def test_minus_top(self):
# 2 - TOP = TOP
self.assertEqual(Interval(2) - TOP, TOP)
# TOP - 2 = TOP
self.assertEqual(TOP - Interval(2), TOP)
# TOP - TOP = TOP
self.assertEqual(TOP - TOP, TOP)
def test_mul_bottom(self):
# 2 * BOTTOM = BOTTOM
self.assertEqual(Interval(2) * BOTTOM, BOTTOM)
# BOTTOM * 2 = BOTTOM
self.assertEqual(BOTTOM * Interval(2), BOTTOM)
# BOTTOM * BOTTOM = BOTTOM
self.assertEqual(BOTTOM * BOTTOM, BOTTOM)
def test_plus_bottom(self):
# BOTTOM + BOTTOM = BOTTOM
self.assertEqual(BOTTOM + BOTTOM, BOTTOM)
# 2 + BOTTOM = BOTTOM
self.assertEqual(Interval(2) + BOTTOM, BOTTOM)
# BOTTOM + 2 = BOTTOM
self.assertEqual(BOTTOM + Interval(2), BOTTOM)
def test_div_bottom(self):
# 2 // BOTTOM = BOTTOM
self.assertEqual(Interval(2) // BOTTOM, BOTTOM)
# BOTTOM // 2 = BOTTOM
self.assertEqual(BOTTOM // Interval(2), BOTTOM)
# BOTTOM // BOTTOM = BOTTOM
self.assertEqual(BOTTOM // BOTTOM, BOTTOM)
def test_minus_bottom(self):
# 2 - BOTTOM = BOTTOM
self.assertEqual(Interval(2) - BOTTOM, BOTTOM)
# BOTTOM - 2 = BOTTOM
self.assertEqual(BOTTOM - Interval(2), BOTTOM)
# BOTTOM - BOTTOM = BOTTOM
self.assertEqual(BOTTOM - BOTTOM, BOTTOM)
def test_plus_top(self):
# TOP + TOP = TOP
self.assertEqual(TOP + TOP, TOP)
# 2 + TOP = TOP
self.assertEqual(Interval(2) + TOP, TOP)
# TOP + 2 = TOP
self.assertEqual(TOP + Interval(2), TOP)
def test_div_top(self):
# TOP // 1 = TOP
self.assertEqual(TOP // Interval(1), TOP)
# 5 // TOP = [-5,5]
self.assertEqual(Interval(5) // TOP, Interval(-5, 5))
# TOP // [1,5] = TOP
self.assertEqual(TOP // Interval(1, 5), TOP)
# [1,5] // TOP = TOP
self.assertEqual(Interval(1, 5) // TOP, Interval(-5, 5))
# [0,inf] // TOP = TOP
self.assertEqual(Interval(0, INFINITY) // TOP, TOP)
# [-inf,0] // TOP = TOP
self.assertEqual(Interval(NEG_INFINITY, 0) // TOP, TOP)
# TOP // [0,inf] = TOP
self.assertEqual(TOP // Interval(0, INFINITY), TOP)
# TOP // [-inf,0] = TOP
self.assertEqual(TOP // Interval(NEG_INFINITY, 0), TOP)
# TOP // TOP = TOP
self.assertEqual(TOP // TOP, TOP)
def test_BOTTOM_comparators(self):
self.assertEqual(BOTTOM >= Interval(1,2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM > Interval(1, 2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM <= Interval(1, 2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM < Interval(1, 2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM == Interval(1, 2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM != Interval(1, 2), BOOLEAN_BOTTOM)
self.assertEqual(BOTTOM == BOTTOM, BOOLEAN_BOTTOM)
def test_TOP_comparators(self):
self.assertEqual(TOP >= Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP > Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP <= Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP < Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP == Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP != Interval(1, 2), BOOLEAN_TOP)
self.assertEqual(TOP == TOP, BOOLEAN_TOP)
def test_div_zero(self):
# [10,20] // 0 = error
with self.assertRaises(ZeroDivisionError):
Interval(10, 20) // Interval(0)
# 1 // 0 = error
with self.assertRaises(ZeroDivisionError):
