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Link: http://codepad.org/28to7lOE    [ raw code | output | fork ]

Python, pasted on Nov 2: 
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def fib1(n):
  def fib_inner(n):
    '''Returns F[n] and L[n]'''
    if n == 0:
      return 0, 2
    m = n >> 1
    u, v = fib_inner(m)
    q = -2 if (m & 1) == 1 else 2
    u, v = u * v, v * v - q
    if n & 1 == 1:
      u1 = (u + v) >> 1
      return u1, 2*u + u1
    else:
      return u, v

  if n <= 0:
    return 0
  m = n >> 1
  u, v = fib_inner(m)
  if (n & 1) == 1:
    u1 = (u + v) >> 1
    return u*u + u1*u1
  else:
    return u * v

def fib2(n):
  def fib_inner(n):
    '''Returns F[n] and F[n+1]'''
    if n == 0:
      return 0, 1
    m = n >> 1
    u, v = fib_inner(m)
    if (n & 1) == 1:
      return u*u + v*v, v * (2*u + v)
    else:
      return u * (2*v - u), u*u + v*v

  if n <= 0:
    return 0
  m = n >> 1
  u, v = fib_inner(m)
  if (n & 1) == 1:
    return u*u + v*v
  else:
    return u * (2*v - u)

def fib3(n):
  def fib_inner(n):
    '''Returns F[n-1] and F[n]'''
    if n == 0:
      return 1, 0
    m = n >> 1
    u, v = fib_inner(m)
    if (n & 1) == 1:
      return v * (2*u + v), u*u + 2*v*(u + v)
    else:
      return u*u + v*v, v * (2*u + v)

  if n <= 0:
    return 0
  m = n >> 1
  u, v = fib_inner(m)
  if (n & 1) == 1:
    return u*u + 2*v*(u + v)
  else:
    return v * (2*u + v)

def fib4(n):
  def fib_inner(n):
    '''Returns F[n] and F[n+1]'''
    if n == 0:
      return 0, 1
    m = n / 3
    u, v = fib_inner(m)
    q = -3 if (m & 1) == 1 else 3
    if n%3 == 0:
      return u*(5*u*u + q), v*v*v + u*u*(3*v - u),
    if n%3 == 1:
      return v*v*v + u*u*(3*v - u), v*v*(v + 3*u) + u*u*u
    else:
      return v*v*(v + 3*u) + u*u*u, v*(5*v*v - q)

  if n <= 0:
    return 0
  m = n / 3
  u, v = fib_inner(m)
  q = -3 if (m & 1) == 1 else 3
  if n%3 == 0:
    return u*(5*u*u + q)
  if n%3 == 1:
    return v*v*v + u*u*(3*v - u)
  else:
    return v*v*(v + 3*u) + u*u*u

from timeit import timeit

runs = 10
for test in ['fib1', 'fib2', 'fib3', 'fib4']:
  print test, 'small values:',
  print timeit(
    setup = 'from __main__ import %s'%test,
    stmt  = 'for n in range(10000): %s(n)'%test,
    number = runs)/runs, 'secs per run'

  print test, 'large values:',
  print timeit(
    setup = "from __main__ import %s\n"%test +
            "from random import seed, randint\n" +
            "seed('fibonacci')",
    stmt  = '%s(randint(1000000, 2000000))'%test,
    number = runs)/runs, 'secs per value'

  print


Output: 
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Traceback (most recent call last):
  Line 95, in <module>
    from timeit import timeit
ImportError: cannot import name timeit


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