Zachary Ware | 38c707e | 2015-04-13 15:00:43 -0500 | [diff] [blame^] | 1 | from test.support import requires_IEEE_754 |
Eric Smith | 3ab08ca | 2010-12-04 15:17:38 +0000 | [diff] [blame] | 2 | from test.test_math import parse_testfile, test_file |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 3 | import unittest |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 4 | import cmath, math |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 5 | from cmath import phase, polar, rect, pi |
Victor Stinner | be3da38 | 2010-11-07 14:14:27 +0000 | [diff] [blame] | 6 | import sysconfig |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 7 | |
| 8 | INF = float('inf') |
| 9 | NAN = float('nan') |
| 10 | |
| 11 | complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]] |
| 12 | complex_infinities = [complex(x, y) for x, y in [ |
| 13 | (INF, 0.0), # 1st quadrant |
| 14 | (INF, 2.3), |
| 15 | (INF, INF), |
| 16 | (2.3, INF), |
| 17 | (0.0, INF), |
| 18 | (-0.0, INF), # 2nd quadrant |
| 19 | (-2.3, INF), |
| 20 | (-INF, INF), |
| 21 | (-INF, 2.3), |
| 22 | (-INF, 0.0), |
| 23 | (-INF, -0.0), # 3rd quadrant |
| 24 | (-INF, -2.3), |
| 25 | (-INF, -INF), |
| 26 | (-2.3, -INF), |
| 27 | (-0.0, -INF), |
| 28 | (0.0, -INF), # 4th quadrant |
| 29 | (2.3, -INF), |
| 30 | (INF, -INF), |
| 31 | (INF, -2.3), |
| 32 | (INF, -0.0) |
| 33 | ]] |
| 34 | complex_nans = [complex(x, y) for x, y in [ |
| 35 | (NAN, -INF), |
| 36 | (NAN, -2.3), |
| 37 | (NAN, -0.0), |
| 38 | (NAN, 0.0), |
| 39 | (NAN, 2.3), |
| 40 | (NAN, INF), |
| 41 | (-INF, NAN), |
| 42 | (-2.3, NAN), |
| 43 | (-0.0, NAN), |
| 44 | (0.0, NAN), |
| 45 | (2.3, NAN), |
| 46 | (INF, NAN) |
| 47 | ]] |
| 48 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 49 | class CMathTests(unittest.TestCase): |
| 50 | # list of all functions in cmath |
| 51 | test_functions = [getattr(cmath, fname) for fname in [ |
| 52 | 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh', |
| 53 | 'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh', |
| 54 | 'sqrt', 'tan', 'tanh']] |
| 55 | # test first and second arguments independently for 2-argument log |
| 56 | test_functions.append(lambda x : cmath.log(x, 1729. + 0j)) |
| 57 | test_functions.append(lambda x : cmath.log(14.-27j, x)) |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 58 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 59 | def setUp(self): |
| 60 | self.test_values = open(test_file) |
| 61 | |
| 62 | def tearDown(self): |
| 63 | self.test_values.close() |
| 64 | |
Mark Dickinson | a837aa6 | 2010-11-07 15:31:41 +0000 | [diff] [blame] | 65 | def assertFloatIdentical(self, x, y): |
| 66 | """Fail unless floats x and y are identical, in the sense that: |
| 67 | (1) both x and y are nans, or |
| 68 | (2) both x and y are infinities, with the same sign, or |
| 69 | (3) both x and y are zeros, with the same sign, or |
| 70 | (4) x and y are both finite and nonzero, and x == y |
| 71 | |
| 72 | """ |
| 73 | msg = 'floats {!r} and {!r} are not identical' |
| 74 | |
| 75 | if math.isnan(x) or math.isnan(y): |
| 76 | if math.isnan(x) and math.isnan(y): |
| 77 | return |
| 78 | elif x == y: |
| 79 | if x != 0.0: |
| 80 | return |
| 81 | # both zero; check that signs match |
| 82 | elif math.copysign(1.0, x) == math.copysign(1.0, y): |
| 83 | return |
| 84 | else: |
| 85 | msg += ': zeros have different signs' |
| 86 | self.fail(msg.format(x, y)) |
| 87 | |
| 88 | def assertComplexIdentical(self, x, y): |
| 89 | """Fail unless complex numbers x and y have equal values and signs. |
| 90 | |
| 91 | In particular, if x and y both have real (or imaginary) part |
| 92 | zero, but the zeros have different signs, this test will fail. |
| 93 | |
| 94 | """ |
| 95 | self.assertFloatIdentical(x.real, y.real) |
