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/Lib/test/test_math.py

http://unladen-swallow.googlecode.com/
Python | 894 lines | 716 code | 91 blank | 87 comment | 53 complexity | ae6ab4ed74f11a85c9805a612cbd17f0 MD5 | raw file
  1# Python test set -- math module
  2# XXXX Should not do tests around zero only
  3
  4from test.test_support import run_unittest, verbose
  5import unittest
  6import math
  7import os
  8import sys
  9import random
 10
 11eps = 1E-05
 12NAN = float('nan')
 13INF = float('inf')
 14NINF = float('-inf')
 15
 16# locate file with test values
 17if __name__ == '__main__':
 18    file = sys.argv[0]
 19else:
 20    file = __file__
 21test_dir = os.path.dirname(file) or os.curdir
 22test_file = os.path.join(test_dir, 'cmath_testcases.txt')
 23
 24def parse_testfile(fname):
 25    """Parse a file with test values
 26
 27    Empty lines or lines starting with -- are ignored
 28    yields id, fn, arg_real, arg_imag, exp_real, exp_imag
 29    """
 30    with open(fname) as fp:
 31        for line in fp:
 32            # skip comment lines and blank lines
 33            if line.startswith('--') or not line.strip():
 34                continue
 35
 36            lhs, rhs = line.split('->')
 37            id, fn, arg_real, arg_imag = lhs.split()
 38            rhs_pieces = rhs.split()
 39            exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
 40            flags = rhs_pieces[2:]
 41
 42            yield (id, fn,
 43                   float(arg_real), float(arg_imag),
 44                   float(exp_real), float(exp_imag),
 45                   flags
 46                  )
 47
 48class MathTests(unittest.TestCase):
 49
 50    def ftest(self, name, value, expected):
 51        if abs(value-expected) > eps:
 52            # Use %r instead of %f so the error message
 53            # displays full precision. Otherwise discrepancies
 54            # in the last few bits will lead to very confusing
 55            # error messages
 56            self.fail('%s returned %r, expected %r' %
 57                      (name, value, expected))
 58
 59    def testConstants(self):
 60        self.ftest('pi', math.pi, 3.1415926)
 61        self.ftest('e', math.e, 2.7182818)
 62
 63    def testAcos(self):
 64        self.assertRaises(TypeError, math.acos)
 65        self.ftest('acos(-1)', math.acos(-1), math.pi)
 66        self.ftest('acos(0)', math.acos(0), math.pi/2)
 67        self.ftest('acos(1)', math.acos(1), 0)
 68        self.assertRaises(ValueError, math.acos, INF)
 69        self.assertRaises(ValueError, math.acos, NINF)
 70        self.assert_(math.isnan(math.acos(NAN)))
 71
 72    def testAcosh(self):
 73        self.assertRaises(TypeError, math.acosh)
 74        self.ftest('acosh(1)', math.acosh(1), 0)
 75        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
 76        self.assertRaises(ValueError, math.acosh, 0)
 77        self.assertRaises(ValueError, math.acosh, -1)
 78        self.assertEquals(math.acosh(INF), INF)
 79        self.assertRaises(ValueError, math.acosh, NINF)
 80        self.assert_(math.isnan(math.acosh(NAN)))
 81
 82    def testAsin(self):
 83        self.assertRaises(TypeError, math.asin)
 84        self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
 85        self.ftest('asin(0)', math.asin(0), 0)
 86        self.ftest('asin(1)', math.asin(1), math.pi/2)
 87        self.assertRaises(ValueError, math.asin, INF)
 88        self.assertRaises(ValueError, math.asin, NINF)
 89        self.assert_(math.isnan(math.asin(NAN)))
 90
 91    def testAsinh(self):
 92        self.assertRaises(TypeError, math.asinh)
 93        self.ftest('asinh(0)', math.asinh(0), 0)
 94        self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
 95        self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
 96        self.assertEquals(math.asinh(INF), INF)
 97        self.assertEquals(math.asinh(NINF), NINF)
 98        self.assert_(math.isnan(math.asinh(NAN)))
 99
100    def testAtan(self):
101        self.assertRaises(TypeError, math.atan)
102        self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
103        self.ftest('atan(0)', math.atan(0), 0)
104        self.ftest('atan(1)', math.atan(1), math.pi/4)
105        self.ftest('atan(inf)', math.atan(INF), math.pi/2)
106        self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
107        self.assert_(math.isnan(math.atan(NAN)))
108
109    def testAtanh(self):
110        self.assertRaises(TypeError, math.atan)
111        self.ftest('atanh(0)', math.atanh(0), 0)
112        self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
113        self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
114        self.assertRaises(ValueError, math.atanh, 1)
115        self.assertRaises(ValueError, math.atanh, -1)
116        self.assertRaises(ValueError, math.atanh, INF)
117        self.assertRaises(ValueError, math.atanh, NINF)
118        self.assert_(math.isnan(math.atanh(NAN)))
119
120    def testAtan2(self):
121        self.assertRaises(TypeError, math.atan2)
122        self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
123        self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
124        self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
125        self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
126        self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
127
128        # math.atan2(0, x)
129        self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
130        self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
131        self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
132        self.assertEqual(math.atan2(0., 0.), 0.)
