factory 0.2.0.4 → 0.2.0.5

raw patch · 19 files changed

+137/−89 lines, 19 filesdep ~toolshedPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

Dependency ranges changed: toolshed

API changes (from Hackage documentation)

Files

• changelog +7/−0
• factory.cabal +3/−3
• makefile +8/−8
• src/Factory/Math/Implementations/Pi/Spigot/Spigot.hs +1/−1
• src/Factory/Math/Implementations/Primality.hs +2/−2
• src/Factory/Math/Implementations/PrimeFactorisation.hs +1/−3
• src/Factory/Math/Implementations/Primes/SieveOfAtkin.hs +6/−6
• src/Factory/Math/Implementations/Primes/TrialDivision.hs +1/−1
• src/Factory/Math/Implementations/Primes/TurnersSieve.hs +1/−1
• src/Factory/Math/Implementations/SquareRoot.hs +4/−4
• src/Factory/Math/PerfectPower.hs +1/−1
• src/Factory/Math/Primes.hs +15/−1
• src/Factory/Math/Probability.hs +4/−4
• src/Factory/Math/SquareRoot.hs +2/−2
• src/Factory/Math/Statistics.hs +2/−2
• src/Factory/Test/Performance/Primes.hs +8/−1
• src/Factory/Test/QuickCheck/Primality.hs +1/−1
• src/Factory/Test/QuickCheck/Primes.hs +1/−1
• src/Main.hs +69/−47

@@ -55,3 +55,10 @@ 0.2.0.4 	* Added classes 'Eq' and 'Show' to many contexts, for migration to 'ghc-7.4'. 	* Minor re-formatting.+0.2.0.5+	* Minor clarification of 'Factory.Math.Implementations.Primality.witnessesCompositeness'.+	* Added details to any failure to parse the command-line arguments.+	* Defined package's name using program's name, in "Main.hs".+	* Added 'Factory.Math.Primes.mersenneNumbers'.+	* Replaced use of 'mod' on positive integers, with the faster 'rem', in 'Factory.Math.Implementations.Pi.Spigot.Spigot.processColumns', 'Factory.Math.Implementations.Primality.witnessesCompositeness', 'Factory.Math.Implementations.Primes.TrialDivision.isIndivisibleBy', 'Factory.Math.Implementations.Primes.SieveOfAtkin.polynomialTypeLookup', 'Factory.Math.Implementations.Primes.SieveOfAtkin.findPolynomialSolutions', 'Factory.Math.Implementations.Primes.TurnersSieve.turnersSieve', 'Factory.Math.PerfectPower.maybeSquareNumber'.+	* Replaced calls to 'realToFrac' with 'toRational' in; "Factory.Math.Implementations.SquareRoot", 'Factory.Math.Statistics.getDispersionFromMean', 'Factory.Math.SquareRoot.getDiscrepancy', 'Factory.Math.SquareRoot.getAccuracy', to more clearly represent the required operation.

@@ -1,6 +1,6 @@ --Package-properties Name:			factory-Version:		0.2.0.4+Version:		0.2.0.5 Cabal-Version:		>= 1.6 Copyright:		(C) 2011 Dr. Alistair Ward License:		GPL@@ -11,7 +11,7 @@ Build-Type:		Simple Description:		A library of number-theory functions, for; factorials, square-roots, Pi and primes. Category:		Math, Number Theory-Tested-With:		GHC == 6.10, GHC == 6.12, GHC == 7.0+Tested-With:		GHC == 6.10, GHC == 6.12, GHC == 7.0, GHC == 7.4 Homepage:		http://functionalley.eu Maintainer:		factory <at> functionalley <dot> eu Bug-reports:		factory <at> functionalley <dot> eu@@ -95,7 +95,7 @@         containers,         primes >= 0.1,         random,-        toolshed == 0.13.*+        toolshed >= 0.13      if flag(threaded)         Build-depends:	parallel >= 3.0

@@ -19,37 +19,37 @@  install: build haddock 	@[ -z "$$CABAL_INSTALL_OPTIONS" ] || echo "INFO: CABAL_INSTALL_OPTIONS='$$CABAL_INSTALL_OPTIONS'"-	runhaskell Setup.hs $@ $$CABAL_INSTALL_OPTIONS+	runhaskell Setup $@ $$CABAL_INSTALL_OPTIONS  prof: 	CABAL_CONFIGURE_OPTIONS="--enable-library-profiling --enable-executable-profiling $$CABAL_CONFIGURE_OPTIONS" make install  copy: build 	@[ -z "$$CABAL_COPY_OPTIONS" ] || echo "INFO: CABAL_COPY_OPTIONS='$$CABAL_COPY_OPTIONS'"-	runhaskell Setup.hs $@ $$CABAL_COPY_OPTIONS+	runhaskell Setup $@ $$CABAL_COPY_OPTIONS  build: configure 	@[ -z "$$CABAL_BUILD_OPTIONS" ] || echo "INFO: CABAL_BUILD_OPTIONS='$$CABAL_BUILD_OPTIONS'"-	runhaskell Setup.hs $@ $$CABAL_BUILD_OPTIONS+	runhaskell Setup $@ $$CABAL_BUILD_OPTIONS  configure: factory.cabal Setup.hs 	@[ -z "$$CABAL_CONFIGURE_OPTIONS" ] || echo "INFO: CABAL_CONFIGURE_OPTIONS='$$CABAL_CONFIGURE_OPTIONS'"-	runhaskell Setup.hs $@ $$CABAL_CONFIGURE_OPTIONS	#--user+	runhaskell Setup $@ $$CABAL_CONFIGURE_OPTIONS	#--user  haddock: configure-	PATH=~/.cabal/bin:$$PATH runhaskell Setup.hs $@ --hyperlink-source	#Amend path to find 'HsColour', as required for 'hyperlink-source'.+	PATH=~/.cabal/bin:$$PATH runhaskell Setup $@ --hyperlink-source	#Amend path to find 'HsColour', as required for 'hyperlink-source'.  hlint: 	@$@ -i 'Use &&' -i 'Reduce duplication' -i 'Redundant bracket' src/ -sdist: configure-	runhaskell Setup.hs $@+sdist:+	runhaskell Setup $@  check: sdist 	cabal upload --check --verbose=3 dist/*.tar.gz;  clean:-	runhaskell Setup.hs $@+	runhaskell Setup $@ 	find src -type f \( -name '*.hc' -o -name '*.hcr' -o -name '*.hi' -o -name '*.o' \) -delete  help:

@@ -111,7 +111,7 @@ processColumns series preDigits l 	| overflowMargin > 1	= preDigits ++ nextRow [digit]				--There's neither overflow, nor risk of impact from subsequent overflow. 	| overflowMargin == 1	= nextRow $ preDigits ++ [digit]			--There's no overflow, but risk of impact from subsequent overflow.-	| otherwise		= map ((`mod` decimal) . succ) preDigits ++ nextRow [0]	--Overflow => propagate the excess to previously withheld preDigits.+	| otherwise		= map ((`rem` decimal) . succ) preDigits ++ nextRow [0]	--Overflow => propagate the excess to previously withheld preDigits. 	where 		results :: [QuotRem] 		results	= init $ scanr carryAndDivide (0, undefined) l

@@ -167,10 +167,10 @@ 	-> i	-- ^ Base. 	-> Bool witnessesCompositeness candidate oddRemainder nPowersOfTwo base	= all (-	$ ((`mod` candidate) . Math.Power.square) `iterate` Math.Power.raiseModulo base oddRemainder candidate	--Repeatedly modulo-square.+	$ ((`rem` candidate) . Math.Power.square) `iterate` Math.Power.raiseModulo base oddRemainder candidate	--Repeatedly modulo-square.  ) [ 	(/= 1) . head,					--Check whether the zeroeth modulo-power is incongruent to one.-	all (/= pred candidate) . take nPowersOfTwo	--Check whether any modulo-power is incongruent to -1.+	notElem (pred candidate) . take nPowersOfTwo	--Check whether any modulo-power is incongruent to -1.  ]  {- |

@@ -73,9 +73,7 @@ 		FermatsMethod	-> Data.PrimeFactors.reduce . factoriseByFermatsMethod 		TrialDivision	-> factoriseByTrialDivision -{- |-	* <http://en.wikipedia.org/wiki/Dixon%27s_factorization_method>.--}+-- | <http://en.wikipedia.org/wiki/Dixon%27s_factorization_method>. factoriseByDixonsMethod :: Integral base => base -> Data.PrimeFactors.Factors base exponent factoriseByDixonsMethod	= undefined 

@@ -113,14 +113,14 @@ --	select :: Integral i => i -> PolynomialType 	select n 		| any (-			(== 0) . (n `mod`)		--Though this is merely /Trial Division/, it's only performed over a short bounded interval of numerators.+			(== 0) . (n `rem`)		--Though this is merely /Trial Division/, it's only performed over a short bounded interval of numerators. 		) primeComponents	= None 		| r `elem` [1, 5]	= ModFour	--We actually require @(n `mod` 4 == 1)@, but this is the equivalent modulo 12, with @(r == 9)@ removed because they're all divisible by /3/. 		| r == 7		= ModSix	--We actually require @(n `mod` 6 == 1)@, but this is the equivalent modulo 12, where @(r == 1)@ has been accounted for above. 		| r == 11		= ModTwelve	--We require @(n `mod` 12 == 11)@. 		| otherwise		= None 		where-			r		= n `mod` atkinsModulus+			r		= n `rem` atkinsModulus 			primeComponents	= drop nInherentPrimes $ Data.PrimeWheel.getPrimeComponents primeWheel  -- | The constant, infinite list of the /squares/, of integers increasing from /1/.@@ -176,19 +176,19 @@ 				x'	<- takeWhile (<= pred maxPrime) $ map (* 4) squares, 				z	<- takeWhile (<= maxPrime) $ map (+ x') oddSquares, 				lookupPolynomialType z == ModFour-		], --Twice the length of the other two lists.+		], --List-comprehension. Twice the length of the other two lists. 		{-# SCC "3x^2+y^2" #-} filterOddRepetitions [ 			z | 				x'	<- takeWhile (<= pred maxPrime) $ map (* 3) squares, 				z	<- takeWhile (<= maxPrime) . map (+ x') $ if even x' then oddSelection else evenSelection, 				lookupPolynomialType z == ModSix-		],+		], --List-comprehension. 		{-# SCC "3x^2-y^2" #-} filterOddRepetitions [ 			z | 				x2	<- takeWhile (<= maxPrime `div` 2) squares, 				z	<- dropWhile (> maxPrime) . map (3 * x2 -) . takeWhile (< x2) $ if even x2 then oddSelection else evenSelection, 				lookupPolynomialType z == ModTwelve-		]+		] --List-comprehension. 	] where 		(evenSquares, oddSquares)	= Data.List.partition even squares @@ -201,7 +201,7 @@ 			selection101 xs			= xs  --		lookupPolynomialType :: (Data.Array.IArray.Ix i, Integral i) => i -> PolynomialType-		lookupPolynomialType	= (polynomialTypeLookup primeWheel maxPrime !) . (`mod` polynomialTypeLookupPeriod primeWheel)+		lookupPolynomialType	= (polynomialTypeLookup primeWheel maxPrime !) . (`rem` polynomialTypeLookupPeriod primeWheel)  -- | Generates the /bounded/ list of multiples, of the /square/ of the specified prime, skipping those which aren't required. generateMultiplesOfSquareTo :: Integral i

