97 lines
2.2 KiB
Python
97 lines
2.2 KiB
Python
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#!/usr/bin/python3
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from collections import deque
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from itertools import count
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import decimal
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# Only for reference.
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def fibonacci(n):
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a = 1
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b = 0
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swp = 0
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for i in range(n):
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swp = a
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a += b
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b = swp
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return a
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_fibonacci_series_context_stack = deque()
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class FibonacciSeriesContext(object):
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def __init__(self):
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self._pre_calculated = {0: 1, 1: 1}
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self._biggest = 1
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def __contains__(self, other):
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return other in self._pre_calculated
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def __getitem__(self, n):
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return self._pre_calculated[n]
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def __setitem__(self, n, v):
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self._pre_calculated[n] = v
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def get_biggest_pair(self):
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return ((self._biggest - 1, self._pre_calculated[self._biggest - 1])
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, (self._biggest, self._pre_calculated[self._biggest]))
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def __enter__(self):
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_fibonacci_series_context_stack.append(self)
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return self
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def __exit__(self, *exc):
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_fibonacci_series_context_stack.pop()
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return False
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_fibonacci_series_context_stack.append(FibonacciSeriesContext())
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def getfibonacciseriescontext():
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return _fibonacci_series_context_stack[-1]
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def fast_ctx_fibonacci(n, context = getfibonacciseriescontext()):
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if(n in context):
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return context[n]
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(n_start_minus_one, b), (n_start, a) = context.get_biggest_pair()
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for i in range(n_start, n):
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swp = a
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a += b
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b = swp
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context[n] = a
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return a
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if( __name__ == "__main__"):
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decimal.getcontext().prec = 5
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golden_ratio = decimal.Decimal((1 + decimal.Decimal(5).sqrt()) / 2)
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print("Seeking n, such that F(n + 1) / F(n) = ", golden_ratio)
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print("Precision is 1e-5.")
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# Try to approximate the result faster using big steps first.
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# At first try steps of 100. This way we can approximate an interval
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# with width 100 where we do the fine approximation.
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for i in count(1, 100):
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if(fast_ctx_fibonacci(i) / decimal.Decimal(fast_ctx_fibonacci(i - 1)) == golden_ratio):
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break
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n_stop = i
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n_start = n_stop - 101
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print("Found that n is in range({}, {})".format(n_start, n_stop))
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for i in range(n_start, n_stop):
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if(fast_ctx_fibonacci(i) / decimal.Decimal(fast_ctx_fibonacci(i - 1)) == golden_ratio):
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break
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n = i + 1
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print("n = ", n)
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print("F(n + 1) / F(n) = %0.6g" % (fast_ctx_fibonacci(n + 1) / fast_ctx_fibonacci(n)))
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