codon/test/stdlib/cmath_test.codon

import math
import cmath

INF = float('inf')
NAN = float('nan')

def float_identical(x, y):
    if math.isnan(x) or math.isnan(y):
        if math.isnan(x) and math.isnan(y):
            return True
    elif x == y:
        if x != 0.0:
            return True
        # both zero; check that signs match
        elif math.copysign(1.0, x) == math.copysign(1.0, y):
            return True
        else:
            return False
    return False

def complex_identical(x, y):
    return float_identical(x.real, y.real) and float_identical(x.imag, y.imag)

###########
# complex #
###########

ZERO_DIVISION = (
    (1+1j, 0+0j),
    (1+1j, 0.0+0j),
    (1+1j, 0+0j),
    (1.0+0j, 0+0j),
    (1+0j, 0+0j),
)

def close_abs(x, y, eps=1e-9):
    """Return true iff floats x and y "are close"."""
    # put the one with larger magnitude second
    if abs(x) > abs(y):
        x, y = y, x
    if y == 0:
        return abs(x) < eps
    if x == 0:
        return abs(y) < eps
    # check that relative difference < eps
    return abs((x-y)/y) < eps

def close_complex(x, y, eps=1e-9):
    a = complex(x)
    b = complex(y)
    return close_abs(a.real, b.real, eps) and close_abs(a.imag, b.imag, eps)

def check_div(x, y):
    """Compute complex z=x*y, and check that z/x==y and z/y==x."""
    z = x * y
    if x != 0:
        q = z / x
        if not close_complex(q, y):
            return False
        q = z.__truediv__(x)
        if not close_complex(q, y):
            return False
    if y != 0:
        q = z / y
        if not close_complex(q, x):
            return False
        q = z.__truediv__(y)
        if not close_complex(q, x):
            return False
    return True

@test
def test_truediv():
    from random import random
    simple_real = [float(i) for i in range(-5, 6)]
    simple_complex = [complex(x, y) for x in simple_real for y in simple_real]
    for x in simple_complex:
        for y in simple_complex:
            assert check_div(x, y)

    # A naive complex division algorithm (such as in 2.0) is very prone to
    # nonsense errors for these (overflows and underflows).
    assert check_div(complex(1e200, 1e200), 1+0j)
    assert check_div(complex(1e-200, 1e-200), 1+0j)

    # Just for fun.
    for i in range(100):
        check_div(complex(random(), random()), complex(random(), random()))

    assert close_complex(complex.__truediv__(2+0j, 1+1j), 1-1j)

    for denom_real, denom_imag in [(0., NAN), (NAN, 0.), (NAN, NAN)]:
        z = complex(0, 0) / complex(denom_real, denom_imag)
        assert math.isnan(z.real)
        assert math.isnan(z.imag)
test_truediv()

@test
def test_richcompare():
    assert not complex.__eq__(1+1j, 1<<10000)
    assert complex.__eq__(1+1j, 1+1j)
    assert not complex.__eq__(1+1j, 2+2j)
    assert not complex.__ne__(1+1j, 1+1j)
    assert complex.__ne__(1+1j, 2+2j), True
    for i in range(1, 100):
        f = i / 100.0
        assert complex.__eq__(f+0j, f)
        assert not complex.__ne__(f+0j, f)
        assert not complex.__eq__(complex(f, f), f)
        assert complex.__ne__(complex(f, f), f)

    import operator
    assert operator.eq(1+1j, 1+1j) == True
    assert operator.eq(1+1j, 2+2j) == False
    assert operator.ne(1+1j, 1+1j) == False
    assert operator.ne(1+1j, 2+2j) == True
test_richcompare()

