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- #!/usr/bin/ruby
- # Daniel "Trizen" Șuteu
- # Date: 03 February 2019
- # https://github.com/trizen
- # Approximate n-th roots, using continued fractions.
- # See also:
- # https://en.wikipedia.org/wiki/Generalized_continued_fraction#Roots_of_positive_numbers
- func cfrac_nth_root (z, m, n, y, r, k=1) {
- return 0 if (r <= 0)
- (k² * n² - m²) * y² / ((2*k + 1)*n*(2*z - y) - __FUNC__(z, m, n, y, r - 1, k+1))
- }
- func nth_root(z, n, r = 100) {
- var (x, y) = z.irootrem(n)
- var m = 1
- var t = cfrac_nth_root(z, m, n, y, r)
- x**m + ((2 * x * m * y) / (n*(2*z - y) - m*y - t))
- }
- say nth_root(1234, 2) #=> 35.12833614050059160587031162535630676454048547878
- say nth_root(12345, 3) #=> 23.11161874980726868087197332958829017451713700262
- say nth_root(123456, 5) #=> 10.43043546409766483375317008568663847055013893731
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