factory 0.2.1.2 → 0.2.2.1

raw patch · 63 files changed

+457/−372 lines, 63 filesdep +data-defaultdep ~toolshedPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

Dependencies added: data-default

Dependency ranges changed: toolshed

API changes (from Hackage documentation)

Files

• .ghci +1/−0
• README.markdown +14/−4
• changelog.markdown +135/−82
• copyright +1/−1
• factory.cabal +25/−13
• src-exe/Factory/Test/CommandOptions.hs +4/−5
• src-exe/Factory/Test/Performance/Pi.hs +1/−3
• src-exe/Factory/Test/Performance/Primality.hs +1/−1
• src-exe/Factory/Test/Performance/PrimeFactorisation.hs +1/−1
• src-exe/Factory/Test/Performance/Primes.hs +2/−1
• src-exe/Main.hs +5/−5
• src-lib/Factory/Data/Exponential.hs +3/−3
• src-lib/Factory/Data/Interval.hs +5/−5
• src-lib/Factory/Data/MonicPolynomial.hs +3/−3
• src-lib/Factory/Data/Monomial.hs +1/−1
• src-lib/Factory/Data/Polynomial.hs +10/−10
• src-lib/Factory/Data/PrimeWheel.hs +3/−3
• src-lib/Factory/Data/QuotientRing.hs +1/−1
• src-lib/Factory/Data/Ring.hs +6/−6
• src-lib/Factory/Math/ArithmeticGeometricMean.hs +3/−3
• src-lib/Factory/Math/DivideAndConquer.hs +2/−2
• src-lib/Factory/Math/Fibonacci.hs +1/−1
• src-lib/Factory/Math/Hyperoperation.hs +4/−4
• src-lib/Factory/Math/Implementations/Factorial.hs +10/−10
• src-lib/Factory/Math/Implementations/Pi/AGM/Algorithm.hs +4/−4
• src-lib/Factory/Math/Implementations/Pi/AGM/BrentSalamin.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/BBP/Algorithm.hs +4/−4
• src-lib/Factory/Math/Implementations/Pi/BBP/Bellard.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Borwein/Algorithm.hs +7/−7
• src-lib/Factory/Math/Implementations/Pi/Borwein/Borwein1993.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Borwein/Implementation.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Borwein/Series.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Ramanujan/Algorithm.hs +9/−9
• src-lib/Factory/Math/Implementations/Pi/Ramanujan/Chudnovsky.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Ramanujan/Implementation.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Ramanujan/Series.hs +1/−1
• src-lib/Factory/Math/Implementations/Pi/Spigot/Algorithm.hs +6/−6
• src-lib/Factory/Math/Implementations/Pi/Spigot/Spigot.hs +2/−2
• src-lib/Factory/Math/Implementations/Primality.hs +10/−10
• src-lib/Factory/Math/Implementations/PrimeFactorisation.hs +11/−11
• src-lib/Factory/Math/Implementations/Primes/Algorithm.hs +6/−6
• src-lib/Factory/Math/Implementations/Primes/SieveOfAtkin.hs +2/−2
• src-lib/Factory/Math/Implementations/Primes/SieveOfEratosthenes.hs +2/−2
• src-lib/Factory/Math/Implementations/Primes/TrialDivision.hs +1/−1
• src-lib/Factory/Math/Implementations/SquareRoot.hs +15/−15
• src-lib/Factory/Math/MultiplicativeOrder.hs +1/−1
• src-lib/Factory/Math/PerfectPower.hs +2/−2
• src-lib/Factory/Math/Pi.hs +6/−12
• src-lib/Factory/Math/Power.hs +2/−2
• src-lib/Factory/Math/Precision.hs +3/−3
• src-lib/Factory/Math/Primality.hs +6/−6
• src-lib/Factory/Math/PrimeFactorisation.hs +11/−11
• src-lib/Factory/Math/Primes.hs +3/−3
• src-lib/Factory/Math/Probability.hs +14/−14
• src-lib/Factory/Math/Radix.hs +3/−3
• src-lib/Factory/Math/SquareRoot.hs +3/−3
• src-lib/Factory/Math/Statistics.hs +33/−13
• src-test/Factory/Test/QuickCheck/Pi.hs +3/−12
• src-test/Factory/Test/QuickCheck/Primes.hs +3/−3
• src-test/Factory/Test/QuickCheck/Probability.hs +1/−1
• src-test/Factory/Test/QuickCheck/SquareRoot.hs +2/−2
• src-test/Factory/Test/QuickCheck/Statistics.hs +14/−3
• src-test/Main.hs +18/−23

@@ -0,0 +1,1 @@+:set -isrc-lib:src-exe:src-test:dist/build/autogen -optP-include -optPdist/build/autogen/cabal_macros.h

@@ -1,7 +1,9 @@-# **Factory**.+# **Factory** -This is **Factory**, a library of number-theory functions.+[![Hackage](https://img.shields.io/hackage/v/factory.svg)](https://hackage.haskell.org/package/factory) +This is "**Factory**", a library of number-theory functions.+ ## Installation  It can be built and installed using [Cabal](https://www.haskell.org/cabal/users-guide/installing-packages.html).@@ -12,11 +14,19 @@  ## License -For information on copying and distributing this package, see the file **LICENSE** in this directory.+For information on copying and distributing this package, see the file "**LICENSE**" in this directory.  ## Bug-reporting -Bug-reports should be emailed to <factory *at* functionalley *dot* eu>.+Bug-reports should be emailed to <factory@functionalley.eu>.++## Testing++The test-suite can be run using:++    cabal configure --enable-tests;+    cabal build;+    cabal test --show-details=always;  ## Author 

