Portability | portable |
---|---|
Stability | experimental |
Maintainer | mik@konecny.aow.cz |
Some important elementary functions for real approximations and their maximal extensions for interval approximations.
- erSqr_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> ira
- erSqr_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> ira
- erPow_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> ira
- erPow_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> ira
- erSqrt_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> ira
- erSqrt_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> ira -> ira
- erRoot_R :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> ira
- erRoot_IR :: (ERIntApprox ira, Ord ira) => EffortIndex -> Integer -> ira -> ira
- erExp_R :: ERIntApprox ira => EffortIndex -> ira -> ira
- erExp_IR :: ERIntApprox ira => EffortIndex -> ira -> ira
- erLog_R :: ERIntApprox ira => EffortIndex -> ira -> ira
- erLog_IR :: ERIntApprox ira => EffortIndex -> ira -> ira
- erSine_R :: ERIntApprox ira => EffortIndex -> ira -> ira
- erSine_IR :: ERIntApprox ira => EffortIndex -> ira -> ira
- erCosine_R :: ERIntApprox ira => EffortIndex -> ira -> ira
- erCosine_IR :: ERIntApprox ira => EffortIndex -> ira -> ira
- erATan_R :: ERIntApprox ira => EffortIndex -> ira -> ira
- erATan_IR :: ERIntApprox ira => EffortIndex -> ira -> ira
- erPi_R :: ERIntApprox ira => EffortIndex -> ira
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).