summaryrefslogtreecommitdiffstats
path: root/Lib/test/test_cmath.py
blob: 2ab5a78a22add325bf46a244279e169dd4bb9dfb (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
from test.support import run_unittest
from test.test_math import parse_testfile, test_file
import unittest
import os, sys
import cmath, math
from cmath import phase, polar, rect, pi

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

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)
        ]]

def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323):
    """Determine whether floating-point values a and b are equal to within
    a (small) rounding error.  The default values for rel_err and
    abs_err are chosen to be suitable for platforms where a float is
    represented by an IEEE 754 double.  They allow an error of between
    9 and 19 ulps."""

    # special values testing
    if math.isnan(a):
        return math.isnan(b)
    if math.isinf(a):
        return a == b

    # if both a and b are zero, check whether they have the same sign
    # (in theory there are examples where it would be legitimate for a
    # and b to have opposite signs; in practice these hardly ever
    # occur).
    if not a and not b:
        return math.copysign(1., a) == math.copysign(1., b)

    # if a-b overflows, or b is infinite, return False.  Again, in
    # theory there are examples where a is within a few ulps of the
    # max representable float, and then b could legitimately be
    # infinite.  In practice these examples are rare.
    try:
        absolute_error = abs(b-a)
    except OverflowError:
        return False
    else:
        return absolute_error <= max(abs_err, rel_err * abs(a))

class CMathTests(unittest.TestCase):
    # list of all functions in cmath
    test_functions = [getattr(cmath, fname) for fname in [
            'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
            'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
            'sqrt', 'tan', 'tanh']]
    # test first and second arguments independently for 2-argument log
    test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
    test_functions.append(lambda x : cmath.log(14.-27j, x))

    def setUp(self):
        self.test_values = open(test_file)

    def tearDown(self):
        self.test_values.close()

    def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323):
        """Check that two floating-point numbers are almost equal."""

        # special values testing
        if math.isnan(a):
            if math.isnan(b):
                return
            self.fail("%s should be nan" % repr(b))

        if math.isinf(a):
            if a == b:
                return
            self.fail("finite result where infinity excpected: "
                      "expected %s, got %s" % (repr(a), repr(b)))

        if not a and not b:
            if math.atan2(a, -1.) != math.atan2(b, -1.):
                self.fail("zero has wrong sign: expected %s, got %s" %
                          (repr(a), repr(b)))

        # test passes if either the absolute error or the relative
        # error is sufficiently small.  The defaults amount to an
        # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
        # machine.

        try:
            absolute_error = abs(b-a)
        except OverflowError:
            pass
        else:
            if absolute_error <= max(abs_err, rel_err * abs(a)):
                return
        self.fail("%s and %s are not sufficiently close" % (repr(a), repr(b)))

    def test_constants(self):
        e_expected = 2.71828182845904523536
        pi_expected = 3.14159265358979323846
        self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
            msg="cmath.pi is %s; should be %s" % (cmath.pi, pi_expected))
        self.assertAlmostEqual(cmath.e, e_expected, places=9,
            msg="cmath.e is %s; should be %s" % (cmath.e, e_expected))

    def test_user_object(self):
        # Test automatic calling of __complex__ and __float__ by cmath
        # functions

        # some random values to use as test values; we avoid values
        # for which any of the functions in cmath is undefined
        # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
        cx_arg = 4.419414439 + 1.497100113j
        flt_arg = -6.131677725

        # a variety of non-complex numbers, used to check that
        # non-complex return values from __complex__ give an error
        non_complexes = ["not complex", 1, 5, 2., None,
                         object(), NotImplemented]

        # Now we introduce a variety of classes whose instances might
        # end up being passed to the cmath functions

        # usual case: new-style class implementing __complex__
        class MyComplex(object):
            def __init__(self, value):
                self.value = value
            def __complex__(self):
                return self.value

        # old-style class implementing __complex__
        class MyComplexOS:
            def __init__(self, value):
                self.value = value
            def __complex__(self):
                return self.value

        # classes for which __complex__ raises an exception
        class SomeException(Exception):
            pass
        class MyComplexException(object):
            def __complex__(self):
                raise SomeException
        class MyComplexExceptionOS:
            def __complex__(self):
                raise SomeException

        # some classes not providing __float__ or __complex__
        class NeitherComplexNorFloat(object):
            pass
        class NeitherComplexNorFloatOS:
            pass
        class MyInt(object):
            def __int__(self): return 2
            def __index__(self): return 2
        class MyIntOS:
            def __int__(self): return 2
            def __index__(self): return 2

