Added gauss() (same as normal but twice as fast) and betavariate();

print more statistics in test_generator()

diff --git a/Lib/random.py b/Lib/random.py
index 51ecb329954638c0687b0350883024f1bad29d57..1fa13773c9278e5adcb39854ab2ed6747ea2b1f9 100644 (file)
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -6,6 +6,7 @@
 #             lognormal
 #             negative exponential
 #             gamma
+#             beta
 #
 #      distributions on the circle (angles 0 to 2pi)
 #      ---------------------------------------------
@@ -15,7 +16,7 @@
 # Translated from anonymously contributed C/C++ source.
 
 from whrandom import random, uniform, randint, choice # Also for export!
-from math import log, exp, pi, e, sqrt, acos, cos
+from math import log, exp, pi, e, sqrt, acos, cos, sin
 
 # Housekeeping function to verify that magic constants have been
 # computed correctly
@@ -172,6 +173,37 @@ def stdgamma(alpha, ainv, bbb, ccc):
                                break
                return x
 
+
+# -------------------- Gauss (faster alternative) --------------------
+
+# When x and y are two variables from [0, 1), uniformly distributed, then
+#
+#    cos(2*pi*x)*log(1-y)
+#    sin(2*pi*x)*log(1-y)
+#
+# are two *independent* variables with normal distribution (mu = 0, sigma = 1).
+# (Lambert Meertens)
+
+gauss_next = None
+def gauss(mu, sigma):
+       global gauss_next
+       if gauss_next != None:
+               z = gauss_next
+               gauss_next = None
+       else:
+               x2pi = random() * TWOPI
+               log1_y = log(1.0 - random())
+               z = cos(x2pi) * log1_y
+               gauss_next = sin(x2pi) * log1_y
+       return mu + z*sigma
+
+# -------------------- beta --------------------
+
+def betavariate(alpha, beta):
+       y = expovariate(alpha)
+       z = expovariate(1.0/beta)
+       return z/(y+z)
+
 # -------------------- test program --------------------
 
 def test():
@@ -179,7 +211,7 @@ def test():
        print 'LOG4          =', LOG4
        print 'NV_MAGICCONST =', NV_MAGICCONST
        print 'SG_MAGICCONST =', SG_MAGICCONST
-       N = 100
+       N = 200
        test_generator(N, 'random()')
        test_generator(N, 'normalvariate(0.0, 1.0)')
        test_generator(N, 'lognormvariate(0.0, 1.0)')
@@ -192,21 +224,30 @@ def test():
        test_generator(N, 'gammavariate(2.0, 1.0)')
        test_generator(N, 'gammavariate(20.0, 1.0)')
        test_generator(N, 'gammavariate(200.0, 1.0)')
+       test_generator(N, 'gauss(0.0, 1.0)')
+       test_generator(N, 'betavariate(3.0, 3.0)')
 
 def test_generator(n, funccall):
-       import sys
-       print '%d calls to %s:' % (n, funccall),
-       sys.stdout.flush()
+       import time
+       print n, 'times', funccall
        code = compile(funccall, funccall, 'eval')
        sum = 0.0
        sqsum = 0.0
+       smallest = 1e10
+       largest = 1e-10
+       t0 = time.time()
        for i in range(n):
                x = eval(code)
                sum = sum + x
                sqsum = sqsum + x*x
+               smallest = min(x, smallest)
+               largest = max(x, largest)
+       t1 = time.time()
+       print round(t1-t0, 3), 'sec,', 
        avg = sum/n
        stddev = sqrt(sqsum/n - avg*avg)
-       print 'avg %g, stddev %g' % (avg, stddev)
+       print 'avg %g, stddev %g, min %g, max %g' % \
+                 (avg, stddev, smallest, largest)
 
 if __name__ == '__main__':
        test()