@@ -38,7 +38,7 @@ 	=> i	-- ^ The numerator. 	-> [i]	-- ^ The denominators of which it must not be a multiple. 	-> Bool-isIndivisibleBy numerator	= all ((/= 0) . (numerator `mod`)) . takeWhile (<= Math.PrimeFactorisation.maxBoundPrimeFactor numerator)+isIndivisibleBy numerator	= all ((/= 0) . (numerator `rem`)) . takeWhile (<= Math.PrimeFactorisation.maxBoundPrimeFactor numerator)  {-# INLINE isIndivisibleBy #-} 

@@ -41,7 +41,7 @@ 		filter ( 			\candidate	-> any ($ candidate) [ 				(< Math.Power.square prime),	--Unconditionally admit any candidate smaller than the square of the last prime.-				(/= 0) . (`mod` prime)		--Ensure indivisibility, of all subsequent candidates, by the last prime discovered.+				(/= 0) . (`rem` prime)		--Ensure indivisibility, of all subsequent candidates, by the last prime discovered. 			] 		) candidates 	 )

@@ -112,9 +112,9 @@ 			dydx	= 2 * x						--The gradient, at the estimated value 'x'. 			dx	= recip $ dydx / dy - recip dydx ---	step NewtonRaphsonIteration y x	= (x + realToFrac y / x) / 2		--This is identical to the /Babylonian Method/.---	step NewtonRaphsonIteration y x	= x / 2 + realToFrac y / (2 * x)	--Faster.-	step NewtonRaphsonIteration y x	= x / 2 + (realToFrac y / 2) / x	--Faster still.+--	step NewtonRaphsonIteration y x	= (x + toRational y / x) / 2		--This is identical to the /Babylonian Method/.+--	step NewtonRaphsonIteration y x	= x / 2 + toRational y / (2 * x)	--Faster.+	step NewtonRaphsonIteration y x	= x / 2 + (toRational y / 2) / x	--Faster still.  	step (TaylorSeries terms) y x	= squareRootByTaylorSeries terms y x @@ -184,7 +184,7 @@ 	| otherwise	= Math.Summation.sumR' . take terms . zipWith (*) taylorSeriesCoefficients $ iterate (* relativeError) x 	where 		relativeError :: Math.SquareRoot.Result-		relativeError	= pred $ realToFrac y / Math.Power.square x	--Pedantically, this is the error in y, which is twice the magnitude of the error in x.+		relativeError	= pred $ toRational y / Math.Power.square x	--Pedantically, this is the error in y, which is twice the magnitude of the error in x.  -- | Iterates from the estimated value, towards the /square-root/, a sufficient number of times to achieve the required accuracy. squareRootByIteration :: Real operand => Algorithm -> ProblemSpecification operand

@@ -45,7 +45,7 @@ maybeSquareNumber :: Integral i => i -> Maybe i maybeSquareNumber i --	| i < 0					= Nothing	--This function is performance-sensitive, but this test is neither strictly nor frequently required.-	| all (\(modulus, valid) -> mod i modulus `elem` valid) [+	| all (\(modulus, valid) -> rem i modulus `elem` valid) [ --							--Distribution of moduli amongst perfect squares	Cumulative failure-detection. 		(16,	[0,1,4,9]),			--All moduli are equally likely.			75% 		(9,	[0,1,4,7]),			--Zero occurs 33%, the others only 22%.			88%

@@ -24,7 +24,8 @@ -- * Types-classes 	Algorithmic(..), -- * Functions-	primorial+	primorial,+	mersenneNumbers ) where  import qualified	Control.DeepSeq@@ -48,3 +49,16 @@ 	Integral		i  ) => algorithm -> [i] primorial	= scanl (*) 1 . primes++{- |+	* Returns the constant ordered infinite list of /Mersenne numbers/.++	* Only the subset composed from a prime exponent is returned; which is a strict superset of the /Mersenne Primes/.++	* <http://en.wikipedia.org/wiki/Mersenne_prime>.++	* <http://mathworld.wolfram.com/MersenneNumber.html>+-}+mersenneNumbers :: (Algorithmic algorithm, Integral i) => algorithm -> [i]+mersenneNumbers algorithm	= map (pred . (2 ^)) (primes algorithm :: [Int])	--Whilst the exponentiation could be parallelised, not all values are known to be required.+

