Data update

Task/Fibonacci-sequence/Python/fibonacci-sequence-2.py

@@ -1,8 +1,28 @@
-def fibIter(n):
-    if n < 2:
-        return n
-    fibPrev = 1
-    fib = 1
-    for _ in range(2, n):
-        fibPrev, fib = fib, fib + fibPrev
-    return fib
+def analytic_fibonacci91(m):
+	"""
+	Binet's algebraic formula for the nth Fibonacci number.
+	Good for up to n=91
+	Uses numpy longdoubles:
+
+	See: https://artofproblemsolving.com/wiki/index.php/Binet%27s_Formula
+	"""
+
+    import numpy as np
+    assert isinstance(m,int), "parameter must be an integer."
+    assert 0<=m<=91 , "n must be in the range 0 .. 91 due to double precision floating point precision limitations."
+    if m < 2: return m
+    # Make sure that nothing causes conversion to single
+    n=np.longdouble(m)
+    C1=np.longdouble(1)
+    C2=np.longdouble(2)
+    C5=np.longdouble(5)
+    Chalf=C1/C2
+    Cfifth=C1/C5
+    root5=C5**Chalf
+    t1=(C1+root5)/C2
+    t2=(C1-root5)/C2
+    f=(t1**n-t2**n)/root5
+    return int(f+0.1)
+
+# Usage
+print(f:=[[i,analytic_fibonacci91(i)] for i in range(92)])