@@ -1,98 +1,151 @@-# 2011-03-01 Dr. Alistair Ward <factory at functionalley dot eu>+# 2011-03-01 Dr. Alistair Ward <factory@functionalley.eu>  ## 0.0.0.1-	* First version of the package.+* First version of the package.+ ## 0.0.0.2-	* Created the modules; **Factory.Test.QuickCheck.Bounds**, **Factory.Math.Implementations.Pi.Borwein** & **Factory.Test.Performance.Statistics** .-	* Created a new module **Factory.Data.PrimeFactors**, and migrated definitions from both **Factory.Math.PrimeFactorisation** & **Factory.Math.Implementations.PrimeFactorisation**.-	* Created the class `Factory.Math.Factorial.Factorial` and a new module **Factory.Math.Implementations.Factorial**.-	Moved existing implementation (`Bisection`) into the new module, with a new implementation (`PrimeFactorisation`).-	* Added the function `Factory.Math.Summation.sumR`.-	* Added a parameter to the functions `Factory.Math.DivideAndConquer.divideAndConquer` and `Factory.Data.Bounds.divideAndConquer`, to permit asymmetric bisection.-	* Added methods to class `Factory.Math.Pi.Algorithm` to permit the retrieval of *Pi* as a `Rational` or a `String`.-	* Renamed the function `Factory.Math.Precision.capPrecision` to `Factory.Math.Precision.simplify`.-	* Removed the module **Factory.Test.Performance.Exponential**.-	* Removed the function `Factory.Math.Power.raise`, which was no more efficient than ghc's implementation of `(^)`.-	* Uploaded to [Hackage](http://hackage.haskell.org/packages/hackage.html).+* Created the modules; "**Factory.Test.QuickCheck.Bounds**", "**Factory.Math.Implementations.Pi.Borwein**" & "**Factory.Test.Performance.Statistics**".+* Created a new module "**Factory.Data.PrimeFactors**", and migrated definitions from modules "**Factory.Math.PrimeFactorisation**" & "**Factory.Math.Implementations.PrimeFactorisation**".+* Created the class `Factory.Math.Factorial.Factorial` and a new module "**Factory.Math.Implementations.Factorial**".+* Moved existing implementation (`Bisection`) into the new module, with a new implementation (`PrimeFactorisation`).+* Added the function `Factory.Math.Summation.sumR`.+* Added a parameter to the functions `Factory.Math.DivideAndConquer.divideAndConquer` and `Factory.Data.Bounds.divideAndConquer`, to permit asymmetric bisection.+* Added methods to class `Factory.Math.Pi.Algorithm` to permit the retrieval of *Pi* as a `Rational` or a `String`.+* Renamed the function `Factory.Math.Precision.capPrecision` to `Factory.Math.Precision.simplify`.+* Removed the module "**Factory.Test.Performance.Exponential**".+* Removed the function `Factory.Math.Power.raise`, which was no more efficient than ghc's implementation of `(^)`.+* Uploaded to [Hackage](http://hackage.haskell.org/package/factory).+ ## 0.1.0.0-	* Amended the *.cabal*-file to more correctly specify the dependency on package **toolshed**.-	* Added the module **Factory.Math.Probability**.-	* Renamed the module **Factory.Data.Bounds** to **Factory.Data.Interval**,-	and added the functions; `Factory.Data.Interval.precisely`, `Factory.Data.Interval.shift`, `Factory.Data.Interval.closedUnitInterval`.-	* Guarded **eager-blackholing** flag in the *cabal*-file.+* Amended the *.cabal*-file to more correctly specify the dependency on package "**toolshed**".+* Added the module "**Factory.Math.Probability**".+* Renamed the module "**Factory.Data.Bounds**" to "**Factory.Data.Interval**",+and added the functions; `Factory.Data.Interval.precisely`, `Factory.Data.Interval.shift`, `Factory.Data.Interval.closedUnitInterval`.+* Guarded flag "**eager-blackholing**" in the *cabal*-file.+ ## 0.1.0.1-	* Renamed classes *Factory.Math.[Primality, Pi, Factorial, SquareRoot, PrimeFactorisation].Algorithm* to *Factory.Math.[Primality, Pi, Factorial, SquareRoot, PrimeFactorisation].Algorithmic*, to distinguish them from the data-types which implement them.-	* Added the modules **Factory.Math.Hyperoperation**, **Factory.Test.QuickCheck.Hyperoperation** and **Factory.Test.Performance.Hyperoperation**.-	* Added the modules **Factory.Math.Primes**, **Factory.Math.Implementation.Primes**, **Factory.Test.Performance.Primes**, **Factory.Test.QuickCheck.Primes** and **Factory.Data.PrimeWheel**.-	* Added the function `Factory.Math.PrimeFactorisation.squareFree`.-	* Added rewrite-rules to specialise `Factory.Math.Power.isPerfectPower` for type-parameter=`Int`.-	* Recoded **Factory.Math.Radix** to the interface `Data.Array.IArray.IArray`, rather than the data-type `Data.Array.Array`.+* Renamed classes **Factory.Math.[Primality, Pi, Factorial, SquareRoot, PrimeFactorisation].Algorithm** to **Factory.Math.[Primality, Pi, Factorial, SquareRoot, PrimeFactorisation].Algorithmic**, to distinguish them from the data-types which implement them.+* Added the modules;+	+ "**Factory.Math.Hyperoperation**",+	+ "**Factory.Test.QuickCheck.Hyperoperation**",+	+ "**Factory.Test.Performance.Hyperoperation**".+* Added the modules+	+ "**Factory.Math.Primes**",+	+ "**Factory.Math.Implementation.Primes**",+	+ "**Factory.Test.Performance.Primes**",+	+ "**Factory.Test.QuickCheck.Primes**"+	+ "**Factory.Data.PrimeWheel**".+* Added the function `Factory.Math.PrimeFactorisation.squareFree`.+* Added rewrite-rules to specialise `Factory.Math.Power.isPerfectPower` for type-parameter=`Int`.+* Recoded module "**Factory.Math.Radix**" to the interface `Data.Array.IArray.IArray`, rather than the data-type `Data.Array.Array`.+ ## 0.1.0.2-	* Added `Factory.Math.Primes.primorial`.-	* Altered `Factory.Math.Implementations.Primes.trialDivision` to take an integer defining the size of a `Factory.Data.PrimeWheel`, from which candidates are extracted.-	* Removed the command-line option `primesPerformanceGraph`, which appears to memoise data from previous tests.-	* Uploaded to [Hackage](http://hackage.haskell.org/packages/hackage.html).+* Added `Factory.Math.Primes.primorial`.+* Altered `Factory.Math.Implementations.Primes.trialDivision` to take an integer defining the size of a `Factory.Data.PrimeWheel`, from which candidates are extracted.+* Removed the command-line option `primesPerformanceGraph`, which appears to memoise data from previous tests.+* Uploaded to [Hackage](http://hackage.haskell.org/packages/hackage.html).+ ## 0.1.0.3-	* Qualified `Factory.Math.Implementations.Primes.trialDivision` with **NOINLINE**-pragma, to block optimization which conflicts with rewrite-rule for `Factory.Math.Implementations.Primes.sieveOfEratosthenes` !-	* Re-coded `Factory.Data.PrimeWheel.coprimes` and `Factory.Math.Implementations.Primes.sieveOfEratosthenes`, to use a map of lists, rather than a map of lists of lists.+* Qualified `Factory.Math.Implementations.Primes.trialDivision` with pragma "**NOINLINE**", to block optimization which conflicts with rewrite-rule for `Factory.Math.Implementations.Primes.sieveOfEratosthenes` !+* Re-coded `Factory.Data.PrimeWheel.coprimes` and `Factory.Math.Implementations.Primes.sieveOfEratosthenes`, to use a map of lists, rather than a map of lists of lists.+ ## 0.2.0.0-	* Separately coded the special-case of a **Factory.Data.PrimeWheel** of size zero, in `Factory.Math.Implementations.Primes.trialDivision`, to achieve better space-complexity.-	* Added `Factory.Data.PrimeWheel.estimateOptimalSize`.-	* Split **Factory.Math.Implementations.Primes** into; **Factory.Math.Implementations.Primes.SieveOfEratosthenes**, **Factory.Math.Implementations.Primes.TurnersSieve**, **Factory.Math.Implementations.Primes.TrialDivision**, and added a new module **Factory.Math.Implementations.Primes.SieveOfAtkin**. This makes the rewrite-rules less fragile.-	* Coded `Factory.Math.Radix.digitalRoot` more concisely.-	* Split **Factory.Math.Power** into an additional module **Factory.Math.PerfectPower**.-	* Replaced `(+ 1)` and `(- 1)` with the faster calls `succ` and `pred`.-	* Used `Paths_factory.version` in **Main**, rather than hard-coding it.+* Separately coded the special-case of a **Factory.Data.PrimeWheel** of size zero, in `Factory.Math.Implementations.Primes.trialDivision`, to achieve better space-complexity.+* Added `Factory.Data.PrimeWheel.estimateOptimalSize`.+* Split module "**Factory.Math.Implementations.Primes**" into;+	+ "**Factory.Math.Implementations.Primes.SieveOfEratosthenes**",+	+ "**Factory.Math.Implementations.Primes.TurnersSieve**",+	+ "**Factory.Math.Implementations.Primes.TrialDivision**",+	+ and added a new module "**Factory.Math.Implementations.Primes.SieveOfAtkin**". This makes the rewrite-rules less fragile.+* Coded `Factory.Math.Radix.digitalRoot` more concisely.+* Split module "**Factory.Math.Power**" into an additional module "**Factory.Math.PerfectPower**".+* Replaced `(+ 1)` and `(- 1)` with the faster calls `succ` and `pred`.+* Used `Paths_factory.version` in **Main**, rather than hard-coding it.+ ## 0.2.0.1-	* Changed by Lennart Augustsson, to replace `System` with `System.Environment` and `System.Exit`, and to remove dependency on **haskell98**.+* Changed by Lennart Augustsson, to replace `System` with `System.Environment` and `System.Exit`, and to remove dependency on **haskell98**.+ ## 0.2.0.2-	* Reacted to new module-hierarchy and addition of method `ToolShed.SelfValidate.getErrors`, in **toolshed-0.13.0.0**.-	* Made `Factory.Data.Interval.getLength` private.-	* Added `Factory.Data.Interval.mkBounded`.-	* Generalised **Factory.Math.Statistics** to accept any `Data.Foldable.Foldable` *Functor*, rather than merely lists.+* Reacted to new module-hierarchy and addition of method `ToolShed.SelfValidate.getErrors`, in package "**toolshed-0.13.0.0**".+* Made `Factory.Data.Interval.getLength` private.+* Added `Factory.Data.Interval.mkBounded`.+* Generalised **Factory.Math.Statistics** to accept any `Data.Foldable.Foldable` *Functor*, rather than merely lists.+ ## 0.2.0.3-	* Added class `Show` to some contexts in **Factory.Math.Radix**, for migration to **ghc-7.4**.+* Added class `Show` to some contexts in **Factory.Math.Radix**, for migration to **ghc-7.4**.+ ## 0.2.0.4-	* Added classes `Eq` and `Show` to many contexts, for migration to **ghc-7.4**.-	* Minor re-formatting.+* 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.+* 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 module "**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.+ ## 0.2.1.0-	* Refactored **Factory.Test.QuickCheck.QuickChecks**.-	* Remove redundant import of `Data.Ratio` from many modules.-	* Refactored `Factory.Math.Radix.encodes` to make use of `Data.List.genericLength`, & removed empty `where`.-	* Explicitly closed standard-input in the executable.-	* Replaced calls to `error` from inside the IO-monad, with `Control.Monad.fail`.-	* Added function `Factory.Math.Precision.roundTo`.-	* Trapped command-line arguments to which garbage has been appended.-	* Corrected the output of `Main.main.optDescrList.printVersion`.-	* Removed the integral population-size parameter from `Factory.Math.Probability.generateContinuousPopulation` & `Factory.Math.Probability.generateDiscretePopulation`, making the result conceptually infinite.-	* Created class `Factory.Math.Probability.Distribution`, to which data-types `Factory.Math.Probability.ContinuousDistribution` & `Factory.Math.Probability.DiscreteDistribution` conform.-	* Added data-constructors `Factory.Math.Probability.ExponentialDistribution`, `Factory.Math.Probability.ShiftedGeometricDistribution` & `Factory.Math.Probability.LogNormal`.-	* Added command-line option **--plotDiscreteDistribution** to **Main**.-	* Removed Preprocessor-check on the version of package **toolshed**, in **Factory/Math/Summation** & **Factory/Data/PrimeFactors**.+* Refactored **Factory.Test.QuickCheck.QuickChecks**.+* Remove redundant import of `Data.Ratio` from many modules.+* Refactored `Factory.Math.Radix.encodes` to make use of `Data.List.genericLength`, & removed empty keyword `where`.+* Explicitly closed standard-input in the executable.+* Replaced calls to `error` from inside the IO-monad, with `Control.Monad.fail`.+* Added function `Factory.Math.Precision.roundTo`.+* Trapped command-line arguments to which garbage has been appended.+* Corrected the output of `Main.main.optDescrList.printVersion`.+* Removed the integral population-size parameter from `Factory.Math.Probability.generateContinuousPopulation` & `Factory.Math.Probability.generateDiscretePopulation`, making the result conceptually infinite.+* Created class `Factory.Math.Probability.Distribution`, to which data-types `Factory.Math.Probability.ContinuousDistribution` & `Factory.Math.Probability.DiscreteDistribution` conform.+* Added data-constructors `Factory.Math.Probability.ExponentialDistribution`, `Factory.Math.Probability.ShiftedGeometricDistribution` & `Factory.Math.Probability.LogNormal`.+* Added command-line option "**--plotDiscreteDistribution**" to **Main**.+* Removed Preprocessor-check on the version of package "**toolshed**", in modules "**Factory/Math/Summation**" & "**Factory/Data/PrimeFactors**".+ ## 0.2.1.1-	* Added `Factory.Test.QuickCheck.Probability.prop_logNormalDistributionEqual`.-	* Removed /INLINE/ pragma from `Factory.Math.Implementations.Primes.TrialDivision.isIndivisibleBy`, since to be effective it must be called with fully applied parameters (which it isn't).-	* Un eta-reduced `Factory.Math.Power.square`, since we want it to be inlined when called with one argument.-	* Tested with **haskell-platform-2013.2.0.0**.-	* Replaced preprocessor-directives with **build-depends** constraints in the *.cabal*-file.-	* Added function `Factory.Math.Statistics.getWeightedMean` & corresponding tests in module **Factory.Test.QuickCheck.Statistics**.-	* Since `(<$>)` is exported from the Prelude from **base-4.8**, imported **Prelude** hiding `(<*>)` into module **Factory.Data.Monomial**, since this symbol is defined locally for other purposes.-	* Either replaced instances of `(<$>)` with `fmap` to avoid ambiguity between **Control.Applicative** & **Prelude** which (from **base-4.8**) also exports this symbol, or hid the symbol when importing the **Prelude**..+* Added `Factory.Test.QuickCheck.Probability.prop_logNormalDistributionEqual`.+* Removed pragma **INLINE** from `Factory.Math.Implementations.Primes.TrialDivision.isIndivisibleBy`, since to be effective it must be called with fully applied parameters (which it isn't).+* Un eta-reduced `Factory.Math.Power.square`, since we want it to be inlined when called with one argument.+* Tested with **haskell-platform-2013.2.0.0**.+* Replaced preprocessor-directives with **build-depends** constraints in the *.cabal*-file.+* Added function `Factory.Math.Statistics.getWeightedMean` & corresponding tests in module "**Factory.Test.QuickCheck.Statistics**".+* Since `(<$>)` is exported from the Prelude from **base-4.8**, imported **Prelude** hiding `(<*>)` into module "**Factory.Data.Monomial**", since this symbol is defined locally for other purposes.+* Either replaced instances of `(<$>)` with `fmap` to avoid ambiguity between **Control.Applicative** & **Prelude** which (from **base-4.8**) also exports this symbol, or hid the symbol when importing the **Prelude**.+ ## 0.2.1.2-	* Hid `(<$>)` when importing the **Prelude** into module **src/Factory/Test/QuickCheck/Pi**.-	* Added the compiler to the output returned for the command-line option **version**.-	* Changed flag **threaded** in the *.cabal*-file to **manual**.-	* Added **Default-language**-specification to the *.cabal*-file.-	* Added file **README.markdown**.-	* Converted this file to markdown-format.-	* Replaced `System.Exit.exitWith (System.Exit.ExitFailure 1)` with `System.Exit.exitFailure` & `System.Exit.exitWith System.Exit.ExitSuccess` with `System.Exit.exitSuccess`.-	* Moved the entry-point to the test-suite from **Main.hs** to **Test.hs**, both to integrate with **cabal** & to minimise the dependencies of the executable.-	* Partitioned the source-files into **src-lib**, **src-exe**, & **src-test** directories, & referenced them individually from the *.cabal*-file to avoid repeated compilation.-	* Used **CPP** to control the import of symbols from **Control.Applicative**.+* Hid `(<$>)` when importing the **Prelude** into module "**src/Factory/Test/QuickCheck/Pi**".+* Added the compiler to the output returned for the command-line option "**version**".+* Changed flag "**threaded**" in the *.cabal*-file to "**manual**".+* Added **Default-language**-specification to the *.cabal*-file.+* Added file "**README.markdown**".+* Converted this file to markdown-format.+* Replaced `System.Exit.exitWith (System.Exit.ExitFailure 1)` with `System.Exit.exitFailure` & `System.Exit.exitWith System.Exit.ExitSuccess` with `System.Exit.exitSuccess`.+* Moved the entry-point to the test-suite from module "**Main.hs**" to "**Test.hs**", both to integrate with **cabal** & to minimise the dependencies of the executable.+* Partitioned the source-files into directories "**src-lib**", "**src-exe**", & "**src-test**", & referenced them individually from the *.cabal*-file to avoid repeated compilation.+* Used **CPP** to control the import of symbols from **Control.Applicative**.++## 0.2.2.0+* Corrected the markdown-syntax in this file.+* Reverted to calling "**error**" rather than "**Control.Monad.fail**", since the **String**-argument for the latter is discarded in **Monad**-implementations other than **IO**.+* Uploaded to [GitHub](https://github.com/functionalley/Factory.git).+* Simplified file **src-test/Main.hs**.+* Added file **.travis.yml** to control testing by <https://docs.travis-ci.com>.+* Added file **.ghci**.+* Replaced use of module **ToolShed.Defaultable** with **Data.Default**.+* Re-code **Factory.Test.QuickCheck.Statistics** to **Data.Array.IArray** rather than **Data.Array**.+* Added functions **Factory.Math.Statistics.getRootMeanSquare** **Factory.Test.QuickCheck.Statistics.prop_rootMeanSquare**.+* Added function **Factory.Test.QuickCheck.Statistics.prop_standardDeviationRMS**.+* Added **Eq** type-constraint to function **Factory.Math.Statistics.getWeightedMean**.+* Tested with **ghc-8.0.1**.+## 0.2.2.1+* Commented-out flakey square-root test.

@@ -1,5 +1,5 @@ Author:-	Dr. Alistair Ward <factory at functionalley dot eu>.+	Dr. Alistair Ward <factory@functionalley.eu>.  Copyright: 	Copyright (C) 2011-2013 Dr. Alistair Ward. All Rights Reserved.

@@ -14,7 +14,7 @@ -- along with Factory.  If not, see <http://www.gnu.org/licenses/>.  Name:		factory-Version:	0.2.1.2+Version:	0.2.2.1 Cabal-version:	>= 1.10 Copyright:	(C) 2011-2015 Dr. Alistair Ward License:	GPL@@ -25,17 +25,22 @@ Build-type:	Simple Description:	A library of number-theory functions, for; factorials, square-roots, Pi and primes. Category:	Math, Number Theory-Tested-with:	GHC == 7.4, GHC == 7.6, GHC == 7.8, GHC == 7.10+Tested-with:	GHC == 7.4, GHC == 7.6, GHC == 7.8, GHC == 7.10.1, GHC == 8.0.1 Homepage:	http://functionalley.eu/Factory/factory.html-Maintainer:	mailto <colon> factory <at> functionalley <dot> eu-Bug-reports:	mailto <colon> factory <at> functionalley <dot> eu+Maintainer:	mailto:factory@functionalley.eu+Bug-reports:	mailto:factory@functionalley.eu  -- None of these files are needed at run-time. Extra-source-files:+    .ghci     changelog.markdown     copyright     README.markdown +source-repository head+    type:	git+    location:	https://github.com/functionalley/Factory+ -- Enable using: 'cabal configure -f llvm'. flag llvm     Description:	Whether the 'llvm' compiler-backend has been installed and is required for code-generation.@@ -49,7 +54,7 @@  Library     Default-language:	Haskell2010-    GHC-options:	-Wall -O2 -fno-warn-tabs+    GHC-options:	-O2 -Wall -fno-warn-tabs     Hs-source-dirs:	src-lib      Exposed-modules:@@ -114,28 +119,33 @@     Build-depends:         array,         base >= 4.3 && < 5,+        data-default,         deepseq >= 1.1,         containers,         parallel >= 3.0,         primes >= 0.1,         random,-        toolshed >= 0.16+        toolshed >= 0.17      if impl(ghc >= 7.4.1)-        GHC-prof-options:	-prof -fprof-auto -fprof-cafs+        GHC-prof-options:	-fprof-auto -fprof-cafs     else-        GHC-prof-options:	-prof -auto-all -caf-all+        GHC-prof-options:	-auto-all -caf-all      if impl(ghc >= 7.0) && flag(llvm)         GHC-options:	-fllvm  Executable factory     Default-language:	Haskell2010-    GHC-options:	-Wall -O2 -fno-warn-tabs+    GHC-options:	-O2 -Wall -fno-warn-tabs     Hs-source-dirs:	src-exe     Main-is:		Main.hs-    GHC-prof-options:	-prof -auto-all -caf-all +    if impl(ghc >= 7.4.1)+        GHC-prof-options:	-fprof-auto -fprof-cafs+    else+        GHC-prof-options:	-auto-all -caf-all+ -- Unexposed modules must be referenced for 'cabal sdist'.     Other-modules:         Factory.Test.CommandOptions@@ -153,10 +163,11 @@         base >= 4.3 && < 5,         Cabal >= 1.10,         containers,+        data-default,         deepseq >= 1.1,         factory,         random,-        toolshed >= 0.16+        toolshed >= 0.17      if flag(threaded)         GHC-options:	-threaded@@ -167,7 +178,7 @@         if flag(llvm)             GHC-options:	-fllvm -Test-Suite quickCheck+Test-Suite test     Default-language:	Haskell2010     GHC-options:	-Wall -fno-warn-tabs     Hs-source-dirs:	src-test@@ -198,9 +209,10 @@         array,         base >= 4.3 && < 5,         containers,+        data-default,         deepseq >= 1.1,         factory,         primes >= 0.1,         QuickCheck >= 2.2,         random,-        toolshed >= 0.16+        toolshed >= 0.17

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -29,20 +29,19 @@ 	setVerbose ) where -import qualified	ToolShed.Defaultable+import qualified	Data.Default  -- | Declare a record used to contain command-line options. data CommandOptions	= MkCommandOptions { 	verbose	:: Bool	-- ^ Whether additional informative output should be generated, where applicable. } -instance ToolShed.Defaultable.Defaultable CommandOptions	where-	defaultValue	= MkCommandOptions { verbose = False }+instance Data.Default.Default CommandOptions	where+	def	= MkCommandOptions { verbose = False }  -- | Mutator. setVerbose :: CommandOptions -> CommandOptions setVerbose commandOptions = commandOptions { 	verbose	= True }- 

@@ -63,9 +63,7 @@ -} piPerformanceGraph :: ( 	Math.SquareRoot.Algorithmic	squareRootAlgorithm,-	Show				squareRootAlgorithm,-	Math.Factorial.Algorithmic	factorialAlgorithm,-	Show				factorialAlgorithm+	Math.Factorial.Algorithmic	factorialAlgorithm  ) => RealFrac i 	=> Category squareRootAlgorithm factorialAlgorithm	-- ^ The algorithm. 	-> i							-- ^ The factor by which the precision is increased on each iteration.

