Python code coverage for Lib/test/test_math.py

#	count	content
1	n/a	# Python test set -- math module
2	n/a	# XXXX Should not do tests around zero only
3	n/a
4	n/a	from test.support import run_unittest, verbose, requires_IEEE_754
5	n/a	from test import support
6	n/a	import unittest
7	n/a	import math
8	n/a	import os
9	n/a	import platform
10	n/a	import struct
11	n/a	import sys
12	n/a	import sysconfig
13	n/a
14	n/a	eps = 1E-05
15	n/a	NAN = float('nan')
16	n/a	INF = float('inf')
17	n/a	NINF = float('-inf')
18	n/a	FLOAT_MAX = sys.float_info.max
19	n/a
20	n/a	# detect evidence of double-rounding: fsum is not always correctly
21	n/a	# rounded on machines that suffer from double rounding.
22	n/a	x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
23	n/a	HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
24	n/a
25	n/a	# locate file with test values
26	n/a	if __name__ == '__main__':
27	n/a	file = sys.argv[0]
28	n/a	else:
29	n/a	file = __file__
30	n/a	test_dir = os.path.dirname(file) or os.curdir
31	n/a	math_testcases = os.path.join(test_dir, 'math_testcases.txt')
32	n/a	test_file = os.path.join(test_dir, 'cmath_testcases.txt')
33	n/a
34	n/a
35	n/a	def to_ulps(x):
36	n/a	"""Convert a non-NaN float x to an integer, in such a way that
37	n/a	adjacent floats are converted to adjacent integers. Then
38	n/a	abs(ulps(x) - ulps(y)) gives the difference in ulps between two
39	n/a	floats.
40	n/a
41	n/a	The results from this function will only make sense on platforms
42	n/a	where native doubles are represented in IEEE 754 binary64 format.
43	n/a
44	n/a	Note: 0.0 and -0.0 are converted to 0 and -1, respectively.
45	n/a	"""
46	n/a	n = struct.unpack('<q', struct.pack('<d', x))[0]
47	n/a	if n < 0:
48	n/a	n = ~(n+2**63)
49	n/a	return n
50	n/a
51	n/a
52	n/a	def ulp(x):
53	n/a	"""Return the value of the least significant bit of a
54	n/a	float x, such that the first float bigger than x is x+ulp(x).
55	n/a	Then, given an expected result x and a tolerance of n ulps,
56	n/a	the result y should be such that abs(y-x) <= n * ulp(x).
57	n/a	The results from this function will only make sense on platforms
58	n/a	where native doubles are represented in IEEE 754 binary64 format.
59	n/a	"""
60	n/a	x = abs(float(x))
61	n/a	if math.isnan(x) or math.isinf(x):
62	n/a	return x
63	n/a
64	n/a	# Find next float up from x.
65	n/a	n = struct.unpack('<q', struct.pack('<d', x))[0]
66	n/a	x_next = struct.unpack('<d', struct.pack('<q', n + 1))[0]
67	n/a	if math.isinf(x_next):
68	n/a	# Corner case: x was the largest finite float. Then it's
69	n/a	# not an exact power of two, so we can take the difference
70	n/a	# between x and the previous float.
71	n/a	x_prev = struct.unpack('<d', struct.pack('<q', n - 1))[0]
72	n/a	return x - x_prev
73	n/a	else:
74	n/a	return x_next - x
75	n/a
76	n/a	# Here's a pure Python version of the math.factorial algorithm, for
77	n/a	# documentation and comparison purposes.
78	n/a	#
79	n/a	# Formula:
80	n/a	#
81	n/a	# factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n))
82	n/a	#
83	n/a	# where
84	n/a	#
85	n/a	# factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j
86	n/a	#
87	n/a	# The outer product above is an infinite product, but once i >= n.bit_length,
88	n/a	# (n >> i) < 1 and the corresponding term of the product is empty. So only the
89	n/a	# finitely many terms for 0 <= i < n.bit_length() contribute anything.
90	n/a	#
91	n/a	# We iterate downwards from i == n.bit_length() - 1 to i == 0. The inner
92	n/a	# product in the formula above starts at 1 for i == n.bit_length(); for each i
93	n/a	# < n.bit_length() we get the inner product for i from that for i + 1 by
94	n/a	# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}. In Python terms,
95	n/a	# this set is range((n >> i+1) + 1 \| 1, (n >> i) + 1 \| 1, 2).
96	n/a
97	n/a	def count_set_bits(n):
98	n/a	"""Number of '1' bits in binary expansion of a nonnnegative integer."""
99	n/a	return 1 + count_set_bits(n & n - 1) if n else 0
100	n/a
101	n/a	def partial_product(start, stop):
102	n/a	"""Product of integers in range(start, stop, 2), computed recursively.