@test
def test_pow():
    def pow(a, b): return a ** b
    assert close_complex(pow(1+1j, 0+0j), 1.0)
    assert close_complex(pow(0+0j, 2+0j), 0.0)
    assert close_complex(pow(1j, -1), 1/(1j))
    assert close_complex(pow(1j, 200), 1)

    a = 3.33+4.43j
    assert a ** (0j) == 1
    assert a ** (0.+0.j) == 1

    assert (3j) ** (0j) == 1
    assert (3j) ** 0 == 1

    # The following is used to exercise certain code paths
    assert a ** 105 == a ** 105
    assert a ** -105 == a ** -105
    assert a ** -30 == a ** -30

    assert (0.0j) ** 0 == 1
test_pow()

@test
def test_conjugate():
    assert close_complex(complex(5.3, 9.8).conjugate(), 5.3-9.8j)
test_conjugate()

@test
def test_cabs():
    nums = [complex(x/3., y/7.) for x in range(-9,9) for y in range(-9,9)]
    for num in nums:
        assert close_complex((num.real**2 + num.imag**2)  ** 0.5, abs(num))
test_cabs()

@test
def test_negative_zero_repr_str():
    def test(v, expected):
        return str(v) == expected

    assert test(complex(0., 1.),   "1j")
    assert test(complex(-0., 1.),  "(-0+1j)")
    assert test(complex(0., -1.),  "-1j")
    assert test(complex(-0., -1.), "(-0-1j)")

    assert test(complex(0., 0.),   "0j")
    assert test(complex(0., -0.),  "-0j")
    assert test(complex(-0., 0.),  "(-0+0j)")
    assert test(complex(-0., -0.), "(-0-0j)")
test_negative_zero_repr_str()

#########
# cmath #
#########

complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
complex_infinities = [complex(x, y) for x, y in [
        (INF, 0.0),  # 1st quadrant
        (INF, 2.3),
        (INF, INF),
        (2.3, INF),
        (0.0, INF),
        (-0.0, INF), # 2nd quadrant
        (-2.3, INF),
        (-INF, INF),
        (-INF, 2.3),
        (-INF, 0.0),
        (-INF, -0.0), # 3rd quadrant
        (-INF, -2.3),
        (-INF, -INF),
        (-2.3, -INF),
        (-0.0, -INF),
        (0.0, -INF), # 4th quadrant
        (2.3, -INF),
        (INF, -INF),
        (INF, -2.3),
        (INF, -0.0)
        ]]
complex_nans = [complex(x, y) for x, y in [
        (NAN, -INF),
        (NAN, -2.3),
        (NAN, -0.0),
        (NAN, 0.0),
        (NAN, 2.3),
        (NAN, INF),
        (-INF, NAN),
        (-2.3, NAN),
        (-0.0, NAN),
        (0.0, NAN),
        (2.3, NAN),
        (INF, NAN)
        ]]

@llvm
@pure
def small() -> float:
    ret double 4.940660e-323

def almost_equal(a, b, rel_err = 2e-15, abs_err = small()):
    if math.isnan(a):
        if math.isnan(b):
            return True
        return False

    if math.isinf(a):
        if a == b:
            return True
        return False

    if not a and not b:
        if math.copysign(1., a) != math.copysign(1., b):
            return False

    absolute_error = abs(b-a)
    if absolute_error <= max(abs_err, rel_err * abs(a)):
        return True
    return False

@test
def test_constants():
    e_expected = 2.71828182845904523536
    pi_expected = 3.14159265358979323846
    assert math.isclose(cmath.pi, pi_expected)
    assert math.isclose(cmath.e, e_expected)
test_constants()

@test
def test_infinity_and_nan_constants():
    assert cmath.inf.real == math.inf
    assert cmath.inf.imag == 0.0
    assert cmath.infj.real == 0.0
    assert cmath.infj.imag == math.inf

    assert math.isnan(cmath.nan.real)
    assert cmath.nan.imag == 0.0
    assert cmath.nanj.real == 0.0
    assert math.isnan(cmath.nanj.imag)

    assert str(cmath.inf) == "inf"
    assert str(cmath.infj) == "infj"
    assert str(cmath.nan) == "nan"
    assert str(cmath.nanj) == "nanj"
test_infinity_and_nan_constants()

