Data commit

Task/Continued-fraction/Python/continued-fraction-1.py

@@ -0,0 +1,67 @@
+from fractions import Fraction
+import itertools
+try: zip = itertools.izip
+except: pass
+
+# The Continued Fraction
+def CF(a, b, t):
+  terms = list(itertools.islice(zip(a, b), t))
+  z = Fraction(1,1)
+  for a, b in reversed(terms):
+    z = a + b / z
+  return z
+
+# Approximates a fraction to a string
+def pRes(x, d):
+  q, x = divmod(x, 1)
+  res = str(q)
+  res += "."
+  for i in range(d):
+    x *= 10
+    q, x = divmod(x, 1)
+    res += str(q)
+  return res
+
+# Test the Continued Fraction for sqrt2
+def sqrt2_a():
+  yield 1
+  for x in itertools.repeat(2):
+    yield x
+
+def sqrt2_b():
+  for x in itertools.repeat(1):
+    yield x
+
+cf = CF(sqrt2_a(), sqrt2_b(), 950)
+print(pRes(cf, 200))
+#1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
+
+
+# Test the Continued Fraction for Napier's Constant
+def Napier_a():
+  yield 2
+  for x in itertools.count(1):
+    yield x
+
+def Napier_b():
+  yield 1
+  for x in itertools.count(1):
+    yield x
+
+cf = CF(Napier_a(), Napier_b(), 950)
+print(pRes(cf, 200))
+#2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193200305992181741359662904357290033429526059563073813232862794349076323382988075319525101901
+
+# Test the Continued Fraction for Pi
+def Pi_a():
+  yield 3
+  for x in itertools.repeat(6):
+    yield x
+
+def Pi_b():
+  for x in itertools.count(1,2):
+    yield x*x
+
+cf = CF(Pi_a(), Pi_b(), 950)
+print(pRes(cf, 10))
+#3.1415926532

Task/Continued-fraction/Python/continued-fraction-2.py

@@ -0,0 +1,24 @@
+from decimal import Decimal, getcontext
+
+def calc(fun, n):
+    temp = Decimal("0.0")
+
+    for ni in xrange(n+1, 0, -1):
+        (a, b) = fun(ni)
+        temp = Decimal(b) / (a + temp)
+
+    return fun(0)[0] + temp
+
+def fsqrt2(n):
+    return (2 if n > 0 else 1, 1)
+
+def fnapier(n):
+    return (n if n > 0 else 2, (n - 1) if n > 1 else 1)
+
+def fpi(n):
+    return (6 if n > 0 else 3, (2 * n - 1) ** 2)
+
+getcontext().prec = 50
+print calc(fsqrt2, 200)
+print calc(fnapier, 200)
+print calc(fpi, 200)