Initial commit. Most formulas retrieved from Wikipedia.com

.project

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<?xml version="1.0" encoding="UTF-8"?>
<projectDescription>
	<name>FibonacciFun</name>
	<comment></comment>
	<projects>
	</projects>
	<buildSpec>
		<buildCommand>
			<name>org.python.pydev.PyDevBuilder</name>
			<arguments>
			</arguments>
		</buildCommand>
	</buildSpec>
	<natures>
		<nature>org.python.pydev.pythonNature</nature>
	</natures>
</projectDescription>

.pydevproject

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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<?eclipse-pydev version="1.0"?>
<pydev_project>
<pydev_property name="org.python.pydev.PYTHON_PROJECT_INTERPRETER">Default</pydev_property>
<pydev_property name="org.python.pydev.PYTHON_PROJECT_VERSION">python 2.7</pydev_property>
<pydev_pathproperty name="org.python.pydev.PROJECT_SOURCE_PATH">
<path>/FibonacciFun/src</path>
</pydev_pathproperty>
</pydev_project>

run.bat

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@echo off
set PATH=C:\Python27
%PATH%\python.exe src/Main.py

run.sh

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#!/bin/sh
python src/Main.py

src/FibonacciBinet.py

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from math import log
phi = (1 + 5 ** 0.5) / 2
def fib(n):
    '''
    Find the Fibonacci number using Binet's formula.
    '''
    
    return int(round((phi ** n - (1 - phi) ** n) / 5 ** 0.5))
def fibinv(f):
    '''
    Inverse Fibonacci function using Binet's formula.
    '''
    
    if f < 2:
        return
    
    return int(round(log(f * 5 ** 0.5) / log(phi)))

src/FibonacciDjikstra.py

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fibs = {0: 0, 1: 1}
def fib(n):
    '''
    Find the Fibonacci number using the Djikstra method.
    '''
    
    if n in fibs:
        return fibs[n]
    elif n % 2 == 0:
        fibs[n] = ((2 * fib((n / 2) - 1)) + fib(n / 2)) * fib(n / 2)
        return fibs[n]
    else:
        fibs[n] = (fib((n - 1) / 2) ** 2) + (fib((n + 1) / 2) ** 2)
        return fibs[n]

src/FibonacciGenerator.py

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def fib():
    '''
    Generate each Fibonacci number in an infinite loop.
    '''
    
    a, b = 0, 1
    
    while 1:
        yield a
        a, b = b, a + b

src/FibonacciIteration.py

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def fib(n):
    '''
    Find the Fibonacci number using iteration.
    '''
    
    a, b = 0, 1
    
    for i in range(n):
        a, b = b, a + b
    
    return a

src/FibonacciLucas.py

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def powLF(n):
    if n == 1:
        return (1, 1)
    
    L, F = powLF(n // 2)
    L, F = (L ** 2 + 5 * F ** 2) >> 1, L*F
    
    if n & 1:
        return ((L + 5 * F) >> 1, (L + F) >> 1)
    
    return (L, F)
def fib(n):
    '''
    Find the Fibonacci number using Lucas numbers.
    '''
    
    if n & 1:
        return powLF(n)[1]
    else:
        L, F = powLF(n // 2)
        return L * F 

src/FibonacciMatrix.py

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def mul(A, B):
    a, b, c = A
    d, e, f = B
    
    return a*d + b*e, a*e + b*f, b*e + c*f
def pow(A, n):
    if n == 1:
        return A
    elif n & 1 == 0:
        return pow(mul(A, A), n//2)
    else:
        return mul(A, pow(mul(A, A), (n - 1)//2))
def fib(n):
    '''
    Find the Fibonacci number using a matrix.
    '''
    
    if n < 2:
        return n
    
    return pow((1, 1, 0), n - 1)[0]

src/FibonacciMemory.py

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memory = {0: 0, 1: 1}
def fib(n):
    '''
    Find the Fibonacci number with the help of cached results.
    '''
    
    if not n in memory:
        memory[n] = fib(n - 1) + fib(n - 2)
    
    return memory[n]

src/FibonacciRecursive.py

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def fib(n):
    '''
    Find the Fibonacci number using a recursive function.
    '''
    
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        return fib(n - 1) + fib(n - 2)

src/Main.py

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#!/usr/bin/python
'''
Created on Jun 10, 2011
@author: BMAllred
'''
import FibonacciBinet
import FibonacciDjikstra
import FibonacciGenerator
import FibonacciIteration
import FibonacciLucas
import FibonacciMatrix
import FibonacciMemory
import FibonacciRecursive
from StopWatch import StopWatch
def displayMenu():
    stopWatch = StopWatch()
    
    while True:
        print
        print "Fun with Fibonacci!!!"
        print
        print "Select your poison:"
        print
        print "\t1. Binet's formula"
        print "\t2. Djikstra's method"
        print "\t3. Iteration"
        print "\t4. Lucas' numbers"
        print "\t5. Matrix"
        print "\t6. Memory"
        print "\t7. Recursive (intensive)"
        print "\t-------------------------"
        print "\t0. Exit"
        print
        
        # Retrieve the user menu choice.
        choice = raw_input("Option: ")
        
        # Exit early if at all possible.
        if choice == "0":
            break
        
        # Let the user pick which number to find.
        n = -1
        while n < 0:
            n = int(raw_input("Number: "))
        
        # Start the timer.
        stopWatch.Start()
        answer = "Not available."
        
        try:
            # Perform the necessary method.
            if choice == "1":
                answer = FibonacciBinet.fib(n)
            elif choice == "2":
                answer = FibonacciDjikstra.fib(n)
            elif choice == "3":
                answer = FibonacciIteration.fib(n)
            elif choice == "4":
                answer = FibonacciLucas.fib(n)
            elif choice == "5":
                answer = FibonacciMatrix.fib(n)
            elif choice == "6":
                answer = FibonacciMemory.fib(n)
            elif choice == "7":
                answer = FibonacciRecursive.fib(n)
        except:
            pass
        
        # Stop the timer.
        stopWatch.Stop()
        
        # Give the user some feedback and statistics.
        print
        print "Answer:\t\t{0}".format(answer)
        print "Time Elapsed:\t{0}".format(stopWatch.TimeElapsed())
        print
        
        # Prepare the stop watch for the next iteration.
        stopWatch.Reset()
        
        raw_input("Press ENTER to continue...")
    
    print
    print "Hope you had as much as I did!"
    print
if __name__ == '__main__':
    displayMenu()

src/StopWatch.py

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'''
Created on Jun 10, 2011
@author: BMAllred
'''
import time
class StopWatch(object):
    '''
    Stop watch object.
    '''
    def __init__(self):
        '''
        Initializes a new instance of the StopWatch class.
        '''
        
        self.StartTime = None
        self.StopTime = None
    
    def Start(self):
        self.StartTime = time.clock()
        self.StopTime = None
        
        return self.StartTime
    
    def Stop(self):
        self.StopTime = time.clock()
    
    def TimeElapsed(self):
        
        if self.StartTime is None:
            return -1
        elif self.StopTime is None:
            return time.clock() - self.StartTime
        
        return self.StopTime - self.StartTime
    
    def Reset(self):
        self.StartTime = None
        self.StopTime = None