133        self.assertEqual(math.atan2(0., 2.3), 0.)
134        self.assertEqual(math.atan2(0., INF), 0.)
135        self.assert_(math.isnan(math.atan2(0., NAN)))
136        # math.atan2(-0, x)
137        self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
138        self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
139        self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
140        self.assertEqual(math.atan2(-0., 0.), -0.)
141        self.assertEqual(math.atan2(-0., 2.3), -0.)
142        self.assertEqual(math.atan2(-0., INF), -0.)
143        self.assert_(math.isnan(math.atan2(-0., NAN)))
144        # math.atan2(INF, x)
145        self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
146        self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
147        self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
148        self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
149        self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
150        self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
151        self.assert_(math.isnan(math.atan2(INF, NAN)))
152        # math.atan2(NINF, x)
153        self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
154        self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
155        self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
156        self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
157        self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
158        self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
159        self.assert_(math.isnan(math.atan2(NINF, NAN)))
160        # math.atan2(+finite, x)
161        self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
162        self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
163        self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
164        self.assertEqual(math.atan2(2.3, INF), 0.)
165        self.assert_(math.isnan(math.atan2(2.3, NAN)))
166        # math.atan2(-finite, x)
167        self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
168        self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
169        self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
170        self.assertEqual(math.atan2(-2.3, INF), -0.)
171        self.assert_(math.isnan(math.atan2(-2.3, NAN)))
172        # math.atan2(NAN, x)
173        self.assert_(math.isnan(math.atan2(NAN, NINF)))
174        self.assert_(math.isnan(math.atan2(NAN, -2.3)))
175        self.assert_(math.isnan(math.atan2(NAN, -0.)))
176        self.assert_(math.isnan(math.atan2(NAN, 0.)))
177        self.assert_(math.isnan(math.atan2(NAN, 2.3)))
178        self.assert_(math.isnan(math.atan2(NAN, INF)))
179        self.assert_(math.isnan(math.atan2(NAN, NAN)))
180
181    def testCeil(self):
182        self.assertRaises(TypeError, math.ceil)
183        # These types will be int in py3k.
184        self.assertEquals(float, type(math.ceil(1)))
185        self.assertEquals(float, type(math.ceil(1L)))
186        self.assertEquals(float, type(math.ceil(1.0)))
187        self.ftest('ceil(0.5)', math.ceil(0.5), 1)
188        self.ftest('ceil(1.0)', math.ceil(1.0), 1)
189        self.ftest('ceil(1.5)', math.ceil(1.5), 2)
190        self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
191        self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
192        self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
193        self.assertEquals(math.ceil(INF), INF)
194        self.assertEquals(math.ceil(NINF), NINF)
195        self.assert_(math.isnan(math.ceil(NAN)))
196
197        class TestCeil(object):
198            def __float__(self):
199                return 41.3
200        class TestNoCeil(object):
201            pass
202        self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
203        self.assertRaises(TypeError, math.ceil, TestNoCeil())
204
205        t = TestNoCeil()
206        t.__ceil__ = lambda *args: args
207        self.assertRaises(TypeError, math.ceil, t)
208        self.assertRaises(TypeError, math.ceil, t, 0)
209
210    if float.__getformat__("double").startswith("IEEE"):
211        def testCopysign(self):
212            self.assertRaises(TypeError, math.copysign)
213            # copysign should let us distinguish signs of zeros
214            self.assertEquals(copysign(1., 0.), 1.)
215            self.assertEquals(copysign(1., -0.), -1.)
216            self.assertEquals(copysign(INF, 0.), INF)
217            self.assertEquals(copysign(INF, -0.), NINF)
218            self.assertEquals(copysign(NINF, 0.), INF)
219            self.assertEquals(copysign(NINF, -0.), NINF)
220            # and of infinities
221            self.assertEquals(copysign(1., INF), 1.)
222            self.assertEquals(copysign(1., NINF), -1.)
223            self.assertEquals(copysign(INF, INF), INF)
224            self.assertEquals(copysign(INF, NINF), NINF)
225            self.assertEquals(copysign(NINF, INF), INF)
226            self.assertEquals(copysign(NINF, NINF), NINF)
227            self.assert_(math.isnan(copysign(NAN, 1.)))
228            self.assert_(math.isnan(copysign(NAN, INF)))
229            self.assert_(math.isnan(copysign(NAN, NINF)))
230            self.assert_(math.isnan(copysign(NAN, NAN)))
231            # copysign(INF, NAN) may be INF or it may be NINF, since
232            # we don't know whether the sign bit of NAN is set on any
233            # given platform.
