source: python/trunk/Lib/test/test_fractions.py

Last change on this file was 391, checked in by dmik, 11 years ago

python: Merge vendor 2.7.6 to trunk.
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Line 
1"""Tests for Lib/fractions.py."""
2
3from decimal import Decimal
4from test.test_support import run_unittest
5import math
6import numbers
7import operator
8import fractions
9import sys
10import unittest
11from copy import copy, deepcopy
12from cPickle import dumps, loads
13F = fractions.Fraction
14gcd = fractions.gcd
15
16# decorator for skipping tests on non-IEEE 754 platforms
17requires_IEEE_754 = unittest.skipUnless(
18 float.__getformat__("double").startswith("IEEE"),
19 "test requires IEEE 754 doubles")
20
21class DummyFloat(object):
22 """Dummy float class for testing comparisons with Fractions"""
23
24 def __init__(self, value):
25 if not isinstance(value, float):
26 raise TypeError("DummyFloat can only be initialized from float")
27 self.value = value
28
29 def _richcmp(self, other, op):
30 if isinstance(other, numbers.Rational):
31 return op(F.from_float(self.value), other)
32 elif isinstance(other, DummyFloat):
33 return op(self.value, other.value)
34 else:
35 return NotImplemented
36
37 def __eq__(self, other): return self._richcmp(other, operator.eq)
38 def __le__(self, other): return self._richcmp(other, operator.le)
39 def __lt__(self, other): return self._richcmp(other, operator.lt)
40 def __ge__(self, other): return self._richcmp(other, operator.ge)
41 def __gt__(self, other): return self._richcmp(other, operator.gt)
42
43 # shouldn't be calling __float__ at all when doing comparisons
44 def __float__(self):
45 assert False, "__float__ should not be invoked for comparisons"
46
47 # same goes for subtraction
48 def __sub__(self, other):
49 assert False, "__sub__ should not be invoked for comparisons"
50 __rsub__ = __sub__
51
52 # Silence Py3k warning
53 __hash__ = None
54
55
56class DummyRational(object):
57 """Test comparison of Fraction with a naive rational implementation."""
58
59 def __init__(self, num, den):
60 g = gcd(num, den)
61 self.num = num // g
62 self.den = den // g
63
64 def __eq__(self, other):
65 if isinstance(other, fractions.Fraction):
66 return (self.num == other._numerator and
67 self.den == other._denominator)
68 else:
69 return NotImplemented
70
71 def __lt__(self, other):
72 return(self.num * other._denominator < self.den * other._numerator)
73
74 def __gt__(self, other):
75 return(self.num * other._denominator > self.den * other._numerator)
76
77 def __le__(self, other):
78 return(self.num * other._denominator <= self.den * other._numerator)
79
80 def __ge__(self, other):
81 return(self.num * other._denominator >= self.den * other._numerator)
82
83 # this class is for testing comparisons; conversion to float
84 # should never be used for a comparison, since it loses accuracy
85 def __float__(self):
86 assert False, "__float__ should not be invoked"
87
88 # Silence Py3k warning
89 __hash__ = None
90
91
92class DummyFraction(fractions.Fraction):
93 """Dummy Fraction subclass for copy and deepcopy testing."""
94
95class GcdTest(unittest.TestCase):
96
97 def testMisc(self):
98 self.assertEqual(0, gcd(0, 0))
99 self.assertEqual(1, gcd(1, 0))
100 self.assertEqual(-1, gcd(-1, 0))
101 self.assertEqual(1, gcd(0, 1))
102 self.assertEqual(-1, gcd(0, -1))
103 self.assertEqual(1, gcd(7, 1))
104 self.assertEqual(-1, gcd(7, -1))
105 self.assertEqual(1, gcd(-23, 15))
106 self.assertEqual(12, gcd(120, 84))
107 self.assertEqual(-12, gcd(84, -120))
108
109
110def _components(r):
111 return (r.numerator, r.denominator)
112
113
114class FractionTest(unittest.TestCase):
115
116 def assertTypedEquals(self, expected, actual):
117 """Asserts that both the types and values are the same."""
118 self.assertEqual(type(expected), type(actual))
119 self.assertEqual(expected, actual)
120
121 def assertRaisesMessage(self, exc_type, message,
122 callable, *args, **kwargs):
123 """Asserts that callable(*args, **kwargs) raises exc_type(message)."""