        # other possible combinations of __float__ and __complex__
        # that should work
        class FloatAndComplex(object):
            def __float__(self):
                return flt_arg
            def __complex__(self):
                return cx_arg
        class FloatAndComplexOS:
            def __float__(self):
                return flt_arg
            def __complex__(self):
                return cx_arg
        class JustFloat(object):
            def __float__(self):
                return flt_arg
        class JustFloatOS:
            def __float__(self):
                return flt_arg

        for f in self.test_functions:
            # usual usage
            self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
            self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
            # other combinations of __float__ and __complex__
            self.assertEqual(f(FloatAndComplex()), f(cx_arg))
            self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
            self.assertEqual(f(JustFloat()), f(flt_arg))
            self.assertEqual(f(JustFloatOS()), f(flt_arg))
            # TypeError should be raised for classes not providing
            # either __complex__ or __float__, even if they provide
            # __int__ or __index__.  An old-style class
            # currently raises AttributeError instead of a TypeError;
            # this could be considered a bug.
            self.assertRaises(TypeError, f, NeitherComplexNorFloat())
            self.assertRaises(TypeError, f, MyInt())
            self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
            self.assertRaises(Exception, f, MyIntOS())
            # non-complex return value from __complex__ -> TypeError
            for bad_complex in non_complexes:
                self.assertRaises(TypeError, f, MyComplex(bad_complex))
                self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
            # exceptions in __complex__ should be propagated correctly
            self.assertRaises(SomeException, f, MyComplexException())
            self.assertRaises(SomeException, f, MyComplexExceptionOS())

    def test_input_type(self):
        # ints and longs should be acceptable inputs to all cmath
        # functions, by virtue of providing a __float__ method
        for f in self.test_functions:
            for arg in [2, 2.]:
                self.assertEqual(f(arg), f(arg.__float__()))

        # but strings should give a TypeError
        for f in self.test_functions:
            for arg in ["a", "long_string", "0", "1j", ""]:
                self.assertRaises(TypeError, f, arg)

    def test_cmath_matches_math(self):
        # check that corresponding cmath and math functions are equal
        # for floats in the appropriate range

        # test_values in (0, 1)
        test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]

        # test_values for functions defined on [-1., 1.]
        unit_interval = test_values + [-x for x in test_values] + \
            [0., 1., -1.]

        # test_values for log, log10, sqrt
        positive = test_values + [1.] + [1./x for x in test_values]
        nonnegative = [0.] + positive

        # test_values for functions defined on the whole real line
        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 fn, values in test_functions.items():
            float_fn = getattr(math, fn)
            complex_fn = getattr(cmath, fn)
            for v in values:
                z = complex_fn(v)
                self.rAssertAlmostEqual(float_fn(v), z.real)
                self.assertEqual(0., z.imag)

        # test two-argument version of log with various bases
        for base in [0.5, 2., 10.]:
            for v in positive:
                z = cmath.log(v, base)
                self.rAssertAlmostEqual(math.log(v, base), z.real)
                self.assertEqual(0., z.imag)

    def test_specific_values(self):
        if not float.__getformat__("double").startswith("IEEE"):
            return

        def rect_complex(z):
            """Wrapped version of rect that accepts a complex number instead of
            two float arguments."""
            return cmath.rect(z.real, z.imag)

        def polar_complex(z):
            """Wrapped version of polar that returns a complex number instead of
            two floats."""
            return complex(*polar(z))

        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
            arg = complex(ar, ai)
            expected = complex(er, ei)
            if fn == 'rect':
                function = rect_complex
            elif fn == 'polar':
                function = polar_complex
            else:
                function = getattr(cmath, fn)
            if 'divide-by-zero' in flags or 'invalid' in flags:
                try:
                    actual = function(arg)
                except ValueError:
                    continue
                else:
                    test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
                    self.fail('ValueError not raised in test %s' % test_str)

            if 'overflow' in flags:
                try:
                    actual = function(arg)
                except OverflowError:
                    continue
                else:
                    test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
                    self.fail('OverflowError not raised in test %s' % test_str)

            actual = function(arg)

            if 'ignore-real-sign' in flags:
                actual = complex(abs(actual.real), actual.imag)
                expected = complex(abs(expected.real), expected.imag)
            if 'ignore-imag-sign' in flags:
                actual = complex(actual.real, abs(actual.imag))
                expected = complex(expected.real, abs(expected.imag))