@@ -45,7 +45,7 @@  -- | Describes a /continuous probability-distribution/; <http://en.wikipedia.org/wiki/List_of_probability_distributions#Continuous_distributions>. data ContinuousDistribution f-	= UniformDistribution (Data.Interval.Interval f)	-- ^ Defines a /Uniform/-distribution within a closed /interval/; <http://en.wikipedia.org/wiki/Uniform_distribution>.+	= UniformDistribution (Data.Interval.Interval f)	-- ^ Defines a /Uniform/-distribution within a /closed interval/; <http://en.wikipedia.org/wiki/Uniform_distribution>. 	| NormalDistribution f f				-- ^ Defines a /Normal/-distribution with a particular /mean/ and /variance/; <http://en.wikipedia.org/wiki/Normal_distribution>. 	deriving (Eq, Read, Show) @@ -61,13 +61,13 @@ 	getErrors (PoissonDistribution lambda)	= ToolShed.SelfValidate.extractErrors [(lambda < 0, "Negative lambda=" ++ show lambda ++ ".")]  {- |-	* Converts a pair of independent /uniformly distributed/ random numbers, within the /semi-closed/ /unit interval/ /(0 .. 1]/,+	* Converts a pair of independent /uniformly distributed/ random numbers, within the /semi-closed unit interval/ /(0,1]/, 	to a pair of independent /normally distributed/ random numbers, of standardized /mean/=0, and /variance/=1.  	* <http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform>. -} boxMullerTransform :: (Floating f, Ord f, Show f)-	=> (f, f)	-- ^ Independent, /uniformly distributed/ random numbers, which must be within the /semi-closed unit interval/, /(0, 1]/.+	=> (f, f)	-- ^ Independent, /uniformly distributed/ random numbers, which must be within the /semi-closed unit interval/, /(0,1]/. 	-> (f, f)	-- ^ Independent, /normally distributed/ random numbers, with standardized /mean/=0 and /variance/=1. boxMullerTransform cartesian 	| not . uncurry (&&) $ ToolShed.Data.Pair.mirror inSemiClosedUnitInterval cartesian	= error $ "Factory.Math.Probability.boxMullerTransform:\tspecified Cartesian coordinates, must be within semi-closed unit-interval (0, 1]; " ++ show cartesian@@ -126,7 +126,7 @@ 	-> [f] generateContinuousPopulation 0 _ _				= [] generateContinuousPopulation populationSize probabilityDistribution randomGen-	| populationSize < 0						= error $ "Factory.Math.Probability.generateDiscretePopulation:\tinvalid population-size=" ++ show populationSize+	| populationSize < 0						= error $ "Factory.Math.Probability.generateContinuousPopulation:\tinvalid population-size=" ++ show populationSize 	| not $ ToolShed.SelfValidate.isValid probabilityDistribution	= error $ "Factory.Math.Probability.generateContinuousPopulation:\t" ++ ToolShed.SelfValidate.getFirstError probabilityDistribution 	| otherwise						= take populationSize $ ( 		case probabilityDistribution of

@@ -98,7 +98,7 @@ 	* CAVEAT: the magnitude is twice the error in the /square-root/. -} getDiscrepancy :: Real operand => operand -> Result -> Result-getDiscrepancy y x	= realToFrac y - Math.Power.square x+getDiscrepancy y x	= toRational y - Math.Power.square x  -- | True if the specified estimate for the /square-root/, is precise. isPrecise :: Real operand => operand -> Result -> Bool@@ -114,7 +114,7 @@ getAccuracy y x 	| absoluteError == 0	= maxBound	--Bodge. --	| otherwise		= length . takeWhile (< 1) $ iterate (* 10) relativeError	--CAVEAT: too slow.-	| otherwise		= length $ show (round $ realToFrac y / absoluteError :: Integer)+	| otherwise		= length $ show (round $ toRational y / absoluteError :: Integer) 	where 		absoluteError :: Result 		absoluteError	= abs (getDiscrepancy y x) / 2	--NB: the magnitude of the error in 'y', is twice the error in its square-root, 'x'.

@@ -48,7 +48,7 @@ -} getMean :: (Data.Foldable.Foldable f, Real r, Fractional result) => f r -> result getMean x-	| denominator == 0	= error "Factory.Math.Statistics.getMean:\tno data => no result."+	| denominator == 0	= error "Factory.Math.Statistics.getMean:\tno data => undefined result." 	| otherwise		= realToFrac numerator / fromIntegral denominator 	where 		(numerator, denominator)	= Data.Foldable.foldr (\s -> (+ s) *** succ) (0, 0 :: Int) x@@ -64,7 +64,7 @@ 	Functor			f, 	Real			r  ) => (Data.Ratio.Rational -> Data.Ratio.Rational) -> f r -> result-getDispersionFromMean weight x	= getMean $ fmap (weight . (+ negate mean) . realToFrac) x	where+getDispersionFromMean weight x	= getMean $ fmap (weight . (+ negate mean) . toRational) x	where 	mean :: Data.Ratio.Rational 	mean	= getMean x 

@@ -22,7 +22,8 @@  module Factory.Test.Performance.Primes( -- * Functions-	primesPerformance+	primesPerformance,+	mersenneNumbersPerformance ) where  import qualified	Control.DeepSeq@@ -38,3 +39,9 @@ 	Integral		i  ) => algorithm -> Int -> IO (Double, i) primesPerformance algorithm	= ToolShed.System.TimePure.getCPUSeconds . (Math.Primes.primes algorithm !!)++-- | Measures the CPU-time required to find the specified number of /Mersenne/-numbers, which is returned together with the requested list.+mersenneNumbersPerformance :: Math.Primes.Algorithmic algorithm => algorithm -> Int -> IO (Double, [Integer])+mersenneNumbersPerformance primalityAlgorithm i+	| i < 0		= error $ "Factory.Test.Performance.Primes.mersenneNumbersPerformance:\tnegative number; " ++ show i+	| otherwise	= ToolShed.System.TimePure.getCPUSeconds . take i $ Math.Primes.mersenneNumbers primalityAlgorithm

@@ -40,7 +40,7 @@ instance Test.QuickCheck.Arbitrary factorisationAlgorithm => Test.QuickCheck.Arbitrary (Math.Implementations.Primality.Algorithm factorisationAlgorithm)	where 	arbitrary	= Test.QuickCheck.oneof [ 		Math.Implementations.Primality.AKS <$> Test.QuickCheck.arbitrary,-		return Math.Implementations.Primality.MillerRabin+		return {-to Gen-monad-} Math.Implementations.Primality.MillerRabin 	 ] #if !(MIN_VERSION_QuickCheck(2,1,0)) 	coarbitrary	= undefined	--CAVEAT: stops warnings from ghc.