@test
def test_user_object():
    class MyComplexOS[T]:
        value: T
        def __init__(self, value: T):
            self.value = value
        def __complex__(self):
            return self.value

    x = MyComplexOS(4.2)
    assert cmath.acos(x) == cmath.acos(x.value)
    assert cmath.acosh(x) == cmath.acosh(x.value)
    assert cmath.asin(x) == cmath.asin(x.value)
    assert cmath.asinh(x) == cmath.asinh(x.value)
    assert cmath.atan(x) == cmath.atan(x.value)
    assert cmath.atanh(x) == cmath.atanh(x.value)
    assert cmath.cos(x) == cmath.cos(x.value)
    assert cmath.cosh(x) == cmath.cosh(x.value)
    assert cmath.exp(x) == cmath.exp(x.value)
    assert cmath.log(x) == cmath.log(x.value)
    assert cmath.log10(x) == cmath.log10(x.value)
    assert cmath.sin(x) == cmath.sin(x.value)
    assert cmath.sinh(x) == cmath.sinh(x.value)
    assert cmath.sqrt(x) == cmath.sqrt(x.value)
    assert cmath.tan(x) == cmath.tan(x.value)
    assert cmath.tanh(x) == cmath.tanh(x.value)
test_user_object()

@test
def test_input_type():
    x = 42
    y = float(x)
    assert cmath.acos(x) == cmath.acos(y)
    assert cmath.acosh(x) == cmath.acosh(y)
    assert cmath.asin(x) == cmath.asin(y)
    assert cmath.asinh(x) == cmath.asinh(y)
    assert cmath.atan(x) == cmath.atan(y)
    assert cmath.atanh(x) == cmath.atanh(y)
    assert cmath.cos(x) == cmath.cos(y)
    assert cmath.cosh(x) == cmath.cosh(y)
    assert cmath.exp(x) == cmath.exp(y)
    assert cmath.log(x) == cmath.log(y)
    assert cmath.log10(x) == cmath.log10(y)
    assert cmath.sin(x) == cmath.sin(y)
    assert cmath.sinh(x) == cmath.sinh(y)
    assert cmath.sqrt(x) == cmath.sqrt(y)
    assert cmath.tan(x) == cmath.tan(y)
    assert cmath.tanh(x) == cmath.tanh(y)
test_input_type()


@test
def test_cmath_matches_math():
    test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
    unit_interval = test_values + [-x for x in test_values] + \
                [0., 1., -1.]
    positive = test_values + [1.] + [1./x for x in test_values]
    nonnegative = [0.] + positive
    real_line = [0.] + positive + [-x for x in positive]

    test_functions = {
        'acos' : unit_interval,
        'asin' : unit_interval,
        'atan' : real_line,
        'cos' : real_line,
        'cosh' : real_line,
        'exp' : real_line,
        'log' : positive,
        'log10' : positive,
        'sin' : real_line,
        'sinh' : real_line,
        'sqrt' : nonnegative,
        'tan' : real_line,
        'tanh' : real_line}

    for v in test_functions['acos']:
        z = cmath.acos(v)
        assert almost_equal(z.real, math.acos(v))
        assert z.imag == 0.

    for v in test_functions['asin']:
        z = cmath.asin(v)
        assert almost_equal(z.real, math.asin(v))
        assert z.imag == 0.

    for v in test_functions['atan']:
        z = cmath.atan(v)
        assert almost_equal(z.real, math.atan(v))
        assert z.imag == 0.

    for v in test_functions['cos']:
        z = cmath.cos(v)
        assert almost_equal(z.real, math.cos(v))
        assert z.imag == 0.

    for v in test_functions['cosh']:
        z = cmath.cosh(v)
        assert almost_equal(z.real, math.cosh(v))
        assert z.imag == 0.

    for v in test_functions['exp']:
        z = cmath.exp(v)
        assert almost_equal(z.real, math.exp(v))
        assert z.imag == 0.