234            self.assert_(math.isinf(copysign(INF, NAN)))
235            # similarly, copysign(2., NAN) could be 2. or -2.
236            self.assertEquals(abs(copysign(2., NAN)), 2.)
237
238    def testCos(self):
239        self.assertRaises(TypeError, math.cos)
240        self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
241        self.ftest('cos(0)', math.cos(0), 1)
242        self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
243        self.ftest('cos(pi)', math.cos(math.pi), -1)
244        try:
245            self.assert_(math.isnan(math.cos(INF)))
246            self.assert_(math.isnan(math.cos(NINF)))
247        except ValueError:
248            self.assertRaises(ValueError, math.cos, INF)
249            self.assertRaises(ValueError, math.cos, NINF)
250        self.assert_(math.isnan(math.cos(NAN)))
251
252    def testCosh(self):
253        self.assertRaises(TypeError, math.cosh)
254        self.ftest('cosh(0)', math.cosh(0), 1)
255        self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
256        self.assertEquals(math.cosh(INF), INF)
257        self.assertEquals(math.cosh(NINF), INF)
258        self.assert_(math.isnan(math.cosh(NAN)))
259
260    def testDegrees(self):
261        self.assertRaises(TypeError, math.degrees)
262        self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
263        self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
264        self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
265
266    def testExp(self):
267        self.assertRaises(TypeError, math.exp)
268        self.ftest('exp(-1)', math.exp(-1), 1/math.e)
269        self.ftest('exp(0)', math.exp(0), 1)
270        self.ftest('exp(1)', math.exp(1), math.e)
271        self.assertEquals(math.exp(INF), INF)
272        self.assertEquals(math.exp(NINF), 0.)
273        self.assert_(math.isnan(math.exp(NAN)))
274
275    def testFabs(self):
276        self.assertRaises(TypeError, math.fabs)
277        self.ftest('fabs(-1)', math.fabs(-1), 1)
278        self.ftest('fabs(0)', math.fabs(0), 0)
279        self.ftest('fabs(1)', math.fabs(1), 1)
280
281    def testFactorial(self):
282        def fact(n):
283            result = 1
284            for i in range(1, int(n)+1):
285                result *= i
286            return result
287        values = range(10) + [50, 100, 500]
288        random.shuffle(values)
289        for x in range(10):
290            for cast in (int, long, float):
291                self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x)))
292        self.assertRaises(ValueError, math.factorial, -1)
293        self.assertRaises(ValueError, math.factorial, math.pi)
294
295    def testFloor(self):
296        self.assertRaises(TypeError, math.floor)
297        # These types will be int in py3k.
298        self.assertEquals(float, type(math.floor(1)))
299        self.assertEquals(float, type(math.floor(1L)))
300        self.assertEquals(float, type(math.floor(1.0)))
301        self.ftest('floor(0.5)', math.floor(0.5), 0)
302        self.ftest('floor(1.0)', math.floor(1.0), 1)
303        self.ftest('floor(1.5)', math.floor(1.5), 1)
304        self.ftest('floor(-0.5)', math.floor(-0.5), -1)
305        self.ftest('floor(-1.0)', math.floor(-1.0), -1)
306        self.ftest('floor(-1.5)', math.floor(-1.5), -2)
307        # pow() relies on floor() to check for integers
308        # This fails on some platforms - so check it here
309        self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
310        self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
311        self.assertEquals(math.ceil(INF), INF)
312        self.assertEquals(math.ceil(NINF), NINF)
313        self.assert_(math.isnan(math.floor(NAN)))
314
315        class TestFloor(object):
316            def __float__(self):
317                return 42.3
318        class TestNoFloor(object):
319            pass
320        self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
321        self.assertRaises(TypeError, math.floor, TestNoFloor())
322
323        t = TestNoFloor()
324        t.__floor__ = lambda *args: args
325        self.assertRaises(TypeError, math.floor, t)
326        self.assertRaises(TypeError, math.floor, t, 0)
327
328    def testFmod(self):
329        self.assertRaises(TypeError, math.fmod)
330        self.ftest('fmod(10,1)', math.fmod(10,1), 0)
331        self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
332        self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
333        self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
334        self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
335        self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
336        self.assert_(math.isnan(math.fmod(NAN, 1.)))
337        self.assert_(math.isnan(math.fmod(1., NAN)))
338        self.assert_(math.isnan(math.fmod(NAN, NAN)))
339        self.assertRaises(ValueError, math.fmod, 1., 0.)
340        self.assertRaises(ValueError, math.fmod, INF, 1.)
341        self.assertRaises(ValueError, math.fmod, NINF, 1.)
342        self.assertRaises(ValueError, math.fmod, INF, 0.)
