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# fibonacci.py

"""

1. Calculates the iterative fibonacci sequence

2. Calculates the fibonacci sequence with a formula

an = [ Phin - (phi)n ]/Sqrt[5]

reference-->Su, Francis E., et al. "Fibonacci Number Formula." Math Fun Facts.

<http://www.math.hmc.edu/funfacts>

"""

import functools

import math

import time

from decimal import Decimal, getcontext

getcontext().prec = 100

def timer_decorator(func):

@functools.wraps(func)

def timer_wrapper(*args, **kwargs):

start = time.time()

func(*args, **kwargs)

end = time.time()

if int(end - start) > 0:

print(f"Run time for {func.__name__}: {(end - start):0.2f}s")

else:

print(f"Run time for {func.__name__}: {(end - start)*1000:0.2f}ms")

return func(*args, **kwargs)

return timer_wrapper

# define Python user-defined exceptions

class Error(Exception):

"""Base class for other exceptions"""

class ValueTooLargeError(Error):

"""Raised when the input value is too large"""

class ValueTooSmallError(Error):

"""Raised when the input value is not greater than one"""

class ValueLessThanZero(Error):

"""Raised when the input value is less than zero"""

def _check_number_input(n, min_thresh, max_thresh=None):

"""

:param n: single integer

:type n: int

:param min_thresh: min threshold, single integer

:type min_thresh: int

:param max_thresh: max threshold, single integer

:type max_thresh: int

:return: boolean

"""

try:

if n >= min_thresh and max_thresh is None:

return True

elif min_thresh <= n <= max_thresh:

return True

elif n < 0:

raise ValueLessThanZero

elif n < min_thresh:

raise ValueTooSmallError

elif n > max_thresh:

raise ValueTooLargeError

except ValueLessThanZero:

print("Incorrect Input: number must not be less than 0")

except ValueTooSmallError:

print(

f"Incorrect Input: input number must be > {min_thresh} for the recursive "

"calculation"

)

except ValueTooLargeError:

print(

f"Incorrect Input: input number must be < {max_thresh} for the recursive "

"calculation"

)

return False

@timer_decorator

def fib_iterative(n):

"""

:param n: calculate Fibonacci to the nth integer

:type n:int

:return: Fibonacci sequence as a list

"""

n = int(n)

if _check_number_input(n, 2):

seq_out = [0, 1]

a, b = 0, 1

for _ in range(n - len(seq_out)):

a, b = b, a + b

seq_out.append(b)

return seq_out

@timer_decorator

def fib_formula(n):

"""

:param n: calculate Fibonacci to the nth integer

:type n:int

:return: Fibonacci sequence as a list

"""

seq_out = [0, 1]

n = int(n)

if _check_number_input(n, 2, 1000000):

sqrt = Decimal(math.sqrt(5))

phi_1 = Decimal(1 + sqrt) / Decimal(2)

phi_2 = Decimal(1 - sqrt) / Decimal(2)

for i in range(2, n):

temp_out = ((phi_1 ** Decimal(i)) - (phi_2 ** Decimal(i))) * (

Decimal(sqrt) ** Decimal(-1)

)

seq_out.append(int(temp_out))

return seq_out

if __name__ == "__main__":

num = 20

# print(f'{fib_recursive(num)}\n')

# print(f'{fib_iterative(num)}\n')

# print(f'{fib_formula(num)}\n')

fib_iterative(num)

fib_formula(num)