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- #!/usr/bin/ruby
- # Recursive computation of Bernoulli numbers.
- # See: https://en.wikipedia.org/wiki/Bernoulli_number#Recursive_definition
- # https://en.wikipedia.org/wiki/Binomial_coefficient#Recursive_formula
- func bernoulli_number{}; # must be declared before used
- func binomial(n, k) is cached {
- (k == 0) || (n == k) ? 1 : (binomial(n - 1, k - 1) + binomial(n - 1, k));
- }
- func bern_helper(n, k) {
- binomial(n, k) * (bernoulli_number(k) / (n - k + 1));
- }
- func bern_diff(n, k, d) {
- n < k ? d : bern_diff(n, k + 1, d - bern_helper(n + 1, k));
- }
- bernoulli_number = func(n) is cached {
- n.is_one && return 1/2;
- n.is_odd && return 0;
- n > 0 ? bern_diff(n - 1, 0, 1) : 1;
- }
- for i in range(0, 20, 2) {
- var num = bernoulli_number(i);
- printf("B(%2d) = %20s / %s\n", i, num.nude);
- }
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