@@ -46,7 +46,7 @@  instance Test.QuickCheck.Arbitrary Math.Implementations.Primes.Algorithm.Algorithm	where 	arbitrary	= Test.QuickCheck.oneof [-		return Math.Implementations.Primes.Algorithm.TurnersSieve,+		return {-to Gen-monad-} Math.Implementations.Primes.Algorithm.TurnersSieve, 		Math.Implementations.Primes.Algorithm.TrialDivision . (`mod` 10) <$> Test.QuickCheck.arbitrary, 		Math.Implementations.Primes.Algorithm.SieveOfEratosthenes . (`mod` 10) <$> Test.QuickCheck.arbitrary 	 ]

@@ -29,6 +29,8 @@ -- ** Type-synonyms --	CommandLineAction, -- * Functions+--	read',+--	readCommandArg, 	main ) where @@ -69,113 +71,131 @@ -- | Used to thread user-defined command-line options, though the list of functions which implement them. type CommandLineAction	= Test.CommandOptions.CommandOptions -> IO Test.CommandOptions.CommandOptions	--Supplied as the type-argument to 'G.OptDescr'. +-- | On failure to parse the specified string, returns an explanatory error.+read' :: Read a => String -> String -> a+read' errorMessage s	= case reads s of+	[(x, _)]	-> x+	_		-> error $ errorMessage ++ show s++-- | On failure to parse a command-line argument, returns an explanatory error.+readCommandArg :: Read a => String -> a+readCommandArg	= read' "Failed to parse command-line argument "+ -- | Parses the command-line arguments, to determine 'Test.CommandOptions.CommandOptions'. main :: IO () main	= do 	progName	<- System.Environment.getProgName-	args		<- System.Environment.getArgs  	let-		usage :: String-		usage	= "Usage:\t" ++ G.usageInfo progName optDescrList+		usageMessage :: String+		usageMessage	= "Usage:\t" ++ G.usageInfo progName optDescrList ---Define the command-line options, and the 'CommandLineAction's used to handle them. 		optDescrList :: [G.OptDescr CommandLineAction] 		optDescrList	= [---				 String	[String]				(G.ArgDescr CommandLineAction)												String-			G.Option "?"	["help"]				(G.NoArg $ const printUsage)												"Display this help-text & then exit.",-			G.Option ""	["verbose"]				(G.NoArg $ return {-to IO-monad-} . Test.CommandOptions.setVerbose)							("Provide additional information where available; default '" ++ show (Test.CommandOptions.verbose ToolShed.Defaultable.defaultValue) ++ "'."),-			G.Option ""	["version"]				(G.NoArg $ const printVersion)												"Print version-information & then exit.",-			G.Option "q"	["runQuickChecks"]			(G.NoArg $ const runQuickChecks)											"Run Quick-checks using arbitrary data & then exit.",-			G.Option ""	["carmichaelNumbersPerformance"]	(carmichaelNumbersPerformance `G.ReqArg` "(Math.Implementations.Primality.Algorithm, Int)")				"Test the performance of 'Math.Primality.carmichaelNumbers'.",-			G.Option ""	["factorialPerformance"]		(factorialPerformance `G.ReqArg` "(Math.Implementations.Factorial.Algorithm, Integer)")					"Test the performance of 'Math.Factorial.factorial'.",-			G.Option ""	["factorialPerformanceGraph"]		(factorialPerformanceGraph `G.ReqArg` "Math.Implementations.Factorial.Algorithm")					"Test the performance of 'Math.Factorial.factorial', with an exponentially increasing operand.",-			G.Option ""	["factorialPerformanceGraphControl"]	(G.NoArg factorialPerformanceGraphControl)										"Test the performance of a naive factorial-implementation, with an exponentially increasing operand.",-			G.Option ""	["hyperoperationPerformance"]		(hyperoperationPerformance `G.ReqArg` "(Integer, Math.Hyperoperation.Base, Math.Hyperoperation.HyperExponent)")		"Test the performance of 'Math.Hyperoperation.hyperoperation', against the specified rank, base and hyper-exponent.",-			G.Option ""	["hyperoperationPerformanceGraphRank"]	(hyperoperationPerformanceGraphRank `G.ReqArg` "(Math.Hyperoperation.Base, Math.Hyperoperation.HyperExponent)")		"Test the performance of 'Math.Hyperoperation.hyperoperation', for the specified base and hyper-exponent, and a linearly increasing rank.",-			G.Option ""	["hyperoperationPerformanceGraphExponent"]	(hyperoperationPerformanceGraphExponent `G.ReqArg` "(Integer, Math.Hyperoperation.Base)")			"Test the performance of 'Math.Hyperoperation.hyperoperation', for the specified rank and base, and a linearly increasing hyper-exponent.",-			G.Option ""	["isPrimePerformance"]			(isPrimePerformance `G.ReqArg` "(Math.Implementations.Primality.Algorithm, Integer)")					"Test the performance of 'Math.Primality.isPrime'.",-			G.Option ""	["isPrimePerformanceGraph"]		(isPrimePerformanceGraph `G.ReqArg` "Math.Implementations.Primality.Algorithm")						"Test the performance of 'Math.Primality.isPrime', against the prime-indexed Fibonacci-numbers.",-			G.Option ""	["nCrPerformance"]			(nCrPerformance `G.ReqArg` "(Math.Implementations.Factorial.Algorithm, Integer, Integer)")				"Test the performance of 'Math.Factorial.factorial'.",-			G.Option ""	["piPerformance"]			(piPerformance `G.ReqArg` "(Math.Pi.Category, Math.Precision.DecimalDigits)")						"Test the performance of 'Math.Pi.openI'.",-			G.Option ""	["piPerformanceGraph"]			(piPerformanceGraph `G.ReqArg` "(Math.Pi.Category, Double, Math.Precision.DecimalDigits)")				"Test the performance of 'Math.Pi.openI', with