diff --git a/README.markdown b/README.markdown --- a/README.markdown +++ b/README.markdown @@ -1,6 +1,9 @@ # **Factory** -[![Hackage](https://img.shields.io/hackage/v/factory.svg)](https://hackage.haskell.org/package/factory) [![Build Status](https://travis-ci.org/functionalley/Factory.svg?branch=master)](https://travis-ci.org/functionalley/Factory) +[![Build Status](https://travis-ci.org/functionalley/Factory.svg?branch=master)](https://travis-ci.org/functionalley/Factory) +[![Hackage](https://img.shields.io/hackage/v/factory.svg)](https://hackage.haskell.org/package/factory) +[![License: GPL v3](https://img.shields.io/badge/License-GPL%20v3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0) +[![Haskell](https://b.repl.ca/v1/language-haskell-yellow.png)](https://haskell.org) This is "**Factory**", a library of number-theory functions. @@ -10,7 +13,7 @@ ## Documentation -More information about this library can be found at [Factory](http://functionalley.eu/Factory/factory.html). +More information about this library can be found at [Factory](https://functionalley.eu/Factory/factory.html). ## License diff --git a/changelog.markdown b/changelog.markdown --- a/changelog.markdown +++ b/changelog.markdown @@ -14,7 +14,7 @@ * 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). +* Uploaded to [Hackage](https://hackage.haskell.org/package/factory). ## 0.1.0.0 * Amended the *.cabal*-file to more correctly specify the dependency on package "**toolshed**". @@ -43,7 +43,7 @@ * 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). +* Uploaded to [Hackage](https://hackage.haskell.org/packages/hackage.html). ## 0.1.0.3 * Qualified `Factory.Math.Implementations.Primes.trialDivision` with pragma "**NOINLINE**", to block optimization which conflicts with rewrite-rule for `Factory.Math.Implementations.Primes.sieveOfEratosthenes` ! @@ -163,4 +163,8 @@ * Added specialisation-pragmas to **Factory.Math.Statistics**. ## 0.3.1.4 + +## 0.3.2.0 +* Added **Paths_factory** to **Other-modules** section of cabal file. +* Accounted for **Semigroup** becoming a superclass of **Monoid** in **ghc-8.4**. diff --git a/copyright b/copyright --- a/copyright +++ b/copyright @@ -5,7 +5,7 @@ Copyright (C) 2011-2013 Dr. Alistair Ward. All Rights Reserved. Home-page: - http://functionalley.eu/Factory/factory.html + https://functionalley.eu/Factory/factory.html License: GNU GENERAL PUBLIC LICENSE Version 3; see '/usr/share/common-licenses/GPL-3' or '/usr/share/doc/licenses/gpl-3.0.txt' where available, or the local packaged file 'LICENSE'. diff --git a/factory.cabal b/factory.cabal --- a/factory.cabal +++ b/factory.cabal @@ -14,7 +14,7 @@ -- along with Factory. If not, see . Name: factory -Version: 0.3.1.4 +Version: 0.3.2.0 Cabal-version: >= 1.10 Copyright: (C) 2011-2015 Dr. Alistair Ward License: GPL @@ -25,8 +25,8 @@ 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, GHC == 8.0, GHC == 8.2 -Homepage: http://functionalley.eu/Factory/factory.html +Tested-with: GHC == 7.4, GHC == 7.6, GHC == 7.8, GHC == 7.10, GHC == 8.0, GHC == 8.2, GHC == 8.4 +Homepage: https://functionalley.eu/Factory/factory.html Maintainer: mailto:factory@functionalley.eu Bug-reports: mailto:factory@functionalley.eu @@ -161,6 +161,7 @@ Factory.Test.Performance.Primes Factory.Test.Performance.SquareRoot Factory.Test.Performance.Statistics + Paths_factory Build-depends: array, diff --git a/src-lib/Factory/Data/Polynomial.hs b/src-lib/Factory/Data/Polynomial.hs --- a/src-lib/Factory/Data/Polynomial.hs +++ b/src-lib/Factory/Data/Polynomial.hs @@ -13,7 +13,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -24,7 +24,7 @@ * . - * . + * . -} module Factory.Data.Polynomial( @@ -167,7 +167,7 @@ {- Uses /Euclidian division/. . - . + . -} _ `quotRem'` MkPolynomial [] = error "Factory.Data.Polynomial.quotRem':\tzero denominator." polynomialN `quotRem'` polynomialD = longDivide polynomialN where @@ -285,7 +285,7 @@ {- | * 'True' if the two specified /polynomials/ are /congruent/ in /modulo/-arithmetic. - * . + * . -} areCongruentModulo :: (Integral c, Num e, Ord e) => Polynomial c e -- ^ LHS. @@ -303,7 +303,7 @@ * . - * . + * . -} getDegree :: Num e => Polynomial c e -> e getDegree (MkPolynomial []) = -1 -- CAVEAT: debatable, but makes some operations more robust and consistent. diff --git a/src-lib/Factory/Data/Ring.hs b/src-lib/Factory/Data/Ring.hs --- a/src-lib/Factory/Data/Ring.hs +++ b/src-lib/Factory/Data/Ring.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE CPP #-} {- Copyright (C) 2011 Dr. Alistair Ward @@ -12,7 +13,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -23,7 +24,7 @@ * . - * . + * . -} module Factory.Data.Ring( @@ -57,7 +58,7 @@ (=+=) :: r -> r -> r -- ^ Addition of two members; required to be /commutative/; . (=*=) :: r -> r -> r -- ^ Multiplication of two members. additiveInverse :: r -> r -- ^ The operand required to yield /zero/ under addition; . - multiplicativeIdentity :: r -- ^ The /identity/-member under multiplication; . + multiplicativeIdentity :: r -- ^ The /identity/-member under multiplication; . additiveIdentity :: r -- ^ The /identity/-member under addition (AKA /zero/); . (=-=) :: r -> r -> r -- ^ Subtract the two specified /ring/-members. @@ -93,9 +94,17 @@ getProduct :: p -- ^ Access the polymorphic payload. } deriving (Read, Show) +-- Added for 'ghc-8.4', when 'Semigroup' became a superclass of 'Monoid'. +#if MIN_VERSION_base(4,11,0) +instance Ring r => Semigroup (Product r) where + MkProduct x <> MkProduct y = MkProduct $ x =*= y +#endif + instance Ring r => Data.Monoid.Monoid (Product r) where mempty = MkProduct multiplicativeIdentity +#if !MIN_VERSION_base(4,11,0) MkProduct x `mappend` MkProduct y = MkProduct $ x =*= y +#endif -- | Returns the /product/ of the list of /ring/-members. product' :: Ring r => Math.DivideAndConquer.BisectionRatio -> Math.DivideAndConquer.MinLength -> [r] -> r @@ -107,9 +116,17 @@ getSum :: s -- ^ Access the polymorphic payload. } deriving (Read, Show) +-- Added for 'ghc-8.4', when 'Semigroup' became a superclass of 'Monoid'. +#if MIN_VERSION_base(4,11,0) +instance Ring r => Semigroup (Sum r) where + MkSum x <> MkSum y = MkSum $ x =+= y +#endif + instance Ring r => Data.Monoid.Monoid (Sum r) where mempty = MkSum additiveIdentity +#if !MIN_VERSION_base(4,11,0) MkSum x `mappend` MkSum y = MkSum $ x =+= y +#endif -- | Returns the /sum/ of the list of /ring/-members. sum' :: Ring r => Math.DivideAndConquer.BisectionRatio -> Math.DivideAndConquer.MinLength -> [r] -> r diff --git a/src-lib/Factory/Math/Factorial.hs b/src-lib/Factory/Math/Factorial.hs --- a/src-lib/Factory/Math/Factorial.hs +++ b/src-lib/Factory/Math/Factorial.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -23,7 +23,7 @@ the simple algorithms appropriate for that forum, leave a large margin for performance-improvement. This module provides the interface for alternative algorithms. - * . + * . -} module Factory.Math.Factorial( diff --git a/src-lib/Factory/Math/Fibonacci.hs b/src-lib/Factory/Math/Fibonacci.hs --- a/src-lib/Factory/Math/Fibonacci.hs +++ b/src-lib/Factory/Math/Fibonacci.