AERN-Net-0.2.1: Compositional lazy dataflow networks for exact real number computation Source code Contents Index

Control.ERNet.Blocks.Real.LFT Portability portable Stability experimental Maintainer mik@konecny.aow.cz

Contents protocol processes arithmetic

Description

A protocol for sending a real number using a stream of LFT digits based on the work of Potts and Edalat (1997).

Synopsis

data QALFTRealQ = QALFTRealQ Int data QALFTRealA = QALFTRealA [LFTDigit] data LFTDigit = LFT_L | LFT_M | LFT_R | LFT_SG_ZER | LFT_SG_INF | LFT_SG_POS | LFT_SG_NEG lftDigit2Tensor :: LFTDigit -> LFTTensor chTLFTReal :: ChannelType lftRealNumberIncremProcess :: (Channel sIn sOut sInAnyProt sOutAnyProt, ERIntApprox ra, Typeable ra) => ERProcessName -> (EffortIndex -> ra) -> ERProcess sInAnyProt sOutAnyProt lftRealNumberBufferForkProcess :: Channel sIn sOut sInAnyProt sOutAnyProt => ERProcessName -> ERProcess sInAnyProt sOutAnyProt data LFTTensor = LFTTensor { lftTNSrank :: Int lftTNScoeffs :: Map [Bool] Integer } lftConst :: Integer -> Integer -> LFTTensor lftMatrix :: Integer -> Integer -> Integer -> Integer -> LFTTensor lftTensorBinary :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> LFTTensor lftTensorInfo :: ERApprox ra => Granularity -> LFTTensor -> ExtInterval ra lftTensorIsPositive :: LFTTensor -> Bool lftTensorCompose :: LFTTensor -> Int -> LFTTensor -> LFTTensor lftTensorComposeUnary :: LFTTensor -> LFTTensor -> LFTTensor

protocol

data QALFTRealQ Source

Constructors QALFTRealQ Int Instances Eq QALFTRealQ Ord QALFTRealQ Show QALFTRealQ Typeable QALFTRealQ HTML QALFTRealQ QAProtocol QALFTRealQ QALFTRealA

data QALFTRealA Source

Constructors QALFTRealA [LFTDigit] Instances Eq QALFTRealA Ord QALFTRealA Show QALFTRealA Typeable QALFTRealA HTML QALFTRealA QAProtocol QALFTRealQ QALFTRealA

data LFTDigit Source

Constructors LFT_L LFT_M LFT_R LFT_SG_ZER LFT_SG_INF LFT_SG_POS LFT_SG_NEG Instances Eq LFTDigit Ord LFTDigit Show LFTDigit Typeable LFTDigit HTML LFTDigit

lftDigit2Tensor :: LFTDigit -> LFTTensor Source

Interpret the LFT digits as LFTs.

chTLFTReal :: ChannelType Source

processes

lftRealNumberIncremProcess Source

:: (Channel sIn sOut sInAnyProt sOutAnyProt, ERIntApprox ra, Typeable ra) => ERProcessName -> EffortIndex -> ra the number to represent; intersection of this sequence has to converge to a singleton -> ERProcess sInAnyProt sOutAnyProt A process communicating a real number to a single client incrementally digit by digit.

lftRealNumberBufferForkProcess :: Channel sIn sOut sInAnyProt sOutAnyProt => ERProcessName -> ERProcess sInAnyProt sOutAnyProt Source

A process that receives a real number incrementally digit by digit and makes it available to multiple clients incrementally or non-incrementally.

arithmetic

data LFTTensor Source

A multi-dimensional linear fractional transformation with integer coefficients. Constructors LFTTensor lftTNSrank :: Int lftTNScoeffs :: Map [Bool] Integer the first Bool indicates whether or not the term is in the numerator of the LFT Instances Show LFTTensor

lftConst :: Integer -> Integer -> LFTTensor Source

Constructor for a 0-ary LFT with integer coefficients.

lftMatrix :: Integer -> Integer -> Integer -> Integer -> LFTTensor Source

Constructor for a unary LFT with integer coefficients.

lftTensorBinary :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> LFTTensor Source

Constructor for a binary LFT with integer coefficients.

lftTensorInfo :: ERApprox ra => Granularity -> LFTTensor -> ExtInterval ra Source

Work out what interval is the image of the lft when all variables are given the value [0,oo]. The returned interval may be slightly bigger than the exact image due to rounding but it always contains the whole exact image.

lftTensorIsPositive :: LFTTensor -> Bool Source

lftTensorCompose :: LFTTensor -> Int -> LFTTensor -> LFTTensor Source

Compose two LFTs, ie substituting one into another using one of its variables.

lftTensorComposeUnary :: LFTTensor -> LFTTensor -> LFTTensor Source

Compose two unary LFTs, ie substituting one into the other.

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