343        self.assertEquals(math.fmod(3.0, INF), 3.0)
344        self.assertEquals(math.fmod(-3.0, INF), -3.0)
345        self.assertEquals(math.fmod(3.0, NINF), 3.0)
346        self.assertEquals(math.fmod(-3.0, NINF), -3.0)
347        self.assertEquals(math.fmod(0.0, 3.0), 0.0)
348        self.assertEquals(math.fmod(0.0, NINF), 0.0)
349
350    def testFrexp(self):
351        self.assertRaises(TypeError, math.frexp)
352
353        def testfrexp(name, (mant, exp), (emant, eexp)):
354            if abs(mant-emant) > eps or exp != eexp:
355                self.fail('%s returned %r, expected %r'%\
356                          (name, (mant, exp), (emant,eexp)))
357
358        testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
359        testfrexp('frexp(0)', math.frexp(0), (0, 0))
360        testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
361        testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
362
363        self.assertEquals(math.frexp(INF)[0], INF)
364        self.assertEquals(math.frexp(NINF)[0], NINF)
365        self.assert_(math.isnan(math.frexp(NAN)[0]))
366
367    def testFsum(self):
368        # math.fsum relies on exact rounding for correct operation.
369        # There's a known problem with IA32 floating-point that causes
370        # inexact rounding in some situations, and will cause the
371        # math.fsum tests below to fail; see issue #2937.  On non IEEE
372        # 754 platforms, and on IEEE 754 platforms that exhibit the
373        # problem described in issue #2937, we simply skip the whole
374        # test.
375
376        if not float.__getformat__("double").startswith("IEEE"):
377            return
378
379        # on IEEE 754 compliant machines, both of the expressions
380        # below should round to 10000000000000002.0.
381        if 1e16+2.0 != 1e16+2.9999:
382            return
383
384        # Python version of math.fsum, for comparison.  Uses a
385        # different algorithm based on frexp, ldexp and integer
386        # arithmetic.
387        from sys import float_info
388        mant_dig = float_info.mant_dig
389        etiny = float_info.min_exp - mant_dig
390
391        def msum(iterable):
392            """Full precision summation.  Compute sum(iterable) without any
393            intermediate accumulation of error.  Based on the 'lsum' function
394            at http://code.activestate.com/recipes/393090/
395
396            """
397            tmant, texp = 0, 0
398            for x in iterable:
399                mant, exp = math.frexp(x)
400                mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
401                if texp > exp:
402                    tmant <<= texp-exp
403                    texp = exp
404                else:
405                    mant <<= exp-texp
406                tmant += mant
407            # Round tmant * 2**texp to a float.  The original recipe
408            # used float(str(tmant)) * 2.0**texp for this, but that's
409            # a little unsafe because str -> float conversion can't be
410            # relied upon to do correct rounding on all platforms.
411            tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
412            if tail > 0:
413                h = 1 << (tail-1)
414                tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
415                texp += tail
416            return math.ldexp(tmant, texp)
417
418        test_values = [
419            ([], 0.0),
420            ([0.0], 0.0),
421            ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
422            ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
423            ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
424            ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
425            ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
426            ([1./n for n in range(1, 1001)],
427             float.fromhex('0x1.df11f45f4e61ap+2')),
428            ([(-1.)**n/n for n in range(1, 1001)],
429             float.fromhex('-0x1.62a2af1bd3624p-1')),
430            ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
431            ([1e16, 1., 1e-16], 10000000000000002.0),
432            ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
433            # exercise code for resizing partials array
434            ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
435             [-2.**1022],
436             float.fromhex('0x1.5555555555555p+970')),
437            ]
438
439        for i, (vals, expected) in enumerate(test_values):
440            try:
441                actual = math.fsum(vals)
442            except OverflowError:
443                self.fail("test %d failed: got OverflowError, expected %r "
444                          "for math.fsum(%.100r)" % (i, expected, vals))
445            except ValueError:
446                self.fail("test %d failed: got ValueError, expected %r "
447                          "for math.fsum(%.100r)" % (i, expected, vals))
448            self.assertEqual(actual, expected)
449
450        from random import random, gauss, shuffle
451        for j in xrange(1000):
452            vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
453            s = 0
454            for i in xrange(200):
455                v = gauss(0, random()) ** 7 - s
456                s += v
457                vals.append(v)
458            shuffle(vals)
459
460            s = msum(vals)
461            self.assertEqual(msum(vals), math.fsum(vals))
462
463    def testHypot(self):
464        self.assertRaises(TypeError, math.hypot)
465        self.ftest('hypot(0,0)', math.hypot(0,0), 0)
466        self.ftest('hypot(3,4)', math.hypot(3,4), 5)
467        self.assertEqual(math.hypot(NAN, INF), INF)
468        self.assertEqual(math.hypot(INF, NAN), INF)
469        self.assertEqual(math.hypot(NAN, NINF), INF)
470        self.assertEqual(math.hypot(NINF, NAN), INF)
471        self.assert_(math.isnan(math.hypot(1.0, NAN)))
472        self.assert_(math.isnan(math.hypot(NAN, -2.0)))
473
474    def testLdexp(self):
475        self.assertRaises(TypeError, math.ldexp)
476        self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
477        self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
478        self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
479        self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
480        self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
481        self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
482        self.assertEquals(math.ldexp(1., -1000000), 0.)
