Float.hs

{-|
    Module      :  AERN2.MP.Float
    Description :  Arbitrary precision floating point numbers
    Copyright   :  (c) Michal Konecny
    License     :  BSD3

    Maintainer  :  mikkonecny@gmail.com
    Stability   :  experimental
    Portability :  portable

    Arbitrary precision floating-point numbers with up/down-rounded operations.
-}

module AERN2.MP.Float
  (
   -- * Precision operations
   module Precision
   -- * Helper structure
   , module Auxi
   -- * The type definition and basic operations
   , module Type
   -- * Arithmetic operations
   , module Arithmetic
   , distUp, distDown, avgUp, avgDown
   -- * Conversions, comparisons and norm, constants such as NaN, infinity
   , module Conversions
   -- * Infix operators for up/down-rounded operations
   , module Operators
   -- * Tests
   , module Tests
   )
where

import MixedTypesNumPrelude
-- import qualified Prelude as P

import AERN2.MP.Precision as Precision
import AERN2.MP.Float.Auxi as Auxi

import AERN2.MP.Float.Type as Type
import AERN2.MP.Float.Arithmetic as Arithmetic
import AERN2.MP.Float.Conversions as Conversions

import AERN2.MP.Float.Operators as Operators
import AERN2.MP.Float.PreludeNum ()
import AERN2.MP.Float.Tests as Tests

-- | Computes an upper bound to the distance @|x - y|@ of @x@ and @y@.
distUp :: MPFloat -> MPFloat -> MPFloat
distUp x y = if x >= y then x -^ y else y -^ x

-- | Computes a lower bound to the distance @|x - y|@ of @x@ and @y@.
distDown :: MPFloat -> MPFloat -> MPFloat
distDown x y = if x >= y then x -. y else y -. x

avgUp :: MPFloat -> MPFloat -> MPFloat
avgUp x y = (x +^ y) /^ (mpFloat 2)

avgDown :: MPFloat -> MPFloat -> MPFloat
avgDown x y = (x +. y) /. (mpFloat 2)