Continued fraction: Difference between revisions

=={{header|Lambdatalk}}==

<lang Scheme>

{def gcf

{def gcf.rec

{lambda {:f :n :r}

{if {< :n 1}

then {+ {car {:f 0}} :r}

else {gcf.rec :f

{- :n 1}

{let { {:r :r}

{:ab {:f :n}}

} {/ {cdr :ab}

{+ {car :ab} :r}} }}}}}

{lambda {:f :n}

{gcf.rec :f :n 0}}}

{def phi

{lambda {:n}

{cons 1 1}}}

{gcf phi 50}

-> 1.618033988749895

{def sqrt2

{lambda {:n}

{cons {if {> :n 0} then 2 else 1} 1}}}

{gcf sqrt2 25}

-> 1.4142135623730951

{def napier

{lambda {:n}

{cons {if {> :n 0} then :n else 2} {if {> :n 1} then {- :n 1} else 1} }}}

{gcf napier 20}

-> 2.7182818284590455

{def fpi

{lambda {:n}

{cons {if {> :n 0} then 6 else 3} {pow {- {* 2 :n} 1} 2} }}}

{gcf fpi 500}

-> 3.1415926 516017554

// only 8 exact decimals for 500 iterations

// A very very slow convergence.

// Here is a quicker version without any obvious pattern

{def pi

{lambda {:n}

{cons {A.get :n {A.new 3 7 15 1 292 1 1 1 2 1 3 1 14 2 1 1}} 1}}}

{gcf pi 15}

-> 3.1415926 53589793

// Much quicker, 15 exact decimals after 15 iterations

</lang>