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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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22
Task/Nth-root/Julia/nth-root.julia
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@ -1,15 +1,17 @@
function nthroot(n::Integer, A::Real)
A < 0 || n == 0 && throw(DomainError())
n < 0 && return 1/nthroot(-n, A)
A == 0 && return A
x = A / n
prevdx = A
function nthroot(n::Integer, r::Real)
r < 0 || n == 0 && throw(DomainError())
n < 0 && return 1 / nthroot(-n, r)
r > 0 || return 0
x = r / n
prevdx = r
while true
y = x^(n-1)
dx = (A - y*x) / (n * y)
abs(dx) >= abs(prevdx) && return x
y = x ^ (n - 1)
dx = (r - y * x) / (n * y)
abs(dx) ≥ abs(prevdx) && return x
x += dx
prevdx = dx
end
end
@vectorize_2arg Number nthroot
@show nthroot.(-5:2:5, 5.0)
@show nthroot.(-5:2:5, 5.0) - 5.0 .^ (1 ./ (-5:2:5))