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -35,7 +35,7 @@ {- | * The subset of 'fibonacci', /indexed/ by a /prime/-number. - * . + * . -} primeIndexedFibonacci :: Integral i => [i] primeIndexedFibonacci = map (fibonacci !!) Data.Numbers.Primes.primes diff --git a/src-lib/Factory/Math/Hyperoperation.hs b/src-lib/Factory/Math/Hyperoperation.hs --- a/src-lib/Factory/Math/Hyperoperation.hs +++ b/src-lib/Factory/Math/Hyperoperation.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -61,11 +61,11 @@ (succession : addition : multiplication : exponentiation : tetration : pentation : hexation : _) = [0 ..] {- | - * Returns the /power-tower/ of the specified /base/; . + * Returns the /power-tower/ of the specified /base/; . * A synonym for /tetration/; , - . + . -} powerTower :: (Integral base, Integral hyperExponent, Show base) => base -> hyperExponent -> base powerTower 0 hyperExponent diff --git a/src-lib/Factory/Math/Implementations/Factorial.hs b/src-lib/Factory/Math/Implementations/Factorial.hs --- a/src-lib/Factory/Math/Implementations/Factorial.hs +++ b/src-lib/Factory/Math/Implementations/Factorial.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -26,9 +26,9 @@ * . - * . + * . - * . + * . -} module Factory.Math.Implementations.Factorial( @@ -89,7 +89,7 @@ * General purpose /prime-factorisation/ has /exponential time-complexity/, so use /Legendre's Theorem/, which relates only to the /prime factors/ of /factorials/. - * . + * . -} primeMultiplicity :: Integral i => i -- ^ A prime number. @@ -97,7 +97,7 @@ -> i -- ^ The number of times the prime occurs in the factorial. primeMultiplicity prime = sum . takeWhile (> 0) . tail . iterate (`div` prime) --- | Returns the /rising factorial/; +-- | Returns the /rising factorial/; risingFactorial :: (Integral i, Show i) => i -- ^ The lower bound of the integer-range, whose product is returned. -> i -- ^ The number of integers in the range above. @@ -106,7 +106,7 @@ risingFactorial 0 _ = 0 risingFactorial x n = Data.Interval.product' (recip 2) 64 $ Data.Interval.normalise (x, pred $ x + n) --- | Returns the /falling factorial/; +-- | Returns the /falling factorial/; fallingFactorial :: (Integral i, Show i) => i -- ^ The upper bound of the integer-range, whose product is returned. -> i -- ^ The number of integers in the range beneath. diff --git a/src-lib/Factory/Math/Implementations/Pi/AGM/BrentSalamin.hs b/src-lib/Factory/Math/Implementations/Pi/AGM/BrentSalamin.hs --- a/src-lib/Factory/Math/Implementations/Pi/AGM/BrentSalamin.hs +++ b/src-lib/Factory/Math/Implementations/Pi/AGM/BrentSalamin.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -21,8 +21,8 @@ * Implements the /Brent-Salamin/ (AKA /Gauss-Legendre/) algorithm; , - , - . + , + . * The precision of the result approximately doubles for each iteration. diff --git a/src-lib/Factory/Math/Implementations/Pi/BBP/Base65536.hs b/src-lib/Factory/Math/Implementations/Pi/BBP/Base65536.hs --- a/src-lib/Factory/Math/Implementations/Pi/BBP/Base65536.hs +++ b/src-lib/Factory/Math/Implementations/Pi/BBP/Base65536.hs @@ -12,12 +12,12 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward - [@DESCRIPTION@] Defines a specific base-@2^16@ /BBP/-formula; + [@DESCRIPTION@] Defines a specific base-@2^16@ /BBP/-formula; -} diff --git a/src-lib/Factory/Math/Implementations/Pi/BBP/Implementation.hs b/src-lib/Factory/Math/Implementations/Pi/BBP/Implementation.hs --- a/src-lib/Factory/Math/Implementations/Pi/BBP/Implementation.hs +++ b/src-lib/Factory/Math/Implementations/Pi/BBP/Implementation.hs @@ -12,14 +12,14 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward [@DESCRIPTION@] - * Implements a /Bailey-Borwein-Plouffe/ formula; + * Implements a /Bailey-Borwein-Plouffe/ formula; * Surprisingly, because of the huge size of the 'Rational' quantities, it is a /single/ call to @Factory.Math.Summation.sum'@, rather than the calculation of the many terms in the series, which is the performance-bottleneck. diff --git a/src-lib/Factory/Math/Implementations/Pi/BBP/Series.hs b/src-lib/Factory/Math/Implementations/Pi/BBP/Series.hs --- a/src-lib/Factory/Math/Implementations/Pi/BBP/Series.hs +++ b/src-lib/Factory/Math/Implementations/Pi/BBP/Series.hs @@ -12,12 +12,12 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward - [@DESCRIPTION@] Defines a /Bailey-Borwein-Plouffe/ formula; + [@DESCRIPTION@] Defines a /Bailey-Borwein-Plouffe/ formula; -} module Factory.Math.Implementations.Pi.BBP.Series( diff --git a/src-lib/Factory/Math/Implementations/Pi/Ramanujan/Classic.hs b/src-lib/Factory/Math/Implementations/Pi/Ramanujan/Classic.hs --- a/src-lib/Factory/Math/Implementations/Pi/Ramanujan/Classic.hs +++ b/src-lib/Factory/Math/Implementations/Pi/Ramanujan/Classic.hs @@ -12,12 +12,12 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward - [@DESCRIPTION@] Defines the /Ramanujan/ series for /Pi/; . + [@DESCRIPTION@] Defines the /Ramanujan/ series for /Pi/; . -} module Factory.Math.Implementations.Pi.Ramanujan.Classic( diff --git a/src-lib/Factory/Math/Implementations/Primality.hs b/src-lib/Factory/Math/Implementations/Primality.hs --- a/src-lib/Factory/Math/Implementations/Primality.hs +++ b/src-lib/Factory/Math/Implementations/Primality.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -23,7 +23,7 @@ * . - * + * * CAVEAT: it doesn't determine the prime-factors of composite numbers, just that they exist. -} @@ -92,17 +92,17 @@ This mind-shift, allows one to introduce concepts like /modular/ arithmetic on polynomials, which merely represent an operation on their coefficients and the pigeon-hole in which they're placed. - [@Manindra Agrawal, Neeraj Kayal and Nitin Saxena@] . + [@Manindra Agrawal, Neeraj Kayal and Nitin Saxena@] . - [@H. W. Lenstra, Jr. and Carl Pomerance@] . + [@H. W. Lenstra, Jr. and Carl Pomerance@] . - [@Salembier and Southerington@] , + [@Salembier and Southerington@] , - [@R. Crandall and J. Papadopoulos@] , + [@R. Crandall and J. Papadopoulos@] , - [@Andreas Klappenecker@] , + [@Andreas Klappenecker@] , - [@Vibhor Bhatt and G. K. Patra@] , + [@Vibhor Bhatt and G. K. Patra@] , -} isPrimeByAKS :: ( Control.DeepSeq.NFData i, @@ -145,7 +145,7 @@ {- | * Uses the specified 'base' in an attempt to prove the /compositeness/ of an integer. - * This is the opposite of the /Miller Test/; . + * This is the opposite of the /Miller Test/; . * If the result is 'True', then the candidate is /composite/; regrettably the converse isn't true. Amongst the set of possible bases, over three-quarters are /witnesses/ to the compositeness of a /composite/ candidate, @@ -173,15 +173,15 @@ * The test becomes deterministic, for any candidate integer, when the number of tests reaches the limit defined by /Eric Bach/. - * A testing of smaller set of bases, is sufficient for candidates smaller than various thresholds; . + * A testing of smaller set of bases, is sufficient for candidates smaller than various thresholds; . * . - * + * - * . + * . - * , . + * , . -} isPrimeByMillerRabin :: (Integral i, Show i) => i -> Bool isPrimeByMillerRabin primeCandidate = not $ witnessesCompositeness primeCandidate ( diff --git a/src-lib/Factory/Math/Implementations/PrimeFactorisation.hs b/src-lib/Factory/Math/Implementations/PrimeFactorisation.hs --- a/src-lib/Factory/Math/Implementations/PrimeFactorisation.hs +++ b/src-lib/Factory/Math/Implementations/PrimeFactorisation.