483        self.assertEquals(math.ldexp(-1., -1000000), -0.)
484        self.assertEquals(math.ldexp(INF, 30), INF)
485        self.assertEquals(math.ldexp(NINF, -213), NINF)
486        self.assert_(math.isnan(math.ldexp(NAN, 0)))
487
488        # large second argument
489        for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
490            self.assertEquals(math.ldexp(INF, -n), INF)
491            self.assertEquals(math.ldexp(NINF, -n), NINF)
492            self.assertEquals(math.ldexp(1., -n), 0.)
493            self.assertEquals(math.ldexp(-1., -n), -0.)
494            self.assertEquals(math.ldexp(0., -n), 0.)
495            self.assertEquals(math.ldexp(-0., -n), -0.)
496            self.assert_(math.isnan(math.ldexp(NAN, -n)))
497
498            self.assertRaises(OverflowError, math.ldexp, 1., n)
499            self.assertRaises(OverflowError, math.ldexp, -1., n)
500            self.assertEquals(math.ldexp(0., n), 0.)
501            self.assertEquals(math.ldexp(-0., n), -0.)
502            self.assertEquals(math.ldexp(INF, n), INF)
503            self.assertEquals(math.ldexp(NINF, n), NINF)
504            self.assert_(math.isnan(math.ldexp(NAN, n)))
505
506    def testLog(self):
507        self.assertRaises(TypeError, math.log)
508        self.ftest('log(1/e)', math.log(1/math.e), -1)
509        self.ftest('log(1)', math.log(1), 0)
510        self.ftest('log(e)', math.log(math.e), 1)
511        self.ftest('log(32,2)', math.log(32,2), 5)
512        self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
513        self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
514        self.assertEquals(math.log(INF), INF)
515        self.assertRaises(ValueError, math.log, NINF)
516        self.assert_(math.isnan(math.log(NAN)))
517
518    def testLog1p(self):
519        self.assertRaises(TypeError, math.log1p)
520        self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
521        self.ftest('log1p(0)', math.log1p(0), 0)
522        self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
523        self.ftest('log1p(1)', math.log1p(1), math.log(2))
524        self.assertEquals(math.log1p(INF), INF)
525        self.assertRaises(ValueError, math.log1p, NINF)
526        self.assert_(math.isnan(math.log1p(NAN)))
527        n= 2**90
528        self.assertAlmostEquals(math.log1p(n), 62.383246250395075)
529        self.assertAlmostEquals(math.log1p(n), math.log1p(float(n)))
530
531    def testLog10(self):
532        self.assertRaises(TypeError, math.log10)
533        self.ftest('log10(0.1)', math.log10(0.1), -1)
534        self.ftest('log10(1)', math.log10(1), 0)
535        self.ftest('log10(10)', math.log10(10), 1)
536        self.assertEquals(math.log(INF), INF)
537        self.assertRaises(ValueError, math.log10, NINF)
538        self.assert_(math.isnan(math.log10(NAN)))
539
540    def testModf(self):
541        self.assertRaises(TypeError, math.modf)
542
543        def testmodf(name, (v1, v2), (e1, e2)):
544            if abs(v1-e1) > eps or abs(v2-e2):
545                self.fail('%s returned %r, expected %r'%\
546                          (name, (v1,v2), (e1,e2)))
547
548        testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
549        testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
550
551        self.assertEquals(math.modf(INF), (0.0, INF))
552        self.assertEquals(math.modf(NINF), (-0.0, NINF))
553
554        modf_nan = math.modf(NAN)
555        self.assert_(math.isnan(modf_nan[0]))
556        self.assert_(math.isnan(modf_nan[1]))
557
558    def testPow(self):
559        self.assertRaises(TypeError, math.pow)
560        self.ftest('pow(0,1)', math.pow(0,1), 0)
561        self.ftest('pow(1,0)', math.pow(1,0), 1)
562        self.ftest('pow(2,1)', math.pow(2,1), 2)
563        self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
564        self.assertEqual(math.pow(INF, 1), INF)
565        self.assertEqual(math.pow(NINF, 1), NINF)
566        self.assertEqual((math.pow(1, INF)), 1.)
567        self.assertEqual((math.pow(1, NINF)), 1.)
568        self.assert_(math.isnan(math.pow(NAN, 1)))
569        self.assert_(math.isnan(math.pow(2, NAN)))
570        self.assert_(math.isnan(math.pow(0, NAN)))
571        self.assertEqual(math.pow(1, NAN), 1)
572
573        # pow(0., x)
574        self.assertEqual(math.pow(0., INF), 0.)
575        self.assertEqual(math.pow(0., 3.), 0.)
576        self.assertEqual(math.pow(0., 2.3), 0.)
577        self.assertEqual(math.pow(0., 2.), 0.)
578        self.assertEqual(math.pow(0., 0.), 1.)
