => FixedPrec e -> FixedPrec f

Cast from any FixedPrec type to another.

upcast :: Precision e => FixedPrec e -> FixedPrec (PPlus3 e)

Cast to a fixed-point type with three additional digits of accuracy.

downcast :: Precision e => FixedPrec (PPlus3 e) -> FixedPrec e

Cast to a fixed-point type with three fewer digits of accuracy.

with_added_digits :: forall a f. Precision f => Int -> (forall e. Precision e => FixedPrec e -> a) -> FixedPrec f -> a

The function with_added_digits d f x evaluates f(x), adding d digits of accuracy to x during the computation.

Other operations

fractional :: Precision e => FixedPrec e -> FixedPrec e

Return the positive fractional part of a fixed-precision number. The result is always in [0,1), regardless of the sign of the input.

solve_quadratic :: Precision e => FixedPrec e -> FixedPrec e -> Maybe (FixedPrec e, FixedPrec e)

Solve the quadratic equation x^2 + bx + c = 0 with maximal possible precision, using a numerically stable method. Return the pair (x1, x2) of solutions with x1 <= x2, or Nothing if no solution exists.

This is far more precise, and probably more efficient, than naively using the quadratic formula.

log_double :: (Floating a, Real a) => a -> Double

A version of the natural logarithm that returns a Double. The logarithm of just about any value can fit into a Double; so if not a lot of precision is required in the mantissa, this function is often faster than log.