def msum(iterable):
"""Full precision summation. Compute sum(iterable) without any
intermediate accumulation of error. Based on the 'lsum' function
at http://code.activestate.com/recipes/393090/
"""
tmant, texp = 0, 0
for x in iterable:
mant, exp = math.frexp(x)
mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
if texp > exp:
tmant <<= texp-exp
texp = exp
else:
mant <<= exp-texp
tmant += mant
# Round tmant * 2**texp to a float. The original recipe
# used float(str(tmant)) * 2.0**texp for this, but that's
# a little unsafe because str -> float conversion can't be
# relied upon to do correct rounding on all platforms.
tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
if tail > 0:
h = 1 << (tail-1)
tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
texp += tail
return math.ldexp(tmant, texp)
def msum(iterable):
"""Full precision summation. Compute sum(iterable) without any
intermediate accumulation of error. Based on the 'lsum' function
at http://code.activestate.com/recipes/393090/
"""
tmant, texp = 0, 0
for x in iterable:
mant, exp = math.frexp(x)
mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
if texp > exp:
tmant <<= texp-exp
texp = exp
else:
mant <<= exp-texp
tmant += mant
# Round tmant * 2**texp to a float. The original recipe
# used float(str(tmant)) * 2.0**texp for this, but that's
# a little unsafe because str -> float conversion can't be
# relied upon to do correct rounding on all platforms.
tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
if tail > 0:
h = 1 << (tail-1)
tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
texp += tail
return math.ldexp(tmant, texp)
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
###self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
###self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
###self.assertEqual(math.ldexp(1., -1000000), 0.)
###self.assertEqual(math.ldexp(-1., -1000000), -0.)
self.assertEqual(math.ldexp(INF, 30), INF)
self.assertEqual(math.ldexp(NINF, -213), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEqual(math.ldexp(INF, -n), INF)
self.assertEqual(math.ldexp(NINF, -n), NINF)
###self.assertEqual(math.ldexp(1., -n), 0.)
###self.assertEqual(math.ldexp(-1., -n), -0.)
self.assertEqual(math.ldexp(0., -n), 0.)
self.assertEqual(math.ldexp(-0., -n), -0.)
self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
###self.assertRaises(OverflowError, math.ldexp, 1., n)
###self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEqual(math.ldexp(0., n), 0.)
self.assertEqual(math.ldexp(-0., n), -0.)
self.assertEqual(math.ldexp(INF, n), INF)
self.assertEqual(math.ldexp(NINF, n), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, n)))
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
self.assertTrue(math.ldexp(1.0,100000)>0)
self.assertTrue(math.ldexp(-1.0,100000)<0)
#cf don't return +-0 for big numbers in ldexp function
#self.assertEquals(math.ldexp(1., -1000000), 0.)
#self.assertEquals(math.ldexp(-1., -1000000), -0.)
self.assertEquals(math.ldexp(INF, 30), INF)
self.assertEquals(math.ldexp(NINF, -213), NINF)
self.assert_(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEquals(math.ldexp(INF, -n), INF)
self.assertEquals(math.ldexp(NINF, -n), NINF)
#cf doesn't return 0/-0
#self.assertEquals(math.ldexp(1., -n), 0.)
#self.assertEquals(math.ldexp(-1., -n), -0.)
self.assertEquals(math.ldexp(0., -n), 0.)
self.assertEquals(math.ldexp(-0., -n), -0.)
self.assert_(math.isnan(math.ldexp(NAN, -n)))
#cf doesn't raise exceptions
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEquals(math.ldexp(0., n), 0.)
self.assertEquals(math.ldexp(-0., n), -0.)
self.assertEquals(math.ldexp(INF, n), INF)
self.assertEquals(math.ldexp(NINF, n), NINF)
self.assert_(math.isnan(math.ldexp(NAN, n)))
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
#self.assertEqual(math.ldexp(1., -1000000), 0.)
#self.assertEqual(math.ldexp(-1., -1000000), -0.)
self.assertEqual(math.ldexp(INF, 30), INF)
self.assertEqual(math.ldexp(NINF, -213), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEqual(math.ldexp(INF, -n), INF)
self.assertEqual(math.ldexp(NINF, -n), NINF)
#self.assertEqual(math.ldexp(1., -n), 0.)
#self.assertEqual(math.ldexp(-1., -n), -0.)
self.assertEqual(math.ldexp(0., -n), 0.)
self.assertEqual(math.ldexp(-0., -n), -0.)
self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEqual(math.ldexp(0., n), 0.)
self.assertEqual(math.ldexp(-0., n), -0.)
self.assertEqual(math.ldexp(INF, n), INF)
self.assertEqual(math.ldexp(NINF, n), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, n)))
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0, 1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1, 1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1, -1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1, 1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
self.assertTrue(math.ldexp(1.0, 100000) > 0)
self.assertTrue(math.ldexp(-1.0, 100000) < 0)
#cf don't return +-0 for big numbers in ldexp function
#self.assertEquals(math.ldexp(1., -1000000), 0.)
#self.assertEquals(math.ldexp(-1., -1000000), -0.)
self.assertEquals(math.ldexp(INF, 30), INF)
self.assertEquals(math.ldexp(NINF, -213), NINF)
self.assert_(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEquals(math.ldexp(INF, -n), INF)
self.assertEquals(math.ldexp(NINF, -n), NINF)
#cf doesn't return 0/-0
#self.assertEquals(math.ldexp(1., -n), 0.)
#self.assertEquals(math.ldexp(-1., -n), -0.)
self.assertEquals(math.ldexp(0., -n), 0.)
self.assertEquals(math.ldexp(-0., -n), -0.)
self.assert_(math.isnan(math.ldexp(NAN, -n)))
#cf doesn't raise exceptions
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEquals(math.ldexp(0., n), 0.)
self.assertEquals(math.ldexp(-0., n), -0.)
self.assertEquals(math.ldexp(INF, n), INF)
self.assertEquals(math.ldexp(NINF, n), NINF)
self.assert_(math.isnan(math.ldexp(NAN, n)))