124 try:
125 callable(*args, **kwargs)
126 except exc_type, e:
127 self.assertEqual(message, str(e))
128 else:
129 self.fail("%s not raised" % exc_type.__name__)
130
131 def testInit(self):
132 self.assertEqual((0, 1), _components(F()))
133 self.assertEqual((7, 1), _components(F(7)))
134 self.assertEqual((7, 3), _components(F(F(7, 3))))
135
136 self.assertEqual((-1, 1), _components(F(-1, 1)))
137 self.assertEqual((-1, 1), _components(F(1, -1)))
138 self.assertEqual((1, 1), _components(F(-2, -2)))
139 self.assertEqual((1, 2), _components(F(5, 10)))
140 self.assertEqual((7, 15), _components(F(7, 15)))
141 self.assertEqual((10**23, 1), _components(F(10**23)))
142
143 self.assertEqual((3, 77), _components(F(F(3, 7), 11)))
144 self.assertEqual((-9, 5), _components(F(2, F(-10, 9))))
145 self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113))))
146
147 self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
148 F, 12, 0)
149 self.assertRaises(TypeError, F, 1.5 + 3j)
150
151 self.assertRaises(TypeError, F, "3/2", 3)
152 self.assertRaises(TypeError, F, 3, 0j)
153 self.assertRaises(TypeError, F, 3, 1j)
154
155 @requires_IEEE_754
156 def testInitFromFloat(self):
157 self.assertEqual((5, 2), _components(F(2.5)))
158 self.assertEqual((0, 1), _components(F(-0.0)))
159 self.assertEqual((3602879701896397, 36028797018963968),
160 _components(F(0.1)))
161 self.assertRaises(TypeError, F, float('nan'))
162 self.assertRaises(TypeError, F, float('inf'))
163 self.assertRaises(TypeError, F, float('-inf'))
164
165 def testInitFromDecimal(self):
166 self.assertEqual((11, 10),
167 _components(F(Decimal('1.1'))))
168 self.assertEqual((7, 200),
169 _components(F(Decimal('3.5e-2'))))
170 self.assertEqual((0, 1),
171 _components(F(Decimal('.000e20'))))
172 self.assertRaises(TypeError, F, Decimal('nan'))
173 self.assertRaises(TypeError, F, Decimal('snan'))
174 self.assertRaises(TypeError, F, Decimal('inf'))
175 self.assertRaises(TypeError, F, Decimal('-inf'))
176
177 def testFromString(self):
178 self.assertEqual((5, 1), _components(F("5")))
179 self.assertEqual((3, 2), _components(F("3/2")))
180 self.assertEqual((3, 2), _components(F(" \n +3/2")))
181 self.assertEqual((-3, 2), _components(F("-3/2 ")))
182 self.assertEqual((13, 2), _components(F(" 013/02 \n ")))
183 self.assertEqual((13, 2), _components(F(u" 013/02 \n ")))
184
185 self.assertEqual((16, 5), _components(F(" 3.2 ")))
186 self.assertEqual((-16, 5), _components(F(u" -3.2 ")))
187 self.assertEqual((-3, 1), _components(F(u" -3. ")))
188 self.assertEqual((3, 5), _components(F(u" .6 ")))
189 self.assertEqual((1, 3125), _components(F("32.e-5")))
190 self.assertEqual((1000000, 1), _components(F("1E+06")))
191 self.assertEqual((-12300, 1), _components(F("-1.23e4")))
192 self.assertEqual((0, 1), _components(F(" .0e+0\t")))
193 self.assertEqual((0, 1), _components(F("-0.000e0")))
194
195
196 self.assertRaisesMessage(
197 ZeroDivisionError, "Fraction(3, 0)",
198 F, "3/0")
199 self.assertRaisesMessage(
200 ValueError, "Invalid literal for Fraction: '3/'",
201 F, "3/")
202 self.assertRaisesMessage(
203 ValueError, "Invalid literal for Fraction: '/2'",
204 F, "/2")
205 self.assertRaisesMessage(
206 ValueError, "Invalid literal for Fraction: '3 /2'",
207 F, "3 /2")
208 self.assertRaisesMessage(
209 # Denominators don't need a sign.
210 ValueError, "Invalid literal for Fraction: '3/+2'",
211 F, "3/+2")
212 self.assertRaisesMessage(
213 # Imitate float's parsing.