    for v in test_functions['log']:
        z = cmath.log(v)
        assert almost_equal(z.real, math.log(v))
        assert z.imag == 0.

    for v in test_functions['log10']:
        z = cmath.log10(v)
        assert almost_equal(z.real, math.log10(v))
        assert z.imag == 0.

    for v in test_functions['sin']:
        z = cmath.sin(v)
        assert almost_equal(z.real, math.sin(v))
        assert z.imag == 0.

    for v in test_functions['sinh']:
        z = cmath.sinh(v)
        assert almost_equal(z.real, math.sinh(v))
        assert z.imag == 0.

    for v in test_functions['sqrt']:
        z = cmath.sqrt(v)
        assert almost_equal(z.real, math.sqrt(v))
        assert z.imag == 0.

    for v in test_functions['tan']:
        z = cmath.tan(v)
        assert almost_equal(z.real, math.tan(v))
        assert z.imag == 0.

    for v in test_functions['tanh']:
        z = cmath.tanh(v)
        assert almost_equal(z.real, math.tanh(v))
        assert z.imag == 0.

    for base in [0.5, 2., 10.]:
        for v in positive:
            z = cmath.log(v, base)
            s = math.log(v, base)
            # added 'or z.real == s' since Codon version gives -0 vs. +0 in one test
            assert almost_equal(z.real, math.log(v, base)) or z.real == s
            assert z.imag == 0.
test_cmath_matches_math()

@test
def test_polar():
    def check(arg, expected):
        got = cmath.polar(arg)
        return all(almost_equal(e, g) for e,g in zip(expected, got))
    pi = cmath.pi
    assert check(0, (0., 0.))
    assert check(1, (1., 0.))
    assert check(-1, (1., pi))
    assert check(1j, (1., pi / 2))
    assert check(-3j, (3., -pi / 2))
    inf = float('inf')
    assert check(complex(inf, 0), (inf, 0.))
    assert check(complex(-inf, 0), (inf, pi))
    assert check(complex(3, inf), (inf, pi / 2))
    assert check(complex(5, -inf), (inf, -pi / 2))
    assert check(complex(inf, inf), (inf, pi / 4))
    assert check(complex(inf, -inf), (inf, -pi / 4))
    assert check(complex(-inf, inf), (inf, 3 * pi / 4))
    assert check(complex(-inf, -inf), (inf, -3 * pi / 4))
    nan = float('nan')
    assert check(complex(nan, 0), (nan, nan))
    assert check(complex(0, nan), (nan, nan))
    assert check(complex(nan, nan), (nan, nan))
    assert check(complex(inf, nan), (inf, nan))
    assert check(complex(-inf, nan), (inf, nan))
    assert check(complex(nan, inf), (inf, nan))
    assert check(complex(nan, -inf), (inf, nan))
test_polar()

@test
def test_phase():
    from cmath import phase, pi
    assert almost_equal(phase(0), 0.)
    assert almost_equal(phase(1.), 0.)
    assert almost_equal(phase(-1.), pi)
    assert almost_equal(phase(-1.+1E-300j), pi)
    assert almost_equal(phase(-1.-1E-300j), -pi)
    assert almost_equal(phase(1j), pi/2)
    assert almost_equal(phase(-1j), -pi/2)

    # zeros
    assert phase(complex(0.0, 0.0)) == 0.0
    assert phase(complex(0.0, -0.0)) == -0.0
    assert phase(complex(-0.0, 0.0)) == pi
    assert phase(complex(-0.0, -0.0)) == -pi