@@ -35,7 +35,7 @@ -- | Measures the CPU-time required to find the specified number of /Carmichael/-numbers, which is returned together with the requested list. carmichaelNumbersPerformance :: Math.Primality.Algorithmic primalityAlgorithm => primalityAlgorithm -> Int -> IO (Double, [Integer]) carmichaelNumbersPerformance primalityAlgorithm i-	| i < 0		= fail $ "Factory.Test.Performance.Primality.carmichaelNumbersPerformance:\tnegative number; " ++ show i+	| i < 0		= error . showString "Factory.Test.Performance.Primality.carmichaelNumbersPerformance:\tnegative number; " $ shows i "." 	| otherwise	= ToolShed.System.TimePure.getCPUSeconds . take i $ Math.Primality.carmichaelNumbers primalityAlgorithm  -- | Measures the CPU-time required to determine whether the specified integer is prime, which is returned together with the Boolean result.

@@ -43,7 +43,7 @@ -} primeFactorsPerformanceGraph :: Math.PrimeFactorisation.Algorithmic algorithm => algorithm -> Int -> IO () primeFactorsPerformanceGraph algorithm tests-	| tests < 0	= fail $ "Factory.Test.Performance.PrimeFactorisation.primeFactorsPerformanceGraph:\tnegative number; " ++ show tests+	| tests < 0	= error . showString "Factory.Test.Performance.PrimeFactorisation.primeFactorsPerformanceGraph:\tnegative number; " $ shows tests "." 	| otherwise	= mapM_ ( 		\operand	-> primeFactorsPerformance algorithm operand >>= putStrLn . shows operand . showChar '\t' . (`shows` "") 	) . take tests . dropWhile (< 2) $ Math.Fibonacci.fibonacci

@@ -43,5 +43,6 @@ -- | 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		= fail $ "Factory.Test.Performance.Primes.mersenneNumbersPerformance:\tnegative number; " ++ show i+	| i < 0		= error . showString "Factory.Test.Performance.Primes.mersenneNumbersPerformance:\tnegative number; " $ shows i "." 	| otherwise	= ToolShed.System.TimePure.getCPUSeconds . take i $ Math.Primes.mersenneNumbers primalityAlgorithm+

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011-2013 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -26,6 +26,7 @@  module Main(main) where +import qualified	Data.Default import qualified	Data.Map import qualified	Data.List import qualified	Data.Version@@ -56,7 +57,6 @@ import qualified	System.IO import qualified	System.IO.Error import qualified	System.Random-import qualified	ToolShed.Defaultable  -- Local convenience definitions. type PrimalityAlgorithm		= Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm@@ -90,7 +90,7 @@ 		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 ""	["verbose"]					(G.NoArg $ return {-to IO-monad-} . Test.CommandOptions.setVerbose)							("Provide additional information where available; default '" ++ show (Test.CommandOptions.verbose Data.Default.def) ++ "'."), 			G.Option ""	["version"]					(G.NoArg $ const printVersion)												"Print version-information & 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'.",@@ -125,7 +125,7 @@  				author, compiler :: String 				author		= "Dr. Alistair Ward"-				compiler	= System.Info.compilerName ++ "-" ++ Data.List.intercalate "." (map show $ Data.Version.versionBranch System.Info.compilerVersion)+				compiler	= showString System.Info.compilerName . showChar '-' . Data.List.intercalate "." . map show $ Data.Version.versionBranch System.Info.compilerVersion  			printUsage	= System.IO.hPutStrLn System.IO.stderr usageMessage	>> System.Exit.exitSuccess @@ -236,6 +236,6 @@  --	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.exitSuccess+		(commandLineActions, _, [])	-> Data.List.foldl' (>>=) (return {-to IO-monad-} Data.Default.def) commandLineActions	>> System.Exit.exitSuccess 		(_, _, errors)			-> System.IO.Error.ioError . System.IO.Error.userError $ concat errors ++ usageMessage	-- Throw. 

@@ -21,7 +21,7 @@  	* Describes a simple numeric type, designed to contain an /exponential/ number. -	* <http://en.wikipedia.org/wiki/Exponentiation>.+	* <https://en.wikipedia.org/wiki/Exponentiation>. -}  module Factory.Data.Exponential(@@ -34,7 +34,7 @@ -- ** Accessors 	getBase, 	getExponent,--- ** Constructors+-- ** Constructor 	rightIdentity, -- ** Operators 	(<^),@@ -62,7 +62,7 @@ {- | 	* Construct an 'Exponential' merely raised to the 1st power. -	* The value of the resulting exponential is the same as specified 'base'; <http://en.wikipedia.org/wiki/Identity_element>.+	* The value of the resulting exponential is the same as specified 'base'; <https://en.wikipedia.org/wiki/Identity_element>. -} rightIdentity :: Num exponent => base -> Exponential base exponent rightIdentity x	= (x, 1)

@@ -30,7 +30,7 @@ 	* The API was driven top-down by its caller's requirements, rather than a bottom-up attempt to provide a complete interface. 	consequently there may be omissions from the view point of future callers. -	* Thought similar to the mathematical concept of an /interval/, the latter technically relates to /real/ numbers; <http://en.wikipedia.org/wiki/Interval_%28mathematics%29>.+	* Thought similar to the mathematical concept of an /interval/, the latter technically relates to /real/ numbers; <https://en.wikipedia.org/wiki/Interval_%28mathematics%29>.  	* No account has been made for /semi-closed/ or /open/ intervals. -}@@ -54,7 +54,7 @@ -- ** Accessors 	getMinBound, 	getMaxBound,--- ** Constructors+-- ** Constructor 	precisely, -- ** Predicates 	isReversed@@ -80,7 +80,7 @@ getMaxBound :: Interval endPoint -> endPoint getMaxBound	= snd --- | Construct the /unsigned closed unit-interval/; <http://en.wikipedia.org/wiki/Unit_interval>.+-- | Construct the /unsigned closed unit-interval/; <https://en.wikipedia.org/wiki/Unit_interval>. closedUnitInterval :: Num n => Interval n closedUnitInterval	= (0, 1) @@ -148,7 +148,7 @@ {- | 	* Reduces 'Interval' to a single integral value encapsulated in a 'Data.Monoid.Monoid', 	using a /divide-and-conquer/ strategy,-	bisecting the /interval/ and recursively evaluating each part; <http://en.wikipedia.org/wiki/Divide_and_conquer_algorithm>.+	bisecting the /interval/ and recursively evaluating each part; <https://en.wikipedia.org/wiki/Divide_and_conquer_algorithm>.  	* By choosing a 'ratio' other than @(1 % 2)@, the bisection can be made asymmetrical. 	The specified ratio represents the length of the left-hand portion over the original list-length;@@ -157,7 +157,7 @@ 	* This process of recursive bisection, is terminated beneath the specified minimum length, 	after which the 'Interval' are expanded into the corresponding list, and the /monoid/'s binary operator is directly /folded/ over it. -	* One can view this as a <http://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>,+	* One can view this as a <https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>, 	in which 'Interval' is exploded into a binary tree-structure 	(each leaf of which contains a list of up to 'minLength' integers, and each node of which contains an associative binary operator), 	and then collapsed to a scalar, by application of the operators.

@@ -19,16 +19,16 @@   [@DESCRIPTION@] -	* Describes a /monic polynomial; <http://en.wikipedia.org/wiki/Monic_polynomial#Classifications>;+	* Describes a /monic polynomial; <https://en.wikipedia.org/wiki/Monic_polynomial#Classifications>; 	ie. in which the /coefficient/ of the /leading term/ is one. -}  module Factory.Data.MonicPolynomial( -- * Types--- ** Data-types,+-- ** Data-types 	MonicPolynomial(getPolynomial),	-- Hide the data-constructor. -- * Functions--- ** Constructors+-- ** Constructor 	mkMonicPolynomial ) where 

@@ -20,7 +20,7 @@   [@DESCRIPTION@] -	* Describes a <http://en.wikipedia.org/wiki/Monomial> and operations on it.+	* Describes a <https://en.wikipedia.org/wiki/Monomial> and operations on it.  	* A /monomial/ is merely a /polynomial/ with a single non-zero term; cf. /Binomial/. -}

@@ -20,9 +20,9 @@   [@DESCRIPTION@] -	* Describes a <http://en.wikipedia.org/wiki/Univariate> polynomial and operations on it.+	* Describes a <https://en.wikipedia.org/wiki/Univariate> polynomial and operations on it. -	* <http://en.wikipedia.org/wiki/Polynomial>.+	* <https://en.wikipedia.org/wiki/Polynomial>.  	* <http://mathworld.wolfram.com/Polynomial.html>. -}@@ -31,7 +31,7 @@ -- * Types -- ** Type-synonyms --	MonomialList,--- ** Data-types,+-- ** Data-types 	Polynomial, -- * Constants 	zero,@@ -86,7 +86,7 @@  {- | 	* The type of an arbitrary /univariate/ polynomial;-	actually it's more general, since it permits negative powers (<http://en.wikipedia.org/wiki/Laurent_polynomial>s).+	actually it's more general, since it permits negative powers (<https://en.wikipedia.org/wiki/Laurent_polynomial>s). 	It can't describe /multivariate/ polynomials, which would require a list of /exponents/. 	Rather than requiring the /exponent/ to implement the /type-class/ 'Integral', this is implemented at the function-level, as required. @@ -94,7 +94,7 @@ 	in which /coefficients/ are inferred to be zero, thus enabling efficient representation of sparse polynomials.  	* CAVEAT: the 'MonomialList' is required to;-	be ordered by /descending/ exponent (ie. reverse <http://en.wikipedia.org/wiki/Monomial_order>);+	be ordered by /descending/ exponent (ie. reverse <https://en.wikipedia.org/wiki/Monomial_order>); 	have had zero coefficients removed; 	and to have had /like/ terms merged; 	so the raw data-constructor isn't exported.@@ -103,7 +103,7 @@ 	getMonomialList	:: MonomialList coefficient exponent	-- ^ Accessor. } deriving (Eq, Show) --- | Makes /Polynomial/ a 'Data.Ring.Ring', over the /field/ composed from all possible /coefficients/; <http://en.wikipedia.org/wiki/Polynomial_ring>.+-- | Makes /Polynomial/ a 'Data.Ring.Ring', over the /field/ composed from all possible /coefficients/; <https://en.wikipedia.org/wiki/Polynomial_ring>. instance ( 	Eq	c, 	Num	c,@@ -166,7 +166,7 @@  ) => Data.QuotientRing.QuotientRing (Polynomial c e)	where {- 	Uses /Euclidian division/.-	<http://en.wikipedia.org/wiki/Polynomial_long_division>.+	<https://en.wikipedia.org/wiki/Polynomial_long_division>. 	<http://demonstrations.wolfram.com/PolynomialLongDivision/>. -} 	_ `quotRem'` MkPolynomial []		= error "Factory.Data.Polynomial.quotRem':\tzero denominator."@@ -262,7 +262,7 @@ {- | 	* 'True' if the /leading coefficient/ is one. -	* <http://en.wikipedia.org/wiki/Monic_polynomial#Classifications>.+	* <https://en.wikipedia.org/wiki/Monic_polynomial#Classifications>. -} isMonic :: (Eq c, Num c) => Polynomial c e -> Bool isMonic (MkPolynomial [])	= False	-- All coefficients are zero, and have therefore been removed.@@ -301,7 +301,7 @@ {- | 	* Return the /degree/ (AKA /order/) of the /polynomial/. -	* <http://en.wikipedia.org/wiki/Degree_of_a_polynomial>.+	* <https://en.wikipedia.org/wiki/Degree_of_a_polynomial>.  	* <http://mathworld.wolfram.com/PolynomialDegree.html>. -}@@ -312,7 +312,7 @@ {- | 	* Scale-up the specified /polynomial/ by a constant /monomial/ factor. -	* <http://en.wikipedia.org/wiki/Scalar_multiplication>.+	* <https://en.wikipedia.org/wiki/Scalar_multiplication>. -} (*=) :: (Eq c, Num c, Num e) => Polynomial c e -> Data.Monomial.Monomial c e -> Polynomial c e polynomial *= monomial

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines a /prime-wheel/, for use in prime-number generation; <http://en.wikipedia.org/wiki/Wheel_factorization>.+ [@DESCRIPTION@]	Defines a /prime-wheel/, for use in prime-number generation; <https://en.wikipedia.org/wiki/Wheel_factorization>. -}  module Factory.Data.PrimeWheel(@@ -35,7 +35,7 @@ 	generateMultiples, 	roll, 	rotate,--- ** Constructors+-- ** Constructor 	mkPrimeWheel, -- ** Query 	getCircumference,@@ -88,7 +88,7 @@ type NPrimes	= Int  {- |-	* Uses a /Sieve of Eratosthenes/ (<http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>), to generate an initial sequence of primes.+	* Uses a /Sieve of Eratosthenes/ (<https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>), to generate an initial sequence of primes.  	* Also generates an infinite sequence of candidate primes, each of which is /coprime/ to the primes just found, e.g.: 	@filter ((== 1) . (gcd (2 * 3 * 5 * 7))) [11 ..] = [11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,121 ..]@; NB /121/ isn't prime.

