added gauss legendre algorithm

AVD087 · Apr 26, 2017 · e0c549e · e0c549e
1 parent c48e5f1
commit e0c549e
Showing 1 changed file with 23 additions and 0 deletions.
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)