Changelog

0.13.0.0

Changed

• Migrate functions under Math.NumberTheory.Recurrences and Math.NumberTheory.Zeta, which operate on infinite lists, to use Infinite from infinite-list package.
• Migrate functions under Math.NumberTheory.Quadratic to return an Infinite list of quadratic primes.

Removed

• Remove deprecated Math.NumberTheory.Powers.Modular.

0.12.1.0

Fixed

• Fix a grave bug in prime factorisation, lurking since arithmoi-0.7.0.0.

0.12.0.2

Fixed

• Compatibility patches for GHC 9.4.

0.12.0.1

Fixed

• Compatibility patches for GHC 9.2.

0.12.0.0

Added

• Define cubic symbol (#194).
• Add instance Unbox (Prime a) and toPrimeIntegral helper (#201).
• Implement Cornacchia’s algorithm for Diophantine equations (#195).
• Define a wrapper PrimeIntSet for sets of primes (#205).

Deprecated

• Deprecate Math.NumberTheory.Powers.Modular, use Data.Mod or Data.Mod.Word instead.

Removed

• Remove modules and functions, deprecated in the previous release.

0.11.0.1

Changed

• Switch to smallcheck-1.2.0.

0.11.0.0

Added

• Brand new machinery to deal with Dirichlet characters (#180).

• Generate preimages of the Jordan and the sum-of-powers-of-divisors functions (#148).

• More flexible interface for Pascal triangle: in addition to binomial we now provide also binomialRotated, binomialLine and binomialDiagonal (#151). There are also factoriseFactorial and factoriseBinomial (#152).

• Add Semiring instance of SomeMod (#174).

• Generate divisors in range (#183).

Changed

• Speed up partition, using better container for memoization (#176).

• Speed up integerRoot, using better starting approximation (#177).

Deprecated

• Deprecate Math.NumberTheory.Euclidean, use Data.Euclidean instead.

• Deprecate chineseRemainder, chineseRemainder2, chineseCoprime, use chinese instead. Deprecate chineseCoprimeSomeMod, use chineseSomeMod.

• Deprecate Math.NumberTheory.Powers except Math.NumberTheory.Powers.Modular. Use Math.NumberTheory.Roots instead.

• Deprecate Math.NumberTheory.Moduli.Jacobi, use Math.NumberTheory.Moduli.Sqrt instead.

• Deprecate Math.NumberTheory.Moduli.{DiscreteLogarithm,PrimitiveRoot}, use Math.NumberTheory.Moduli.Multiplicative instead.

Removed

• Remove modules and functions, deprecated in the previous release.

Fixed

• Fix subtraction of SomeMod (#174).

0.10.0.0

Added

• The machinery of cyclic groups, primitive roots and discrete logarithms has been completely overhauled and rewritten using singleton types (#169).

  There is also a new singleton type, linking a type-level modulo with a term-level factorisation. It allows both to have a nicely-typed API of Mod m and avoid repeating factorisations (#169).

  Refer to a brand new module Math.NumberTheory.Moduli.Singleton for details.

• Add a new function factorBack.

• Add Ord SomeMod instance (#165).

• Add Semiring and Ring instances for Eisenstein and Gaussian integers.

Changed

• Embrace the new Semiring -> GcdDomain -> Euclidean hierarchy of classes, refining Num and Integral constraints.

• Reshuffle exports from Math.NumberTheory.Zeta, do not advertise its submodules as available to import.

• Add a proxy argument storing vector’s flavor to Math.NumberTheory.MoebiusInversion.{generalInversion,totientSum}.

• solveQuadratic and sqrtsMod require an additional argument: a singleton linking a type-level modulo with a term-level factorisation (#169).

• Generalize sieveBlock to handle any flavor of Vector (#164).

Deprecated

• Deprecate Math.NumberTheory.Primes.Factorisation, use Math.NumberTheory.Primes.factorise instead. Deprecate Math.NumberTheory.Primes.Sieve, use Enum instance instead.