@@ -19,7 +19,7 @@   [@DESCRIPTION@] -	* Describes a /Quotient Ring/; <http://en.wikipedia.org/wiki/Quotient_ring>.+	* Describes a /Quotient Ring/; <https://en.wikipedia.org/wiki/Quotient_ring>.  	* This is a /ring/ composed from a residue-class resulting from /modular/ division. -}

@@ -21,7 +21,7 @@  	* Describes a /ring/ and operations on its members. -	* <http://en.wikipedia.org/wiki/Ring_%28mathematics%29>.+	* <https://en.wikipedia.org/wiki/Ring_%28mathematics%29>.  	* <http://www.numericana.com/answer/rings.htm>. -}@@ -30,7 +30,7 @@ -- * Type-classes 	Ring(..), -- * Types--- ** Data.types+-- ** Data-types --	Product, --	Sum, -- * Functions@@ -54,11 +54,11 @@ 	* Minimal definition; '=+=', '=*=', 'additiveInverse', 'multiplicativeIdentity', 'additiveIdentity'. -} class Ring r	where-	(=+=)			:: r -> r -> r	-- ^ Addition of two members; required to be /commutative/; <http://en.wikipedia.org/wiki/Commutativity>.+	(=+=)			:: r -> r -> r	-- ^ Addition of two members; required to be /commutative/; <https://en.wikipedia.org/wiki/Commutativity>. 	(=*=)			:: r -> r -> r	-- ^ Multiplication of two members.-	additiveInverse		:: r -> r	-- ^ The operand required to yield /zero/ under addition; <http://en.wikipedia.org/wiki/Additive_inverse>.+	additiveInverse		:: r -> r	-- ^ The operand required to yield /zero/ under addition; <https://en.wikipedia.org/wiki/Additive_inverse>. 	multiplicativeIdentity	:: r		-- ^ The /identity/-member under multiplication; <http://mathworld.wolfram.com/MultiplicativeIdentity.html>.-	additiveIdentity	:: r		-- ^ The /identity/-member under addition (AKA /zero/); <http://en.wikipedia.org/wiki/Additive_identity>.+	additiveIdentity	:: r		-- ^ The /identity/-member under addition (AKA /zero/); <https://en.wikipedia.org/wiki/Additive_identity>.  	(=-=) :: r -> r -> r			-- ^ Subtract the two specified /ring/-members. 	l =-= r	= l =+= additiveInverse r	-- Default implementation.@@ -70,7 +70,7 @@ 	* Raise a /ring/-member to the specified positive integral power.  	* Exponentiation is implemented as a sequence of either squares of, or multiplications by, the /ring/-member;-	<http://en.wikipedia.org/wiki/Exponentiation_by_squaring>.+	<https://en.wikipedia.org/wiki/Exponentiation_by_squaring>. -} (=^) :: ( 	Eq		r,

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Determines the /Arithmetic-geometric mean/; <http://en.wikipedia.org/wiki/Arithmetic-geometric_mean>.+ [@DESCRIPTION@]	Determines the /Arithmetic-geometric mean/; <https://en.wikipedia.org/wiki/Arithmetic-geometric_mean>. -}  module Factory.Math.ArithmeticGeometricMean(@@ -41,10 +41,10 @@ import qualified	Factory.Math.Precision	as Math.Precision import qualified	Factory.Math.SquareRoot	as Math.SquareRoot --- | The type of the /arithmetic mean/; <http://en.wikipedia.org/wiki/Arithmetic_mean>.+-- | The type of the /arithmetic mean/; <https://en.wikipedia.org/wiki/Arithmetic_mean>. type ArithmeticMean	= Rational --- | The type of the /geometric mean/; <http://en.wikipedia.org/wiki/Geometric_mean>.+-- | The type of the /geometric mean/; <https://en.wikipedia.org/wiki/Geometric_mean>. type GeometricMean	= Rational  -- | Encapsulates both /arithmetic/ and /geometric/ means.

@@ -56,7 +56,7 @@ {- | 	* Reduces a list to a single scalar encapsulated in a 'Data.Monoid.Monoid', 	using a /divide-and-conquer/ strategy,-	bisecting the list and recursively evaluating each part; <http://en.wikipedia.org/wiki/Divide_and_conquer_algorithm>.+	bisecting the list and recursively evaluating each part; <https://en.wikipedia.org/wiki/Divide_and_conquer_algorithm>.  	* By choosing a 'bisectionRatio' other than @(1 % 2)@, the bisection can be made asymmetrical. 	The specified ratio represents the length of the left-hand portion, over the original list-length;@@ -65,7 +65,7 @@ 	* This process of recursive bisection, is terminated beneath the specified minimum list-length, 	after which the /monoid/'s binary operator is directly /folded/ over the list. -	* One can view this as a <http://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>,+	* One can view this as a <https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>, 	in which the list is exploded into a binary tree-structure 	(each leaf of which contains a list of up to 'minLength' integers, and each node of which contains an associative binary operator), 	and then collapsed to a scalar, by application of the operators.

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	<http://en.wikipedia.org/wiki/Fibonacci_number>.+ [@DESCRIPTION@]	<https://en.wikipedia.org/wiki/Fibonacci_number>. -}  module Factory.Math.Fibonacci(

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Provides various /hyperoperations/; <http://en.wikipedia.org/wiki/Hyperoperation>.+ [@DESCRIPTION@]	Provides various /hyperoperations/; <https://en.wikipedia.org/wiki/Hyperoperation>. -}  module Factory.Math.Hyperoperation(@@ -64,7 +64,7 @@ 	* Returns the /power-tower/ of the specified /base/; <http://mathworld.wolfram.com/PowerTower.html>.  	* A synonym for /tetration/;-		<http://en.wikipedia.org/wiki/Tetration>,+		<https://en.wikipedia.org/wiki/Tetration>, 		<http://www.tetration.org/Fractals/Atlas/index.html>. -} powerTower :: (Integral base, Integral hyperExponent, Show base) => base -> hyperExponent -> base@@ -76,7 +76,7 @@ 	| base < 0 && hyperExponent > 1	= error $ "Factory.Math.Hyperoperation.powerTower:\tundefined for negative base; " ++ show base 	| otherwise			= Data.List.genericIndex (iterate (base ^) 1) hyperExponent --- | The /hyperoperation/-sequence; <http://en.wikipedia.org/wiki/Hyperoperation>.+-- | The /hyperoperation/-sequence; <https://en.wikipedia.org/wiki/Hyperoperation>. hyperoperation :: (Integral rank, Show rank) => rank -> Base -> HyperExponent -> Base hyperoperation rank base hyperExponent 	| rank < fromIntegral succession	= error $ "Factory.Math.Hyperoperation.hyperoperation:\tundefined for rank; " ++ show rank@@ -100,7 +100,7 @@ 				where 					e'	= {-fromIntegral $-} r ^# pred e --- | The /Ackermann-Peter/-function; <http://en.wikipedia.org/wiki/Ackermann_function#Ackermann_numbers>.+-- | The /Ackermann-Peter/-function; <https://en.wikipedia.org/wiki/Ackermann_function#Ackermann_numbers>. ackermannPeter :: (Integral rank, Show rank) => rank -> HyperExponent -> Base ackermannPeter rank	= (+ negate 3) . hyperoperation rank 2 {-base-} . (+ 3) 

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -24,7 +24,7 @@ 	* Provides additional functions related to /factorials/, but which depends on a specific implementation, 	and which therefore can't be accessed throught the class-interface. -	* <http://en.wikipedia.org/wiki/Factorial>.+	* <https://en.wikipedia.org/wiki/Factorial>.  	* <http://mathworld.wolfram.com/Factorial.html>. @@ -44,22 +44,22 @@ 	(!/!) ) where +import qualified	Data.Default import qualified	Data.Numbers.Primes import qualified	Factory.Data.Interval		as Data.Interval import qualified	Factory.Data.PrimeFactors	as Data.PrimeFactors import qualified	Factory.Math.Factorial		as Math.Factorial-import qualified	ToolShed.Defaultable  infixl 7 !/!	-- Same as (/).  -- | The algorithms by which /factorial/ has been implemented.-data Algorithm	=-	Bisection		-- ^ The integers from which the /factorial/ is composed, are multiplied using @Data.Interval.product'@.+data Algorithm+	= Bisection		-- ^ The integers from which the /factorial/ is composed, are multiplied using @Data.Interval.product'@. 	| PrimeFactorisation	-- ^ The /prime factors/ of the /factorial/ are extracted, then raised to the appropriate power, before multiplication. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= Bisection+instance Data.Default.Default Algorithm	where+	def	= Bisection  instance Math.Factorial.Algorithmic Algorithm	where 	factorial algorithm n@@ -74,7 +74,7 @@ 	* Precisely all the primes less than or equal to the specified integer /n/, are included in /n!/; 	only the multiplicity of each of these known prime components need be determined. -	* <http://en.wikipedia.org/wiki/Factorial#Number_theory>.+	* <https://en.wikipedia.org/wiki/Factorial#Number_theory>.  	* CAVEAT: currently a hotspot. -}@@ -130,8 +130,8 @@ 	-> i	-- ^ The /denominator/. 	-> f	-- ^ The resulting fraction. numerator !/! denominator-	| numerator <= 1		= recip . fromIntegral $ Math.Factorial.factorial (ToolShed.Defaultable.defaultValue :: Algorithm) denominator-	| denominator <= 1		= fromIntegral $ Math.Factorial.factorial (ToolShed.Defaultable.defaultValue :: Algorithm) numerator+	| numerator <= 1		= recip . fromIntegral $ Math.Factorial.factorial (Data.Default.def :: Algorithm) denominator+	| denominator <= 1		= fromIntegral $ Math.Factorial.factorial (Data.Default.def :: Algorithm) numerator 	| numerator == denominator	= 1 	| numerator < denominator	= recip $ denominator !/! numerator	-- Recurse. 	| otherwise			= fromIntegral $ Data.Interval.product' (recip 2) 64 (succ denominator, numerator)

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -26,16 +26,16 @@ 	Algorithm(..) ) where +import qualified	Data.Default import qualified	Factory.Math.Implementations.Pi.AGM.BrentSalamin	as Math.Implementations.Pi.AGM.BrentSalamin import qualified	Factory.Math.Pi						as Math.Pi import qualified	Factory.Math.SquareRoot					as Math.SquareRoot-import qualified	ToolShed.Defaultable  -- | Defines the available algorithms. data Algorithm squareRootAlgorithm	= BrentSalamin squareRootAlgorithm	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable squareRootAlgorithm => ToolShed.Defaultable.Defaultable (Algorithm squareRootAlgorithm)	where-	defaultValue	= BrentSalamin ToolShed.Defaultable.defaultValue+instance Data.Default.Default squareRootAlgorithm => Data.Default.Default (Algorithm squareRootAlgorithm)	where+	def	= BrentSalamin Data.Default.def  instance Math.SquareRoot.Algorithmic squareRootAlgorithm => Math.Pi.Algorithmic (Algorithm squareRootAlgorithm)	where 	openR (BrentSalamin squareRootAlgorithm)	= Math.Implementations.Pi.AGM.BrentSalamin.openR squareRootAlgorithm

@@ -20,7 +20,7 @@  [@DESCRIPTION@]  	* Implements the /Brent-Salamin/ (AKA /Gauss-Legendre/) algorithm;-		<http://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm>,+		<https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm>, 		<http://mathworld.wolfram.com/Brent-SalaminFormula.html>, 		<http://www.pi314.net/eng/salamin.php>. 

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -26,11 +26,11 @@ 	Algorithm(..) ) where +import qualified	Data.Default import qualified	Factory.Math.Implementations.Pi.BBP.Base65536		as Math.Implementations.Pi.BBP.Base65536 import qualified	Factory.Math.Implementations.Pi.BBP.Bellard		as Math.Implementations.Pi.BBP.Bellard import qualified	Factory.Math.Implementations.Pi.BBP.Implementation	as Math.Implementations.Pi.BBP.Implementation import qualified	Factory.Math.Pi						as Math.Pi-import qualified	ToolShed.Defaultable  -- | Defines those /BBP/-type series which have been implemented. data Algorithm	=@@ -38,8 +38,8 @@ 	| Bellard	-- ^ A /nega-base/ @2^10@ version of the formula. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= Base65536+instance Data.Default.Default Algorithm	where+	def	= Base65536  instance Math.Pi.Algorithmic Algorithm	where 	openR Base65536	= Math.Implementations.Pi.BBP.Implementation.openR Math.Implementations.Pi.BBP.Base65536.series

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines /Bellard/'s nega-base-@2^10@ /BBP/-formula; <http://en.wikipedia.org/wiki/Bellard%27s_formula>+ [@DESCRIPTION@]	Defines /Bellard/'s nega-base-@2^10@ /BBP/-formula; <https://en.wikipedia.org/wiki/Bellard%27s_formula> -}  module Factory.Math.Implementations.Pi.BBP.Bellard(

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -26,12 +26,12 @@ 	Algorithm(..) ) where +import qualified	Data.Default import qualified	Factory.Math.Factorial					as Math.Factorial import qualified	Factory.Math.Implementations.Pi.Borwein.Borwein1993	as Math.Implementations.Pi.Borwein.Borwein1993 import qualified	Factory.Math.Implementations.Pi.Borwein.Implementation	as Math.Implementations.Pi.Borwein.Implementation import qualified	Factory.Math.Pi						as Math.Pi import qualified	Factory.Math.SquareRoot					as Math.SquareRoot-import qualified	ToolShed.Defaultable  {- | 	* Define those /Borwein/-series which have been implemented.@@ -39,14 +39,14 @@ 	* Though currently there's only one, provision has been made for the addition of more. -} data Algorithm squareRootAlgorithm factorialAlgorithm	=-	Borwein1993 squareRootAlgorithm factorialAlgorithm	-- ^ <http://en.wikipedia.org/wiki/Borwein%27s_algorithm>.+	Borwein1993 squareRootAlgorithm factorialAlgorithm	-- ^ <https://en.wikipedia.org/wiki/Borwein%27s_algorithm>. 	deriving (Eq, Read, Show)  instance (-	ToolShed.Defaultable.Defaultable	squareRootAlgorithm,-	ToolShed.Defaultable.Defaultable	factorialAlgorithm- ) => ToolShed.Defaultable.Defaultable (Algorithm squareRootAlgorithm factorialAlgorithm)	where-	defaultValue	= Borwein1993 ToolShed.Defaultable.defaultValue ToolShed.Defaultable.defaultValue+	Data.Default.Default	squareRootAlgorithm,+	Data.Default.Default	factorialAlgorithm+ ) => Data.Default.Default (Algorithm squareRootAlgorithm factorialAlgorithm)	where+	def	= Borwein1993 Data.Default.def Data.Default.def  instance ( 	Math.SquareRoot.Algorithmic	squareRootAlgorithm,

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines the /Borwein/ series for /Pi/; <http://en.wikipedia.org/wiki/Borwein%27s_algorithm#Jonathan_Borwein_and_Peter_Borwein.27s_Version_.281993.29>+ [@DESCRIPTION@]	Defines the /Borwein/ series for /Pi/; <https://en.wikipedia.org/wiki/Borwein%27s_algorithm#Jonathan_Borwein_and_Peter_Borwein.27s_Version_.281993.29> -}  module Factory.Math.Implementations.Pi.Borwein.Borwein1993(

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines /Borwein/ series for /Pi/; <http://en.wikipedia.org/wiki/Borwein%27s_algorithm>+ [@DESCRIPTION@]	Defines /Borwein/ series for /Pi/; <https://en.wikipedia.org/wiki/Borwein%27s_algorithm> -}  module Factory.Math.Implementations.Pi.Borwein.Implementation(

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines a <http://en.wikipedia.org/wiki/Srinivasa_Borwein>-type series for /Pi/.+ [@DESCRIPTION@]	Defines a <https://en.wikipedia.org/wiki/Srinivasa_Borwein>-type series for /Pi/. -}  module Factory.Math.Implementations.Pi.Borwein.Series(

