added gauss legendre algorithm

nickolaswiebe · nickolaswiebe · commit e0c549ee50b3 · 2017-04-26T15:19:53.000-05:00
diff --git a/math/gauss_legendre.py b/math/gauss_legendre.py
@@ -0,0 +1,23 @@
+from decimal import *
+
+"""
+Gauss-Legendre algorithm for calculating pi
+the number of correct bits generated doubles with each extra iteration
+"""
+def gauss_legendre(bits, iterations):
+	with localcontext() as ctx:
+		ctx.prec = bits # set decimal precision
+
+		a = 1
+		b = Decimal(1) / Decimal(2).sqrt()
+		t = Decimal(1) / Decimal(4)
+		p = 1
+
+		for _ in xrange(iterations):
+			a_new = (a + b) / 2
+			b = (a * b).sqrt()
+			t -= p * (a - a_new) ** 2
+			p *= 2
+			a = a_new
+
+		return ((a + b) ** 2) / (4 * t)
