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Expand stirlings1 and stirlings2 to work with very large integers #84

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Expand stirlings1 and stirlings2 to work with very large integers #84

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86518c7
Broaden types accepted by stirlings1 and stirlings2 functions
wherrera10 Aug 16, 2019
4b2c99a
Update numbers.jl
wherrera10 Aug 18, 2019
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32 changes: 22 additions & 10 deletions src/numbers.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -125,19 +125,23 @@ function lucasnum(n::Integer)
return z[]
end

function stirlings1(n::Int, k::Int, signed::Bool=false)
stirlings1cache = Dict()

function stirlings1(n::Integer, k::Integer, signed::Bool=false)
if signed == true
return (-1)^(n - k) * stirlings1(n, k)
end

if n < 0
if haskey(stirlings1cache, Pair(n, k))
return stirlings1cache[Pair(n, k)]
elseif n < 0
throw(DomainError(n, "n must be nonnegative"))
elseif n == k == 0
return 1
return one(n)
elseif n == 0 || k == 0
return 0
return zero(n)
elseif n == k
return 1
return one(n)
elseif k == 1
return factorial(n-1)
elseif k == n - 1
Expand All @@ -148,21 +152,29 @@ function stirlings1(n::Int, k::Int, signed::Bool=false)
return binomial(n, 2) * binomial(n, 4)
end

return (n - 1) * stirlings1(n - 1, k) + stirlings1(n - 1, k - 1)
ret = (n - 1) * stirlings1(n - 1, k) + stirlings1(n - 1, k - 1)
stirlings1cache[Pair(n, k)] = ret
return ret
end

function stirlings2(n::Int, k::Int)
stirlings2cache = Dict()

function stirlings2(n::Integer, k::Integer)
if n < 0
throw(DomainError(n, "n must be nonnegative"))
elseif haskey(stirlings2cache, Pair(n, k))
return stirlings2cache[Pair(n, k)]
elseif n == k == 0
return 1
return one(n)
elseif n == 0 || k == 0
return 0
return zero(n)
elseif k == n - 1
return binomial(n, 2)
elseif k == 2
return 2^(n-1) - 1
end

return k * stirlings2(n - 1, k) + stirlings2(n - 1, k - 1)
ret = k * stirlings2(n - 1, k) + stirlings2(n - 1, k - 1)
stirlings2cache[Pair(n, k)] = ret
ret
end