Interval(1) // Interval(0)
# [10,20] // [0,0] = error
with self.assertRaises(ZeroDivisionError):
Interval(10, 20) // Interval(0, 0)
def test_mul_top(self):
# [-inf,1] * [-1,2] = TOP
self.assertEqual(Interval(NEG_INFINITY, 1) * Interval(-1, 2), TOP)
# [-10,inf] * [-1,2] = TOP
self.assertEqual(Interval(-10, INFINITY) * Interval(-1, 2), TOP)
# 2 * TOP = TOP
self.assertEqual(Interval(2) * TOP, TOP)
# TOP * 2 = TOP
self.assertEqual(TOP * Interval(2), TOP)
# TOP * TOP = TOP
self.assertEqual(TOP * TOP, TOP)
def test_nequals_interval(self):
self.assertEqual(Interval(1, 3) != Interval(1, 3), BOOLEAN_TOP)
self.assertEqual(Interval(1, 2) != Interval(2, 3), BOOLEAN_TOP)
self.assertEqual(Interval(1, 2) != Interval(3, 5), TRUE)
def test_mul_infinity_simple(self):
# 1 * [0,inf] = [0,inf]
self.assertEqual(
Interval(1) * Interval(0, INFINITY), Interval(0, INFINITY))
# 1 * [-inf,0] = [-inf,0]
self.assertEqual(
Interval(1) * Interval(NEG_INFINITY, 0), Interval(NEG_INFINITY, 0))
# [0,inf] * 1 = [0,inf]
self.assertEqual(
Interval(0, INFINITY) * Interval(1), Interval(0, INFINITY))
# [-inf,0] * 1 = [-inf,0]
self.assertEqual(
Interval(NEG_INFINITY, 0) * Interval(1), Interval(NEG_INFINITY, 0))
# [-inf,0] * 0 = 0
self.assertEqual(Interval(NEG_INFINITY, 0) * Interval(0), Interval(0))
# [0,inf] * 0 = 0
self.assertEqual(Interval(0, INFINITY) * Interval(0), Interval(0))
# 0 * [0,inf] = 0
self.assertEqual(Interval(0) * Interval(0, INFINITY), Interval(0))
# 0 * [-inf,0] = 0
self.assertEqual(Interval(0) * Interval(NEG_INFINITY, 0), Interval(0))
# [-inf,0] * [-inf,0] = [0,inf]
self.assertEqual(
Interval(NEG_INFINITY, 0) * Interval(NEG_INFINITY, 0),
Interval(0, INFINITY))
# [0,inf] * [0,inf] = [0,inf]
self.assertEqual(
Interval(0, INFINITY) * Interval(0, INFINITY),
Interval(0, INFINITY))
# [-inf,0] * [0,inf] = [-inf,0]
self.assertEqual(
Interval(NEG_INFINITY, 0) * Interval(0, INFINITY),
Interval(NEG_INFINITY, 0))
def test_infinity_comparators_report(self):
self.assertEqual(Interval(0, INFINITY) == Interval(0, INFINITY), BOOLEAN_TOP)
self.assertEqual(Interval(NEG_INFINITY, 0) != Interval(1, INFINITY), TRUE)
self.assertEqual(Interval(0, INFINITY) > Interval(NEG_INFINITY, -1), TRUE)
self.assertEqual(Interval(0, INFINITY) >= Interval(NEG_INFINITY, 0), TRUE)
self.assertEqual(Interval(NEG_INFINITY, 0) < Interval(1, INFINITY), TRUE)
self.assertEqual(Interval(NEG_INFINITY, 0) <= Interval(0, INFINITY), TRUE)
self.assertEqual(Interval(0, INFINITY) > Interval(999999), BOOLEAN_TOP)
self.assertEqual(Interval(0, INFINITY) >= Interval(999999), BOOLEAN_TOP)
self.assertEqual(Interval(NEG_INFINITY, 0) < Interval(-999999), BOOLEAN_TOP)
self.assertEqual(Interval(NEG_INFINITY, 0) <= Interval(-999999), BOOLEAN_TOP)
def test_plus_infinity(self):
# [0,inf] + 2 = [2, inf]
self.assertEqual(
Interval(0, INFINITY) + Interval(2), Interval(2, INFINITY))
# [-inf,0] + 2 = [-inf, 2]
self.assertEqual(
Interval(NEG_INFINITY, 0) + Interval(2), Interval(NEG_INFINITY, 2))
# 1 + [0, inf] = [1,inf]
self.assertEqual(
Interval(1) + Interval(0, INFINITY), Interval(1, INFINITY))
