Add a much more detailed suite of tests for arb.

Author: Maegereg

requirements-dev.txt

@@ -9,3 +9,4 @@ pytest-cov
 sphinx
 sphinx-rtd-theme
 furo
+scipy

src/flint/test/meson.build

@@ -4,6 +4,7 @@ pyfiles = [
   '__init__.py',
   '__main__.py',
   'test_all.py',
+  'test_arb.py',
   'test_docstrings.py',
 ]
 

src/flint/test/test_all.py

@@ -12,6 +12,8 @@
 import flint.flint_base.flint_base as flint_base
 from flint.utils.flint_exceptions import DomainError, IncompatibleContextError
 
+from flint.test.test_arb import all_tests as arb_tests
+
 
 PYPY = platform.python_implementation() == "PyPy"
 
@@ -5233,4 +5235,4 @@ def test_all_tests():
     test_python_threads,
 
     test_all_tests,
-]
+] + arb_tests

src/flint/test/test_arb.py

@@ -0,0 +1,350 @@
+"""Test for python-flint's `arb` type."""
+
+import math
+
+from flint import arb, ctx
+
+from scipy.special import erf, erfc
+
+def assert_almost_equal(x, y, places=7):
+    """Helper method for approximate comparisons."""
+    assert round(x-y, ndigits=places) == 0
+
+def test_from_int():
+    """Tests instantiating `arb`s from ints."""
+    for val in [
+        -42 * 10**9,
+        -42 * 10**7,
+        -42,
+        0,
+        42,
+        42 * 10**7,
+        42 * 10**9,
+        42 * 10**11,
+    ]:
+        x = arb(val)
+        man, exp = x.man_exp()
+        assert (man * 2**exp) == val
+
+def test_from_float():
+    """Tests instantiating `arb`s from floats."""
+    for val in [0.0, 1.1, -1.1, 9.9 * 0.123, 99.12]:
+        x = arb(val)
+        man, exp = x.man_exp()
+        assert (int(man) * 2 ** int(exp)) == val
+
+def test_from_float_inf():
+    """Tests `arb` works with +/- inf."""
+    posinf = arb(float("inf"))
+    neginf = arb(float("-inf"))
+
+    assert not posinf.is_finite()
+    assert not neginf.is_finite()
+    assert float(posinf) == float("inf")
+    assert float(neginf) == float("-inf")
+
+def test_from_man_exp():
+    """Tests instantiating `arb`s with mantissa and exponent."""
+    for man, exp in [(2, 30), (4, 300), (5 * 10**2, 7**8)]:
+        x = arb(mid=(man, exp))
+        m, e = x.man_exp()
+        assert (m * 2**e) == (man * 2**exp)
+
+def test_from_midpoint_radius():
+    """Tests instantiating `arb`s with midpoint and radius."""
+    for mid, rad in [(10, 1), (10000, 5), (10, 1), (10, 1)]:
+        mid_arb = arb(mid)
+        rad_arb = arb(rad)
+        x = arb(mid_arb, rad_arb)
+        assert x.mid() == mid_arb
+        actual_radius = float(x.rad())
+        assert_almost_equal(actual_radius, rad)
+
+def test_is_exact():
+    """Tests `arb.is_exact`."""
+    for arb_val, exact in [
+        (arb(10), True),
+        (arb(0.01), True),
+        (arb(-float("inf")), True),
+        (arb(1, 0), True),
+        (arb(1, 1), False),
+    ]:
+        assert arb_val.is_exact() == exact
+
+def test_is_finite():
+    """Tests `arb.is_finite`."""
+    assert not (arb(-float("inf")).is_finite())
+    assert not (arb(float("inf")).is_finite())
+    assert (arb(10).is_finite())
+
+def test_is_nan():
+    """Tests `arb.is_nan`."""
+    assert (arb(float("nan")).is_nan())
+    assert not (arb(0.0).is_nan())
+
+def test_lower():
+    """Tests `arb.lower`."""
+    with ctx.workprec(100):
+        arb_val = arb(1, 0.5)
+        assert_almost_equal(float(arb_val.lower()), 0.5)
+
+def test_upper():
+    """Tests `arb.upper`."""
+    with ctx.workprec(100):
+        arb_val = arb(1, 0.5)
+        assert_almost_equal(float(arb_val.upper()), 1.5)
+
+def test_contains():
+    """`y.__contains__(x)` returns True iff every number in `x` is also in `y`."""
+    for x, y, expected in [
+        (
+            arb(mid=9, rad=1),
+            arb(mid=10, rad=2),