| 96 | self.assertFloatIdentical(x.imag, y.imag) |
Victor Stinner | be3da38 | 2010-11-07 14:14:27 +0000 | [diff] [blame] | 97 | |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 98 | def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323, |
| 99 | msg=None): |
| 100 | """Fail if the two floating-point numbers are not almost equal. |
| 101 | |
| 102 | Determine whether floating-point values a and b are equal to within |
| 103 | a (small) rounding error. The default values for rel_err and |
| 104 | abs_err are chosen to be suitable for platforms where a float is |
| 105 | represented by an IEEE 754 double. They allow an error of between |
| 106 | 9 and 19 ulps. |
| 107 | """ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 108 | |
| 109 | # special values testing |
| 110 | if math.isnan(a): |
| 111 | if math.isnan(b): |
| 112 | return |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 113 | self.fail(msg or '{!r} should be nan'.format(b)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 114 | |
| 115 | if math.isinf(a): |
| 116 | if a == b: |
| 117 | return |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 118 | self.fail(msg or 'finite result where infinity expected: ' |
| 119 | 'expected {!r}, got {!r}'.format(a, b)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 120 | |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 121 | # if both a and b are zero, check whether they have the same sign |
| 122 | # (in theory there are examples where it would be legitimate for a |
| 123 | # and b to have opposite signs; in practice these hardly ever |
| 124 | # occur). |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 125 | if not a and not b: |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 126 | if math.copysign(1., a) != math.copysign(1., b): |
| 127 | self.fail(msg or 'zero has wrong sign: expected {!r}, ' |
| 128 | 'got {!r}'.format(a, b)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 129 | |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 130 | # if a-b overflows, or b is infinite, return False. Again, in |
| 131 | # theory there are examples where a is within a few ulps of the |
| 132 | # max representable float, and then b could legitimately be |
| 133 | # infinite. In practice these examples are rare. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 134 | try: |
| 135 | absolute_error = abs(b-a) |
| 136 | except OverflowError: |
| 137 | pass |
| 138 | else: |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 139 | # test passes if either the absolute error or the relative |
| 140 | # error is sufficiently small. The defaults amount to an |
| 141 | # error of between 9 ulps and 19 ulps on an IEEE-754 compliant |
| 142 | # machine. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 143 | if absolute_error <= max(abs_err, rel_err * abs(a)): |
| 144 | return |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 145 | self.fail(msg or |
| 146 | '{!r} and {!r} are not sufficiently close'.format(a, b)) |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 147 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 148 | def test_constants(self): |
| 149 | e_expected = 2.71828182845904523536 |
| 150 | pi_expected = 3.14159265358979323846 |
Mark Dickinson | da89245 | 2009-12-20 19:56:09 +0000 | [diff] [blame] | 151 | self.assertAlmostEqual(cmath.pi, pi_expected, places=9, |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 152 | msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected)) |
Mark Dickinson | da89245 | 2009-12-20 19:56:09 +0000 | [diff] [blame] | 153 | self.assertAlmostEqual(cmath.e, e_expected, places=9, |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 154 | msg="cmath.e is {}; should be {}".format(cmath.e, e_expected)) |
