"""
 fib_table.py

 Generate a list of 20 Fibonacci numbers F(n)
 where the n's are 7 apart starting at 100,
 e.g. n = [100, 107, 114, ...], and output
 as a csv (comma separated values) table.

 According to http://en.wikipedia.org/wiki/Fibonacci_number,
 the series starts like this :
   n       0  1  2  3  4 ...
   fib(n)  0  1  1  2  3 ...
 where each term is the sum of the previous two.

 Running it this way will create fib_data.csv.

   $ python fib_table.py > fib_data.csv

 --- fib_data.csv ---
 n,fib
 100,354224848179261915075
 107,10284720757613717413913
 ...

 Jim Mahoney | Jan 2013 | MIT License
"""

def generate_fibs(max_n):
    """ Return list of fibonnaci numbers f[0 ... max_n]
        >>> generate_fibs(10)  # fib[0] through fib[10]
        [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
    """
    f = [0]*(max_n + 1)     # list to hold result
    (f[0], f[1]) = (0, 1)   # initial values
    for i in xrange(2, max_n + 1):
        f[i] = f[i-1] + f[i-2]
    return f

def skip_list(start, skip, length):
    """ Return list with given start, skip, and length
        >>> skip_list(10, 3, 5)
        [10, 13, 16, 19, 22]
    """
    return [start + i*skip for i in range(length)]

def print_csv(lists, names=[]):
    """ Print a table of comma-separated-values
        from the given lists, with optional column names.
        >>> print_csv([ [0,1,2], [10,11,12] ], ['a', 'b'])
        a,b
        0,10
        1,11
        2,12
    """
    if len(names) > 0:
        print ','.join(names)
    for n_line in range(len(lists[0])):
        data_line = [str(data[n_line]) for data in lists]
        print ','.join(data_line)

def main(start=100, count=20):
    n = skip_list(start, 7, count)  # [100, 107, ...]
    fibs = generate_fibs(n[-1])     # [f(0), f(1), ...]
    fibs_n = [fibs[i] for i in n]   # [f(100, f(107), ...]
    #
    ## 1st try at dealing with big numbers (i.e. fib[10000])
    ## fails for really big ones; can't convert to float.
    #fibs_n = ["{:.5g}".format(fibs[i]) for i in n]
    #
    ## 2nd try at dealing with big numbers : use log_2()
    #from math import log
    #fibs_n = [log(fibs[i], 2) for i in n]
    #
    print_csv([n, fibs_n], ['n', 'fib'])

main()

if __name__ == "__main__":
    import doctest
    doctest.testmod()