+            True,
+        ),
+        (
+            arb(mid=10, rad=2),
+            arb(mid=9, rad=1),
+            False,
+        ),
+        (arb(10), arb(mid=9, rad=1), True),
+        (arb(10.1), arb(mid=9, rad=1), False),
+    ]:
+        assert (x in y) == expected
+
+# TODO: Re-enable this if we ever add the ability to hash arbs.
+# def test_hash():
+#     """`x` and `y` hash to the same value if they have the same midpoint and radius.
+
+#     Args:
+#         x: An arb.
+#         y: An arb.
+#         expected: Whether `x` and `y` should hash to the same value.
+#     """
+#     def arb_pi(prec):
+#         """Helper to calculate arb to a given precision."""
+#         with ctx.workprec(prec):
+#             return arb.pi()
+#     for x, y, expected in [
+#         (arb(10), arb(10), True),
+#         (arb(10), arb(11), False),
+#         (arb(10.0), arb(10), True),
+#         (
+#             arb(mid=10, rad=2),
+#             arb(mid=10, rad=2),
+#             True,
+#         ),
+#         (
+#             arb(mid=10, rad=2),
+#             arb(mid=10, rad=3),
+#             False,
+#         ),
+#         (arb_pi(100), arb_pi(100), True),
+#         (arb_pi(100), arb_pi(1000), False),
+#     ]:
+#         assert (hash(x) == hash(y)) == expected
+
+
+
+# Tests for arithmetic functions in `flint.arb`.
+
+# NOTE: Correctness of an arb function `F` is specified as follows:
+
+#     If `f` is the corresponding real-valued arithmetic function, `F` is correct
+#     only if, for any Arb X and any real number x in the interval X,
+#     `f(x)` is in `F(X)`.
+
+# These tests assume arb.__contains__ is correct.
+
+def test_arb_sub():
+    """`arb.__sub__` works as expected."""
+    arb1 = arb(2, 0.5)
+    arb2 = arb(1, 1)
+    with ctx.workprec(100):
+        actual = arb1 - arb2
+    # Smallest value in diff => 1.5 - 2 = -0.5
+    # Largest value in diff => 2.5 - 0 = 2.5
+    true_interval = arb(1, 1.5)  # [-0.5, 2.5]
+    assert true_interval in actual
+
+def test_arb_add():
+    """`arb.__add__` works as expected."""
+    arb1 = arb(2, 1)
+    arb2 = arb(1, 1)
+    with ctx.workprec(100):
+        actual = arb1 + arb2
+    true_interval = arb(3, 2)  # [1, 5]
+    assert true_interval in actual
+
+def test_arb_mul():
+    """`arb.__mul__` works as expected."""
+    arb1 = arb(2, 1)
+    arb2 = arb(1, 1)
+    with ctx.workprec(100):
+        actual = arb1 * arb2
+    true_interval = arb(3, 3)  # [0, 6]
+    assert true_interval in actual
+
+def test_arb_div():
+    """`arb.__div__` works as expected."""
+    arb1 = arb(4, 1)
+    arb2 = arb(2, 1)
+    with ctx.workprec(100):
+        actual = arb1 / arb2
+    true_interval = arb(4, 1)  # [3, 5]
+    assert true_interval in actual
+
+def test_arb_log():
+    """`arb.log` works as expected."""
+    midpoint = (1 + math.exp(10)) / 2
+    arb_val = arb(midpoint, midpoint - 1)  # [1, exp(10)]
+    with ctx.workprec(100):
+        actual = arb_val.log()
+    true_interval = arb(5, 5)  # [0,10]
+    assert true_interval in actual
+
+def test_arb_exp():
+    """`arb.exp` works as expected."""
+    midpoint = math.log(9) / 2
+    arb_val = arb(midpoint, midpoint)  # [0, log(9)]
+    with ctx.workprec(100):
+        actual = arb_val.exp()
+    true_interval = arb(5, 4)  # [1,9]
+    assert true_interval in actual
+
+def test_arb_max():
+    """`arb.max` works as expected."""
+    arb1 = arb(1.5, 0.5)  # [1, 2]
+    arb2 = arb(1, 2)  # [-1, 3]
+    with ctx.workprec(100):
+        actual = arb1.max(arb2)
+    true_interval = arb(2, 1)  # [1, 3]
+    assert true_interval in actual
+
+def test_arb_min():
+    """`arb.min` works as expected."""
+    arb1 = arb(1.5, 0.5)  # [1, 2]