Roger E. Masse | 3daddda | 1996-12-09 22:59:15 +0000 | [diff] [blame] | 155 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 156 | def test_user_object(self): |
| 157 | # Test automatic calling of __complex__ and __float__ by cmath |
| 158 | # functions |
Roger E. Masse | fab8ab8 | 1996-12-20 22:36:52 +0000 | [diff] [blame] | 159 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 160 | # some random values to use as test values; we avoid values |
| 161 | # for which any of the functions in cmath is undefined |
| 162 | # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow |
| 163 | cx_arg = 4.419414439 + 1.497100113j |
| 164 | flt_arg = -6.131677725 |
Roger E. Masse | fab8ab8 | 1996-12-20 22:36:52 +0000 | [diff] [blame] | 165 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 166 | # a variety of non-complex numbers, used to check that |
| 167 | # non-complex return values from __complex__ give an error |
| 168 | non_complexes = ["not complex", 1, 5, 2., None, |
| 169 | object(), NotImplemented] |
| 170 | |
| 171 | # Now we introduce a variety of classes whose instances might |
| 172 | # end up being passed to the cmath functions |
| 173 | |
| 174 | # usual case: new-style class implementing __complex__ |
| 175 | class MyComplex(object): |
| 176 | def __init__(self, value): |
| 177 | self.value = value |
| 178 | def __complex__(self): |
| 179 | return self.value |
| 180 | |
| 181 | # old-style class implementing __complex__ |
| 182 | class MyComplexOS: |
| 183 | def __init__(self, value): |
| 184 | self.value = value |
| 185 | def __complex__(self): |
| 186 | return self.value |
| 187 | |
| 188 | # classes for which __complex__ raises an exception |
| 189 | class SomeException(Exception): |
| 190 | pass |
| 191 | class MyComplexException(object): |
| 192 | def __complex__(self): |
| 193 | raise SomeException |
| 194 | class MyComplexExceptionOS: |
| 195 | def __complex__(self): |
| 196 | raise SomeException |
| 197 | |
| 198 | # some classes not providing __float__ or __complex__ |
| 199 | class NeitherComplexNorFloat(object): |
| 200 | pass |
| 201 | class NeitherComplexNorFloatOS: |
| 202 | pass |
| 203 | class MyInt(object): |
| 204 | def __int__(self): return 2 |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 205 | def __index__(self): return 2 |
| 206 | class MyIntOS: |
| 207 | def __int__(self): return 2 |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 208 | def __index__(self): return 2 |
| 209 | |
| 210 | # other possible combinations of __float__ and __complex__ |
| 211 | # that should work |
| 212 | class FloatAndComplex(object): |
| 213 | def __float__(self): |
| 214 | return flt_arg |
| 215 | def __complex__(self): |
| 216 | return cx_arg |
| 217 | class FloatAndComplexOS: |
| 218 | def __float__(self): |
| 219 | return flt_arg |
| 220 | def __complex__(self): |
| 221 | return cx_arg |
| 222 | class JustFloat(object): |
| 223 | def __float__(self): |
| 224 | return flt_arg |
| 225 | class JustFloatOS: |
| 226 | def __float__(self): |
| 227 | return flt_arg |
| 228 | |
| 229 | for f in self.test_functions: |
| 230 | # usual usage |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 231 | self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg)) |
| 232 | self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg)) |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 233 | # other combinations of __float__ and __complex__ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 234 | self.assertEqual(f(FloatAndComplex()), f(cx_arg)) |
| 235 | self.assertEqual(f(FloatAndComplexOS()), f(cx_arg)) |
| 236 | self.assertEqual(f(JustFloat()), f(flt_arg)) |