214 ValueError, "Invalid literal for Fraction: '+ 3/2'",
215 F, "+ 3/2")
216 self.assertRaisesMessage(
217 # Avoid treating '.' as a regex special character.
218 ValueError, "Invalid literal for Fraction: '3a2'",
219 F, "3a2")
220 self.assertRaisesMessage(
221 # Don't accept combinations of decimals and fractions.
222 ValueError, "Invalid literal for Fraction: '3/7.2'",
223 F, "3/7.2")
224 self.assertRaisesMessage(
225 # Don't accept combinations of decimals and fractions.
226 ValueError, "Invalid literal for Fraction: '3.2/7'",
227 F, "3.2/7")
228 self.assertRaisesMessage(
229 # Allow 3. and .3, but not .
230 ValueError, "Invalid literal for Fraction: '.'",
231 F, ".")
232
233 def testImmutable(self):
234 r = F(7, 3)
235 r.__init__(2, 15)
236 self.assertEqual((7, 3), _components(r))
237
238 self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
239 self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
240 self.assertEqual((7, 3), _components(r))
241
242 # But if you _really_ need to:
243 r._numerator = 4
244 r._denominator = 2
245 self.assertEqual((4, 2), _components(r))
246 # Which breaks some important operations:
247 self.assertNotEqual(F(4, 2), r)
248
249 def testFromFloat(self):
250 self.assertRaises(TypeError, F.from_float, 3+4j)
251 self.assertEqual((10, 1), _components(F.from_float(10)))
252 bigint = 1234567890123456789
253 self.assertEqual((bigint, 1), _components(F.from_float(bigint)))
254 self.assertEqual((0, 1), _components(F.from_float(-0.0)))
255 self.assertEqual((10, 1), _components(F.from_float(10.0)))
256 self.assertEqual((-5, 2), _components(F.from_float(-2.5)))
257 self.assertEqual((99999999999999991611392, 1),
258 _components(F.from_float(1e23)))
259 self.assertEqual(float(10**23), float(F.from_float(1e23)))
260 self.assertEqual((3602879701896397, 1125899906842624),
261 _components(F.from_float(3.2)))
262 self.assertEqual(3.2, float(F.from_float(3.2)))
263
264 inf = 1e1000
265 nan = inf - inf
266 self.assertRaisesMessage(
267 TypeError, "Cannot convert inf to Fraction.",
268 F.from_float, inf)
269 self.assertRaisesMessage(
270 TypeError, "Cannot convert -inf to Fraction.",
271 F.from_float, -inf)
272 self.assertRaisesMessage(
273 TypeError, "Cannot convert nan to Fraction.",
274 F.from_float, nan)
275
276 def testFromDecimal(self):
277 self.assertRaises(TypeError, F.from_decimal, 3+4j)
278 self.assertEqual(F(10, 1), F.from_decimal(10))
279 self.assertEqual(F(0), F.from_decimal(Decimal("-0")))
280 self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5")))
281 self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3")))
282 self.assertEqual(F(5000), F.from_decimal(Decimal("5e3")))
283 self.assertEqual(1 - F(1, 10**30),
284 F.from_decimal(Decimal("0." + "9" * 30)))
285
286 self.assertRaisesMessage(
287 TypeError, "Cannot convert Infinity to Fraction.",
288 F.from_decimal, Decimal("inf"))
289 self.assertRaisesMessage(
290 TypeError, "Cannot convert -Infinity to Fraction.",
291 F.from_decimal, Decimal("-inf"))
292 self.assertRaisesMessage(
293 TypeError, "Cannot convert NaN to Fraction.",
294 F.from_decimal, Decimal("nan"))
295 self.assertRaisesMessage(
296 TypeError, "Cannot convert sNaN to Fraction.",
297 F.from_decimal, Decimal("snan"))
298
299 def testLimitDenominator(self):
300 rpi = F('3.1415926535897932')
301 self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
302 self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
303 self.assertEqual(rpi.limit_denominator(113), F(355, 113))
304 self.assertEqual(rpi.limit_denominator(112), F(333, 106))
305 self.assertEqual(F(201, 200).limit_denominator(100), F(1))
306 self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
307 self.assertEqual(F(0).limit_denominator(10000), F(0))
308 for i in (0, -1):
309 self.assertRaisesMessage(
310 ValueError, "max_denominator should be at least 1",
311 F(1).limit_denominator, i)
312
313 def testConversions(self):
314 self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
315 self.assertTypedEquals(-1, int(F(-11, 10)))
316 self.assertTypedEquals(1, math.trunc(F(11, 10)))
317 self.assertEqual(False, bool(F(0, 1)))
318 self.assertEqual(True, bool(F(3, 2)))
319 self.assertTypedEquals(0.1, float(F(1, 10)))
320
321 # Check that __float__ isn't implemented by converting the
322 # numerator and denominator to float before dividing.
