| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Factory.Math.Precision
Description
AUTHOR- Dr. Alistair Ward
DESCRIPTION- Defines the unit with which precision is measured, and operations on it.
- type ConvergenceOrder = Int
- type ConvergenceRate = Double
- type DecimalDigits = Int
- linearConvergence :: ConvergenceOrder
- quadraticConvergence :: ConvergenceOrder
- cubicConvergence :: ConvergenceOrder
- quarticConvergence :: ConvergenceOrder
- getIterationsRequired :: Integral i => ConvergenceOrder -> DecimalDigits -> DecimalDigits -> i
- getTermsRequired :: Integral i => ConvergenceRate -> DecimalDigits -> i
- roundTo :: (RealFrac a, Fractional f) => DecimalDigits -> a -> f
- promote :: Num n => n -> DecimalDigits -> n
- simplify :: RealFrac operand => DecimalDigits -> operand -> Rational
Types
Type-synonyms
type ConvergenceOrder = Int Source
The order of convergence; http://en.wikipedia.org/wiki/Rate_of_convergence.
type ConvergenceRate = Double Source
The rate of convergence; http://en.wikipedia.org/wiki/Rate_of_convergence.
type DecimalDigits = Int Source
A number of decimal digits; presumably positive.
Constants
linearConvergence :: ConvergenceOrder Source
Linear convergence-rate; which may be qualified by the rate of convergence.
quadraticConvergence :: ConvergenceOrder Source
Quadratic convergence-rate.
cubicConvergence :: ConvergenceOrder Source
Cubic convergence-rate.
quarticConvergence :: ConvergenceOrder Source
Quartic convergence-rate.
Functions
Arguments
| :: Integral i | |
| => ConvergenceOrder | |
| -> DecimalDigits | The precision of the initial estimate. |
| -> DecimalDigits | The required precision. |
| -> i |
The predicted number of iterations, required to achieve a specific accuracy, at a given order of convergence.
Arguments
| :: Integral i | |
| => ConvergenceRate | |
| -> DecimalDigits | The additional number of correct decimal digits. |
| -> i |
- The predicted number of terms which must be extracted from a series, if it is to converge to the required accuracy, at the specified linear convergence-rate.
- The convergence-rate of a series, is the error in the series after summation of
(n+1)thterms, divided by the error after onlynterms, as the latter tends to infinity. As such, for a convergent series (in which the error get smaller with successive terms), it's value lies in the range0 .. 1. - http://en.wikipedia.org/wiki/Rate_of_convergence.
roundTo :: (RealFrac a, Fractional f) => DecimalDigits -> a -> f Source
Rounds the specified number, to a positive number of DecimalDigits.
promote :: Num n => n -> DecimalDigits -> n Source
Promotes the specified number, by a positive number of DecimalDigits.
Arguments
| :: RealFrac operand | |
| => DecimalDigits | The number of places after the decimal point, which are required. |
| -> operand | |
| -> Rational |
- Reduces a
Rationalto the minimal form required for the specified number of fractional decimal places; irrespective of the number of integral decimal places. - A
Rationalapproximation to an irrational number, may be very long, and provide an unknown excess precision. Whilst this doesn't sound harmful, it costs in performance and memory-requirement, and being unpredictable isn't actually useful.