| 237 | self.assertEqual(f(JustFloatOS()), f(flt_arg)) |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 238 | # TypeError should be raised for classes not providing |
| 239 | # either __complex__ or __float__, even if they provide |
Mark Dickinson | cce2f21 | 2009-01-15 19:32:23 +0000 | [diff] [blame] | 240 | # __int__ or __index__. An old-style class |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 241 | # currently raises AttributeError instead of a TypeError; |
| 242 | # this could be considered a bug. |
| 243 | self.assertRaises(TypeError, f, NeitherComplexNorFloat()) |
| 244 | self.assertRaises(TypeError, f, MyInt()) |
| 245 | self.assertRaises(Exception, f, NeitherComplexNorFloatOS()) |
| 246 | self.assertRaises(Exception, f, MyIntOS()) |
| 247 | # non-complex return value from __complex__ -> TypeError |
| 248 | for bad_complex in non_complexes: |
| 249 | self.assertRaises(TypeError, f, MyComplex(bad_complex)) |
| 250 | self.assertRaises(TypeError, f, MyComplexOS(bad_complex)) |
| 251 | # exceptions in __complex__ should be propagated correctly |
| 252 | self.assertRaises(SomeException, f, MyComplexException()) |
| 253 | self.assertRaises(SomeException, f, MyComplexExceptionOS()) |
| 254 | |
| 255 | def test_input_type(self): |
Serhiy Storchaka | 9594942 | 2013-08-27 19:40:23 +0300 | [diff] [blame] | 256 | # ints should be acceptable inputs to all cmath |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 257 | # functions, by virtue of providing a __float__ method |
| 258 | for f in self.test_functions: |
| 259 | for arg in [2, 2.]: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 260 | self.assertEqual(f(arg), f(arg.__float__())) |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 261 | |
| 262 | # but strings should give a TypeError |
| 263 | for f in self.test_functions: |
| 264 | for arg in ["a", "long_string", "0", "1j", ""]: |
| 265 | self.assertRaises(TypeError, f, arg) |
| 266 | |
| 267 | def test_cmath_matches_math(self): |
| 268 | # check that corresponding cmath and math functions are equal |
| 269 | # for floats in the appropriate range |
| 270 | |
| 271 | # test_values in (0, 1) |
| 272 | test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99] |
| 273 | |
| 274 | # test_values for functions defined on [-1., 1.] |
| 275 | unit_interval = test_values + [-x for x in test_values] + \ |
| 276 | [0., 1., -1.] |
| 277 | |
| 278 | # test_values for log, log10, sqrt |
| 279 | positive = test_values + [1.] + [1./x for x in test_values] |
| 280 | nonnegative = [0.] + positive |
| 281 | |
| 282 | # test_values for functions defined on the whole real line |
| 283 | real_line = [0.] + positive + [-x for x in positive] |
| 284 | |
| 285 | test_functions = { |
| 286 | 'acos' : unit_interval, |
| 287 | 'asin' : unit_interval, |
| 288 | 'atan' : real_line, |
| 289 | 'cos' : real_line, |
| 290 | 'cosh' : real_line, |
| 291 | 'exp' : real_line, |
| 292 | 'log' : positive, |
| 293 | 'log10' : positive, |
| 294 | 'sin' : real_line, |
| 295 | 'sinh' : real_line, |
| 296 | 'sqrt' : nonnegative, |
| 297 | 'tan' : real_line, |
| 298 | 'tanh' : real_line} |
| 299 | |
| 300 | for fn, values in test_functions.items(): |
| 301 | float_fn = getattr(math, fn) |
| 302 | complex_fn = getattr(cmath, fn) |
| 303 | for v in values: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 304 | z = complex_fn(v) |
| 305 | self.rAssertAlmostEqual(float_fn(v), z.real) |
| 306 | self.assertEqual(0., z.imag) |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 307 | |
| 308 | # test two-argument version of log with various bases |
| 309 | for base in [0.5, 2., 10.]: |
| 310 | for v in positive: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 311 | z = cmath.log(v, base) |
| 312 | self.rAssertAlmostEqual(math.log(v, base), z.real) |
| 313 | self.assertEqual(0., z.imag) |