# 1 + [-inf, 0] = [-inf,1]
self.assertEqual(
Interval(1) + Interval(NEG_INFINITY, 0), Interval(NEG_INFINITY, 1))
# [0, inf] + [-1,2] = [-1, inf]
self.assertEqual(
Interval(0, INFINITY) + Interval(-1, 2), Interval(-1, INFINITY))
# [-inf,0] + [-1,2] = [-inf, 2]
self.assertEqual(
Interval(NEG_INFINITY, 0) + Interval(-1, 2),
Interval(NEG_INFINITY, 2))
# [-10,1] + [-inf,2] = [-inf,3]
self.assertEqual(
Interval(-10, 1) + Interval(NEG_INFINITY, 2),
Interval(NEG_INFINITY, 3))
# [-10,1] + [-1,inf] = [-11,inf]
self.assertEqual(
Interval(-10, 1) + Interval(-1, INFINITY), Interval(-11, INFINITY))
# [0,inf] + [-inf,0] = TOP]
self.assertEqual(
Interval(0, INFINITY) + Interval(NEG_INFINITY, 0),
Interval(NEG_INFINITY, INFINITY))
def test_div_around_zero(self):
# [1,10] // [-2,2] = [-10, 10]
self.assertEqual(Interval(1, 10) // Interval(-2, 2), Interval(-10, 10))
# [-10,1] // [-2,2] = [-10,10]
self.assertEqual(
Interval(-10, 1) // Interval(-2, 2), Interval(-10, 10))
# [-10,1] // [0,2] = [-10,1]
self.assertEqual(Interval(-10, 1) // Interval(0, 2), Interval(-10, 1))
# [-10,1] // [-2,0] = [-1,10]
self.assertEqual(Interval(-10, 1) // Interval(-2, 0), Interval(-1, 10))
def test_div_infinity(self):
# Application of -1 // 8 = -1
# 5 // [-inf,0] = [-5,-1]
self.assertEqual(
Interval(5) // Interval(NEG_INFINITY, 0), Interval(-5, -1))
# 5 // [0,inf] = [0,5]
self.assertEqual(Interval(5) // Interval(0, INFINITY), Interval(0, 5))
# -5 // [-inf,0] = [0,5]
self.assertEqual(
Interval(-5) // Interval(NEG_INFINITY, 0), Interval(0, 5))
# -5 // [0,inf] = [-5,-1]
self.assertEqual(
Interval(-5) // Interval(0, INFINITY), Interval(-5, -1))
# [-inf,0] // -1 = [0,inf]
self.assertEqual(
Interval(NEG_INFINITY, 0) // Interval(-1), Interval(0, INFINITY))
# [0,inf] // -1 = [-inf,0]
self.assertEqual(
Interval(0, INFINITY) // Interval(-1), Interval(NEG_INFINITY, 0))
# [0,inf] // [0,inf] = [0,inf]
self.assertEqual(
Interval(0, INFINITY) // Interval(0, INFINITY),
Interval(0, INFINITY))
# [0,inf] // [-inf,0] = [-inf,0]
self.assertEqual(
Interval(0, INFINITY) // Interval(NEG_INFINITY, 0),
Interval(NEG_INFINITY, 0))
# [-inf,0] // [0,inf] = [-inf,0]
self.assertEqual(
Interval(NEG_INFINITY, 0) // Interval(0, INFINITY),
Interval(NEG_INFINITY, 0))
def test_div_interval(self):
# [2,4] // 1 = [2,4]
self.assertEqual(Interval(2, 4) // Interval(1), Interval(2, 4))
# 4 // [1,2] = [2,4]
self.assertEqual(Interval(4) // Interval(1, 2), Interval(2, 4))
# [2,4] // -1 = [-4,-2]
self.assertEqual(Interval(2, 4) // Interval(-1), Interval(-4, -2))
# -4 // [1,2] = [-4,-2]
self.assertEqual(Interval(-4) // Interval(1, 2), Interval(-4, -2))
# [-10,1] // [1,2] = [-10,1]
self.assertEqual(Interval(-10, 1) // Interval(1, 2), Interval(-10, 1))
# [-10,1] // [-2,-1] = [-1,10]
self.assertEqual(
Interval(-10, 1) // Interval(-2, -1), Interval(-1, 10))
# [-1,1] // [-1,1] = [-1,1]
self.assertEqual(Interval(-1, 1) // Interval(-1, 1), Interval(-1, 1))
def test_infinity_comparators_report_false(self):
self.assertEqual(Interval(0, INFINITY) != Interval(0, INFINITY), BOOLEAN_TOP)