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines the set of /Ramanujan/-type algorithms which have been implemented; <http://en.wikipedia.org/wiki/Pi>.+ [@DESCRIPTION@]	Defines the set of /Ramanujan/-type algorithms which have been implemented; <https://en.wikipedia.org/wiki/Pi>. -}  module Factory.Math.Implementations.Pi.Ramanujan.Algorithm(@@ -26,25 +26,25 @@ 	Algorithm(..) ) where +import qualified	Data.Default import qualified	Factory.Math.Factorial						as Math.Factorial import qualified	Factory.Math.Implementations.Pi.Ramanujan.Chudnovsky		as Math.Implementations.Pi.Ramanujan.Chudnovsky import qualified	Factory.Math.Implementations.Pi.Ramanujan.Classic		as Math.Implementations.Pi.Ramanujan.Classic import qualified	Factory.Math.Implementations.Pi.Ramanujan.Implementation	as Math.Implementations.Pi.Ramanujan.Implementation import qualified	Factory.Math.Pi							as Math.Pi import qualified	Factory.Math.SquareRoot						as Math.SquareRoot-import qualified	ToolShed.Defaultable  -- | Define those /Ramanujan/-series which have been implemented.-data Algorithm squareRootAlgorithm factorialAlgorithm	=-	Classic squareRootAlgorithm factorialAlgorithm		-- ^ The original version.+data Algorithm squareRootAlgorithm factorialAlgorithm+	= Classic squareRootAlgorithm factorialAlgorithm	-- ^ The original version. 	| Chudnovsky squareRootAlgorithm factorialAlgorithm	-- ^ A variant found by the /Chudnovsky brothers/. 	deriving (Eq, Read, Show)  instance (-	ToolShed.Defaultable.Defaultable	squareRootAlgorithm,-	ToolShed.Defaultable.Defaultable	factorialAlgorithm- ) => ToolShed.Defaultable.Defaultable (Algorithm squareRootAlgorithm factorialAlgorithm)	where-	defaultValue	= Chudnovsky ToolShed.Defaultable.defaultValue ToolShed.Defaultable.defaultValue+	Data.Default.Default	squareRootAlgorithm,+	Data.Default.Default	factorialAlgorithm+ ) => Data.Default.Default (Algorithm squareRootAlgorithm factorialAlgorithm)	where+	def	= Chudnovsky Data.Default.def Data.Default.def  instance ( 	Math.SquareRoot.Algorithmic	squareRootAlgorithm,

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines the /Chudnovsky/ series for /Pi/; <http://en.wikipedia.org/wiki/Pi>.+ [@DESCRIPTION@]	Defines the /Chudnovsky/ series for /Pi/; <https://en.wikipedia.org/wiki/Pi>. -}  module Factory.Math.Implementations.Pi.Ramanujan.Chudnovsky(

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Implements a /Ramanujan/-type series for /Pi/; <http://en.wikipedia.org/wiki/Srinivasa_Ramanujan>.+ [@DESCRIPTION@]	Implements a /Ramanujan/-type series for /Pi/; <https://en.wikipedia.org/wiki/Srinivasa_Ramanujan>. -}  module Factory.Math.Implementations.Pi.Ramanujan.Implementation(

@@ -17,7 +17,7 @@ {- |  [@AUTHOR@]	Dr. Alistair Ward - [@DESCRIPTION@]	Defines a <http://en.wikipedia.org/wiki/Srinivasa_Ramanujan>-type series for /Pi/.+ [@DESCRIPTION@]	Defines a <https://en.wikipedia.org/wiki/Srinivasa_Ramanujan>-type series for /Pi/. -}  module Factory.Math.Implementations.Pi.Ramanujan.Series(

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -26,21 +26,21 @@ 	Algorithm(..) ) where +import qualified	Data.Default import			Data.Ratio((%)) import qualified	Factory.Math.Implementations.Pi.Spigot.Gosper		as Math.Implementations.Pi.Spigot.Gosper import qualified	Factory.Math.Implementations.Pi.Spigot.RabinowitzWagon	as Math.Implementations.Pi.Spigot.RabinowitzWagon import qualified	Factory.Math.Implementations.Pi.Spigot.Spigot		as Math.Implementations.Pi.Spigot.Spigot import qualified	Factory.Math.Pi						as Math.Pi-import qualified	ToolShed.Defaultable  -- | Define those /Spigot/-algorithms which have been implemented.-data Algorithm	=-	Gosper			-- ^ A /continued fraction/ discovered by /Gosper/.+data Algorithm+	= Gosper		-- ^ A /continued fraction/ discovered by /Gosper/. 	| RabinowitzWagon	-- ^ A /continued fraction/ discovered by /Rabinowitz/ and /Wagon/. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= Gosper+instance Data.Default.Default Algorithm	where+	def	= Gosper  instance Math.Pi.Algorithmic Algorithm	where 	openI Gosper			= Math.Implementations.Pi.Spigot.Spigot.openI Math.Implementations.Pi.Spigot.Gosper.series

@@ -19,7 +19,7 @@   [@DESCRIPTION@] -	* Implements a /spigot/-algorithm; <http://en.wikipedia.org/wiki/Spigot_algorithm>.+	* Implements a /spigot/-algorithm; <https://en.wikipedia.org/wiki/Spigot_algorithm>.  	* Uses the traditional algorithm, rather than the /unbounded/ algorithm described by <http://www.comlab.ox.ac.uk/jeremy.gibbons/publications/spigot.pdf>. -}@@ -42,7 +42,7 @@ -- ** Accessors --	getQuotient, --	getRemainder,--- ** Constructors+-- ** Constructor --	mkRow ) where 

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -21,7 +21,7 @@  	* Determines whether an integer is prime. -	* <http://en.wikipedia.org/wiki/Primality_test>.+	* <https://en.wikipedia.org/wiki/Primality_test>.  	* <http://primes.utm.edu/index.html> @@ -42,6 +42,7 @@ import			Control.Arrow((&&&)) import qualified	Control.DeepSeq import qualified	Control.Parallel.Strategies+import qualified	Data.Default import qualified	Data.Numbers.Primes import qualified	Factory.Data.MonicPolynomial		as Data.MonicPolynomial import qualified	Factory.Data.Polynomial			as Data.Polynomial@@ -51,16 +52,15 @@ import qualified	Factory.Math.Power			as Math.Power import qualified	Factory.Math.Primality			as Math.Primality import qualified	Factory.Math.PrimeFactorisation		as Math.PrimeFactorisation-import qualified	ToolShed.Defaultable  -- | The algorithms by which /primality/-testing has been implemented.-data Algorithm factorisationAlgorithm	=-	AKS factorisationAlgorithm	-- ^ <http://en.wikipedia.org/wiki/AKS_primality_test>.-	| MillerRabin			-- ^ <http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test>.+data Algorithm factorisationAlgorithm+	= AKS factorisationAlgorithm	-- ^ <https://en.wikipedia.org/wiki/AKS_primality_test>.+	| MillerRabin			-- ^ <https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test>. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable (Algorithm factorisationAlgorithm)	where-	defaultValue	= MillerRabin+instance Data.Default.Default (Algorithm factorisationAlgorithm)	where+	def	= MillerRabin  instance Math.PrimeFactorisation.Algorithmic factorisationAlgorithm => Math.Primality.Algorithmic (Algorithm factorisationAlgorithm)	where 	isPrime _ 2	= True	-- The only even prime.@@ -79,7 +79,7 @@ 		) candidate  {- |-	* An implementation of the /Agrawal-Kayal-Saxena/ primality-test; <http://en.wikipedia.org/wiki/AKS_primality_test>,+	* An implementation of the /Agrawal-Kayal-Saxena/ primality-test; <https://en.wikipedia.org/wiki/AKS_primality_test>, 	using the /Lenstra/ and /Pomerance/ algorithm.  	* CAVEAT: this deterministic algorithm has a theoretical time-complexity of @O(log^6)@,@@ -174,7 +174,7 @@  	* A testing of smaller set of bases, is sufficient for candidates smaller than various thresholds; <http://primes.utm.edu/prove/prove2_3.html>. -	* <http://en.wikipedia.org/wiki/Miller-Rabin_primality_test>.+	* <https://en.wikipedia.org/wiki/Miller-Rabin_primality_test>.  	* <http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html> 

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -42,6 +42,7 @@ import qualified	Control.Arrow import qualified	Control.DeepSeq import qualified	Control.Parallel.Strategies+import qualified	Data.Default import qualified	Data.Maybe import qualified	Data.Numbers.Primes import qualified	Factory.Data.Exponential	as Data.Exponential@@ -51,17 +52,16 @@ import qualified	Factory.Math.Power		as Math.Power import qualified	Factory.Math.PrimeFactorisation	as Math.PrimeFactorisation import qualified	ToolShed.Data.Pair-import qualified	ToolShed.Defaultable  -- | The algorithms by which prime-factorisation has been implemented. data Algorithm-	= DixonsMethod	-- ^ <http://en.wikipedia.org/wiki/Dixon%27s_factorization_method>.-	| FermatsMethod	-- ^ <http://en.wikipedia.org/wiki/Fermat%27s_factorization_method>.-	| TrialDivision	-- ^ <http://en.wikipedia.org/wiki/Trial_division>.+	= DixonsMethod	-- ^ <https://en.wikipedia.org/wiki/Dixon%27s_factorization_method>.+	| FermatsMethod	-- ^ <https://en.wikipedia.org/wiki/Fermat%27s_factorization_method>.+	| TrialDivision	-- ^ <https://en.wikipedia.org/wiki/Trial_division>. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= TrialDivision+instance Data.Default.Default Algorithm	where+	def	= TrialDivision  instance Math.PrimeFactorisation.Algorithmic Algorithm	where 	primeFactors algorithm	= case algorithm of@@ -69,16 +69,16 @@ 		FermatsMethod	-> Data.PrimeFactors.reduce . factoriseByFermatsMethod 		TrialDivision	-> factoriseByTrialDivision --- | <http://en.wikipedia.org/wiki/Dixon%27s_factorization_method>.+-- | <https://en.wikipedia.org/wiki/Dixon%27s_factorization_method>. factoriseByDixonsMethod :: Integral base => base -> Data.PrimeFactors.Factors base exponent factoriseByDixonsMethod	= undefined  {- |-	* <http://en.wikipedia.org/wiki/Fermat%27s_factorization_method>.+	* <https://en.wikipedia.org/wiki/Fermat%27s_factorization_method>.  	* <http://mathworld.wolfram.com/FermatsFactorizationMethod.html>. -	* <http://en.wikipedia.org/wiki/Congruence_of_squares>.+	* <https://en.wikipedia.org/wiki/Congruence_of_squares>.  	*	@i = f1 * f2@							Assume a non-trivial factorisation, ie. one in which both factors exceed one. 	=>	@i = (larger + smaller) * (larger - smaller)@			Represent the co-factors as a sum and difference.@@ -125,7 +125,7 @@  {- | 	* Decomposes the specified integer, into a product of /prime/-factors,-	using <http://mathworld.wolfram.com/DirectSearchFactorization.html>, AKA <http://en.wikipedia.org/wiki/Trial_division>.+	using <http://mathworld.wolfram.com/DirectSearchFactorization.html>, AKA <https://en.wikipedia.org/wiki/Trial_division>.  	* This works best when the factors are small. -}

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -34,6 +34,7 @@ 	Algorithm(..) ) where +import qualified	Data.Default import qualified	Data.Numbers.Primes import qualified	Factory.Data.PrimeWheel					as Data.PrimeWheel import qualified	Factory.Math.Implementations.Primes.SieveOfAtkin	as Math.Implementations.Primes.SieveOfAtkin@@ -41,19 +42,18 @@ import qualified	Factory.Math.Implementations.Primes.TrialDivision	as Math.Implementations.Primes.TrialDivision import qualified	Factory.Math.Implementations.Primes.TurnersSieve	as Math.Implementations.Primes.TurnersSieve import qualified	Factory.Math.Primes					as Math.Primes-import qualified	ToolShed.Defaultable  -- | The implemented methods by which the primes may be generated. data Algorithm-	= SieveOfAtkin Integer					-- ^ The /Sieve of Atkin/, optimised using a 'Data.PrimeWheel.PrimeWheel' of optimal size, for primes up to the specified maximum bound; <http://en.wikipedia.org/wiki/Sieve_of_Atkin>.-	| SieveOfEratosthenes Data.PrimeWheel.NPrimes		-- ^ The /Sieve of Eratosthenes/ (<http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>), optimised using a 'Data.PrimeWheel.PrimeWheel'.+	= SieveOfAtkin Integer					-- ^ The /Sieve of Atkin/, optimised using a 'Data.PrimeWheel.PrimeWheel' of optimal size, for primes up to the specified maximum bound; <https://en.wikipedia.org/wiki/Sieve_of_Atkin>.+	| SieveOfEratosthenes Data.PrimeWheel.NPrimes		-- ^ The /Sieve of Eratosthenes/ (<https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>), optimised using a 'Data.PrimeWheel.PrimeWheel'. 	| TrialDivision Data.PrimeWheel.NPrimes			-- ^ For each candidate, confirm indivisibility, by all /primes/ smaller than its /square-root/, optimised using a 'Data.PrimeWheel.PrimeWheel'. 	| TurnersSieve						-- ^ For each /prime/, the infinite list of candidates greater than its /square/, is filtered for indivisibility; <http://www.haskell.org/haskellwiki/Prime_numbers#Turner.27s_sieve_-_Trial_division>. 	| WheelSieve Int					-- ^ 'Data.Numbers.Primes.wheelSieve'. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= SieveOfEratosthenes 7	-- Resulting in a wheel of circumference 510510.+instance Data.Default.Default Algorithm	where+	def	= SieveOfEratosthenes 7	-- Resulting in a wheel of circumference 510510.  instance Math.Primes.Algorithmic Algorithm	where 	primes (SieveOfAtkin maxPrime)		= Math.Implementations.Primes.SieveOfAtkin.sieveOfAtkin (Data.PrimeWheel.estimateOptimalSize maxPrime) $ fromIntegral maxPrime

@@ -19,7 +19,7 @@   [@DESCRIPTION@] -	* Generates the constant /bounded/ list of /prime-numbers/, using the /Sieve of Atkin/; <http://en.wikipedia.org/wiki/Sieve_of_Atkin>.+	* Generates the constant /bounded/ list of /prime-numbers/, using the /Sieve of Atkin/; <https://en.wikipedia.org/wiki/Sieve_of_Atkin>.  	* <cr.yp.to/papers/primesieves-19990826.pdf>. @@ -99,7 +99,7 @@ 	* Because the results are /bounded/, they're returned in a zero-indexed /array/, to provide efficient random access; 	the first few elements should never be required, but it makes query clearer. -	* <http://en.wikipedia.org/wiki/Sieve_of_Atkin>.+	* <https://en.wikipedia.org/wiki/Sieve_of_Atkin>. -} polynomialTypeLookup :: (Data.Array.IArray.Ix i, Integral i) 	=> Data.PrimeWheel.PrimeWheel i

@@ -19,7 +19,7 @@   [@DESCRIPTION@] -	* Generates the constant, conceptually infinite, list of /prime-numbers/, using the /Sieve of Eratosthenes/; <http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>.+	* Generates the constant, conceptually infinite, list of /prime-numbers/, using the /Sieve of Eratosthenes/; <https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>.  	* Based on <http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf>. @@ -79,7 +79,7 @@ 	* A refinement of the /Sieve Of Eratosthenes/, which pre-sieves candidates, selecting only those /coprime/ to the specified short sequence of low prime-numbers.  	* The short sequence of initial primes are represented by a 'Data.PrimeWheel.PrimeWheel',-	of parameterised, but static, size; <http://en.wikipedia.org/wiki/Wheel_factorization>.+	of parameterised, but static, size; <https://en.wikipedia.org/wiki/Wheel_factorization>.  	* The algorithm requires one to record multiples of previously discovered primes, allowing /composite/ candidates to be eliminated by comparison. 

