On Tuesday, March 24, 2015 at 10:51:11 AM UTC+5:30, Ian wrote: > On Mon, Mar 23, 2015 at 4:53 PM, Terry Reedy wrote: > > Iteration with caching, using a mutable default arg to keep the cache > > private and the function self-contained. This should be faster. > > > > def fib(n, _cache=[0,1]): > > '''Return fibonacci(n). > > > > _cache is initialized with base values and augmented as needed. > > ''' > > for k in range(len(_cache), n+1): > > _cache.append(_cache[k-2] + _cache[k-1]) > > return _cache[n] > > > > print(fib(1), fib(3), fib(6), fib(5)) > > # 1 2 8 5 > > Iteration in log space. On my desktop, this calculates fib(1000) in > about 9 us, fib(100000) in about 5 ms, and fib(10000000) in about 7 > seconds. > > def fib(n): > assert n >= 0 > if n == 0: > return 0 > > a = b = x = 1 > c = y = 0 > n -= 1 > > while True: > n, r = divmod(n, 2) > if r == 1: > x, y = x*a + y*b, x*b + y*c > if n == 0: > return x > b, c = a*b + b*c, b*b + c*c > a = b + c
This is rather arcane! What are the identities used above? -- https://mail.python.org/mailman/listinfo/python-list
