AERN-Real-0.9.7.1: arbitrary precision interval arithmetic for approximating exact real numbers

Portabilityportable
Stabilityexperimental
Maintainermik@konecny.aow.cz

Data.Number.ER.Real.Arithmetic.Elementary

Contents

Description

Some important elementary functions for real approximations and their maximal extensions for interval approximations.

Synopsis

specialised exponentiation

erSqr_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> iraSource

erSqr_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> iraSource

erPow_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> iraSource

erPow_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> iraSource

erSqrt_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> iraSource

erSqrt_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> iraSource

erRoot_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> iraSource

erRoot_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> iraSource

exponentiation and logarithm

erExp_R :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erExp_IR :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erLog_R :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erLog_IR :: ERIntApprox ira => EffortIndex -> ira -> iraSource

trigonometrics

erSine_R :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erSine_IR :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erCosine_R :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erCosine_IR :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erATan_R :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erATan_IR :: ERIntApprox ira => EffortIndex -> ira -> iraSource

erPi_R :: ERIntApprox ira => EffortIndex -> iraSource

pi using Bellard's formula

Convergence properties:

  • shrinking sequence
  • rate at least 2^(-i).