| 314 | |
Eric Smith | 3ab08ca | 2010-12-04 15:17:38 +0000 | [diff] [blame] | 315 | @requires_IEEE_754 |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 316 | def test_specific_values(self): |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 317 | def rect_complex(z): |
| 318 | """Wrapped version of rect that accepts a complex number instead of |
| 319 | two float arguments.""" |
| 320 | return cmath.rect(z.real, z.imag) |
| 321 | |
| 322 | def polar_complex(z): |
| 323 | """Wrapped version of polar that returns a complex number instead of |
| 324 | two floats.""" |
| 325 | return complex(*polar(z)) |
| 326 | |
| 327 | for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): |
| 328 | arg = complex(ar, ai) |
| 329 | expected = complex(er, ei) |
| 330 | if fn == 'rect': |
| 331 | function = rect_complex |
| 332 | elif fn == 'polar': |
| 333 | function = polar_complex |
| 334 | else: |
| 335 | function = getattr(cmath, fn) |
| 336 | if 'divide-by-zero' in flags or 'invalid' in flags: |
| 337 | try: |
| 338 | actual = function(arg) |
| 339 | except ValueError: |
| 340 | continue |
| 341 | else: |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 342 | self.fail('ValueError not raised in test ' |
| 343 | '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 344 | |
| 345 | if 'overflow' in flags: |
| 346 | try: |
| 347 | actual = function(arg) |
| 348 | except OverflowError: |
| 349 | continue |
| 350 | else: |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 351 | self.fail('OverflowError not raised in test ' |
| 352 | '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 353 | |
| 354 | actual = function(arg) |
| 355 | |
| 356 | if 'ignore-real-sign' in flags: |
| 357 | actual = complex(abs(actual.real), actual.imag) |
| 358 | expected = complex(abs(expected.real), expected.imag) |
| 359 | if 'ignore-imag-sign' in flags: |
| 360 | actual = complex(actual.real, abs(actual.imag)) |
| 361 | expected = complex(expected.real, abs(expected.imag)) |
| 362 | |
| 363 | # for the real part of the log function, we allow an |
| 364 | # absolute error of up to 2e-15. |
| 365 | if fn in ('log', 'log10'): |
| 366 | real_abs_err = 2e-15 |
| 367 | else: |
| 368 | real_abs_err = 5e-323 |
| 369 | |
Mark Dickinson | 4d1e50d | 2009-12-20 20:37:56 +0000 | [diff] [blame] | 370 | error_message = ( |
| 371 | '{}: {}(complex({!r}, {!r}))\n' |
| 372 | 'Expected: complex({!r}, {!r})\n' |
| 373 | 'Received: complex({!r}, {!r})\n' |
| 374 | 'Received value insufficiently close to expected value.' |
| 375 | ).format(id, fn, ar, ai, |
| 376 | expected.real, expected.imag, |
| 377 | actual.real, actual.imag) |
| 378 | self.rAssertAlmostEqual(expected.real, actual.real, |
| 379 | abs_err=real_abs_err, |
| 380 | msg=error_message) |
| 381 | self.rAssertAlmostEqual(expected.imag, actual.imag, |
| 382 | msg=error_message) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 383 | |
| 384 | def assertCISEqual(self, a, b): |
| 385 | eps = 1E-7 |
| 386 | if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps: |
| 387 | self.fail((a ,b)) |
| 388 | |
| 389 | def test_polar(self): |
| 390 | self.assertCISEqual(polar(0), (0., 0.)) |
| 391 | self.assertCISEqual(polar(1.), (1., 0.)) |
| 392 | self.assertCISEqual(polar(-1.), (1., pi)) |
| 393 | self.assertCISEqual(polar(1j), (1., pi/2)) |
| 394 | self.assertCISEqual(polar(-1j), (1., -pi/2)) |
| 395 | |
| 396 | def test_phase(self): |
| 397 | self.assertAlmostEqual(phase(0), 0.) |
| 398 | self.assertAlmostEqual(phase(1.), 0.) |
| 399 | self.assertAlmostEqual(phase(-1.), pi) |
| 400 | self.assertAlmostEqual(phase(-1.+1E-300j), pi) |
| 401 | self.assertAlmostEqual(phase(-1.-1E-300j), -pi) |
| 402 | self.assertAlmostEqual(phase(1j), pi/2) |