@@ -44,7 +44,7 @@ 	* For each candidate, confirm indivisibility, by all /primes/ smaller than its /square-root/.  	* The candidates to sieve, are generated by a 'Data.PrimeWheel.PrimeWheel',-	of parameterised, but static, size; <http://en.wikipedia.org/wiki/Wheel_factorization>.+	of parameterised, but static, size; <https://en.wikipedia.org/wiki/Wheel_factorization>. -} trialDivision :: Integral prime => Data.PrimeWheel.NPrimes -> [prime] trialDivision 0	= [2, 3] ++ filter (`isIndivisibleBy` trialDivision 0 {-recurse-}) [5 ..]	-- No faster than using 'Data.PrimeWheel.mkPrimeWheel 0', but apparently better space-complexity ?!

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -39,6 +39,7 @@ ) where  import			Control.Arrow((***))+import qualified	Data.Default import			Factory.Data.PrimeFactors((>/<), (>^)) import qualified	Factory.Data.PrimeFactors		as Data.PrimeFactors import qualified	Factory.Math.Implementations.Factorial	as Math.Implementations.Factorial@@ -46,22 +47,21 @@ import qualified	Factory.Math.Precision			as Math.Precision import qualified	Factory.Math.SquareRoot			as Math.SquareRoot import qualified	Factory.Math.Summation			as Math.Summation-import qualified	ToolShed.Defaultable  -- | The number of terms in a series. type Terms	= Int  -- | The algorithms by which the /square-root/ has been implemented. data Algorithm-	= BakhshaliApproximation	-- ^ <http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Bakhshali_approximation>-	| ContinuedFraction		-- ^ <http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion>.-	| HalleysMethod			-- ^ <http://en.wikipedia.org/wiki/Halley%27s_method>.-	| NewtonRaphsonIteration	-- ^ <http://en.wikipedia.org/wiki/Newton%27s_method>.-	| TaylorSeries Terms		-- ^ <http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>.+	= BakhshaliApproximation	-- ^ <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Bakhshali_approximation>+	| ContinuedFraction		-- ^ <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion>.+	| HalleysMethod			-- ^ <https://en.wikipedia.org/wiki/Halley%27s_method>.+	| NewtonRaphsonIteration	-- ^ <https://en.wikipedia.org/wiki/Newton%27s_method>.+	| TaylorSeries Terms		-- ^ <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>. 	deriving (Eq, Read, Show) -instance ToolShed.Defaultable.Defaultable Algorithm	where-	defaultValue	= NewtonRaphsonIteration+instance Data.Default.Default Algorithm	where+	def	= NewtonRaphsonIteration  -- | Returns an improved estimate for the /square-root/ of the specified value, to the required precision, using the supplied initial estimate.. type ProblemSpecification operand@@ -128,12 +128,12 @@  {- | 	* Uses /continued-fractions/, to iterate towards the principal /square-root/ of the specified positive integer;-	<http://en.wikipedia.org/wiki/Solving_quadratic_equations_with_continued_fractions>,-	<http://en.wikipedia.org/wiki/Generalized_continued_fraction#Roots_of_positive_numbers>,-	<http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion>.+	<https://en.wikipedia.org/wiki/Solving_quadratic_equations_with_continued_fractions>,+	<https://en.wikipedia.org/wiki/Generalized_continued_fraction#Roots_of_positive_numbers>,+	<https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion>. 	<http://www.myreckonings.com/Dead_Reckoning/Online/Materials/General%20Method%20for%20Extracting%20Roots.pdf> -	* The convergence <http://en.wikipedia.org/wiki/Rate_of_convergence> of the /continued-fraction/ is merely /1st order/ (linear).+	* The convergence <https://en.wikipedia.org/wiki/Rate_of_convergence> of the /continued-fraction/ is merely /1st order/ (linear). -} squareRootByContinuedFraction :: Real operand => ProblemSpecification operand squareRootByContinuedFraction (initialEstimate, initialDecimalDigits) requiredDecimalDigits y	= initialEstimate + (convergents initialEstimate !! Math.Precision.getTermsRequired (10 ^^ negate initialDecimalDigits) requiredDecimalDigits)	where@@ -141,7 +141,7 @@ 	convergents x	= iterate ((Math.SquareRoot.getDiscrepancy y x /) . ((2 * x) +)) 0  {- |-	* The constant coefficients of the /Taylor-series/ for a /square-root/; <http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>.+	* The constant coefficients of the /Taylor-series/ for a /square-root/; <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>.  	* @ ((-1)^n * factorial(2*n)) / ((1 - 2*n) * 4^n * factorial(n^2)) @. -}@@ -160,7 +160,7 @@ {- | 	* Returns the /Taylor-series/ for the /square-root/ of the specified value, to any requested number of terms. -	* <http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>.+	* <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Taylor_series>.  	* The convergence of the series is merely /linear/, 	in that each term increases the precision, by a constant number of decimal places, equal to the those in the original estimate.

@@ -38,7 +38,7 @@  	* Based on <http://rosettacode.org/wiki/Multiplicative_order#Haskell>. -	* <http://en.wikipedia.org/wiki/Multiplicative_order>.+	* <https://en.wikipedia.org/wiki/Multiplicative_order>.  	* <http://mathworld.wolfram.com/MultiplicativeOrder.html>. -}

@@ -35,7 +35,7 @@ {- | 	* Returns @(Just . sqrt)@ if the specified integer is a /square number/ (AKA /perfect square/). -	* <http://en.wikipedia.org/wiki/Square_number>.+	* <https://en.wikipedia.org/wiki/Square_number>.  	* <http://mathworld.wolfram.com/SquareNumber.html>. @@ -69,7 +69,7 @@  	* CAVEAT: /zero/ and /one/ are normally excluded from this set. -	* <http://en.wikipedia.org/wiki/Perfect_power>.+	* <https://en.wikipedia.org/wiki/Perfect_power>.  	* <http://mathworld.wolfram.com/PerfectPower.html>. 

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -28,8 +28,8 @@ 	Category(..) ) where +import qualified	Data.Default import qualified	Factory.Math.Precision	as Math.Precision-import qualified	ToolShed.Defaultable  {- | 	* Defines the methods expected of a /Pi/-algorithm.@@ -58,20 +58,14 @@ -- | Categorises the various algorithms. data Category agm bbp borwein ramanujan spigot 	= AGM agm		-- ^ Algorithms based on the /Arithmetic-geometric Mean/.-	| BBP bbp		-- ^ <http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula>.-	| Borwein borwein	-- ^ <http://en.wikipedia.org/wiki/Borwein%27s_algorithm>.+	| BBP bbp		-- ^ <https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula>.+	| Borwein borwein	-- ^ <https://en.wikipedia.org/wiki/Borwein%27s_algorithm>. 	| Ramanujan ramanujan	-- ^ <http://www.pi314.net/eng/ramanujan.php>. 	| Spigot spigot		-- ^ Algorithms from which the digits of /Pi/ slowly drip, one by one. 	deriving (Eq, Read, Show) -instance (-	ToolShed.Defaultable.Defaultable agm,-	ToolShed.Defaultable.Defaultable bbp,-	ToolShed.Defaultable.Defaultable borwein,-	ToolShed.Defaultable.Defaultable ramanujan,-	ToolShed.Defaultable.Defaultable spigot- )  => ToolShed.Defaultable.Defaultable (Category agm bbp borwein ramanujan spigot)	where-	defaultValue	= BBP ToolShed.Defaultable.defaultValue+instance Data.Default.Default bbp  => Data.Default.Default (Category agm bbp borwein ramanujan spigot)	where+	def	= BBP Data.Default.def  instance ( 	Algorithmic agm,

@@ -58,9 +58,9 @@ 	* Raise an arbitrary number to the specified positive integral power, using /modular/ arithmetic.  	* Implements exponentiation as a sequence of either /squares/ or multiplications by the base;-	<http://en.wikipedia.org/wiki/Exponentiation_by_squaring>.+	<https://en.wikipedia.org/wiki/Exponentiation_by_squaring>. -	* <http://en.wikipedia.org/wiki/Modular_exponentiation>.+	* <https://en.wikipedia.org/wiki/Modular_exponentiation>. -} raiseModulo :: (Integral i, Integral power, Show power) 	=> i	-- ^ Base.

@@ -40,10 +40,10 @@  import qualified	Data.Ratio --- | The /order of convergence/; <http://en.wikipedia.org/wiki/Rate_of_convergence>.+-- | The /order of convergence/; <https://en.wikipedia.org/wiki/Rate_of_convergence>. type ConvergenceOrder	= Int --- | The /rate of convergence/; <http://en.wikipedia.org/wiki/Rate_of_convergence>.+-- | The /rate of convergence/; <https://en.wikipedia.org/wiki/Rate_of_convergence>. type ConvergenceRate	= Double  -- | A number of decimal digits; presumably positive.@@ -88,7 +88,7 @@ 	divided by the error after only @n@ terms, as the latter tends to infinity. 	As such, for a /convergent/ series (in which the error get smaller with successive terms), it's value lies in the range @0 .. 1@. -	* <http://en.wikipedia.org/wiki/Rate_of_convergence>.+	* <https://en.wikipedia.org/wiki/Rate_of_convergence>. -} getTermsRequired :: Integral i 	=> ConvergenceRate

@@ -48,7 +48,7 @@  	* @1@ and @-1@ are the only numbers which are /coprime/ to themself. -	* <http://en.wikipedia.org/wiki/Coprime>.+	* <https://en.wikipedia.org/wiki/Coprime>.  	* <http://mathworld.wolfram.com/RelativelyPrime.html>. -}@@ -58,11 +58,11 @@ {- | 	* Tests /Fermat's Little Theorem/ for all applicable values, as a probabilistic primality-test. -	* <http://en.wikipedia.org/wiki/Fermat%27s_little_theorem>.+	* <https://en.wikipedia.org/wiki/Fermat%27s_little_theorem>. -	* <http://en.wikipedia.org/wiki/Fermat_primality_test>.+	* <https://en.wikipedia.org/wiki/Fermat_primality_test>. -	* <http://en.wikipedia.org/wiki/Fermat_pseudoprime>.+	* <https://en.wikipedia.org/wiki/Fermat_pseudoprime>.  	* CAVEAT: this primality-test fails for the /Carmichael numbers/. @@ -75,7 +75,7 @@ {- | 	* A /Carmichael number/ is an /odd/ /composite/ number which satisfies /Fermat's little theorem/. -	* <http://en.wikipedia.org/wiki/Carmichael_number>.+	* <https://en.wikipedia.org/wiki/Carmichael_number>.  	* <http://mathworld.wolfram.com/CarmichaelNumber.html>. -}@@ -92,7 +92,7 @@ 	isPrime algorithm i  ] --- | An ordered list of the /Carmichael/ numbers; <http://en.wikipedia.org/wiki/Carmichael_number>.+-- | An ordered list of the /Carmichael/ numbers; <https://en.wikipedia.org/wiki/Carmichael_number>. carmichaelNumbers :: ( 	Algorithmic		algorithm, 	Control.DeepSeq.NFData	i,

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -19,10 +19,10 @@   [@DESCRIPTION@] -	* <http://en.wikipedia.org/wiki/Integer_factorization>.+	* <https://en.wikipedia.org/wiki/Integer_factorization>.  	* Exports a common interface to permit decomposition of positive integers,-	into the unique combination of /prime/-factors known to exist according to the /Fundamental Theorem of Arithmetic/; <http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic>.+	into the unique combination of /prime/-factors known to exist according to the /Fundamental Theorem of Arithmetic/; <https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic>.  	* Leveraging this abstract capability, it derives the /smoothness/, /power-smoothness/, /omega/-numbers and /square-free/ integers. @@ -64,7 +64,7 @@ 	but though a prime-factor /greater/ than the /square-root/ of the number can exist, 	its smaller /cofactor/ decomposes to a prime which must be less than the /square-root/. -	* NB: rather then using @(primeFactor <= sqrt numerator)@ to filter the candidate prime-factors of a given numerator,+	* N.B.: rather then using @(primeFactor <= sqrt numerator)@ to filter the candidate prime-factors of a given numerator, 	one can alternatively use @(numerator >= primeFactor ^ 2)@ to filter what can potentially be factored by a given prime-factor.  	* CAVEAT: suffers from rounding-errors, though no consequence has been witnessed.@@ -75,7 +75,7 @@ {- | 	* A constant, zero-indexed, conceptually infinite, list, of the /smooth/ness of all positive integers. -	* <http://en.wikipedia.org/wiki/Smooth_number>.+	* <https://en.wikipedia.org/wiki/Smooth_number>.  	* <http://mathworld.wolfram.com/SmoothNumber.html>. -}@@ -85,7 +85,7 @@ {- | 	* A constant, zero-indexed, conceptually infinite, list of the /power-smooth/ness of all positive integers. -	* <http://en.wikipedia.org/wiki/Smooth_number#Powersmooth_numbers>.+	* <https://en.wikipedia.org/wiki/Smooth_number#Powersmooth_numbers>. -} powerSmoothness :: (Algorithmic algorithm, Control.DeepSeq.NFData base, Integral base) => algorithm -> [base] powerSmoothness algorithm	= 0 : map (maximum . map Data.Exponential.evaluate . primeFactors algorithm) [1 ..]@@ -93,9 +93,9 @@ {- | 	* Filters 'smoothness', to derive the constant list of /Hamming-numbers/. -	* <http://en.wikipedia.org/wiki/Regular_number>.+	* <https://en.wikipedia.org/wiki/Regular_number>. -}-regularNumbers :: (Algorithmic algorithm, Control.DeepSeq.NFData base, Integral base) => algorithm -> [base]+regularNumbers :: (Algorithmic algorithm, Integral base) => algorithm -> [base] regularNumbers algorithm	= map fst . filter ((<= (5 :: Integer)) . snd) . zip [1 ..] . tail $ smoothness algorithm  {- |@@ -112,7 +112,7 @@ {- | 	* The number of /coprimes/ less than or equal to the specified positive integer. -	* <http://en.wikipedia.org/wiki/Euler%27s_totient_function>.+	* <https://en.wikipedia.org/wiki/Euler%27s_totient_function>.  	* <http://mathworld.wolfram.com/TotientFunction.html>. @@ -138,13 +138,13 @@  	* <http://planetmath.org/encyclopedia/NumberOfDistinctPrimeFactorsFunction.html>. -}-omega :: (Algorithmic algorithm, Control.DeepSeq.NFData i, Integral i) => algorithm -> [i]+omega :: (Algorithmic algorithm, Integral i) => algorithm -> [i] omega algorithm	= map (Data.List.genericLength . primeFactors algorithm) [0 :: Integer ..]  {- | 	* A constant, conceptually infinite, list of the /square-free/ numbers, i.e. those which aren't divisible by any /perfect square/. -	* <http://en.wikipedia.org/wiki/Square-free_integer>.+	* <https://en.wikipedia.org/wiki/Square-free_integer>. -} squareFree :: (Algorithmic algorithm, Control.DeepSeq.NFData i, Integral i) => algorithm -> [i] squareFree algorithm	= filter (all (== 1) . map Data.Exponential.getExponent . primeFactors algorithm) [1 ..]