• Deprecate Math.NumberTheory.Primes.Factorisation.Certified and Math.NumberTheory.Primes.Testing.Certificates.

• Deprecate Math.NumberTheory.MoebiusInversion.Int.

• Deprecate Math.NumberTheory.SmoothNumbers.{fromSet,fromSmoothUpperBound}. Use Math.NumberTheory.SmoothNumbers.fromList instead.

• Deprecate Math.NumberTheory.SmoothNumbers.smoothOverInRange in favor of smoothOver and Math.NumberTheory.SmoothNumbers.smoothOverInRange in favor of isSmooth.

Removed

• Move Euclidean type class to semirings package (#168).

• Remove deprecated earlier Math.NumberTheory.Recurrencies.* and Math.NumberTheory.UniqueFactorisation modules. Use Math.NumberTheory.Recurrences.* and Math.NumberTheory.Primes instead.

• Remove deprecated earlier an old interface of Math.NumberTheory.Moduli.Sqrt.

0.9.0.0

Added

• Introduce Prime newtype. This newtype is now used extensively in public API:

  primes :: Integral a => [Prime a]
  primeList :: Integral a => PrimeSieve -> [Prime a]
  sieveFrom :: Integer -> [Prime Integer]
  nthPrime :: Integer -> Prime Integer
  

• New functions nextPrime and precPrime. Implement an instance of Enum for primes (#153):

  > [nextPrime 101 .. precPrime 130]
  [Prime 101,Prime 103,Prime 107,Prime 109,Prime 113,Prime 127]
  

• Add the Hurwitz zeta function on non-negative integer arguments (#126).

• Implement efficient tests of n-freeness: pointwise and in interval. See isNFree and nFreesBlock (#145).

• Generate preimages of the totient and the sum-of-divisors functions (#142):

  > inverseTotient 120 :: [Integer]
  [155,310,183,366,225,450,175,350,231,462,143,286,244,372,396,308,248]
  

• Generate coefficients of Faulhaber polynomials faulhaberPoly (#70).

Changed

• Support Gaussian and Eisenstein integers in smooth numbers (#138).

• Change types of primes, primeList, sieveFrom, nthPrime, etc., to use Prime newtype.

• Math.NumberTheory.Primes.{Factorisation,Testing,Counting,Sieve} are no longer re-exported from Math.NumberTheory.Primes. Merge Math.NumberTheory.UniqueFactorisation into Math.NumberTheory.Primes (#135, #153).

• From now on Math.NumberTheory.Primes.Factorisation.factorise and similar functions return [(Integer, Word)] instead of [(Integer, Int)].

• sbcFunctionOnPrimePower now accepts Prime Word instead of Word.

• Better precision for exact values of Riemann zeta and Dirichlet beta functions (#123).

• Speed up certain cases of modular multiplication (#160).

• Extend Chinese theorem to non-coprime moduli (#71).

Deprecated

• Deprecate Math.NumberTheory.Recurrencies.*. Use Math.NumberTheory.Recurrences.* instead (#146).

Removed

• Remove Prime type family.

• Remove deprecated Math.NumberTheory.GCD and Math.NumberTheory.GCD.LowLevel.

0.8.0.0

Added

• A new interface for Math.NumberTheory.Moduli.Sqrt, more robust and type safe (#87, #108).

• Implement Ramanujan tau function (#112):

  > map ramanujan [1..10]
  [1,-24,252,-1472,4830,-6048,-16744,84480,-113643,-115920]
  

• Implement partition function (#115):

  > take 10 partition
  [1,1,2,3,5,7,11,15,22,30]
  

• Add the Dirichlet beta function on non-negative integer arguments (#120). E. g.,

  > take 5 $ Math.NumberTheory.Zeta.Dirichlet.betas 1e-15
  [0.5,0.7853981633974483,0.9159655941772191,0.9689461462593693,0.9889445517411055]
  

• Solve linear and quadratic congruences (#129).

• Support Eisenstein integers (#121).

• Implement discrete logarithm (#88).