    # infinities
    assert almost_equal(phase(complex(-INF, -0.0)), -pi)
    assert almost_equal(phase(complex(-INF, -2.3)), -pi)
    assert almost_equal(phase(complex(-INF, -INF)), -0.75*pi)
    assert almost_equal(phase(complex(-2.3, -INF)), -pi/2)
    assert almost_equal(phase(complex(-0.0, -INF)), -pi/2)
    assert almost_equal(phase(complex(0.0, -INF)), -pi/2)
    assert almost_equal(phase(complex(2.3, -INF)), -pi/2)
    assert almost_equal(phase(complex(INF, -INF)), -pi/4)
    assert phase(complex(INF, -2.3)) == -0.0
    assert phase(complex(INF, -0.0)) == -0.0
    assert phase(complex(INF, 0.0)) == 0.0
    assert phase(complex(INF, 2.3)) == 0.0
    assert almost_equal(phase(complex(INF, INF)), pi/4)
    assert almost_equal(phase(complex(2.3, INF)), pi/2)
    assert almost_equal(phase(complex(0.0, INF)), pi/2)
    assert almost_equal(phase(complex(-0.0, INF)), pi/2)
    assert almost_equal(phase(complex(-2.3, INF)), pi/2)
    assert almost_equal(phase(complex(-INF, INF)), 0.75*pi)
    assert almost_equal(phase(complex(-INF, 2.3)), pi)
    assert almost_equal(phase(complex(-INF, 0.0)), pi)

    # real or imaginary part NaN
    for z in complex_nans:
        assert math.isnan(phase(z))
test_phase()

@test
def test_abs():
    # zeros
    for z in complex_zeros:
        assert abs(z) == 0.0

    # infinities
    for z in complex_infinities:
        assert abs(z) == INF

    # real or imaginary part NaN
    assert abs(complex(NAN, -INF)) == INF
    assert math.isnan(abs(complex(NAN, -2.3)))
    assert math.isnan(abs(complex(NAN, -0.0)))
    assert math.isnan(abs(complex(NAN, 0.0)))
    assert math.isnan(abs(complex(NAN, 2.3)))
    assert abs(complex(NAN, INF)) == INF
    assert abs(complex(-INF, NAN)) == INF
    assert math.isnan(abs(complex(-2.3, NAN)))
    assert math.isnan(abs(complex(-0.0, NAN)))
    assert math.isnan(abs(complex(0.0, NAN)))
    assert math.isnan(abs(complex(2.3, NAN)))
    assert abs(complex(INF, NAN)) == INF
    assert math.isnan(abs(complex(NAN, NAN)))
test_abs()

def c_equal(a, b):
    eps = 1E-7
    if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
        return False
    return True

@test
def test_rect():
    from cmath import rect, pi
    assert c_equal(rect(0, 0), (0, 0))
    assert c_equal(rect(1, 0), (1., 0))
    assert c_equal(rect(1, -pi), (-1., 0))
    assert c_equal(rect(1, pi/2), (0, 1.))
    assert c_equal(rect(1, -pi/2), (0, -1.))
test_rect()

@test
def test_isfinite():
    real_vals = [float('-inf'), -2.3, -0.0,
                 0.0, 2.3, float('inf'), float('nan')]
    for x in real_vals:
        for y in real_vals:
            z = complex(x, y)
            assert cmath.isfinite(z) == (math.isfinite(x) and math.isfinite(y))
test_isfinite()

@test
def test_isnan():
    assert not cmath.isnan(1)
    assert not cmath.isnan(1j)
    assert not cmath.isnan(INF)
    assert cmath.isnan(NAN)
    assert cmath.isnan(complex(NAN, 0))
    assert cmath.isnan(complex(0, NAN))
    assert cmath.isnan(complex(NAN, NAN))
    assert cmath.isnan(complex(NAN, INF))
    assert cmath.isnan(complex(INF, NAN))
test_isnan()

@test
def test_isinf():
    assert not cmath.isinf(1)
    assert not cmath.isinf(1j)
    assert not cmath.isinf(NAN)
    assert cmath.isinf(INF)
    assert cmath.isinf(complex(INF, 0))
    assert cmath.isinf(complex(0, INF))
    assert cmath.isinf(complex(INF, INF))
    assert cmath.isinf(complex(NAN, INF))
    assert cmath.isinf(complex(INF, NAN))
test_isinf()

@test
def test_tanh_sign():
    for z in complex_zeros:
        assert complex_identical(cmath.tanh(z), z)
test_tanh_sign()