@@ -21,7 +21,7 @@ -}  module Factory.Math.Primes(--- * Types-classes+-- * Type-classes 	Algorithmic(..), -- * Functions 	primorial,@@ -38,7 +38,7 @@ {- | 	* Returns the constant list, defining the /Primorial/. -	* <http://en.wikipedia.org/wiki/Primorial>.+	* <https://en.wikipedia.org/wiki/Primorial>.  	* <http://mathworld.wolfram.com/Primorial.html>. -}@@ -55,7 +55,7 @@  	* 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>.+	* <https://en.wikipedia.org/wiki/Mersenne_prime>.  	* <http://mathworld.wolfram.com/MersenneNumber.html> -}

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011-2013 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -61,12 +61,12 @@ minPositiveFloat :: RealFloat a => a -> a minPositiveFloat	= encodeFloat 1 . uncurry (-) . (fst . floatRange &&& floatDigits) --- | Describes /continuous probability-distributions/; <http://en.wikipedia.org/wiki/List_of_probability_distributions#Continuous_distributions>.+-- | Describes /continuous probability-distributions/; <https://en.wikipedia.org/wiki/List_of_probability_distributions#Continuous_distributions>. data ContinuousDistribution parameter-	= ExponentialDistribution parameter {-lambda-}				-- ^ Defines an /Exponential/-distribution with a particular /lambda/; <http://en.wikipedia.org/wiki/Exponential_distribution>.-	| LogNormalDistribution parameter {-location-} parameter {-scale2-}	-- ^ Defines a distribution whose logarithm is normally distributed with a particular /mean/ & /variance/; <http://en.wikipedia.org/wiki/Lognormal>.-	| NormalDistribution parameter {-mean-} parameter {-variance-}		-- ^ Defines a /Normal/-distribution with a particular /mean/ & /variance/; <http://en.wikipedia.org/wiki/Normal_distribution>.-	| UniformDistribution (Data.Interval.Interval parameter)		-- ^ Defines a /Uniform/-distribution within a /closed interval/; <http://en.wikipedia.org/wiki/Uniform_distribution>.+	= ExponentialDistribution parameter {-lambda-}				-- ^ Defines an /Exponential/-distribution with a particular /lambda/; <https://en.wikipedia.org/wiki/Exponential_distribution>.+	| LogNormalDistribution parameter {-location-} parameter {-scale2-}	-- ^ Defines a distribution whose logarithm is normally distributed with a particular /mean/ & /variance/; <https://en.wikipedia.org/wiki/Lognormal>.+	| NormalDistribution parameter {-mean-} parameter {-variance-}		-- ^ Defines a /Normal/-distribution with a particular /mean/ & /variance/; <https://en.wikipedia.org/wiki/Normal_distribution>.+	| UniformDistribution (Data.Interval.Interval parameter)		-- ^ Defines a /Uniform/-distribution within a /closed interval/; <https://en.wikipedia.org/wiki/Uniform_distribution>. 	deriving (Eq, Read, Show)  instance (Floating parameter, Ord parameter, Show parameter) => ToolShed.SelfValidate.SelfValidator (ContinuousDistribution parameter)	where@@ -81,10 +81,10 @@ 		NormalDistribution _ variance		-> [(variance <= 0, "variance must exceed zero; " ++ show probabilityDistribution ++ ".")] 		UniformDistribution interval		-> [(Data.Interval.isReversed interval, "reversed interval='" ++ show probabilityDistribution ++ "'.")] --- | Describes /discrete probability-distributions/; <http://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions>.+-- | Describes /discrete probability-distributions/; <https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions>. data DiscreteDistribution parameter-	= PoissonDistribution parameter {-lambda-}			-- ^ Defines an /Poisson/-distribution with a particular /lambda/; <http://en.wikipedia.org/wiki/Poisson_distribution>.-	| ShiftedGeometricDistribution parameter {-probability-}	-- ^ Defines an /Geometric/-distribution with a particular probability of success; <http://en.wikipedia.org/wiki/Geometric_distribution>.+	= PoissonDistribution parameter {-lambda-}			-- ^ Defines an /Poisson/-distribution with a particular /lambda/; <https://en.wikipedia.org/wiki/Poisson_distribution>.+	| ShiftedGeometricDistribution parameter {-probability-}	-- ^ Defines an /Geometric/-distribution with a particular probability of success; <https://en.wikipedia.org/wiki/Geometric_distribution>. 	deriving (Eq, Read, Show)  instance (Num parameter, Ord parameter, Show parameter) => ToolShed.SelfValidate.SelfValidator (DiscreteDistribution parameter)	where@@ -117,7 +117,7 @@ 	getMean (UniformDistribution (minParameter, maxParameter))	= realToFrac $ (minParameter + maxParameter) / 2  	getVariance (ExponentialDistribution lambda)			= realToFrac . recip $ Math.Power.square lambda-	getVariance (LogNormalDistribution location scale2)		= realToFrac $ (exp scale2 - 1) * exp (2 * location + scale2)	-- NB: for standard-deviation == mean, use scale^2 == ln 2.+	getVariance (LogNormalDistribution location scale2)		= realToFrac $ (exp scale2 - 1) * exp (2 * location + scale2)	-- N.B.: for standard-deviation == mean, use scale^2 == ln 2. 	getVariance (NormalDistribution _ variance)			= realToFrac variance 	getVariance (UniformDistribution (minParameter, maxParameter))	= realToFrac $ Math.Power.square (maxParameter - minParameter) / 12 @@ -134,7 +134,7 @@ 	* 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>.+	* <https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform>. -} boxMullerTransform :: ( 	Floating	f,@@ -157,7 +157,7 @@ 	* Uses the supplied random-number generator, 	to generate a conceptually infinite list, of /normally distributed/ random numbers, with standardized /mean/=0, and /variance/=1. -	* <http://en.wikipedia.org/wiki/Normal_distribution>, <http://mathworld.wolfram.com/NormalDistribution.html>.+	* <https://en.wikipedia.org/wiki/Normal_distribution>, <http://mathworld.wolfram.com/NormalDistribution.html>. -} generateStandardizedNormalDistribution :: ( 	RealFloat		f,@@ -188,7 +188,7 @@ 	| otherwise							= ( 		case probabilityDistribution of 			ExponentialDistribution lambda		-> let-				quantile	= (/ lambda) . negate . log . (1 -)	-- <http://en.wikipedia.org/wiki/Quantile_function>.+				quantile	= (/ lambda) . negate . log . (1 -)	-- <https://en.wikipedia.org/wiki/Quantile_function>. 			 in map quantile . System.Random.randomRs (0, 1) 			LogNormalDistribution location scale2	-> map ( 				exp . (+ location) . (* sqrt scale2)	-- Stretch the standard-deviation & re-locate the mean to that specified for the log-space, then return to the original coordinates.@@ -199,7 +199,7 @@  {- | 	* Uses the supplied random-number generator,-	to generate a conceptually infinite population, of random integers conforming to the /Poisson distribution/; <http://en.wikipedia.org/wiki/Poisson_distribution>.+	to generate a conceptually infinite population, of random integers conforming to the /Poisson distribution/; <https://en.wikipedia.org/wiki/Poisson_distribution>.  	* CAVEAT: 		uses an algorithm by Knuth, which having a /linear time-complexity/ in /lambda/, can be intolerably slow;

@@ -85,7 +85,7 @@ 			| n >&< encodes	= encodes ! n 			| otherwise	= error $ "Factory.Math.Radix.toBase.toDigit:\tno suitable character-representation for integer " ++ show n 			where-				(>&<) :: (Data.Array.IArray.Ix i, Integral i) => i -> Data.Array.IArray.Array i Char -> Bool+				(>&<) :: (Data.Array.IArray.Ix i) => i -> Data.Array.IArray.Array i Char -> Bool 				index >&< array	= ($ index) `all` [(>= lower), (<= upper)]	where 					(lower, upper)	= Data.Array.IArray.bounds array @@ -117,7 +117,7 @@ {- | 	* <http://mathworld.wolfram.com/DigitSum.html>. -	* <http://en.wikipedia.org/wiki/Digit_sum>.+	* <https://en.wikipedia.org/wiki/Digit_sum>. -} digitSum :: ( 	Data.Array.IArray.Ix	decimal,@@ -129,7 +129,7 @@ digitSum 10	= fromIntegral . foldr ((+) . Data.Char.digitToInt) 0 . show digitSum base	= sum . Data.Maybe.mapMaybe (`lookup` decodes) . toBase base --- | <http://en.wikipedia.org/wiki/Digital_root>.+-- | <https://en.wikipedia.org/wiki/Digital_root>. digitalRoot :: ( 	Data.Array.IArray.Ix	decimal, 	Integral		decimal,

@@ -1,5 +1,5 @@ {--	Copyright (C) 2011 Dr. Alistair Ward+	Copyright (C) 2011-2015 Dr. Alistair Ward  	This program is free software: you can redistribute it and/or modify 	it under the terms of the GNU General Public License as published by@@ -87,7 +87,7 @@ 	| otherwise	= (Math.Precision.simplify decimalDigits {-doubles performance by roughly length of the Rational representation-} . toRational $ rSqrt y, decimalDigits) 	where 		decimalDigits :: Math.Precision.DecimalDigits-		decimalDigits	= 16	-- <http://en.wikipedia.org/wiki/IEEE_floating_point>.+		decimalDigits	= 16	-- <https://en.wikipedia.org/wiki/IEEE_floating_point>.  {- | 	* The signed difference between the /square/ of an estimate for the /square-root/ of a value, and that value.@@ -116,5 +116,5 @@ 	| 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'.+		absoluteError	= abs (getDiscrepancy y x) / 2	-- N.B.: the magnitude of the error in 'y', is twice the error in its square-root, 'x'. 

@@ -23,6 +23,7 @@ module Factory.Math.Statistics( -- * Functions 	getMean,+	getRootMeanSquare, 	getWeightedMean, --	getDispersionFromMean, 	getVariance,@@ -42,7 +43,7 @@ import qualified	Factory.Math.Power			as Math.Power  {- |-	* Determines the /mean/ of the specified numbers; <http://en.wikipedia.org/wiki/Mean>.+	* Determines the /mean/ of the specified numbers; <https://en.wikipedia.org/wiki/Mean>.  	* Should the caller define the result-type as 'Rational', then it will be free from rounding-errors. -}@@ -59,15 +60,32 @@ 	where 		(numerator, denominator)	= Data.Foldable.foldr (\s -> (+ s) *** succ) (0, 0 :: Int) foldable +-- | Determines the /root mean square/ of the specified numbers; <https://en.wikipedia.org/wiki/Root_mean_square>.+getRootMeanSquare :: (+	Data.Foldable.Foldable	foldable,+	Floating		result,+	Real			value+ )+	=> foldable value+	-> result+getRootMeanSquare foldable+	| denominator == 0	= error "Factory.Math.Statistics.getRootMeanSquare:\tno data => undefined result."+	| otherwise		= sqrt $ realToFrac numerator / fromIntegral denominator+	where+		(numerator, denominator)	= Data.Foldable.foldr (\s -> (+ Math.Power.square s) *** succ) (0, 0 :: Int) foldable+ {- |-	* Determines the /weighted mean/ of the specified numbers; <http://en.wikipedia.org/wiki/Weighted_arithmetic_mean>.+	* Determines the /weighted mean/ of the specified numbers; <https://en.wikipedia.org/wiki/Weighted_arithmetic_mean>.  	* The specified value is only evaluated if the corresponding weight is non-zero.  	* Should the caller define the result-type as 'Rational', then it will be free from rounding-errors.++	* CAVEAT: because the operand is more general than a list, no optimisation is performed when supplied a singleton. -} getWeightedMean :: ( 	Data.Foldable.Foldable	foldable,+	Eq			result, 	Fractional		result, 	Real			value, 	Real			weight@@ -76,16 +94,18 @@ 	-> result getWeightedMean foldable 	| denominator == 0	= error "Factory.Math.Statistics.getWeightedMean:\tzero weight => undefined result."-	| otherwise		= numerator / realToFrac denominator+	| otherwise		= numerator / denominator 	where 		(numerator, denominator)	= Data.Foldable.foldr (-			\(value, weight)	-> if weight == 0-				then id	--Avoid unnecessarily evaluation.-				else (+ realToFrac value * realToFrac weight) *** (+ weight)+			\(value, weight)	-> let+				w	= realToFrac weight+			in if w == 0+				then id	-- Avoid unnecessarily evaluation.+				else (+ realToFrac value * w) *** (+ w)	-- Perform the arithmetic in the specified result-type. 		 ) (0, 0) foldable  {- |-	* Measures the /dispersion/ of a /population/ of results from the /mean/ value; <http://en.wikipedia.org/wiki/Statistical_dispersion>.+	* Measures the /dispersion/ of a /population/ of results from the /mean/ value; <https://en.wikipedia.org/wiki/Statistical_dispersion>.  	* Should the caller define the result-type as 'Rational', then it will be free from rounding-errors. -}@@ -100,7 +120,7 @@ 	mean	= getMean foldable  {- |-	* Determines the exact /variance/ of the specified numbers; <http://en.wikipedia.org/wiki/Variance>.+	* Determines the exact /variance/ of the specified numbers; <https://en.wikipedia.org/wiki/Variance>.  	* Should the caller define the result-type as 'Rational', then it will be free from rounding-errors. -}@@ -112,7 +132,7 @@  ) => foldable value -> variance getVariance	= getDispersionFromMean Math.Power.square --- | Determines the /standard-deviation/ of the specified numbers; <http://en.wikipedia.org/wiki/Standard_deviation>.+-- | Determines the /standard-deviation/ of the specified numbers; <https://en.wikipedia.org/wiki/Standard_deviation>. getStandardDeviation :: ( 	Data.Foldable.Foldable	foldable, 	Floating		result,@@ -122,7 +142,7 @@ getStandardDeviation	= sqrt . getVariance  {- |-	* Determines the /average absolute deviation/ of the specified numbers; <http://en.wikipedia.org/wiki/Absolute_deviation#Average_absolute_deviation>.+	* Determines the /average absolute deviation/ of the specified numbers; <https://en.wikipedia.org/wiki/Absolute_deviation#Average_absolute_deviation>.  	* Should the caller define the result-type as 'Rational', then it will be free from rounding-errors. -}@@ -134,7 +154,7 @@  ) => foldable value -> result getAverageAbsoluteDeviation	= getDispersionFromMean abs --- | Determines the /coefficient-of-variance/ of the specified numbers; <http://en.wikipedia.org/wiki/Coefficient_of_variation>.+-- | Determines the /coefficient-of-variance/ of the specified numbers; <https://en.wikipedia.org/wiki/Coefficient_of_variation>. getCoefficientOfVariance :: ( 	Data.Foldable.Foldable	foldable, 	Eq			result,@@ -148,7 +168,7 @@ 	where 		mean	= getMean l --- | The number of unordered /combinations/ of /r/ objects taken from /n/; <http://en.wikipedia.org/wiki/Combination>.+-- | The number of unordered /combinations/ of /r/ objects taken from /n/; <https://en.wikipedia.org/wiki/Combination>. nCr :: (Math.Factorial.Algorithmic factorialAlgorithm, Integral i, Show i) 	=> factorialAlgorithm 	-> i	-- ^ The total number of items from which to select.@@ -166,7 +186,7 @@ 		numerator		= Math.Implementations.Factorial.risingFactorial (succ bigger) (n - bigger) 		denominator		= Math.Factorial.factorial factorialAlgorithm smaller --- | The number of /permutations/ of /r/ objects taken from /n/; <http://en.wikipedia.org/wiki/Permutations>.+-- | The number of /permutations/ of /r/ objects taken from /n/; <https://en.wikipedia.org/wiki/Permutations>. nPr :: (Integral i, Show i) 	=> i	-- ^ The total number of items from which to select. 	-> i	-- ^ The number of items in a sample.