579        self.assertEqual(math.pow(0., -0.), 1.)
580        self.assertRaises(ValueError, math.pow, 0., -2.)
581        self.assertRaises(ValueError, math.pow, 0., -2.3)
582        self.assertRaises(ValueError, math.pow, 0., -3.)
583        self.assertRaises(ValueError, math.pow, 0., NINF)
584        self.assert_(math.isnan(math.pow(0., NAN)))
585
586        # pow(INF, x)
587        self.assertEqual(math.pow(INF, INF), INF)
588        self.assertEqual(math.pow(INF, 3.), INF)
589        self.assertEqual(math.pow(INF, 2.3), INF)
590        self.assertEqual(math.pow(INF, 2.), INF)
591        self.assertEqual(math.pow(INF, 0.), 1.)
592        self.assertEqual(math.pow(INF, -0.), 1.)
593        self.assertEqual(math.pow(INF, -2.), 0.)
594        self.assertEqual(math.pow(INF, -2.3), 0.)
595        self.assertEqual(math.pow(INF, -3.), 0.)
596        self.assertEqual(math.pow(INF, NINF), 0.)
597        self.assert_(math.isnan(math.pow(INF, NAN)))
598
599        # pow(-0., x)
600        self.assertEqual(math.pow(-0., INF), 0.)
601        self.assertEqual(math.pow(-0., 3.), -0.)
602        self.assertEqual(math.pow(-0., 2.3), 0.)
603        self.assertEqual(math.pow(-0., 2.), 0.)
604        self.assertEqual(math.pow(-0., 0.), 1.)
605        self.assertEqual(math.pow(-0., -0.), 1.)
606        self.assertRaises(ValueError, math.pow, -0., -2.)
607        self.assertRaises(ValueError, math.pow, -0., -2.3)
608        self.assertRaises(ValueError, math.pow, -0., -3.)
609        self.assertRaises(ValueError, math.pow, -0., NINF)
610        self.assert_(math.isnan(math.pow(-0., NAN)))
611
612        # pow(NINF, x)
613        self.assertEqual(math.pow(NINF, INF), INF)
614        self.assertEqual(math.pow(NINF, 3.), NINF)
615        self.assertEqual(math.pow(NINF, 2.3), INF)
616        self.assertEqual(math.pow(NINF, 2.), INF)
617        self.assertEqual(math.pow(NINF, 0.), 1.)
618        self.assertEqual(math.pow(NINF, -0.), 1.)
619        self.assertEqual(math.pow(NINF, -2.), 0.)
620        self.assertEqual(math.pow(NINF, -2.3), 0.)
621        self.assertEqual(math.pow(NINF, -3.), -0.)
622        self.assertEqual(math.pow(NINF, NINF), 0.)
623        self.assert_(math.isnan(math.pow(NINF, NAN)))
624
625        # pow(-1, x)
626        self.assertEqual(math.pow(-1., INF), 1.)
627        self.assertEqual(math.pow(-1., 3.), -1.)
628        self.assertRaises(ValueError, math.pow, -1., 2.3)
629        self.assertEqual(math.pow(-1., 2.), 1.)
630        self.assertEqual(math.pow(-1., 0.), 1.)
631        self.assertEqual(math.pow(-1., -0.), 1.)
632        self.assertEqual(math.pow(-1., -2.), 1.)
633        self.assertRaises(ValueError, math.pow, -1., -2.3)
634        self.assertEqual(math.pow(-1., -3.), -1.)
635        self.assertEqual(math.pow(-1., NINF), 1.)
636        self.assert_(math.isnan(math.pow(-1., NAN)))
637
638        # pow(1, x)
639        self.assertEqual(math.pow(1., INF), 1.)
640        self.assertEqual(math.pow(1., 3.), 1.)
641        self.assertEqual(math.pow(1., 2.3), 1.)
642        self.assertEqual(math.pow(1., 2.), 1.)
643        self.assertEqual(math.pow(1., 0.), 1.)
644        self.assertEqual(math.pow(1., -0.), 1.)
645        self.assertEqual(math.pow(1., -2.), 1.)
646        self.assertEqual(math.pow(1., -2.3), 1.)
647        self.assertEqual(math.pow(1., -3.), 1.)
648        self.assertEqual(math.pow(1., NINF), 1.)
649        self.assertEqual(math.pow(1., NAN), 1.)
650
651        # pow(x, 0) should be 1 for any x
652        self.assertEqual(math.pow(2.3, 0.), 1.)
653        self.assertEqual(math.pow(-2.3, 0.), 1.)
654        self.assertEqual(math.pow(NAN, 0.), 1.)
655        self.assertEqual(math.pow(2.3, -0.), 1.)
656        self.assertEqual(math.pow(-2.3, -0.), 1.)
657        self.assertEqual(math.pow(NAN, -0.), 1.)