323 self.assertRaises(OverflowError, float, long('2'*400+'7'))
324 self.assertAlmostEqual(2.0/3,
325 float(F(long('2'*400+'7'), long('3'*400+'1'))))
326
327 self.assertTypedEquals(0.1+0j, complex(F(1,10)))
328
329
330 def testArithmetic(self):
331 self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
332 self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
333 self.assertEqual(F(1, 25), F(1, 10) * F(2, 5))
334 self.assertEqual(F(1, 4), F(1, 10) / F(2, 5))
335 self.assertTypedEquals(2, F(9, 10) // F(2, 5))
336 self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
337 self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2))
338 self.assertEqual(F(8, 27), F(2, 3) ** F(3))
339 self.assertEqual(F(27, 8), F(2, 3) ** F(-3))
340 self.assertTypedEquals(2.0, F(4) ** F(1, 2))
341 self.assertEqual(F(1, 1), +F(1, 1))
342 # Will return 1j in 3.0:
343 self.assertRaises(ValueError, pow, F(-1), F(1, 2))
344
345 def testMixedArithmetic(self):
346 self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
347 self.assertTypedEquals(1.1, F(1, 10) + 1.0)
348 self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
349 self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
350 self.assertTypedEquals(1.1, 1.0 + F(1, 10))
351 self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
352
353 self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
354 self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
355 self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
356 self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
357 self.assertTypedEquals(0.9, 1.0 - F(1, 10))
358 self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
359
360 self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
361 self.assertTypedEquals(0.1, F(1, 10) * 1.0)
362 self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
363 self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
364 self.assertTypedEquals(0.1, 1.0 * F(1, 10))
365 self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
366
367 self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
368 self.assertTypedEquals(0.1, F(1, 10) / 1.0)
369 self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
370 self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
371 self.assertTypedEquals(10.0, 1.0 / F(1, 10))
372 self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
373
374 self.assertTypedEquals(0, F(1, 10) // 1)
375 self.assertTypedEquals(0.0, F(1, 10) // 1.0)
376 self.assertTypedEquals(10, 1 // F(1, 10))
377 self.assertTypedEquals(10**23, 10**22 // F(1, 10))
378 self.assertTypedEquals(10.0, 1.0 // F(1, 10))
379
380 self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
381 self.assertTypedEquals(0.1, F(1, 10) % 1.0)
382 self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
383 self.assertTypedEquals(0.0, 1.0 % F(1, 10))
384
385 # No need for divmod since we don't override it.
386
387 # ** has more interesting conversion rules.
388 self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
389 self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
390 self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
391 self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
392 self.assertTypedEquals(4 , 2 ** F(2, 1))
393 # Will return 1j in 3.0:
394 self.assertRaises(ValueError, pow, (-1), F(1, 2))
395 self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
396 self.assertTypedEquals(2.0 , 4 ** F(1, 2))
397 self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
398 self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
399
400 def testMixingWithDecimal(self):
401 # Decimal refuses mixed comparisons.
