I'm trying to continue on my previous question in which I'm trying to calculate Fibonacci numbers using Benet's algorithm. To work with arbitrary precision I found mpmath. However the implementation seems to fail above certain value. For instance the 99th value gives:
218922995834555891712
This should be (ref):
218922995834555169026
Here is my code:
from mpmath import *
def Phi():
return (1 + sqrt(5)) / 2
def phi():
return (1 - sqrt(5)) / 2
def F(n):
return (power(Phi(), n) - power(phi(), n)) / sqrt(5)
start = 99
end = 100
for x in range(start, end):
print(x, int(F(x)))
mpmath provides arbitrary precision (as set in mpmath.mp.dps), but still inaccuate calculation. For example, mpmath.sqrt(5) is not accurate, so any calculation based on that will also be inaccurate.
To get an accurate result for sqrt(5), you have to use a library which supports abstract calculation, e.g. http://sympy.org/ .
To get an accurate result for Fibonacci numbers, probably the simplest way is using an algorithm which does only integer arithmetics. For example:
def fib(n):
if n < 0:
raise ValueError
def fib_rec(n):
if n == 0:
return 0, 1
else:
a, b = fib_rec(n >> 1)
c = a * ((b << 1) - a)
d = b * b + a * a
if n & 1:
return d, c + d
else:
return c, d
return fib_rec(n)[0]
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