### -*-bc-*-
### ====================================================================
### 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]
### ====================================================================

### bc supports arbitrary precision floating-point arithmetic.  For
### comparison with other programming languages, we limit it to 
### 64-bit arithmetic: log10(2^64) = 19.2659..., so we set scale = 20
scale = 20
golden_ratio = (1 + sqrt(5))/2
limit =  2^63 - 1

lo = hi = n = 1
print n, "\t", lo, "\n"

while (hi < limit)
{
    n = n + 1
    ratio = hi/lo
    scale = 0
    print n, "\t", hi, "\t"
    scale = 20
    print ratio, "\t", (ratio - golden_ratio), "\n"
    hi = lo + hi
    lo = hi - lo
}