658
659        # pow(x, y) is invalid if x is negative and y is not integral
660        self.assertRaises(ValueError, math.pow, -1., 2.3)
661        self.assertRaises(ValueError, math.pow, -15., -3.1)
662
663        # pow(x, NINF)
664        self.assertEqual(math.pow(1.9, NINF), 0.)
665        self.assertEqual(math.pow(1.1, NINF), 0.)
666        self.assertEqual(math.pow(0.9, NINF), INF)
667        self.assertEqual(math.pow(0.1, NINF), INF)
668        self.assertEqual(math.pow(-0.1, NINF), INF)
669        self.assertEqual(math.pow(-0.9, NINF), INF)
670        self.assertEqual(math.pow(-1.1, NINF), 0.)
671        self.assertEqual(math.pow(-1.9, NINF), 0.)
672
673        # pow(x, INF)
674        self.assertEqual(math.pow(1.9, INF), INF)
675        self.assertEqual(math.pow(1.1, INF), INF)
676        self.assertEqual(math.pow(0.9, INF), 0.)
677        self.assertEqual(math.pow(0.1, INF), 0.)
678        self.assertEqual(math.pow(-0.1, INF), 0.)
679        self.assertEqual(math.pow(-0.9, INF), 0.)
680        self.assertEqual(math.pow(-1.1, INF), INF)
681        self.assertEqual(math.pow(-1.9, INF), INF)
682
683        # pow(x, y) should work for x negative, y an integer
684        self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
685        self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
686        self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
687        self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
688        self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
689        self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
690        self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
691        self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
692        self.assertRaises(ValueError, math.pow, -2.0, -0.5)
693        self.assertRaises(ValueError, math.pow, -2.0, 0.5)
694
695        # the following tests have been commented out since they don't
696        # really belong here:  the implementation of ** for floats is
697        # independent of the implemention of math.pow
698        #self.assertEqual(1**NAN, 1)
699        #self.assertEqual(1**INF, 1)
700        #self.assertEqual(1**NINF, 1)
701        #self.assertEqual(1**0, 1)
702        #self.assertEqual(1.**NAN, 1)
703        #self.assertEqual(1.**INF, 1)
704        #self.assertEqual(1.**NINF, 1)
705        #self.assertEqual(1.**0, 1)
706
707    def testRadians(self):
708        self.assertRaises(TypeError, math.radians)
709        self.ftest('radians(180)', math.radians(180), math.pi)
710        self.ftest('radians(90)', math.radians(90), math.pi/2)
711        self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
712
713    def testSin(self):
714        self.assertRaises(TypeError, math.sin)
715        self.ftest('sin(0)', math.sin(0), 0)
716        self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
717        self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
718        try:
719            self.assert_(math.isnan(math.sin(INF)))
720            self.assert_(math.isnan(math.sin(NINF)))
721        except ValueError:
722            self.assertRaises(ValueError, math.sin, INF)
723            self.assertRaises(ValueError, math.sin, NINF)
724        self.assert_(math.isnan(math.sin(NAN)))
725
726    def testSinh(self):
727        self.assertRaises(TypeError, math.sinh)
728        self.ftest('sinh(0)', math.sinh(0), 0)
729        self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
730        self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
731        self.assertEquals(math.sinh(INF), INF)
732        self.assertEquals(math.sinh(NINF), NINF)
733        self.assert_(math.isnan(math.sinh(NAN)))
734
735    def testSqrt(self):
736        self.assertRaises(TypeError, math.sqrt)
737        self.ftest('sqrt(0)', math.sqrt(0), 0)
738        self.ftest('sqrt(1)', math.sqrt(1), 1)
739        self.ftest('sqrt(4)', math.sqrt(4), 2)
740        self.assertEquals(math.sqrt(INF), INF)
741        self.assertRaises(ValueError, math.sqrt, NINF)
742        self.assert_(math.isnan(math.sqrt(NAN)))
743
744    def testTan(self):
745        self.assertRaises(TypeError, math.tan)
746        self.ftest('tan(0)', math.tan(0), 0)
747        self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
748        self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
749        try:
750            self.assert_(math.isnan(math.tan(INF)))
751            self.assert_(math.isnan(math.tan(NINF)))
752        except:
753            self.assertRaises(ValueError, math.tan, INF)
754            self.assertRaises(ValueError, math.tan, NINF)
755        self.assert_(math.isnan(math.tan(NAN)))
756
757    def testTanh(self):
758        self.assertRaises(TypeError, math.tanh)
759        self.ftest('tanh(0)', math.tanh(0), 0)
760        self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
761        self.ftest('tanh(inf)', math.tanh(INF), 1)
762        self.ftest('tanh(-inf)', math.tanh(NINF), -1)
763        self.assert_(math.isnan(math.tanh(NAN)))
764        # check that tanh(-0.) == -0. on IEEE 754 systems
765        if float.__getformat__("double").startswith("IEEE"):
766            self.assertEqual(math.tanh(-0.), -0.)