| 403 | self.assertAlmostEqual(phase(-1j), -pi/2) |
| 404 | |
| 405 | # zeros |
| 406 | self.assertEqual(phase(complex(0.0, 0.0)), 0.0) |
| 407 | self.assertEqual(phase(complex(0.0, -0.0)), -0.0) |
| 408 | self.assertEqual(phase(complex(-0.0, 0.0)), pi) |
| 409 | self.assertEqual(phase(complex(-0.0, -0.0)), -pi) |
| 410 | |
| 411 | # infinities |
| 412 | self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi) |
| 413 | self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi) |
| 414 | self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi) |
| 415 | self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2) |
| 416 | self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2) |
| 417 | self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2) |
| 418 | self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2) |
| 419 | self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4) |
| 420 | self.assertEqual(phase(complex(INF, -2.3)), -0.0) |
| 421 | self.assertEqual(phase(complex(INF, -0.0)), -0.0) |
| 422 | self.assertEqual(phase(complex(INF, 0.0)), 0.0) |
| 423 | self.assertEqual(phase(complex(INF, 2.3)), 0.0) |
| 424 | self.assertAlmostEqual(phase(complex(INF, INF)), pi/4) |
| 425 | self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2) |
| 426 | self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2) |
| 427 | self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2) |
| 428 | self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2) |
| 429 | self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi) |
| 430 | self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi) |
| 431 | self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi) |
| 432 | |
| 433 | # real or imaginary part NaN |
| 434 | for z in complex_nans: |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 435 | self.assertTrue(math.isnan(phase(z))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 436 | |
| 437 | def test_abs(self): |
| 438 | # zeros |
| 439 | for z in complex_zeros: |
| 440 | self.assertEqual(abs(z), 0.0) |
| 441 | |
| 442 | # infinities |
| 443 | for z in complex_infinities: |
| 444 | self.assertEqual(abs(z), INF) |
| 445 | |
| 446 | # real or imaginary part NaN |
| 447 | self.assertEqual(abs(complex(NAN, -INF)), INF) |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 448 | self.assertTrue(math.isnan(abs(complex(NAN, -2.3)))) |
| 449 | self.assertTrue(math.isnan(abs(complex(NAN, -0.0)))) |
| 450 | self.assertTrue(math.isnan(abs(complex(NAN, 0.0)))) |
| 451 | self.assertTrue(math.isnan(abs(complex(NAN, 2.3)))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 452 | self.assertEqual(abs(complex(NAN, INF)), INF) |
| 453 | self.assertEqual(abs(complex(-INF, NAN)), INF) |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 454 | self.assertTrue(math.isnan(abs(complex(-2.3, NAN)))) |
| 455 | self.assertTrue(math.isnan(abs(complex(-0.0, NAN)))) |
| 456 | self.assertTrue(math.isnan(abs(complex(0.0, NAN)))) |
| 457 | self.assertTrue(math.isnan(abs(complex(2.3, NAN)))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 458 | self.assertEqual(abs(complex(INF, NAN)), INF) |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 459 | self.assertTrue(math.isnan(abs(complex(NAN, NAN)))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 460 | |
Eric Smith | 3ab08ca | 2010-12-04 15:17:38 +0000 | [diff] [blame] | 461 | |
| 462 | @requires_IEEE_754 |
| 463 | def test_abs_overflows(self): |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 464 | # result overflows |
Eric Smith | 3ab08ca | 2010-12-04 15:17:38 +0000 | [diff] [blame] | 465 | self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 466 | |
| 467 | def assertCEqual(self, a, b): |
| 468 | eps = 1E-7 |