an exponential precision-requirement (of the specified exponent), up to the specified limit.",-			G.Option ""	["primeFactorsPerformance"]		(primeFactorsPerformance `G.ReqArg` "(Math.Implementations.PrimeFactorisation.Algorithm, Integer)")			"Test the performance of 'Math.PrimeFactorisation.primeFactors'.",-			G.Option ""	["primeFactorsPerformanceGraph"]	(primeFactorsPerformanceGraph `G.ReqArg` "(Math.Implementations.PrimeFactorisation.Algorithm, Int)")			"Test the performance of 'Math.PrimeFactorisation.primeFactors', on the specified number of odd integers from the Fibonacci-sequence.",-			G.Option ""	["primesPerformance"]			(primesPerformance `G.ReqArg` "(Math.Implementations.Primes.Algorithm.Algorithm, Int)")					"Test the performance of 'Math.Primes.primes'.",-			G.Option ""	["squareRootPerformance"]		(squareRootPerformance `G.ReqArg` "(Math.Implementations.SquareRoot.Algorithm, Data.Ratio.Rational, DecimalDigits)")	"Test the performance of 'Math.SquareRoot.squareRoot'.",-			G.Option ""	["squareRootPerformanceGraph"]		(squareRootPerformanceGraph `G.ReqArg` "(Math.Implementations.SquareRoot.Algorithm, Data.Ratio.Rational)")		"Test the performance of 'Math.SquareRoot.squareRoot', with an exponentially increasing precision-requirement."+--				 String	[String]					(G.ArgDescr CommandLineAction)												String+			G.Option "?"	["help"]					(G.NoArg $ const printUsage)												"Display this help-text & then exit.",+			G.Option ""	["verbose"]					(G.NoArg $ return {-to IO-monad-} . Test.CommandOptions.setVerbose)							("Provide additional information where available; default '" ++ show (Test.CommandOptions.verbose ToolShed.Defaultable.defaultValue) ++ "'."),+			G.Option ""	["version"]					(G.NoArg $ const printVersion)												"Print version-information & then exit.",+			G.Option "q"	["runQuickChecks"]				(G.NoArg $ const runQuickChecks)											"Run Quick-checks using arbitrary data & then exit.",+			G.Option ""	["carmichaelNumbersPerformance"]		(carmichaelNumbersPerformance `G.ReqArg` "(Math.Implementations.Primality.Algorithm, Int)")				"Test the performance of 'Math.Primality.carmichaelNumbers'.",+			G.Option ""	["factorialPerformance"]			(factorialPerformance `G.ReqArg` "(Math.Implementations.Factorial.Algorithm, Integer)")					"Test the performance of 'Math.Factorial.factorial'.",+			G.Option ""	["factorialPerformanceGraph"]			(factorialPerformanceGraph `G.ReqArg` "Math.Implementations.Factorial.Algorithm")					"Test the performance of 'Math.Factorial.factorial', with an exponentially increasing operand.",+			G.Option ""	["factorialPerformanceGraphControl"]		(G.NoArg factorialPerformanceGraphControl)										"Test the performance of a naive factorial-implementation, with an exponentially increasing operand.",+			G.Option ""	["hyperoperationPerformance"]			(hyperoperationPerformance `G.ReqArg` "(Integer, Math.Hyperoperation.Base, Math.Hyperoperation.HyperExponent)")		"Test the performance of 'Math.Hyperoperation.hyperoperation', against the specified rank, base and hyper-exponent.",+			G.Option ""	["hyperoperationPerformanceGraphRank"]		(hyperoperationPerformanceGraphRank `G.ReqArg` "(Math.Hyperoperation.Base, Math.Hyperoperation.HyperExponent)")		"Test the performance of 'Math.Hyperoperation.hyperoperation', for the specified base and hyper-exponent, and a linearly increasing rank.",+			G.Option ""	["hyperoperationPerformanceGraphExponent"]	(hyperoperationPerformanceGraphExponent `G.ReqArg` "(Integer, Math.Hyperoperation.Base)")				"Test the performance of 'Math.Hyperoperation.hyperoperation', for the specified rank and base, and a linearly increasing hyper-exponent.",+			G.Option ""	["isPrimePerformance"]				(isPrimePerformance `G.ReqArg` "(Math.Implementations.Primality.Algorithm, Integer)")					"Test the performance of 'Math.Primality.isPrime'.",+			G.Option ""	["isPrimePerformanceGraph"]			(isPrimePerformanceGraph `G.ReqArg` "Math.Implementations.Primality.Algorithm")						"Test the performance of 'Math.Primality.isPrime', against the prime-indexed Fibonacci-numbers.",+			G.Option ""	["mersenneNumbersPerformance"]			(mersenneNumbersPerformance `G.ReqArg` "(Math.Implementations.Primes.Algorithm.Algorithm, Int)")			"Test the performance of 'Math.Primes.mersenneNumbers'.",+			G.Option ""	["factorialPerformance"]			(factorialPerformance `G.ReqArg` "(Math.Implementations.Factorial.Algorithm, Integer)")					"Test the performance of 'Math.Factorial.factorial'.",+			G.Option ""	["nCrPerformance"]				(nCrPerformance `G.ReqArg` "(Math.Implementations.Factorial.Algorithm, Integer, Integer)")				"Test the performance of 'Math.Factorial.factorial'.",+			G.Option ""	["piPerformance"]				(piPerformance `G.ReqArg` "(Math.Pi.Category, Math.Precision.DecimalDigits)")						"Test the performance of 'Math.Pi.openI'.",+			G.Option ""	["piPerformanceGraph"]				(piPerformanceGraph `G.ReqArg` "(Math.Pi.Category, Double, Math.Precision.DecimalDigits)")				"Test the performance of 'Math.Pi.openI', with an exponential precision-requirement (of the specified exponent), up to the specified limit.",+			G.Option ""	["primeFactorsPerformance"]			