767            self.assertEqual(math.copysign(1., math.tanh(-0.)),
768                             math.copysign(1., -0.))
769
770    def test_trunc(self):
771        self.assertEqual(math.trunc(1), 1)
772        self.assertEqual(math.trunc(-1), -1)
773        self.assertEqual(type(math.trunc(1)), int)
774        self.assertEqual(type(math.trunc(1.5)), int)
775        self.assertEqual(math.trunc(1.5), 1)
776        self.assertEqual(math.trunc(-1.5), -1)
777        self.assertEqual(math.trunc(1.999999), 1)
778        self.assertEqual(math.trunc(-1.999999), -1)
779        self.assertEqual(math.trunc(-0.999999), -0)
780        self.assertEqual(math.trunc(-100.999), -100)
781
782        class TestTrunc(object):
783            def __trunc__(self):
784                return 23
785
786        class TestNoTrunc(object):
787            pass
788
789        self.assertEqual(math.trunc(TestTrunc()), 23)
790
791        self.assertRaises(TypeError, math.trunc)
792        self.assertRaises(TypeError, math.trunc, 1, 2)
793        # XXX: This is not ideal, but see the comment in math_trunc().
794        self.assertRaises(AttributeError, math.trunc, TestNoTrunc())
795
796        t = TestNoTrunc()
797        t.__trunc__ = lambda *args: args
798        self.assertEquals((), math.trunc(t))
799        self.assertRaises(TypeError, math.trunc, t, 0)
800
801    def testCopysign(self):
802        self.assertEqual(math.copysign(1, 42), 1.0)
803        self.assertEqual(math.copysign(0., 42), 0.0)
804        self.assertEqual(math.copysign(1., -42), -1.0)
805        self.assertEqual(math.copysign(3, 0.), 3.0)
806        self.assertEqual(math.copysign(4., -0.), -4.0)
807
808    def testIsnan(self):
809        self.assert_(math.isnan(float("nan")))
810        self.assert_(math.isnan(float("inf")* 0.))
811        self.failIf(math.isnan(float("inf")))
812        self.failIf(math.isnan(0.))
813        self.failIf(math.isnan(1.))
814
815    def testIsinf(self):
816        self.assert_(math.isinf(float("inf")))
817        self.assert_(math.isinf(float("-inf")))
818        self.assert_(math.isinf(1E400))
819        self.assert_(math.isinf(-1E400))
820        self.failIf(math.isinf(float("nan")))
821        self.failIf(math.isinf(0.))
822        self.failIf(math.isinf(1.))
823
824    # RED_FLAG 16-Oct-2000 Tim
825    # While 2.0 is more consistent about exceptions than previous releases, it
826    # still fails this part of the test on some platforms.  For now, we only
827    # *run* test_exceptions() in verbose mode, so that this isn't normally
828    # tested.
829
830    if verbose:
831        def test_exceptions(self):
832            try:
833                x = math.exp(-1000000000)
834            except:
835                # mathmodule.c is failing to weed out underflows from libm, or
836                # we've got an fp format with huge dynamic range
837                self.fail("underflowing exp() should not have raised "
838                          "an exception")
839            if x != 0:
840                self.fail("underflowing exp() should have returned 0")
841
842            # If this fails, probably using a strict IEEE-754 conforming libm, and x
843            # is +Inf afterwards.  But Python wants overflows detected by default.
844            try:
845                x = math.exp(1000000000)
846            except OverflowError:
847                pass
848            else:
849                self.fail("overflowing exp() didn't trigger OverflowError")
850
851            # If this fails, it could be a puzzle.  One odd possibility is that
852            # mathmodule.c's macros are getting confused while comparing
853            # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
854            # as a result (and so raising OverflowError instead).
855            try:
856                x = math.sqrt(-1.0)
857            except ValueError:
858                pass
859            else:
860                self.fail("sqrt(-1) didn't raise ValueError")
861
862    def test_testfile(self):
863        if not float.__getformat__("double").startswith("IEEE"):
864            return
865        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
866            # Skip if either the input or result is complex, or if
867            # flags is nonempty
868            if ai != 0. or ei != 0. or flags:
869                continue
870            if fn in ['rect', 'polar']:
871                # no real versions of rect, polar
872                continue
873            func = getattr(math, fn)
874            try:
875                result = func(ar)
876            except ValueError:
877                message = ("Unexpected ValueError in " +
878                           "test %s:%s(%r)\n" % (id, fn, ar))
879                self.fail(message)
880            except OverflowError:
881                message = ("Unexpected OverflowError in " +
882                           "test %s:%s(%r)\n" % (id, fn, ar))
883                self.fail(message)
884            self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)
885
886def test_main():
887    from doctest import DocFileSuite
888    suite = unittest.TestSuite()
889    suite.addTest(unittest.makeSuite(MathTests))
890    suite.addTest(DocFileSuite("ieee754.txt"))
891    run_unittest(suite)
892
893if __name__ == '__main__':
894    test_main()