--  -*-lua-*-
--  ====================================================================
--  Print ascending members of the Fibonacci sequence that are
--  representable as 64-bit signed integers, prefixed by their term
--  numbers, and followed by the ratio of successive terms, to
--  demonstrate the 1.618...^n growth (the ratio approaches the golden
--  ratio, (1 + sqrt(5))/2 = 1.6180339887498949, and reaches it (to
--  machine precision) at 41 terms: the fourth item on each line is
--  the difference from the golden ratio).
--  [04-May-2006]
--  ====================================================================

function printf(...)
 io.write(string.format(...))
end

golden_ratio = (1.0 + math.sqrt(5.0))/2.0

lo = 1
hi = 1
n = 1
printf("%5d\t%d\n", n, lo)
limit =  2^52 + (2^52 - 1)
while (hi < limit) do
    n = n + 1
    ratio = hi/lo
    printf("%5d\t%16.0f\t%.15f\t%.15f\n", n, hi, ratio, (ratio - golden_ratio))
    hi = lo + hi
    lo = hi - lo
end