(primeFactorsPerformance `G.ReqArg` "(Math.Implementations.PrimeFactorisation.Algorithm, Integer)")			"Test the performance of 'Math.PrimeFactorisation.primeFactors'.",+			G.Option ""	["primeFactorsPerformanceGraph"]		(primeFactorsPerformanceGraph `G.ReqArg` "(Math.Implementations.PrimeFactorisation.Algorithm, Int)")			"Test the performance of 'Math.PrimeFactorisation.primeFactors', on the specified number of odd integers from the Fibonacci-sequence.",+			G.Option ""	["primesPerformance"]				(primesPerformance `G.ReqArg` "(Math.Implementations.Primes.Algorithm.Algorithm, Int)")					"Test the performance of 'Math.Primes.primes'.",+			G.Option ""	["squareRootPerformance"]			(squareRootPerformance `G.ReqArg` "(Math.Implementations.SquareRoot.Algorithm, Data.Ratio.Rational, DecimalDigits)")	"Test the performance of 'Math.SquareRoot.squareRoot'.",+			G.Option ""	["squareRootPerformanceGraph"]			(squareRootPerformanceGraph `G.ReqArg` "(Math.Implementations.SquareRoot.Algorithm, Data.Ratio.Rational)")		"Test the performance of 'Math.SquareRoot.squareRoot', with an exponentially increasing precision-requirement." 		 ] where 			printVersion, printUsage, runQuickChecks :: IO Test.CommandOptions.CommandOptions-			printVersion	= System.IO.hPutStrLn System.IO.stderr (Distribution.Text.display packageIdentifier ++ "\n\nCopyright (C) 2011 Dr. Alistair Ward.\nThis program comes with ABSOLUTELY NO WARRANTY.\nThis is free software, and you are welcome to redistribute it under certain conditions.\n\nWritten by Dr. Alistair Ward.")	>> System.Exit.exitWith System.Exit.ExitSuccess	where+			printVersion	= System.IO.hPutStrLn System.IO.stderr (Distribution.Text.display packageIdentifier ++ "\n\nCopyright (C) 2011 " ++ author ++ ".\nThis program comes with ABSOLUTELY NO WARRANTY.\nThis is free software, and you are welcome to redistribute it under certain conditions.\n\nWritten by " ++ author ++ ".")	>> System.Exit.exitWith System.Exit.ExitSuccess	where 				packageIdentifier :: Distribution.Package.PackageIdentifier 				packageIdentifier	= Distribution.Package.PackageIdentifier {-					Distribution.Package.pkgName	= Distribution.Package.PackageName "factory",+					Distribution.Package.pkgName	= Distribution.Package.PackageName progName,	--CAVEAT: coincidentally. 					Distribution.Package.pkgVersion	= Distribution.Version.Version (Data.Version.versionBranch Paths.version) [] 				} -			printUsage	= System.IO.hPutStrLn System.IO.stderr usage		>> System.Exit.exitWith System.Exit.ExitSuccess+				author :: String+				author	= "Dr. Alistair Ward"++			printUsage	= System.IO.hPutStrLn System.IO.stderr usageMessage	>> System.Exit.exitWith System.Exit.ExitSuccess+ 			runQuickChecks	= Test.QuickCheck.QuickChecks.run			>> System.Exit.exitWith System.Exit.ExitSuccess  			factorialPerformanceGraphControl :: Test.CommandOptions.CommandOptions -> IO Test.CommandOptions.CommandOptions 			factorialPerformanceGraphControl commandOptions	= Test.Performance.Factorial.factorialPerformanceGraphControl (Test.CommandOptions.verbose commandOptions)	>> System.Exit.exitWith (System.Exit.ExitFailure 1) -			carmichaelNumbersPerformance, factorialPerformance, factorialPerformanceGraph, hyperoperationPerformance, hyperoperationPerformanceGraphRank, hyperoperationPerformanceGraphExponent, isPrimePerformance, isPrimePerformanceGraph, piPerformance, piPerformanceGraph, primeFactorsPerformance, primesPerformance, squareRootPerformance, squareRootPerformanceGraph :: String -> CommandLineAction+			carmichaelNumbersPerformance, factorialPerformance, factorialPerformanceGraph, hyperoperationPerformance, hyperoperationPerformanceGraphRank, hyperoperationPerformanceGraphExponent, isPrimePerformance, isPrimePerformanceGraph, mersenneNumbersPerformance, piPerformance, piPerformanceGraph, primeFactorsPerformance, primesPerformance, squareRootPerformance, squareRootPerformanceGraph :: String -> CommandLineAction  			carmichaelNumbersPerformance arg _	= Test.Performance.Primality.carmichaelNumbersPerformance algorithm i >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm :: PrimalityAlgorithm-				(algorithm, i)	= read arg+				(algorithm, i)	= readCommandArg arg  			factorialPerformance arg _	= Test.Performance.Factorial.factorialPerformance algorithm i >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm	:: Math.Implementations.Factorial.Algorithm 				i		:: Integer-				(algorithm, i)	= read arg+				(algorithm, i)	= readCommandArg arg -			factorialPerformanceGraph arg commandOptions	= Test.Performance.Factorial.factorialPerformanceGraph (Test.CommandOptions.verbose commandOptions) (read arg :: Math.Implementations.Factorial.Algorithm)	>> System.Exit.exitWith (System.Exit.ExitFailure 1)+			factorialPerformanceGraph arg commandOptions	= Test.Performance.Factorial.factorialPerformanceGraph (Test.CommandOptions.verbose commandOptions) (readCommandArg arg :: Math.Implementations.Factorial.Algorithm)	>> System.Exit.exitWith (System.Exit.ExitFailure 1)  			hyperoperationPerformance arg _	= Test.Performance.Hyperoperation.hyperoperationPerformance rank base hyperExponent >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				rank		:: Integer 				base		:: Math.Hyperoperation.Base 				hyperExponent	:: Math.Hyperoperation.HyperExponent-				(rank, base, hyperExponent)	= read arg+				(rank, base, hyperExponent)	= readCommandArg arg  			hyperoperationPerformanceGraphRank arg commandOptions	= Test.Performance.Hyperoperation.hyperoperationPerformanceGraphRank (Test.CommandOptions.verbose commandOptions) base hyperExponent >> System.Exit.exitWith (System.Exit.ExitFailure 1)	where 				base		:: Math.Hyperoperation.Base 				hyperExponent	:: Math.Hyperoperation.HyperExponent-				(base, hyperExponent)	= read arg+				(base, hyperExponent)	= readCommandArg arg  			hyperoperationPerformanceGraphExponent arg commandOptions	= Test.Performance.Hyperoperation.hyperoperationPerformanceGraphExponent (Test.CommandOptions.verbose commandOptions) rank base >> System.Exit.exitWith (System.Exit.ExitFailure 1)	where 				rank	:: Integer 				base	:: Math.Hyperoperation.Base-				(rank, base)	= read arg+				(rank, base)	= readCommandArg arg  			isPrimePerformance arg _	= Test.Performance.Primality.isPrimePerformance algorithm i >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm	:: PrimalityAlgorithm 				i		:: Integer-				(algorithm, i)	= read arg+				(algorithm, i)	= readCommandArg arg -			isPrimePerformanceGraph arg _	= Test.Performance.Primality.isPrimePerformanceGraph (read arg :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm) >> System.Exit.exitWith (System.Exit.ExitFailure 1)+			isPrimePerformanceGraph arg _	= Test.Performance.Primality.isPrimePerformanceGraph (readCommandArg arg :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm) >> System.Exit.exitWith (System.Exit.ExitFailure 1) +			mersenneNumbersPerformance arg _	= Test.Performance.Primes.mersenneNumbersPerformance algorithm i >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where+				algorithm :: Math.Implementations.Primes.Algorithm.Algorithm+				(algorithm, i)	= readCommandArg arg+ 			nCrPerformance arg _	= Test.Performance.Statistics.nCrPerformance algorithm n r >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm	:: Math.Implementations.Factorial.Algorithm 				n, r		:: Integer-				(algorithm, n, r)	= read arg+				(algorithm, n, r)	= readCommandArg arg  			piPerformance arg _	= Test.Performance.Pi.piPerformance category decimalDigits >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				category :: PiCategory-				(category, decimalDigits)	= read arg+				(category, decimalDigits)	= readCommandArg arg  			piPerformanceGraph arg commandOptions	= Test.Performance.Pi.piPerformanceGraph category factor maxDecimalDigits (Test.CommandOptions.verbose commandOptions) >> System.Exit.exitWith (System.Exit.ExitFailure 1)	where 				category	:: PiCategory 				factor		:: Double-				(category, factor, maxDecimalDigits)	= read arg+				(category, factor, maxDecimalDigits)	= readCommandArg arg  			primeFactorsPerformance arg _	= Test.Performance.PrimeFactorisation.primeFactorsPerformance algorithm i >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm :: Math.Implementations.PrimeFactorisation.Algorithm-				(algorithm, i)	= read arg+				(algorithm, i)	= readCommandArg arg  			primeFactorsPerformanceGraph arg _	= Test.Performance.PrimeFactorisation.primeFactorsPerformanceGraph algorithm index >> System.Exit.exitWith (System.Exit.ExitFailure 1)	where 				algorithm :: Math.Implementations.PrimeFactorisation.Algorithm-				(algorithm, index)	= read arg+				(algorithm, index)	= readCommandArg arg  			primesPerformance arg _	= ( 				(@@ -195,20 +215,22 @@ 				) 			 ) >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm :: Math.Implementations.Primes.Algorithm.Algorithm-				(algorithm, index)	= read arg+				(algorithm, index)	= readCommandArg arg  			squareRootPerformance arg _	= Test.Performance.SquareRoot.squareRootPerformance algorithm operand decimalDigits >>= print >> System.Exit.exitWith System.Exit.ExitSuccess	where 				algorithm	:: Math.Implementations.SquareRoot.Algorithm 				operand		:: Data.Ratio.Rational-				(algorithm, operand, decimalDigits)	= read arg+				(algorithm, operand, decimalDigits)	= readCommandArg arg  			squareRootPerformanceGraph arg _	= Test.Performance.SquareRoot.squareRootPerformanceGraph algorithm operand >> System.Exit.exitWith (System.Exit.ExitFailure 1)	where 				algorithm	:: Math.Implementations.SquareRoot.Algorithm 				operand		:: Data.Ratio.Rational-				(algorithm, operand)	= read arg+				(algorithm, operand)	= readCommandArg arg +	args	<- System.Environment.getArgs+ --	G.getOpt :: G.ArgOrder CommandLineAction -> [G.OptDescr Action] -> [String] -> ([Action], [String], [String]) 	case G.getOpt G.RequireOrder optDescrList args of 		(commandLineActions, _, [])	-> Data.List.foldl' (>>=) (return {-to IO-monad-} ToolShed.Defaultable.defaultValue) commandLineActions	>> System.Exit.exitWith System.Exit.ExitSuccess-		(_, _, errors)			-> System.IO.Error.ioError . System.IO.Error.userError $ concat errors ++ usage	--Throw.+		(_, _, errors)			-> System.IO.Error.ioError . System.IO.Error.userError $ concat errors ++ usageMessage	--Throw.