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -21,7 +21,7 @@ * Implements several different prime-factorisation algorithms. - * . + * . -} module Factory.Math.Implementations.PrimeFactorisation( @@ -76,7 +76,7 @@ {- | * . - * . + * . * . @@ -125,7 +125,7 @@ {- | * Decomposes the specified integer, into a product of /prime/-factors, - using , AKA . + using , AKA . * This works best when the factors are small. -} diff --git a/src-lib/Factory/Math/Implementations/Primes/Algorithm.hs b/src-lib/Factory/Math/Implementations/Primes/Algorithm.hs --- a/src-lib/Factory/Math/Implementations/Primes/Algorithm.hs +++ b/src-lib/Factory/Math/Implementations/Primes/Algorithm.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -21,11 +21,11 @@ * Generates the constant list of /prime-numbers/, by a variety of different algorithms. - * . + * . - * . + * . - * . + * . -} module Factory.Math.Implementations.Primes.Algorithm( @@ -48,7 +48,7 @@ = SieveOfAtkin Integer -- ^ The /Sieve of Atkin/, optimised using a 'Data.PrimeWheel.PrimeWheel' of optimal size, for primes up to the specified maximum bound; . | SieveOfEratosthenes Data.PrimeWheel.NPrimes -- ^ The /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; . + | TurnersSieve -- ^ For each /prime/, the infinite list of candidates greater than its /square/, is filtered for indivisibility; . | WheelSieve Int -- ^ 'Data.Numbers.Primes.wheelSieve'. deriving (Eq, Read, Show) diff --git a/src-lib/Factory/Math/Implementations/Primes/SieveOfAtkin.hs b/src-lib/Factory/Math/Implementations/Primes/SieveOfAtkin.hs --- a/src-lib/Factory/Math/Implementations/Primes/SieveOfAtkin.hs +++ b/src-lib/Factory/Math/Implementations/Primes/SieveOfAtkin.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -209,7 +209,7 @@ {- | * Generates the constant /bounded/ list of /prime-numbers/. - * + * -} sieveOfAtkin :: (Control.DeepSeq.NFData i, Data.Array.IArray.Ix i, Integral i) => Data.PrimeWheel.NPrimes -- ^ Other implementations effectively use a hard-coded value either /2/ or /3/, but /6/ seems better. diff --git a/src-lib/Factory/Math/Implementations/SquareRoot.hs b/src-lib/Factory/Math/Implementations/SquareRoot.hs --- a/src-lib/Factory/Math/Implementations/SquareRoot.hs +++ b/src-lib/Factory/Math/Implementations/SquareRoot.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -97,7 +97,7 @@ dx' = Math.Power.square dx / dydx' {- - * /Halley's/ method; + * /Halley's/ method; > X(n+1) = Xn - f(Xn) / [f'(Xn) - f''(Xn) * f(Xn) / 2 * f'(Xn)] > => Xn - (Xn^2 - Y) / [2Xn - 2 * (Xn^2 - Y) / 2 * 2Xn] where Y = X^2, f(X) = X^2 - Y, f'(X) = 2X, f''(X) = 2 @@ -131,7 +131,7 @@ , , . - + * The convergence of the /continued-fraction/ is merely /1st order/ (linear). -} diff --git a/src-lib/Factory/Math/MultiplicativeOrder.hs b/src-lib/Factory/Math/MultiplicativeOrder.hs --- a/src-lib/Factory/Math/MultiplicativeOrder.hs +++ b/src-lib/Factory/Math/MultiplicativeOrder.