| 469 | if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps: |
| 470 | self.fail((a ,b)) |
| 471 | |
| 472 | def test_rect(self): |
| 473 | self.assertCEqual(rect(0, 0), (0, 0)) |
| 474 | self.assertCEqual(rect(1, 0), (1., 0)) |
| 475 | self.assertCEqual(rect(1, -pi), (-1., 0)) |
| 476 | self.assertCEqual(rect(1, pi/2), (0, 1.)) |
| 477 | self.assertCEqual(rect(1, -pi/2), (0, -1.)) |
| 478 | |
Mark Dickinson | 8e0c996 | 2010-07-11 17:38:24 +0000 | [diff] [blame] | 479 | def test_isfinite(self): |
| 480 | real_vals = [float('-inf'), -2.3, -0.0, |
| 481 | 0.0, 2.3, float('inf'), float('nan')] |
| 482 | for x in real_vals: |
| 483 | for y in real_vals: |
| 484 | z = complex(x, y) |
Mark Dickinson | 68c5de6 | 2010-07-11 19:12:10 +0000 | [diff] [blame] | 485 | self.assertEqual(cmath.isfinite(z), |
Mark Dickinson | 8e0c996 | 2010-07-11 17:38:24 +0000 | [diff] [blame] | 486 | math.isfinite(x) and math.isfinite(y)) |
| 487 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 488 | def test_isnan(self): |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 489 | self.assertFalse(cmath.isnan(1)) |
| 490 | self.assertFalse(cmath.isnan(1j)) |
| 491 | self.assertFalse(cmath.isnan(INF)) |
| 492 | self.assertTrue(cmath.isnan(NAN)) |
| 493 | self.assertTrue(cmath.isnan(complex(NAN, 0))) |
| 494 | self.assertTrue(cmath.isnan(complex(0, NAN))) |
| 495 | self.assertTrue(cmath.isnan(complex(NAN, NAN))) |
| 496 | self.assertTrue(cmath.isnan(complex(NAN, INF))) |
| 497 | self.assertTrue(cmath.isnan(complex(INF, NAN))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 498 | |
| 499 | def test_isinf(self): |
Benjamin Peterson | c9c0f20 | 2009-06-30 23:06:06 +0000 | [diff] [blame] | 500 | self.assertFalse(cmath.isinf(1)) |
| 501 | self.assertFalse(cmath.isinf(1j)) |
| 502 | self.assertFalse(cmath.isinf(NAN)) |
| 503 | self.assertTrue(cmath.isinf(INF)) |
| 504 | self.assertTrue(cmath.isinf(complex(INF, 0))) |
| 505 | self.assertTrue(cmath.isinf(complex(0, INF))) |
| 506 | self.assertTrue(cmath.isinf(complex(INF, INF))) |
| 507 | self.assertTrue(cmath.isinf(complex(NAN, INF))) |
| 508 | self.assertTrue(cmath.isinf(complex(INF, NAN))) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 509 | |
Victor Stinner | be3da38 | 2010-11-07 14:14:27 +0000 | [diff] [blame] | 510 | @requires_IEEE_754 |
| 511 | @unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0, |
| 512 | "system tanh() function doesn't copy the sign") |
| 513 | def testTanhSign(self): |
Mark Dickinson | 5ccafba | 2010-11-13 10:43:40 +0000 | [diff] [blame] | 514 | for z in complex_zeros: |
| 515 | self.assertComplexIdentical(cmath.tanh(z), z) |
Victor Stinner | be3da38 | 2010-11-07 14:14:27 +0000 | [diff] [blame] | 516 | |
Mark Dickinson | 4ccc137 | 2010-11-20 11:08:27 +0000 | [diff] [blame] | 517 | # The algorithm used for atan and atanh makes use of the system |
| 518 | # log1p function; If that system function doesn't respect the sign |
| 519 | # of zero, then atan and atanh will also have difficulties with |
| 520 | # the sign of complex zeros. |
| 521 | @requires_IEEE_754 |
Mark Dickinson | 4ccc137 | 2010-11-20 11:08:27 +0000 | [diff] [blame] | 522 | def testAtanSign(self): |
| 523 | for z in complex_zeros: |
| 524 | self.assertComplexIdentical(cmath.atan(z), z) |
| 525 | |
| 526 | @requires_IEEE_754 |
Mark Dickinson | 4ccc137 | 2010-11-20 11:08:27 +0000 | [diff] [blame] | 527 | def testAtanhSign(self): |
| 528 | for z in complex_zeros: |
| 529 | self.assertComplexIdentical(cmath.atanh(z), z) |
| 530 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 531 | |
Guido van Rossum | d8faa36 | 2007-04-27 19:54:29 +0000 | [diff] [blame] | 532 | if __name__ == "__main__": |
Zachary Ware | 38c707e | 2015-04-13 15:00:43 -0500 | [diff] [blame^] | 533 | unittest.main() |