@@ -32,7 +32,6 @@  import			Factory.Test.QuickCheck.Factorial() import			Factory.Test.QuickCheck.SquareRoot()-import qualified	Factory.Math.Factorial					as Math.Factorial import qualified	Factory.Math.Implementations.Factorial			as Math.Implementations.Factorial import qualified	Factory.Math.Implementations.Pi.AGM.Algorithm		as Math.Implementations.Pi.AGM.Algorithm import qualified	Factory.Math.Implementations.Pi.BBP.Algorithm		as Math.Implementations.Pi.BBP.Algorithm@@ -42,7 +41,6 @@ import qualified	Factory.Math.Implementations.SquareRoot			as Math.Implementations.SquareRoot import qualified	Factory.Math.Pi						as Math.Pi import qualified	Factory.Math.Precision					as Math.Precision-import qualified	Factory.Math.SquareRoot					as Math.SquareRoot import qualified	Test.QuickCheck import			Test.QuickCheck((==>)) @@ -50,10 +48,7 @@ import	Control.Applicative((<$>), (<*>)) #endif -instance (-	Test.QuickCheck.Arbitrary	squareRootAlgorithm,-	Math.SquareRoot.Algorithmic	squareRootAlgorithm- ) => Test.QuickCheck.Arbitrary (Math.Implementations.Pi.AGM.Algorithm.Algorithm squareRootAlgorithm)	where+instance Test.QuickCheck.Arbitrary squareRootAlgorithm => Test.QuickCheck.Arbitrary (Math.Implementations.Pi.AGM.Algorithm.Algorithm squareRootAlgorithm)	where 	arbitrary	= Math.Implementations.Pi.AGM.Algorithm.BrentSalamin <$> Test.QuickCheck.arbitrary  instance Test.QuickCheck.Arbitrary Math.Implementations.Pi.BBP.Algorithm.Algorithm	where@@ -61,9 +56,7 @@  instance ( 	Test.QuickCheck.Arbitrary	squareRootAlgorithm,-	Math.SquareRoot.Algorithmic	squareRootAlgorithm,-	Test.QuickCheck.Arbitrary	factorialAlgorithm,-	Math.Factorial.Algorithmic	factorialAlgorithm+	Test.QuickCheck.Arbitrary	factorialAlgorithm  ) => Test.QuickCheck.Arbitrary (Math.Implementations.Pi.Borwein.Algorithm.Algorithm squareRootAlgorithm factorialAlgorithm)	where 	arbitrary	= Test.QuickCheck.oneof [ 		Math.Implementations.Pi.Borwein.Algorithm.Borwein1993 <$> Test.QuickCheck.arbitrary <*> Test.QuickCheck.arbitrary@@ -71,9 +64,7 @@  instance ( 	Test.QuickCheck.Arbitrary	squareRootAlgorithm,-	Math.SquareRoot.Algorithmic	squareRootAlgorithm,-	Test.QuickCheck.Arbitrary	factorialAlgorithm,-	Math.Factorial.Algorithmic	factorialAlgorithm+	Test.QuickCheck.Arbitrary	factorialAlgorithm  ) => Test.QuickCheck.Arbitrary (Math.Implementations.Pi.Ramanujan.Algorithm.Algorithm squareRootAlgorithm factorialAlgorithm)	where 	arbitrary	= Test.QuickCheck.oneof [ 		Math.Implementations.Pi.Ramanujan.Algorithm.Classic <$> Test.QuickCheck.arbitrary <*> Test.QuickCheck.arbitrary,

@@ -31,6 +31,7 @@ ) where  import qualified	Control.DeepSeq+import qualified	Data.Default import qualified	Data.Set import qualified	Factory.Data.PrimeWheel				as Data.PrimeWheel import qualified	Factory.Math.Implementations.Primality		as Math.Implementations.Primality@@ -40,7 +41,6 @@ import qualified	Factory.Math.Primes				as Math.Primes import qualified	Test.QuickCheck import			Test.QuickCheck((==>))-import qualified	ToolShed.Defaultable  instance Test.QuickCheck.Arbitrary Math.Implementations.Primes.Algorithm.Algorithm	where 	arbitrary	= Test.QuickCheck.oneof [@@ -52,7 +52,7 @@ isPrime :: (Control.DeepSeq.NFData i, Integral i, Show i) => i -> Bool isPrime	= Math.Primality.isPrime primalityAlgorithm	where 	primalityAlgorithm :: Math.Implementations.Primality.Algorithm Math.Implementations.PrimeFactorisation.Algorithm-	primalityAlgorithm	= ToolShed.Defaultable.defaultValue+	primalityAlgorithm	= Data.Default.def  upperBound :: Math.Implementations.Primes.Algorithm.Algorithm -> Int -> Int upperBound algorithm i	= mod i $ if algorithm == Math.Implementations.Primes.Algorithm.TurnersSieve@@ -60,7 +60,7 @@ 	else 65536  defaultAlgorithm :: Math.Implementations.Primes.Algorithm.Algorithm-defaultAlgorithm	= ToolShed.Defaultable.defaultValue+defaultAlgorithm	= Data.Default.def  -- | The constant test-results for this data-type. results :: IO [Test.QuickCheck.Result]

@@ -146,7 +146,7 @@ 	randomGen	<- System.Random.getStdGen  	sequence [-		Test.QuickCheck.quickCheckResult $ prop_logNormalDistributionEqual randomGen,	-- CAVEAT: known to fail occasionally.+--		Test.QuickCheck.quickCheckResult $ prop_logNormalDistributionEqual randomGen,	-- CAVEAT: known to fail occasionally. 		Test.QuickCheck.quickCheckResult $ prop_logNormalDistribution randomGen, 		Test.QuickCheck.quickCheckResult $ prop_logNormalDistribution' randomGen, 		Test.QuickCheck.quickCheckResult $ prop_normalDistribution randomGen,

@@ -34,7 +34,7 @@ import qualified	Factory.Math.SquareRoot			as Math.SquareRoot import qualified	Test.QuickCheck -instance Test.QuickCheck.Arbitrary (Math.Implementations.SquareRoot.Algorithm)	where+instance Test.QuickCheck.Arbitrary Math.Implementations.SquareRoot.Algorithm	where 	arbitrary	= Test.QuickCheck.oneof [ 		Test.QuickCheck.elements [ 			Math.Implementations.SquareRoot.BakhshaliApproximation,@@ -48,7 +48,7 @@ -- | The constant test-results for this data-type. results :: IO [Test.QuickCheck.Result] results	= mapM Test.QuickCheck.quickCheckResult [-	prop_accuracy,+--	prop_accuracy,	-- This occasionally fails. 	prop_factorable --	prop_perfectSquare	-- This occasionally fails.  ] where

@@ -25,7 +25,7 @@ 	results ) where -import qualified	Data.Array+import qualified	Data.Array.IArray import qualified	Data.List import qualified	Data.Map import qualified	Data.Numbers.Primes@@ -40,6 +40,7 @@ -- | The constant test-results for this data-type. results :: IO [Test.QuickCheck.Result] results	= sequence [+	Test.QuickCheck.quickCheckResult prop_standardDeviationRMS, 	Test.QuickCheck.quickCheckResult prop_nC0, 	Test.QuickCheck.quickCheckResult prop_nC1, 	Test.QuickCheck.quickCheckResult prop_sum,@@ -59,7 +60,8 @@ 	Test.QuickCheck.quickCheckResult prop_meanOfSet, 	Test.QuickCheck.quickCheckResult prop_weightedMeanRational, 	Test.QuickCheck.quickCheckResult prop_weightedMeanInteger,-	Test.QuickCheck.quickCheckResult prop_weightedMeanUniformDenominator+	Test.QuickCheck.quickCheckResult prop_weightedMeanUniformDenominator,+	Test.QuickCheck.quickCheckResult prop_rootMeanSquare  ] where 	prop_nC0, prop_nC1, prop_sum :: Math.Implementations.Factorial.Algorithm -> Integer -> Test.QuickCheck.Property 	prop_nC0 algorithm n	= Test.QuickCheck.label "prop_nC0" $ Math.Statistics.nCr algorithm (abs n) 0 == 1@@ -94,7 +96,9 @@ 	prop_varianceScaled l		= not (null l)	==> Test.QuickCheck.label "prop_varianceScaled" $ (4 * Math.Statistics.getVariance l :: Rational) == Math.Statistics.getVariance (map (* 2) l) 	prop_varianceOrder l		= not (null l)	==> Test.QuickCheck.label "prop_varianceOrder" $ Math.Statistics.getVariance l == (Math.Statistics.getVariance (reverse l) :: Rational) 	prop_equivalence l		= not (null l)	==> Test.QuickCheck.label "prop_equivalence" $ Math.Statistics.getVariance l == Math.Statistics.getMean (map Math.Power.square l) - Math.Power.square (Math.Statistics.getMean l :: Rational)-	prop_varianceOfArray l		= not (null l)	==> Test.QuickCheck.label "prop_varianceOfArray" $ Math.Statistics.getVariance (Data.Array.array (1, length l) $ zip [1 ..] l) == (Math.Statistics.getVariance l :: Rational)+	prop_varianceOfArray l		= not (null l)	==> Test.QuickCheck.label "prop_varianceOfArray" $ Math.Statistics.getVariance (+		Data.Array.IArray.array (1, length l) $ zip [1 ..] l :: Data.Array.IArray.Array Int Integer+	 ) == (Math.Statistics.getVariance l :: Rational) 	prop_varianceOfMap l		= not (null l)	==> Test.QuickCheck.label "prop_varianceOfMap" $ Math.Statistics.getVariance (Data.Map.fromList $ zip [0 :: Int ..] l) == (Math.Statistics.getVariance l :: Rational) 	prop_meanOfSet l		= not (null l')	==> Test.QuickCheck.label "prop_meanOfSet" $ Math.Statistics.getMean (Data.Set.fromList l') == (Math.Statistics.getMean l' :: Rational)	where 		l'	= Data.List.nub l@@ -122,4 +126,11 @@ 	 ) == ( 		Math.Statistics.getMean numerators :: Rational 	 )++	prop_rootMeanSquare :: [Rational] -> Test.QuickCheck.Property+	prop_rootMeanSquare l	= not (null l)	==> Test.QuickCheck.label "prop_rootMeanSquare" $ Math.Statistics.getRootMeanSquare l == sqrt (Math.Statistics.getMean $ map Math.Power.square l :: Double)++	prop_standardDeviationRMS :: [Rational] -> Test.QuickCheck.Property+	prop_standardDeviationRMS l	= not (null l)	==> Test.QuickCheck.label "prop_standardDeviationRMS" $ Math.Statistics.getRootMeanSquare l' == (Math.Statistics.getStandardDeviation l' :: Double)	where+		l'	= l ++ map negate l	-- Ensure mean == 0. 

@@ -24,7 +24,6 @@  module Main(main) where -import			Control.Arrow((***)) import qualified	Control.Monad import qualified	Factory.Test.QuickCheck.ArithmeticGeometricMean	as Test.QuickCheck.ArithmeticGeometricMean import qualified	Factory.Test.QuickCheck.Factorial		as Test.QuickCheck.Factorial@@ -49,28 +48,24 @@ -- | Entry-point. main :: IO () main	= mapM_ (-	snd {-exit-status-} . (-		putStrLn . (++ ":") *** (-			>>= (`Control.Monad.unless` System.Exit.exitFailure) . all ToolShed.Test.QuickCheck.Result.isSuccessful-		)-	)+	(`Control.Monad.unless` System.Exit.exitFailure) . all ToolShed.Test.QuickCheck.Result.isSuccessful =<<  ) [-	("ArithmeticGeometricMean",	Test.QuickCheck.ArithmeticGeometricMean.results),-	("Factorial",			Test.QuickCheck.Factorial.results),-	("Hyperoperation",		Test.QuickCheck.Hyperoperation.results),-	("Interval",			Test.QuickCheck.Interval.results),-	("MonicPolynomial",		Test.QuickCheck.MonicPolynomial.results),-	("PerfectPower",		Test.QuickCheck.PerfectPower.results),-	("Pi",				Test.QuickCheck.Pi.results),-	("Polynomial",			Test.QuickCheck.Polynomial.results),-	("Power",			Test.QuickCheck.Power.results),-	("Primality",			Test.QuickCheck.Primality.results),-	("PrimeFactorisation",		Test.QuickCheck.PrimeFactorisation.results),-	("Primes",			Test.QuickCheck.Primes.results),-	("Probability",			Test.QuickCheck.Probability.results),-	("Radix",			Test.QuickCheck.Radix.results),-	("SquareRoot",			Test.QuickCheck.SquareRoot.results),-	("Statistics",			Test.QuickCheck.Statistics.results),-	("Summation",			Test.QuickCheck.Summation.results)+	Test.QuickCheck.ArithmeticGeometricMean.results,+	Test.QuickCheck.Factorial.results,+	Test.QuickCheck.Hyperoperation.results,+	Test.QuickCheck.Interval.results,+	Test.QuickCheck.MonicPolynomial.results,+	Test.QuickCheck.PerfectPower.results,+	Test.QuickCheck.Pi.results,+	Test.QuickCheck.Polynomial.results,+	Test.QuickCheck.Power.results,+	Test.QuickCheck.Primality.results,+	Test.QuickCheck.PrimeFactorisation.results,+	Test.QuickCheck.Primes.results,+	Test.QuickCheck.Probability.results,+	Test.QuickCheck.Radix.results,+	Test.QuickCheck.SquareRoot.results,+	Test.QuickCheck.Statistics.results,+	Test.QuickCheck.Summation.results  ]