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1. divisorsSmallA :: ArithmeticFunction Int IntSet

   arithmoi	Math.NumberTheory.ArithmeticFunctions

   Same as divisors, but with better performance on cost of type restriction.

2. smallOmega :: (UniqueFactorisation n, Num a) => n -> a

   arithmoi	Math.NumberTheory.ArithmeticFunctions

   See smallOmegaA.

3. smallOmegaA :: Num a => ArithmeticFunction n a

   arithmoi	Math.NumberTheory.ArithmeticFunctions

   Number of distinct prime factors.

   smallOmegaA = additive (\_ _ -> 1)
   

4. evalAll :: forall (n :: Nat) . KnownNat n => DirichletCharacter n -> Vector (OrZero RootOfUnity)

   arithmoi	Math.NumberTheory.DirichletCharacters

   In general, evaluating a DirichletCharacter at a point involves solving the discrete logarithm problem, which can be hard: the implementations here are around O(sqrt n). However, evaluating a dirichlet character at every point amounts to solving the discrete logarithm problem at every point also, which can be done together in O(n) time, better than using a complex algorithm at each point separately. Thus, if a large number of evaluations of a dirichlet character are required, evalAll will be better than evalGeneral, since computations can be shared.

5. binomialLine :: (Enum a, GcdDomain a) => a -> [a]

   arithmoi	Math.NumberTheory.Recurrences.Bilinear

   The n-th (zero-based) line of binomial (and the n-th diagonal of binomialRotated).

   >>> binomialLine 5
   [1,5,10,10,5,1]
   

6. generalLucas :: Num a => a -> a -> Int -> (a, a, a, a)

   arithmoi	Math.NumberTheory.Recurrences.Linear

   generalLucas p q k calculates the quadruple (U(k), U(k+1), V(k), V(k+1)) where U(i) is the Lucas sequence of the first kind and V(i) the Lucas sequence of the second kind for the parameters p and q, where p^2-4q /= 0. Both sequences satisfy the recurrence relation A(j+2) = p*A(j+1) - q*A(j), the starting values are U(0) = 0, U(1) = 1 and V(0) = 2, V(1) = p. The Fibonacci numbers form the Lucas sequence of the first kind for the parameters p = 1, q = -1 and the Lucas numbers form the Lucas sequence of the second kind for these parameters. Here, the index must be non-negative, since the terms of the sequence for negative indices are in general not integers.

7. parallely :: forall (m :: Type -> Type) a b . Applicative m => Automaton m a b -> Automaton m [a] [b]

   automaton	Data.Automaton

   Launch arbitrarily many copies of the automaton in parallel.

   • The copies of the automaton are launched on demand as the input lists grow.
   • The n-th copy will always receive the n-th input.
   • If the input list has length n, the n+1-th automaton copy will not be stepped.
   Caution: Uses memory of the order of the largest list that was ever input during runtime.

8. liftCallCC' :: Monoid w => CallCC m (a, s, w) (b, s, w) -> CallCC (RWST r w s m) a b

   automaton	Data.Automaton.Trans.RWS

   In-situ lifting of a callCC operation to the new monad. This version uses the current state on entering the continuation.

9. DecimalL :: Decimal -> LogicalTypeLong

   avro	Data.Avro

   An arbitrary-precision signed decimal number. See Decimal.

10. DecimalL :: Decimal -> LogicalTypeLong

    avro	Data.Avro.Schema.ReadSchema

    An arbitrary-precision signed decimal number. See Decimal.

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