Changelog for arithmoi- This release supports GHC 7.6, 7.8, 7.10 and 8.0. 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). Fix incorrect indexing of FactorSieve (#35). This release supports GHC 7.6, 7.8, 7.10 and 8.0. Add new cabal flag check-bounds, which replaces all unsafe array functions with safe ones. Add basic functions on Gaussian integers. Add Moebius mu-function. Forbid non-positive moduli in Math.NumberTheory.Moduli. Fix out-of-bounds error 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). Add integerLog10 variants at Bas van Dijk's request and expose Math.NumberTheory.Powers.Integer, with an added integerWordPower. 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. Relaxed dependencies on mtl and containers Fixed warnings from GHC-7.5, Word(..) moved to GHC.Types Removed SPECIALISE pragma from inline function (warning from 7.5, probably pointless anyway) Sped up factor sieves. They need more space now, but the speedup is worth it, IMO. Raised spec-constr limit in MoebiusInversion.Int Fixed Haddock bug Added generalised Moebius inversion, to be continued Added modular square roots and Chinese remainder theorem Performance tweaks for powerModInteger (~10%) and invertMod (~25%). Fix bug in psieveFrom Fix bug in nthPrime Fix bug in powerMod Relax bounds on array dependency for 7.4.* Fix copy-pasto (only relevant for 7.3.*) Fix imports for ghc >= 7.3 Added certificates and certified testing/factorisation Fixed doc bugs Elaborate on overflow, work more on native Ints in Eratosthenes First release