+    arb2 = arb(1, 2)  # [-1, 3]
+    with ctx.workprec(100):
+        actual = arb1.min(arb2)
+    true_interval = arb(0.5, 1.5)  # [-1, 2]
+    assert true_interval in actual
+
+def test_arb_abs():
+    """`arb.__abs__` works as expected."""
+    arb_val = arb(1, 2)  # [-1,3]
+    actual = abs(arb_val)
+    true_interval = arb(1.5, 1.5)
+    assert true_interval in actual
+
+def test_arb_neg():
+    """`arb.neg` works as expected."""
+    arb_val = arb(1, 2)  # [-1,3]
+    actual = arb_val.neg(exact=True)
+    true_interval = arb(-2, 1)  # [-3,1]
+    assert true_interval in actual
+
+def test_arb_neg_dunder():
+    """`arb.__neg__` works as expected."""
+    arb_val = arb(1, 2)  # [-1,3]
+    actual = -arb_val
+    true_interval = arb(-2, 1)  # [-3,1]
+    assert true_interval in actual
+
+def test_arb_sgn():
+    """`arb.sgn` works as expected."""
+    arb1 = arb(1, 0.5)  # [0.5,1.5]
+    arb2 = arb(-1, 0.5)  # [-1.5,-0.5]
+    arb3 = arb(1, 2)  # [-1,3]
+    assert_almost_equal(float(arb1.sgn()), 1)
+    assert_almost_equal(float(arb2.sgn()), -1)
+    # arb3 contains both positive and negative numbers
+    # So, arb_sgn returns [0, 1]
+    assert_almost_equal(float(arb3.sgn().mid()), 0)
+    assert_almost_equal(float(arb3.sgn().rad()), 1)
+
+def test_arb_erfinv():
+    """`arb.erfinv` works as expected."""
+    midpoint = (erf(1 / 8) + erf(1 / 16)) / 2
+    radius = midpoint - erf(1 / 16)
+    arb_val = arb(midpoint, radius)
+    with ctx.workprec(100):
+        actual = arb_val.erfinv()
+    true_interval = arb(3 / 32, 1 / 32)  # [1/16, 1/8]
+    assert true_interval in actual
+
+def test_arb_erf():
+    """`arb.erf` works as expected."""
+    arb_val = arb(2, 1)
+    with ctx.workprec(100):
+        actual = arb_val.erf()
+    true_interval = arb((erf(1) + erf(3)) / 2, (erf(1) + erf(3)) / 2 - erf(1))
+    assert true_interval in actual
+
+def test_arb_erfc():
+    """`arb.erfc` works as expected."""
+    arb_val = arb(2, 1)
+    with ctx.workprec(100):
+        actual = arb_val.erfc()
+    true_interval = arb((erfc(1) + erfc(3)) / 2, (erfc(1) + erfc(3)) / 2 - erfc(3))
+    assert true_interval in actual
+
+def test_arb_const_pi():
+    """`arb.pi` works as expected."""
+    with ctx.workprec(100):
+        actual = arb.pi()
+    interval_around_pi = arb(math.pi, 1e-10)
+    assert actual in interval_around_pi
+
+def test_arb_union():
+    """`arb.union` works as expected."""
+    arb1 = arb(1, 0.5)  # [0.5,1.5]
+    arb2 = arb(3, 0.5)  # [2.5,3.5]
+    with ctx.workprec(100):
+        actual = arb1.union(arb2)
+    true_interval = arb(2, 1.5)  # [0.5, 3.5]
+    assert true_interval in actual
+
+def test_arb_sum():
+    """`arb.__sum__` works as expected."""
+    arb1 = arb(1, 0.5)  # [0.5,1.5]
+    arb2 = arb(2, 0.5)  # [1.5,2.5]
+    arb3 = arb(3, 0.5)  # [2.5,3.5]
+    with ctx.workprec(100):
+        actual = arb1 + arb2 + arb3
+    true_interval = arb(6, 1.5)  # [4.5, 7.5]
+    assert true_interval in actual
+
+all_tests = [
+    test_from_int,
+    test_from_float,
+    test_from_float_inf,
+    test_from_man_exp,
+    test_from_midpoint_radius,
+    test_is_exact,
+    test_is_finite,
+    test_is_nan,
+    test_lower,
+    test_upper,
+    test_contains,
+    # TODO: Re-enable this if we ever add the ability to hash arbs.
+    # test_hash,
+    test_arb_sub,
+    test_arb_add,
+    test_arb_mul,
+    test_arb_div,
+    test_arb_log,
+    test_arb_exp,
+    test_arb_max,
+    test_arb_min,
+    test_arb_abs,
+    test_arb_neg,
+    test_arb_neg_dunder,
+    test_arb_sgn,
+    test_arb_erfinv,
+    test_arb_erf,
+    test_arb_erfc,
+    test_arb_const_pi,
+    test_arb_union,
+    test_arb_sum,
+]