Changed

• Stop reporting units (1, -1, i, -i) as a part of factorisation for integers and Gaussian integers (#101). Now factorise (-2) is [(2, 1)] and not [(-1, 1), (2, 1)].

• Move splitIntoCoprimes to Math.NumberTheory.Euclidean.Coprimes.

• Change types of splitIntoCoprimes, fromFactors and prefFactors using newtype Coprimes (#89).

• Sort Gaussian primes by norm (#124).

• Make return type of primes and primeList polymorphic instead of being limited to Integer only (#109).

• Speed up factorisation of Gaussian integers (#116).

• Speed up computation of primitive roots for prime powers (#127).

Deprecated

• Deprecate an old interface of Math.NumberTheory.Moduli.Sqrt.

• Deprecate Math.NumberTheory.GCD and Math.NumberTheory.GCD.LowLevel (#80). Use Math.NumberTheory.Euclidean instead (#128).

• Deprecate jacobi' (#103).

• Deprecate Math.NumberTheory.GaussianIntegers in favor of Math.NumberTheory.Quadratic.GaussianIntegers.

0.7.0.0

Added

• A general framework for bulk evaluation of arithmetic functions (#77):

  > runFunctionOverBlock carmichaelA 1 10
  [1,1,2,2,4,2,6,2,6,4]
  

• Implement a sublinear algorithm for Mertens function (#90):

  > map (mertens . (10 ^)) [0..9]
  [1,-1,1,2,-23,-48,212,1037,1928,-222]
  

• Add basic support for cyclic groups and primitive roots (#86).

• Implement an efficient modular exponentiation (#86).

• Write routines for lazy generation of smooth numbers (#91).

  > smoothOverInRange (fromJust (fromList [3,5,7])) 1000 2000
  [1029,1125,1215,1225,1323,1575,1701,1715,1875]
  

Changed

• Now moebius returns not a number, but a value of Moebius type (#90).

• Now factorisation of large integers and Gaussian integers produces factors as lazy as possible (#72, #76).

Deprecated

• Deprecate Math.NumberTheory.Primes.Heap. Use Math.NumberTheory.Primes.Sieve instead.

• Deprecate FactorSieve, TotientSieve, CarmichaelSieve and accompanying functions. Use new general approach for bulk evaluation of arithmetic functions instead (#77).

Removed

• Remove Math.NumberTheory.Powers.Integer, deprecated in 0.5.0.0.

0.6.0.1

Changed

• Switch to smallcheck-1.1.3.

0.6.0.0

Added

• Brand new Math.NumberTheory.Moduli.Class (#56), providing flexible and type safe modular arithmetic. Due to use of GMP built-ins it is also significantly faster.

• New function divisorsList, which is lazier than divisors and does not require Ord constraint (#64). Thus, it can be used for GaussianInteger.

Changed

• Math.NumberTheory.Moduli was split into Math.NumberTheory.Moduli.{Chinese,Class,Jacobi,Sqrt}.

• Functions jacobi and jacobi' return JacobiSymbol instead of Int.

• Speed up factorisation over elliptic curve up to 15x (#65).

• Polymorphic fibonacci and lucas functions, which previously were restricted to Integer only (#63). This is especially useful for modular computations, e. g., map fibonacci [1..10] :: [Mod 7].

• Make totientSum more robust and idiomatic (#58).

Removed

• Functions invertMod, powerMod and powerModInteger were removed, as well as their unchecked counterparts. Use new interface to modular computations, provided by Math.NumberTheory.Moduli.Class.

0.5.0.1

Changed

Switch to QuickCheck-2.10.

