fib.awk


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#!/usr/bin/awk -f

### fib.awk
# print nth Fibonacci number, based on R. Hamming's solution to a diff eqn
# form of the sequence


BEGIN {
    ARGV[1] ? n = ARGV[1] : n = 0
    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"

    # fib sol'n from Hamming
    C1 = 1.0/sqrt(5.0)
    C2 = -1.0/sqrt(5.0)
    print C1*(0.5*(1 + sqrt(5.0)))^n + C2*(0.5*(1 - sqrt(5.0)))^n

    phi = 0.5*(1 + sqrt(5.0))
    binet = (phi^n - (-1.0/phi)^n)/sqrt(5.0)
    print binet
}