self.assertEqual(Interval(0) != Interval(0), FALSE)
self.assertEqual(Interval(NEG_INFINITY, 0) == Interval(1, INFINITY), FALSE)
self.assertEqual(Interval(0, INFINITY) < Interval(NEG_INFINITY, 0), FALSE)
self.assertEqual(Interval(1, INFINITY) <= Interval(NEG_INFINITY, 0), FALSE)
self.assertEqual(Interval(NEG_INFINITY, 0) > Interval(0, INFINITY), FALSE)
self.assertEqual(Interval(NEG_INFINITY, 0) >= Interval(1, INFINITY), FALSE)
self.assertEqual(Interval(0, INFINITY) < Interval(-1), FALSE)
self.assertEqual(Interval(0, INFINITY) <= Interval(-1), FALSE)
self.assertEqual(Interval(NEG_INFINITY, 0) > Interval(1), FALSE)
self.assertEqual(Interval(NEG_INFINITY, 0) >= Interval(1), FALSE)
def test_smaller(self):
self.assertEqual(Interval(5) < Interval(6), TRUE)
self.assertEqual(Interval(-1) < Interval(1), TRUE)
self.assertEqual(Interval(0) < Interval(-1), FALSE)
self.assertEqual(Interval(1) < Interval(1), FALSE)
def test_div_simple(self):
# 4 // 2 = 2
self.assertEqual(Interval(4) // Interval(2), Interval(2))
# -4 // 2 = -2
self.assertEqual(Interval(-4) // Interval(2), Interval(-2))
# 4 // -2 = -2
self.assertEqual(Interval(4) // Interval(-2), Interval(-2))
# -4 // -2 = 2
self.assertEqual(Interval(-4) // Interval(-2), Interval(2))
# 1 // 2 = 0
self.assertEqual(Interval(1) // Interval(2), Interval(0))
# -1 // 2 = -1
self.assertEqual(Interval(-1) // Interval(2), Interval(-1))
# 8 // -7 = -2
self.assertEqual(Interval(8) // Interval(-7), Interval(-2))
def test_nequals(self):
self.assertEqual(Interval(0) != Interval(0), FALSE)
self.assertEqual(Interval(-1) != Interval(1), TRUE)
self.assertEqual(Interval(0) != Interval(-1), TRUE)
def test_minus_integer(self):
# 3 - 2 = 1
self.assertEqual(Interval(3) - Interval(2), Interval(1))
# 1 - 1 = 0
self.assertEqual(Interval(1) - Interval(1), Interval(0))
# -1 - -1 = 0
self.assertEqual(Interval(-1) - Interval(-1), Interval(0))
# 0 - -1 = 1
self.assertEqual(Interval(0) - Interval(-1), Interval(1))
# 0 - 1 = -1
self.assertEqual(Interval(0) - Interval(1), Interval(-1))
# 1 - 2 = -1
self.assertEqual(Interval(1) - Interval(2), Interval(-1))
def test_minus_infinity(self):
# [0,inf] - 2 = [-2,inf]
self.assertEqual(
Interval(0, INFINITY) - Interval(2), Interval(-2, INFINITY))
# [-inf,0] - 2 = [-inf, -2]
self.assertEqual(
Interval(NEG_INFINITY, 0) - Interval(2),
Interval(NEG_INFINITY, -2))
# 2 - [0,inf] = [-inf,2]
self.assertEqual(
Interval(2) - Interval(0, INFINITY), Interval(NEG_INFINITY, 2))
# 2 - [-inf,0] = [2,inf]
self.assertEqual(
Interval(2) - Interval(NEG_INFINITY, 0), Interval(2, INFINITY))
# [-inf,0] - [-1,2] = [-inf, 1]
self.assertEqual(
Interval(NEG_INFINITY, 0) - Interval(-1, 2),
Interval(NEG_INFINITY, 1))
# [0,inf] - [-1,2] = [-2,inf]
self.assertEqual(
Interval(0, INFINITY) - Interval(-1, 2), Interval(-2, INFINITY))
# [-1,2] - [-inf,0] = [-1,inf]
self.assertEqual(
Interval(-1, 2) - Interval(NEG_INFINITY, 0),
Interval(-1, INFINITY))
# [-1,2] - [0,inf] = [-inf,2]
self.assertEqual(
Interval(-1, 2) - Interval(0, INFINITY), Interval(NEG_INFINITY, 2))
# [0,inf] - [-inf,0] = [0,inf]
self.assertEqual(
