def test_fifth(self):
"Nearest rounding of 1/5 is upwards."
from operator import truediv
assert 1 / 5.0 == fpu.up (lambda: truediv(1.0, 5.0))
assert 1 / 5.0 > fpu.down(lambda: truediv(1.0, 5.0))
assert -1 / 5.0 == fpu.down(lambda: truediv(1.0, -5.0))
assert -1 / 5.0 < fpu.up (lambda: truediv(1.0, -5.0))
def test_fourth(self):
" 1/4 is exact."
from operator import truediv
assert 1 / 4.0 == fpu.down(lambda: truediv(1.0, 4.0))
assert 1 / 4.0 == fpu.up (lambda: truediv(1.0, 4.0))
assert -1 / 4.0 == fpu.up (lambda: truediv(1.0, -4.0))
assert -1 / 4.0 == fpu.down(lambda: truediv(1.0, -4.0))
def test_third(self):
"Nearest rounding of 1/3 is downwards."
from operator import truediv
assert 1 / 3.0 == fpu.down(lambda: truediv(1.0, 3.0))
assert 1 / 3.0 < fpu.up (lambda: truediv(1.0, 3.0))
assert -1 / 3.0 == fpu.up (lambda: truediv(1.0, -3.0))
assert -1 / 3.0 > fpu.down(lambda: truediv(1.0, -3.0))
def test_power(self):
x = 1 / 3.0
# The cube of one third should depend on the rounding mode
assert fpu.down(lambda: x * x * x) < fpu.up(lambda: x * x * x)
# But using the built-in power operator, it doesn't necessarily do it
# fpu.down(lambda: x ** 3) < fpu.up(lambda: x ** 3))
# So we define an integer power methods that does
assert fpu.power_rd( x, 3) < fpu.power_ru( x, 3)
assert fpu.power_rd(-x, 3) < fpu.power_ru(-x, 3)
assert fpu.power_rd( x, 4) < fpu.power_ru( x, 4)
assert fpu.power_rd(-x, 4) < fpu.power_ru(-x, 4)
assert (fpu.down(lambda: x * x * x), fpu.up(lambda: x * x * x)) == (fpu.power_rd(x, 3), fpu.power_ru(x, 3))
def test_power(self):
self.assertRaises(TypeError, lambda: interval[1, 2] ** (1.3))
self.assertEqual((-interval[1, 2]).inverse(), (-interval[1, 2]) ** -1)
self.assertEqual(interval[0, 4], interval[-1, 2] ** 2)
self.assertEqual(interval[-27, 8], interval[-3, 2] ** 3)
self.assertEqual(interval[-1, 2], (interval[-1,2]**-1)**-1)
self.assertEqual(interval([-0.38712442133802405]) ** 3, interval([-0.058016524353106828, -0.058016524353106808]))
self.assertEqual(
interval[fpu.down(lambda: (1/3.0)*(1/3.0)), fpu.up(lambda: (1/3.0)*(1/3.0))],
(interval[1]/3.0) ** 2)
self.assertEqual(
interval[fpu.down(lambda: (1/3.0)*(1/3.0)*(1/3.0)), fpu.up(lambda: (1/3.0)*(1/3.0)*(1/3.0))],
(interval[1]/3.0) ** 3)
def test_power(self):
self.assertRaises(TypeError, lambda: interval[1, 2] ** (1.3))
assert (-interval[1, 2]).inverse() == (-interval[1, 2]) ** -1
assert interval[0, 4] == interval[-1, 2] ** 2
assert interval[-27, 8] == interval[-3, 2] ** 3
assert interval[-1, 2] == (interval[-1, 2] ** -1) ** -1
assert interval([-0.38712442133802405]) ** 3 == interval([-0.058016524353106828, -0.058016524353106808])
from operator import truediv
assert (
interval[
fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0)),
fpu.up (lambda: truediv(1, 3.0) * truediv(1, 3.0))] ==
(interval[1] / 3.0) ** 2)
assert (
interval[
fpu.down(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0)),
fpu.up(lambda: truediv(1, 3.0) * truediv(1, 3.0) * truediv(1, 3.0))] ==
(interval[1] / 3.0) ** 3)
def measure(x):
from interval import fpu
return fpu.up(lambda: sum((c.sup - c.inf for c in x), 0))
def test_fifth(self):
"Nearest rounding of 1/5 is upwards."
self.assertEqual(1/5.0, fpu.up(lambda: 1.0 / 5.0))
self.assertTrue(1/5.0 > fpu.down(lambda: 1.0 / 5.0))
self.assertEqual(-1/5.0, fpu.down(lambda: 1.0 / -5.0))
self.assertTrue(-1/5.0 < fpu.up(lambda: 1.0 / -5.0))
def test_fourth(self):
" 1/4 is exact."
self.assertEqual(1/4.0, fpu.down(lambda: 1.0 / 4.0))
self.assertEqual(1/4.0, fpu.up(lambda: 1.0 / 4.0))
self.assertEqual(-1/4.0, fpu.up(lambda: 1.0 / -4.0))
self.assertEqual(-1/4.0, fpu.down(lambda: 1.0 / -4.0))
def test_third(self):
"Nearest rounding of 1/3 is downwards."
self.assertEqual(1/3.0, fpu.down(lambda: 1.0 / 3.0))
self.assertTrue(1/3.0 < fpu.up(lambda: 1.0 / 3.0))
self.assertEqual(-1/3.0, fpu.up(lambda: 1.0 / -3.0))
self.assertTrue(-1/3.0 > fpu.down(lambda: 1.0 / -3.0))
def measure(x):
"""See https://github.com/taschini/pyinterval/issues/2"""
return int(fpu.up(lambda: sum((c.sup - c.inf for c in x), 0)))