### -*-hoc-*-
### ====================================================================
### 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).
### [19-Apr-2002]
### ====================================================================
golden_ratio := (1.0 + sqrt(5.0))/2.0
lo = hi = n = 1
println n, "\t", lo
limit = 2^52 + (2^52 - 1)
while (hi < limit) \
{
n++
ratio = hi/lo
println n, "\t", hi, "\t", ratio, "\t", (ratio - golden_ratio)
hi = lo + hi
lo = hi - lo
}