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -36,11 +36,11 @@ * The smallest positive integral power to which the specified integral base must be raised, to be congruent with one, in the specified /modular/ arithmetic. - * Based on . + * Based on . * . - * . + * . -} multiplicativeOrder :: (Math.PrimeFactorisation.Algorithmic primeFactorisationAlgorithm, Control.DeepSeq.NFData i, Integral i, Show i) => primeFactorisationAlgorithm diff --git a/src-lib/Factory/Math/PerfectPower.hs b/src-lib/Factory/Math/PerfectPower.hs --- a/src-lib/Factory/Math/PerfectPower.hs +++ b/src-lib/Factory/Math/PerfectPower.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -37,7 +37,7 @@ * . - * . + * . * @(Math.Power.square . sqrt)@ is expensive, so the modulus of the operand is tested first, in an attempt to prove it isn't a /perfect square/. The set of tests, and the valid moduli within each test, are ordered to maximize the rate of failure-detection. @@ -71,7 +71,7 @@ * . - * . + * . * A generalisation of the concept of /perfect squares/, in which only the exponent '2' is significant. -} diff --git a/src-lib/Factory/Math/Primality.hs b/src-lib/Factory/Math/Primality.hs --- a/src-lib/Factory/Math/Primality.hs +++ b/src-lib/Factory/Math/Primality.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -50,7 +50,7 @@ * . - * . + * . -} areCoprime :: Integral i => i -> i -> Bool areCoprime i = (== 1) . gcd i @@ -77,7 +77,7 @@ * . - * . + * . -} isCarmichaelNumber :: ( Algorithmic algorithm, diff --git a/src-lib/Factory/Math/PrimeFactorisation.hs b/src-lib/Factory/Math/PrimeFactorisation.hs --- a/src-lib/Factory/Math/PrimeFactorisation.hs +++ b/src-lib/Factory/Math/PrimeFactorisation.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -76,7 +76,7 @@ * . - * . + * . -} smoothness :: (Algorithmic algorithm, Control.DeepSeq.NFData base, Integral base) => algorithm -> [base] smoothness algorithm = 0 : map (Data.Exponential.getBase . last . primeFactors algorithm) [1 ..] @@ -113,7 +113,7 @@ * . - * . + * . * AKA /EulerPhi/. -} @@ -131,11 +131,11 @@ {- | * A constant, zero-indexed, conceptually infinite, list of the /small omega/ numbers (i.e. the number of /distinct/ prime factors); cf. /big omega/. - * . + * . - * + * - * . + * . -} omega :: (Algorithmic algorithm, Integral i) => algorithm -> [i] omega algorithm = map (fromIntegral . length . primeFactors algorithm) [0 :: Integer ..] diff --git a/src-lib/Factory/Math/Primes.hs b/src-lib/Factory/Math/Primes.hs --- a/src-lib/Factory/Math/Primes.hs +++ b/src-lib/Factory/Math/Primes.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -40,7 +40,7 @@ * . - * . + * . -} primorial :: ( Algorithmic algorithm, @@ -57,7 +57,7 @@ * . - * + * -} mersenneNumbers :: (Algorithmic algorithm, Integral i) => algorithm -> [i] mersenneNumbers algorithm = map (pred . (2 ^)) (primes algorithm :: [Int]) -- Whilst the exponentiation could be parallelised, not all values are known to be required. diff --git a/src-lib/Factory/Math/Probability.hs b/src-lib/Factory/Math/Probability.hs --- a/src-lib/Factory/Math/Probability.hs +++ b/src-lib/Factory/Math/Probability.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -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. - * , . + * , . -} generateStandardizedNormalDistribution :: ( RealFloat f, diff --git a/src-lib/Factory/Math/Radix.hs b/src-lib/Factory/Math/Radix.hs --- a/src-lib/Factory/Math/Radix.hs +++ b/src-lib/Factory/Math/Radix.hs @@ -12,7 +12,7 @@ GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program. If not, see . + along with this program. If not, see . -} {- | [@AUTHOR@] Dr. Alistair Ward @@ -121,7 +121,7 @@ _ -> error $ "Factory.Math.Radix.fromBase.fromDigit:\tunrecognised char " ++ show c {- | - * . + * . * . -}