402 self.assertRaisesMessage(
403 TypeError,
404 "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
405 operator.add, F(3,11), Decimal('3.1415926'))
406 self.assertRaisesMessage(
407 TypeError,
408 "unsupported operand type(s) for +: 'Decimal' and 'Fraction'",
409 operator.add, Decimal('3.1415926'), F(3,11))
410 self.assertNotEqual(F(5, 2), Decimal('2.5'))
411
412 def testComparisons(self):
413 self.assertTrue(F(1, 2) < F(2, 3))
414 self.assertFalse(F(1, 2) < F(1, 2))
415 self.assertTrue(F(1, 2) <= F(2, 3))
416 self.assertTrue(F(1, 2) <= F(1, 2))
417 self.assertFalse(F(2, 3) <= F(1, 2))
418 self.assertTrue(F(1, 2) == F(1, 2))
419 self.assertFalse(F(1, 2) == F(1, 3))
420 self.assertFalse(F(1, 2) != F(1, 2))
421 self.assertTrue(F(1, 2) != F(1, 3))
422
423 def testComparisonsDummyRational(self):
424 self.assertTrue(F(1, 2) == DummyRational(1, 2))
425 self.assertTrue(DummyRational(1, 2) == F(1, 2))
426 self.assertFalse(F(1, 2) == DummyRational(3, 4))
427 self.assertFalse(DummyRational(3, 4) == F(1, 2))
428
429 self.assertTrue(F(1, 2) < DummyRational(3, 4))
430 self.assertFalse(F(1, 2) < DummyRational(1, 2))
431 self.assertFalse(F(1, 2) < DummyRational(1, 7))
432 self.assertFalse(F(1, 2) > DummyRational(3, 4))
433 self.assertFalse(F(1, 2) > DummyRational(1, 2))
434 self.assertTrue(F(1, 2) > DummyRational(1, 7))
435 self.assertTrue(F(1, 2) <= DummyRational(3, 4))
436 self.assertTrue(F(1, 2) <= DummyRational(1, 2))
437 self.assertFalse(F(1, 2) <= DummyRational(1, 7))
438 self.assertFalse(F(1, 2) >= DummyRational(3, 4))
439 self.assertTrue(F(1, 2) >= DummyRational(1, 2))
440 self.assertTrue(F(1, 2) >= DummyRational(1, 7))
441
442 self.assertTrue(DummyRational(1, 2) < F(3, 4))
443 self.assertFalse(DummyRational(1, 2) < F(1, 2))
444 self.assertFalse(DummyRational(1, 2) < F(1, 7))
445 self.assertFalse(DummyRational(1, 2) > F(3, 4))
446 self.assertFalse(DummyRational(1, 2) > F(1, 2))
447 self.assertTrue(DummyRational(1, 2) > F(1, 7))
448 self.assertTrue(DummyRational(1, 2) <= F(3, 4))
449 self.assertTrue(DummyRational(1, 2) <= F(1, 2))
450 self.assertFalse(DummyRational(1, 2) <= F(1, 7))
451 self.assertFalse(DummyRational(1, 2) >= F(3, 4))
452 self.assertTrue(DummyRational(1, 2) >= F(1, 2))
453 self.assertTrue(DummyRational(1, 2) >= F(1, 7))
454
455 def testComparisonsDummyFloat(self):
456 x = DummyFloat(1./3.)
457 y = F(1, 3)
458 self.assertTrue(x != y)
459 self.assertTrue(x < y or x > y)
460 self.assertFalse(x == y)
461 self.assertFalse(x <= y and x >= y)
462 self.assertTrue(y != x)
463 self.assertTrue(y < x or y > x)
464 self.assertFalse(y == x)
465 self.assertFalse(y <= x and y >= x)
466
467 def testMixedLess(self):
468 self.assertTrue(2 < F(5, 2))
469 self.assertFalse(2 < F(4, 2))
470 self.assertTrue(F(5, 2) < 3)
471 self.assertFalse(F(4, 2) < 2)
472
473 self.assertTrue(F(1, 2) < 0.6)
474 self.assertFalse(F(1, 2) < 0.4)
475 self.assertTrue(0.4 < F(1, 2))
476 self.assertFalse(0.5 < F(1, 2))
477
478 self.assertFalse(float('inf') < F(1, 2))
479 self.assertTrue(float('-inf') < F(0, 10))
480 self.assertFalse(float('nan') < F(-3, 7))
481 self.assertTrue(F(1, 2) < float('inf'))
482 self.assertFalse(F(17, 12) < float('-inf'))
483 self.assertFalse(F(144, -89) < float('nan'))
484
485 def testMixedLessEqual(self):
486 self.assertTrue(0.5 <= F(1, 2))
487 self.assertFalse(0.6 <= F(1, 2))
488 self.assertTrue(F(1, 2) <= 0.5)
489 self.assertFalse(F(1, 2) <= 0.4)
490 self.assertTrue(2 <= F(4, 2))
491 self.assertFalse(2 <= F(3, 2))
492 self.assertTrue(F(4, 2) <= 2)
493 self.assertFalse(F(5, 2) <= 2)
494
495 self.assertFalse(float('inf') <= F(1, 2))
496 self.assertTrue(float('-inf') <= F(0, 10))
497 self.assertFalse(float('nan') <= F(-3, 7))
498 self.assertTrue(F(1, 2) <= float('inf'))
499 self.assertFalse(F(17, 12) <= float('-inf'))
500 self.assertFalse(F(144, -89) <= float('nan'))
501
502 def testBigFloatComparisons(self):
503 # Because 10**23 can't be represented exactly as a float:
504 self.assertFalse(F(10**23) == float(10**23))
505 # The first test demonstrates why these are important.
