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階乗

factorial

$ n! = n(n-1)!

$ 0!\coloneqq 1 と定義する

code:jl

factorial.(collect(0:20))

# 1

# 2

# 6

# 24

# 120

# 720

# 5040

# 40320

# 362880

# 3628800

# 39916800

# 479001600

# 6227020800

# 87178291200

# 1307674368000

# 20922789888000

# 355687428096000

# 6402373705728000

# 121645100408832000

# 2432902008176640000

20! = 2^(18) * 3^8 * 5^4 * 7^2 * 11*13*17*19

同じ方法で末尾の0の長さがわかるあんも.icon

code:jl

factorial(20) # 2432902008176640000

typemax(Int64) # 9223372036854775807

factorial(big(21)) # 51090942171709440000

https://github.com/JuliaLang/julia/blob/master/base/combinatorics.jl

20まで計算しておいて、オーバーフローする21からはエラーを返す

条件の短絡評価で関数を抜ける

code:jl

# https://github.com/JuliaLang/julia/blob/master/base/combinatorics.jl

const _fact_table64 = let _fact_table64 = Vector{Int64}(undef, 20)

_fact_table641 = 1

for n in 2:20

_fact_table64n = _fact_table64n-1 * n

end

Tuple(_fact_table64)

end

function factorial_lookup(

n::Union{Checked.SignedInt,Checked.UnsignedInt},

table::Union{NTuple{20,Int64},NTuple{34,UInt128}}, lim::Int)

idx = Int(n)

idx < 0 && throw(DomainError(n, "n must not be negative."))

idx > lim && throw(OverflowError(lazy"$n is too large to look up in the table; consider using factorial(big($n)) instead"))

idx == 0 && return one(n)

f = getfield(table, idx)

return oftype(n, f)

end

factorial(n::Union{Int64,UInt64}) = factorial_lookup(n, _fact_table64, 20)