Interval(0, INFINITY) - Interval(NEG_INFINITY, 0),
Interval(0, INFINITY))
def test_mul_interval(self):
# [0,2] * 2 = [0,4]
self.assertEqual(Interval(0, 2) * Interval(2), Interval(0, 4))
# 2 * [0,2] = [0,4]
self.assertEqual(Interval(2) * Interval(0, 2), Interval(0, 4))
# [1,2] * [1,2] = [1,4]
self.assertEqual(Interval(1, 2) * Interval(1, 2), Interval(1, 4))
# [-10,1] * [-1,2] = [-20,10]
self.assertEqual(Interval(-10, 1) * Interval(-1, 2), Interval(-20, 10))
# [1,2] * [-2,2] = [-4,4]
self.assertEqual(Interval(1, 2) * Interval(-2, 2), Interval(-4, 4))
# [-4,-3] * [-2,3] = [-12,8]
self.assertEqual(Interval(-4, -3) * Interval(-2, 3), Interval(-12, 8))
# [-1,1] * [0,1] = [-1,1]
self.assertEqual(Interval(-1, 1) * Interval(0, 1), Interval(-1, 1))
def test_mul_simple(self):
# 1 * 2 = 2
self.assertEqual(Interval(1) * Interval(2), Interval(2))
# 1 * -1 = -1
self.assertEqual(Interval(1) * Interval(-1), Interval(-1))
# -1 * 2 = -2
self.assertEqual(Interval(-1) * Interval(2), Interval(-2))
# -2 * -2 = 4
self.assertEqual(Interval(-2) * Interval(-2), Interval(4))
# 0 * 2 = 0
self.assertEqual(Interval(0) * Interval(2), Interval(0))
# 2 * 0 = 0
self.assertEqual(Interval(2) * Interval(0), Interval(0))
def test_plus_integers(self):
# 1 + 2 = 3
self.assertEqual(Interval(1) + Interval(2), Interval(3))
# -1 + 1 = 0
self.assertEqual(Interval(-1) + Interval(1), Interval(0))
# 1 + -1 = 0
self.assertEqual(Interval(1) + Interval(-1), Interval(0))
# 0 + 1 = 1
self.assertEqual(Interval(0) + Interval(1), Interval(1))
# 1 + 0 = 1
self.assertEqual(Interval(1) + Interval(0), Interval(1))
def test_plus_intervals(self):
# [1,2] + [1,2] = [2,4]
self.assertEqual(Interval(1, 2) + Interval(1, 2), Interval(2, 4))
# [-10,1] + [-0,1] = [-10,2]
self.assertEqual(Interval(-10, 1) + Interval(-1, 2), Interval(-11, 3))
# [-10,1] + [-1,0] = [-11,1]
self.assertEqual(Interval(-10, 1) + Interval(-1, 2), Interval(-11, 3))
# [-10,1] + [-1,2] = [-11,3]
self.assertEqual(Interval(-10, 1) + Interval(-1, 2), Interval(-11, 3))
# [-1,0] + [1,1] = [0,1]
self.assertEqual(Interval(-1, 0) + Interval(1), Interval(0, 1))
# [0,1] + [-1,-1] = [-1,0]
self.assertEqual(Interval(0, 1) + Interval(-1), Interval(-1, 0))
def test_minus_interval(self):
# [1,2] - 1 = [0,1]
self.assertEqual(Interval(1, 2) - Interval(1, 1), Interval(0, 1))
# [-10,1] - [-1,2] = [-12,2]
self.assertEqual(Interval(-10, 1) - Interval(-1, 2), Interval(-12, 2))
# [1,2] - [1,2] = [-1,1]
self.assertEqual(Interval(1, 2) - Interval(1, 2), Interval(-1, 1))
# [-1,1] - [-1,1] = [-2,2]
self.assertEqual(Interval(-1, 1) - Interval(-1, 1), Interval(-2, 2))
# [0,1] - [-1,0] = [0,2]
self.assertEqual(Interval(0, 1) - Interval(-1, 0), Interval(0, 2))
# [2,3] - [3,4] = [-2,0]
self.assertEqual(Interval(2, 3) - Interval(3, 4), Interval(-2, 0))
# [0,1] - [-5,-4] = [4,6]
self.assertEqual(Interval(0, 1) - Interval(-5, -4), Interval(4, 6))
def test_equals_interval(self):
self.assertEqual(Interval(1, 3) == Interval(1, 3), BOOLEAN_TOP)
self.assertEqual(Interval(1, 2) == Interval(2, 3), BOOLEAN_TOP)
self.assertEqual(Interval(1, 2) == Interval(3, 5), FALSE)