506 self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
507 self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
508 self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
509 self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
510 self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
511
512 def testBigComplexComparisons(self):
513 self.assertFalse(F(10**23) == complex(10**23))
514 self.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23))
515 self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23))
516
517 x = F(3, 8)
518 z = complex(0.375, 0.0)
519 w = complex(0.375, 0.2)
520 self.assertTrue(x == z)
521 self.assertFalse(x != z)
522 self.assertFalse(x == w)
523 self.assertTrue(x != w)
524 for op in operator.lt, operator.le, operator.gt, operator.ge:
525 self.assertRaises(TypeError, op, x, z)
526 self.assertRaises(TypeError, op, z, x)
527 self.assertRaises(TypeError, op, x, w)
528 self.assertRaises(TypeError, op, w, x)
529
530 def testMixedEqual(self):
531 self.assertTrue(0.5 == F(1, 2))
532 self.assertFalse(0.6 == F(1, 2))
533 self.assertTrue(F(1, 2) == 0.5)
534 self.assertFalse(F(1, 2) == 0.4)
535 self.assertTrue(2 == F(4, 2))
536 self.assertFalse(2 == F(3, 2))
537 self.assertTrue(F(4, 2) == 2)
538 self.assertFalse(F(5, 2) == 2)
539 self.assertFalse(F(5, 2) == float('nan'))
540 self.assertFalse(float('nan') == F(3, 7))
541 self.assertFalse(F(5, 2) == float('inf'))
542 self.assertFalse(float('-inf') == F(2, 5))
543
544 def testStringification(self):
545 self.assertEqual("Fraction(7, 3)", repr(F(7, 3)))
546 self.assertEqual("Fraction(6283185307, 2000000000)",
547 repr(F('3.1415926535')))
548 self.assertEqual("Fraction(-1, 100000000000000000000)",
549 repr(F(1, -10**20)))
550 self.assertEqual("7/3", str(F(7, 3)))
551 self.assertEqual("7", str(F(7, 1)))
552
553 def testHash(self):
554 self.assertEqual(hash(2.5), hash(F(5, 2)))
555 self.assertEqual(hash(10**50), hash(F(10**50)))
556 self.assertNotEqual(hash(float(10**23)), hash(F(10**23)))
557
558 def testApproximatePi(self):
559 # Algorithm borrowed from
560 # http://docs.python.org/lib/decimal-recipes.html
561 three = F(3)
562 lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
563 while abs(s - lasts) > F(1, 10**9):
564 lasts = s
565 n, na = n+na, na+8
566 d, da = d+da, da+32
567 t = (t * n) / d
568 s += t
569 self.assertAlmostEqual(math.pi, s)
570
571 def testApproximateCos1(self):
572 # Algorithm borrowed from
573 # http://docs.python.org/lib/decimal-recipes.html
574 x = F(1)
575 i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
576 while abs(s - lasts) > F(1, 10**9):
577 lasts = s
578 i += 2
579 fact *= i * (i-1)
580 num *= x * x
581 sign *= -1
582 s += num / fact * sign
583 self.assertAlmostEqual(math.cos(1), s)
584
585 def test_copy_deepcopy_pickle(self):
586 r = F(13, 7)
587 dr = DummyFraction(13, 7)
588 self.assertEqual(r, loads(dumps(r)))
589 self.assertEqual(id(r), id(copy(r)))
590 self.assertEqual(id(r), id(deepcopy(r)))
591 self.assertNotEqual(id(dr), id(copy(dr)))
592 self.assertNotEqual(id(dr), id(deepcopy(dr)))
593 self.assertTypedEquals(dr, copy(dr))
594 self.assertTypedEquals(dr, deepcopy(dr))
595
596 def test_slots(self):
597 # Issue 4998
598 r = F(13, 7)
599 self.assertRaises(AttributeError, setattr, r, 'a', 10)
600
601def test_main():
602 run_unittest(FractionTest, GcdTest)
603
604if __name__ == '__main__':
605 test_main()
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