            # for the real part of the log function, we allow an
            # absolute error of up to 2e-15.
            if fn in ('log', 'log10'):
                real_abs_err = 2e-15
            else:
                real_abs_err = 5e-323

            if not (almostEqualF(expected.real, actual.real,
                                 abs_err = real_abs_err) and
                    almostEqualF(expected.imag, actual.imag)):
                error_message = (
                    "%s: %s(complex(%r, %r))\n" % (id, fn, ar, ai) +
                    "Expected: complex(%r, %r)\n" %
                                    (expected.real, expected.imag) +
                    "Received: complex(%r, %r)\n" %
                                    (actual.real, actual.imag) +
                    "Received value insufficiently close to expected value.")
                self.fail(error_message)

    def assertCISEqual(self, a, b):
        eps = 1E-7
        if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
            self.fail((a ,b))

    def test_polar(self):
        self.assertCISEqual(polar(0), (0., 0.))
        self.assertCISEqual(polar(1.), (1., 0.))
        self.assertCISEqual(polar(-1.), (1., pi))
        self.assertCISEqual(polar(1j), (1., pi/2))
        self.assertCISEqual(polar(-1j), (1., -pi/2))

    def test_phase(self):
        self.assertAlmostEqual(phase(0), 0.)
        self.assertAlmostEqual(phase(1.), 0.)
        self.assertAlmostEqual(phase(-1.), pi)
        self.assertAlmostEqual(phase(-1.+1E-300j), pi)
        self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
        self.assertAlmostEqual(phase(1j), pi/2)
        self.assertAlmostEqual(phase(-1j), -pi/2)

        # zeros
        self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
        self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
        self.assertEqual(phase(complex(-0.0, 0.0)), pi)
        self.assertEqual(phase(complex(-0.0, -0.0)), -pi)

        # infinities
        self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
        self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
        self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
        self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
        self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
        self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
        self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
        self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
        self.assertEqual(phase(complex(INF, -2.3)), -0.0)
        self.assertEqual(phase(complex(INF, -0.0)), -0.0)
        self.assertEqual(phase(complex(INF, 0.0)), 0.0)
        self.assertEqual(phase(complex(INF, 2.3)), 0.0)
        self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
        self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
        self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
        self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
        self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
        self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
        self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
        self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)

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

    def test_abs(self):
        # zeros
        for z in complex_zeros:
            self.assertEqual(abs(z), 0.0)

        # infinities
        for z in complex_infinities:
            self.assertEqual(abs(z), INF)

        # real or imaginary part NaN
        self.assertEqual(abs(complex(NAN, -INF)), INF)
        self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
        self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
        self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
        self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
        self.assertEqual(abs(complex(NAN, INF)), INF)
        self.assertEqual(abs(complex(-INF, NAN)), INF)
        self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
        self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
        self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
        self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
        self.assertEqual(abs(complex(INF, NAN)), INF)
        self.assertTrue(math.isnan(abs(complex(NAN, NAN))))

        # result overflows
        if float.__getformat__("double").startswith("IEEE"):
            self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))

    def assertCEqual(self, a, b):
        eps = 1E-7
        if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
            self.fail((a ,b))

    def test_rect(self):
        self.assertCEqual(rect(0, 0), (0, 0))
        self.assertCEqual(rect(1, 0), (1., 0))
        self.assertCEqual(rect(1, -pi), (-1., 0))
        self.assertCEqual(rect(1, pi/2), (0, 1.))
        self.assertCEqual(rect(1, -pi/2), (0, -1.))

    def test_isnan(self):
        self.assertFalse(cmath.isnan(1))
        self.assertFalse(cmath.isnan(1j))
        self.assertFalse(cmath.isnan(INF))
        self.assertTrue(cmath.isnan(NAN))
        self.assertTrue(cmath.isnan(complex(NAN, 0)))
        self.assertTrue(cmath.isnan(complex(0, NAN)))
        self.assertTrue(cmath.isnan(complex(NAN, NAN)))
        self.assertTrue(cmath.isnan(complex(NAN, INF)))
        self.assertTrue(cmath.isnan(complex(INF, NAN)))

    def test_isinf(self):
        self.assertFalse(cmath.isinf(1))
        self.assertFalse(cmath.isinf(1j))
        self.assertFalse(cmath.isinf(NAN))
        self.assertTrue(cmath.isinf(INF))
        self.assertTrue(cmath.isinf(complex(INF, 0)))
        self.assertTrue(cmath.isinf(complex(0, INF)))
        self.assertTrue(cmath.isinf(complex(INF, INF)))
        self.assertTrue(cmath.isinf(complex(NAN, INF)))
        self.assertTrue(cmath.isinf(complex(INF, NAN)))


def test_main():
    run_unittest(CMathTests)

if __name__ == "__main__":
    test_main()