0.5.0.0

Added

• Add basic combinatorial sequences: binomial coefficients, Stirling numbers of both kinds, Eulerian numbers of both kinds, Bernoulli numbers (#39). E. g.,

  > take 10 $ Math.NumberTheory.Recurrencies.Bilinear.bernoulli
  [1 % 1,(-1) % 2,1 % 6,0 % 1,(-1) % 30,0 % 1,1 % 42,0 % 1,(-1) % 30,0 % 1]
  

• Add the Riemann zeta function on non-negative integer arguments (#44). E. g.,

  > take 5 $ Math.NumberTheory.Zeta.zetas 1e-15
  [-0.5,Infinity,1.6449340668482262,1.2020569031595945,1.0823232337111381]
  

Changed

• Rename Math.NumberTheory.Lucas to Math.NumberTheory.Recurrencies.Linear.

• Speed up isPrime twice; rework millerRabinV and isStrongFermatPP (#22, #25).

Deprecated

• Deprecate integerPower and integerWordPower from Math.NumberTheory.Powers.Integer. Use (^) instead (#51).

Removed

• Remove deprecated interface to arithmetic functions (divisors, tau, sigma, totient, jordan, moebius, liouville, smallOmega, bigOmega, carmichael, expMangoldt). New interface is exposed via Math.NumberTheory.ArithmeticFunctions (#30).

• Math.NumberTheory.Logarithms has been moved to the separate package integer-logarithms (#51).

0.4.3.0

Added

• Add Math.NumberTheory.ArithmeticFunctions with brand-new machinery for arithmetic functions: divisors, tau, sigma, totient, jordan, moebius, liouville, smallOmega, bigOmega, carmichael, expMangoldt (#30). Old implementations (exposed via Math.NumberTheory.Primes.Factorisation and Math.NumberTheory.Powers.Integer) are deprecated and will be removed in the next major release.

• Add Karatsuba sqrt algorithm, improving performance on large integers (#6).

Fixed

• Fix incorrect indexing of FactorSieve (#35).

0.4.2.0

Added

• Add new cabal flag check-bounds, which replaces all unsafe array functions with safe ones.

• Add basic functions on Gaussian integers.

• Add Möbius mu-function.

Changed

• Forbid non-positive moduli in Math.NumberTheory.Moduli.

Fixed

• Fix out-of-bounds errors in Math.NumberTheory.Primes.Heap, Math.NumberTheory.Primes.Sieve and Math.NumberTheory.MoebiusInversion.

• Fix 32-bit build.

• Fix binaryGCD on negative numbers.

• Fix highestPower (various issues).

0.4.1.0

Added

• Add integerLog10 variants at Bas van Dijk’s request and expose Math.NumberTheory.Powers.Integer, with an added integerWordPower.

0.4.0.4

Fixed

• Update for GHC 7.8, the type of some primops changed, they return Int# now instead of Bool.

• Fixed bugs in modular square roots and factorisation.

0.4.0.3

Changed

• Relaxed dependencies on mtl and containers.

Fixed

• Fixed warnings from GHC 7.5, Word(..) moved to GHC.Types.

• Removed SPECIALISE pragma from inline function (warning from GHC 7.5, probably pointless anyway).

0.4.0.2

Changed

• Sped up factor sieves. They need more space now, but the speedup is worth it, IMO.

• Raised spec-constr limit in MoebiusInversion.Int.

0.4.0.1

Fixed

• Fixed Haddock bug.

0.4.0.0

Added

• Added generalised Möbius inversion, to be continued.

0.3.0.0

Added

• Added modular square roots and Chinese remainder theorem.

0.2.0.6

Changed

• Performance tweaks for powerModInteger (~10%) and invertMod (~25%).

0.2.0.5

Fixed

• Fix bug in psieveFrom.

0.2.0.4

Fixed

• Fix bug in nthPrime.

0.2.0.3

Fixed

• Fix bug in powerMod.

0.2.0.2

Changed

• Relax bounds on array dependency for GHC 7.4.

0.2.0.1

Fixed

• Fix copy-pasto (only relevant for GHC 7.3).

• Fix imports for GHC 7.3.

0.2.0.0

Added

• Added certificates and certified testing/factorisation

0.1.0.2

Fixed

• Fixed doc bugs

0.1.0.1

Changed

• Elaborate on overflow, work more on native Ints in Eratosthenes.

0.1.0.0

Added

• First release.