{-| Module : Data.Number.ER.BasicTypes Description : generic types for exact real number processing Copyright : (c) Michal Konecny License : BSD3 Maintainer : mik@konecny.aow.cz Stability : experimental Portability : portable generic types for exact real number processing -} module Data.Number.ER.BasicTypes where import qualified Data.Number.ER.ExtendedInteger as EI import qualified Data.Map as Map {-| Precision represents an upper bound on the measure of an approximation viewed as a set; not to be confused with the precision of an 'Data.Number.ER.Real.Base.Float.ERFloat' and similar. In an approximation comprising a number of instances of 'Data.Number.ER.Real.Base.ERRealBase', we will refer to the bit-precision of these base components as the 'Granularity' of the approximation. -} type Precision = EI.ExtendedInteger {-| The bit size of the floating point numbers (or similar) used internally in real number and function approximations. -} type Granularity = Int prec2gran :: Precision -> Granularity prec2gran = fromInteger . toInteger {-| This type synonym should be used for funciton parameter(s) that guide the convergence of the function's result to a perfect (exact) result. The name should remind us that there is no universally valid relationship between this integer the quality (precision) of the result. The only condition usually assumed is that in the limit when the effort index rises to infinity, the result should be exact. -} type EffortIndex = Integer effIx2gran :: EffortIndex -> Granularity effIx2gran = fromInteger . toInteger effIx2prec :: EffortIndex -> Precision effIx2prec = fromInteger . toInteger effIx2int :: EffortIndex -> Int effIx2int = fromInteger . toInteger int2effIx :: Int -> EffortIndex int2effIx = fromInteger . toInteger prec2effIx :: Precision -> EffortIndex prec2effIx = fromInteger . toInteger gran2effIx :: Granularity -> EffortIndex gran2effIx = fromInteger . toInteger {-| A variable identifier for axes in function domains, polynomials etc. -} type VarID = Int defaultVar :: VarID defaultVar = 0 {-| A many-dimensional point or interval. -} type Box ira = Map.Map VarID ira