@test
def test_atan_sign():
    for z in complex_zeros:
        assert complex_identical(cmath.atan(z), z)
test_atan_sign()

@test
def test_atanh_sign():
    for z in complex_zeros:
        assert complex_identical(cmath.atanh(z), z)
test_atanh_sign()

@test
def test_is_close():
    # test complex values that are close to within 12 decimal places
    complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
                        (1.0+1.0j, 1.0+1.000000000001j),
                        (-1.0+1.0j, -1.000000000001+1.0j),
                        (1.0-1.0j, 1.0-0.999999999999j),
                        ]

    for a,b in complex_examples:
        assert cmath.isclose(a, b, rel_tol=1e-12)
        assert not cmath.isclose(a, b, rel_tol=1e-13)

    # test values near zero that are near to within three decimal places
    near_zero_examples = [(0.001j, 0),
                          (0.001 + 0j, 0),
                          (0.001+0.001j, 0),
                          (-0.001+0.001j, 0),
                          (0.001-0.001j, 0),
                          (-0.001-0.001j, 0),
                          ]

    for a,b in near_zero_examples:
        assert cmath.isclose(a, b, abs_tol=1.5e-03)
        assert not cmath.isclose(a, b, abs_tol=0.5e-03)

    assert cmath.isclose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
    assert not cmath.isclose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
test_is_close()

@test
def test_cmath_testcases():
    def check(exp, got, flags):
        def close(a, b):
            if math.isnan(a):
                return math.isnan(b)
            elif math.isnan(b):
                return math.isnan(a)
            return math.isclose(a, b, rel_tol = 1e-10, abs_tol=1e-15)

        x1 = exp.real
        y1 = exp.imag

        x2 = got.real
        y2 = got.imag

        if 'ignore-real-sign' in flags:
            x1 = math.fabs(x1)
            x2 = math.fabs(x2)

        if 'ignore-imag-sign' in flags:
            y1 = math.fabs(y1)
            y2 = math.fabs(y2)

        return close(x1, x2) and close(y1, y2)

    def run_test(test):
        v = test.split()
        if not v:
            return True
        name = v[0]
        func = v[1]
        inp = complex(float(v[2]), float(v[3]))
        exp = complex(float(v[5]), float(v[6]))
        flags = v[7:]

        got = complex()
        if func == 'rect':
            got = cmath.rect(inp.real, inp.imag)
        elif func == 'polar':
            got = complex(*cmath.polar(inp))
        elif func == 'exp':
            got = cmath.exp(inp)
        elif func == 'log':
            got = cmath.log(inp)
        elif func == 'log10':
            got = cmath.log10(inp)
        elif func == 'sqrt':
            got = cmath.sqrt(inp)
        elif func == 'acos':
            got = cmath.acos(inp)
        elif func == 'asin':
            got = cmath.asin(inp)
        elif func == 'atan':
            got = cmath.atan(inp)
        elif func == 'cos':
            got = cmath.cos(inp)
        elif func == 'sin':
            got = cmath.sin(inp)
        elif func == 'tan':
            got = cmath.tan(inp)
        elif func == 'acosh':
            got = cmath.acosh(inp)
        elif func == 'asinh':
            got = cmath.asinh(inp)
        elif func == 'atanh':
            got = cmath.atanh(inp)
        elif func == 'cosh':
            got = cmath.cosh(inp)
        elif func == 'sinh':
            got = cmath.sinh(inp)
        elif func == 'tanh':
            got = cmath.tanh(inp)
        else:
            assert False, f'ERROR: unknown function: {func}'

        if not check(exp, got, flags):
            print(f'{name} {func} {inp=} {got=} {exp=} {flags=}')
            return False
        return True

    tests = []
    with open('test/stdlib/cmath_testcases.txt') as f:
        for line in f:
            line = line.strip()
            if not line.startswith('--'):
                tests.append(line)

    for test in tests:
        assert run_test(test)
test_cmath_testcases()