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87 lines
4.7 KiB
Haskell
87 lines
4.7 KiB
Haskell
-----------------------------------------------------------------------------
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-- |
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-- Module : Data.SBV.Tools.ExpectedValue
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-- Copyright : (c) Levent Erkok
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-- License : BSD3
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-- Maintainer : erkokl@gmail.com
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-- Stability : experimental
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--
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-- Computing the expected value of a symbolic variable
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-----------------------------------------------------------------------------
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{-# LANGUAGE PatternGuards #-}
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module Data.SBV.Tools.ExpectedValue (expectedValue, expectedValueWith) where
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import Control.DeepSeq (rnf)
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import System.Random (newStdGen, StdGen)
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import Numeric
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import Data.SBV.BitVectors.Data
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-- | Generalized version of 'expectedValue', allowing the user to specify the
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-- warm-up count and the convergence factor. Maximum iteration count can also
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-- be specified, at which point convergence won't be sought. The boolean controls verbosity.
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expectedValueWith :: Outputtable a => Bool -> Int -> Maybe Int -> Double -> Symbolic a -> IO [Double]
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expectedValueWith chatty warmupCount mbMaxIter epsilon m
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| warmupCount < 0 || epsilon < 0
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= error $ "SBV.expectedValue: warmup count and epsilon both must be non-negative, received: " ++ show (warmupCount, epsilon)
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| True
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= warmup warmupCount (repeat 0) >>= go warmupCount
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where progress s | not chatty = return ()
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| True = putStr $ "\r*** " ++ s
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warmup :: Int -> [Integer] -> IO [Integer]
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warmup 0 v = do progress $ "Warmup complete, performed " ++ show warmupCount ++ " rounds.\n"
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return v
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warmup n v = do progress $ "Performing warmup, round: " ++ show (warmupCount - n)
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g <- newStdGen
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t <- runOnce g
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let v' = zipWith (+) v t
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rnf v' `seq` warmup (n-1) v'
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runOnce :: StdGen -> IO [Integer]
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runOnce g = do (_, Result _ _ _ _ cs _ _ _ _ _ cstrs os) <- runSymbolic' (Concrete g) (m >>= output)
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let cval o = case o `lookup` cs of
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Nothing -> error "SBV.expectedValue: Cannot compute expected-values in the presence of uninterpreted constants!"
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Just cw -> case (cwKind cw, cwVal cw) of
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(KBool, _) -> if cwToBool cw then 1 else 0
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(KBounded{}, CWInteger v) -> v
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(KUnbounded, CWInteger v) -> v
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(KReal, _) -> error "Cannot compute expected-values for real valued results."
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_ -> error $ "SBV.expectedValueWith: Unexpected CW: " ++ show cw
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if all ((== 1) . cval) cstrs
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then return $ map cval os
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else runOnce g -- constraint not satisfied try again with the same set of constraints
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go :: Int -> [Integer] -> IO [Double]
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go cases curSums
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| Just n <- mbMaxIter, n < curRound
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= do progress "\n"
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progress "Maximum iteration count reached, stopping.\n"
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return curEVs
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| True
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= do g <- newStdGen
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t <- runOnce g
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let newSums = zipWith (+) curSums t
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newEVs = map ev' newSums
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diffs = zipWith (\x y -> abs (x - y)) newEVs curEVs
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if all (< epsilon) diffs
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then do progress $ "Converges with epsilon " ++ show epsilon ++ " after " ++ show curRound ++ " rounds.\n"
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return newEVs
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else do progress $ "Tuning, round: " ++ show curRound ++ " (margin: " ++ showFFloat (Just 6) (maximum (0:diffs)) "" ++ ")"
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go newCases newSums
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where curRound = cases - warmupCount
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newCases = cases + 1
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ev, ev' :: Integer -> Double
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ev x = fromIntegral x / fromIntegral cases
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ev' x = fromIntegral x / fromIntegral newCases
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curEVs = map ev curSums
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-- | Given a symbolic computation that produces a value, compute the
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-- expected value that value would take if this computation is run
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-- with its free variables drawn from uniform distributions of its
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-- respective values, satisfying the given constraints specified by
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-- 'constrain' and 'pConstrain' calls. This is equivalent to calling
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-- 'expectedValueWith' the following parameters: verbose, warm-up
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-- round count of @10000@, no maximum iteration count, and with
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-- convergence margin @0.0001@.
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expectedValue :: Outputtable a => Symbolic a -> IO [Double]
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expectedValue = expectedValueWith True 10000 Nothing 0.0001
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