continued_fraction.sf

#!/usr/bin/ruby

# Generic implementation of continued fractions.

func continued_fraction(a, b, f, n = 1000, r = 1) {
    f(func (r) {
        r < n ? (a(r) / (b(r) + __FUNC__(r+1))) : 0
    }(r))
}

var params = Hash(
    "φ"  => [ { 1 }, { 1 }, { 1 + _ } ],
    "√2" => [ { 1 }, { 2 }, { 1 + _ } ],
    "e"  => [ { _ }, { _ }, { 1 + 1/_ } ],
    "π"  => [ { (2*_ - 1)**2 }, { 6 }, { 3 + _ } ],
    "τ"  => [ { _**2 }, { 2*_ + 1 }, { 8 / (1 + _) } ],     # very fast convergence
)

for k in (params.keys.sort) {
    printf("%2s ≈ %s\n", k, continued_fraction(params{k}...))
}

__END__
 e ≈ 2.7182818284590452353602874713526624977572470937
 π ≈ 3.14159265383979292596359650286939597045138933078
 τ ≈ 6.28318530717958647692528676655900576839433879875
 φ ≈ 1.61803398874989484820458683436563811772030917981
√2 ≈ 1.41421356237309504880168872420969807856967187538