103	n/a	start and stop should both be odd, with start <= stop.
104	n/a
105	n/a	"""
106	n/a	numfactors = (stop - start) >> 1
107	n/a	if not numfactors:
108	n/a	return 1
109	n/a	elif numfactors == 1:
110	n/a	return start
111	n/a	else:
112	n/a	mid = (start + numfactors) \| 1
113	n/a	return partial_product(start, mid) * partial_product(mid, stop)
114	n/a
115	n/a	def py_factorial(n):
116	n/a	"""Factorial of nonnegative integer n, via "Binary Split Factorial Formula"
117	n/a	described at http://www.luschny.de/math/factorial/binarysplitfact.html
118	n/a
119	n/a	"""
120	n/a	inner = outer = 1
121	n/a	for i in reversed(range(n.bit_length())):
122	n/a	inner *= partial_product((n >> i + 1) + 1 \| 1, (n >> i) + 1 \| 1)
123	n/a	outer *= inner
124	n/a	return outer << (n - count_set_bits(n))
125	n/a
126	n/a	def ulp_abs_check(expected, got, ulp_tol, abs_tol):
127	n/a	"""Given finite floats `expected` and `got`, check that they're
128	n/a	approximately equal to within the given number of ulps or the
129	n/a	given absolute tolerance, whichever is bigger.
130	n/a
131	n/a	Returns None on success and an error message on failure.
132	n/a	"""
133	n/a	ulp_error = abs(to_ulps(expected) - to_ulps(got))
134	n/a	abs_error = abs(expected - got)
135	n/a
136	n/a	# Succeed if either abs_error <= abs_tol or ulp_error <= ulp_tol.
137	n/a	if abs_error <= abs_tol or ulp_error <= ulp_tol:
138	n/a	return None
139	n/a	else:
140	n/a	fmt = ("error = {:.3g} ({:d} ulps); "
141	n/a	"permitted error = {:.3g} or {:d} ulps")
142	n/a	return fmt.format(abs_error, ulp_error, abs_tol, ulp_tol)
143	n/a
144	n/a	def parse_mtestfile(fname):
145	n/a	"""Parse a file with test values
146	n/a
147	n/a	-- starts a comment
148	n/a	blank lines, or lines containing only a comment, are ignored
149	n/a	other lines are expected to have the form
150	n/a	id fn arg -> expected [flag]*
151	n/a
152	n/a	"""
153	n/a	with open(fname) as fp:
154	n/a	for line in fp:
155	n/a	# strip comments, and skip blank lines
156	n/a	if '--' in line:
157	n/a	line = line[:line.index('--')]
158	n/a	if not line.strip():
159	n/a	continue
160	n/a
161	n/a	lhs, rhs = line.split('->')
162	n/a	id, fn, arg = lhs.split()
163	n/a	rhs_pieces = rhs.split()
164	n/a	exp = rhs_pieces[0]
165	n/a	flags = rhs_pieces[1:]
166	n/a
167	n/a	yield (id, fn, float(arg), float(exp), flags)
168	n/a
169	n/a
170	n/a	def parse_testfile(fname):
171	n/a	"""Parse a file with test values
172	n/a
173	n/a	Empty lines or lines starting with -- are ignored
174	n/a	yields id, fn, arg_real, arg_imag, exp_real, exp_imag
175	n/a	"""
176	n/a	with open(fname) as fp:
177	n/a	for line in fp:
178	n/a	# skip comment lines and blank lines
179	n/a	if line.startswith('--') or not line.strip():
180	n/a	continue
181	n/a
182	n/a	lhs, rhs = line.split('->')
183	n/a	id, fn, arg_real, arg_imag = lhs.split()
184	n/a	rhs_pieces = rhs.split()
185	n/a	exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
186	n/a	flags = rhs_pieces[2:]
187	n/a
188	n/a	yield (id, fn,
189	n/a	float(arg_real), float(arg_imag),
190	n/a	float(exp_real), float(exp_imag),
191	n/a	flags)
192	n/a
193	n/a
194	n/a	def result_check(expected, got, ulp_tol=5, abs_tol=0.0):
195	n/a	# Common logic of MathTests.(ftest, test_testcases, test_mtestcases)
196	n/a	"""Compare arguments expected and got, as floats, if either
197	n/a	is a float, using a tolerance expressed in multiples of
198	n/a	ulp(expected) or absolutely (if given and greater).
199	n/a
200	n/a	As a convenience, when neither argument is a float, and for
201	n/a	non-finite floats, exact equality is demanded. Also, nan==nan
202	n/a	as far as this function is concerned.
203	n/a
204	n/a	Returns None on success and an error message on failure.
205	n/a	"""
206	n/a
207	n/a	# Check exactly equal (applies also to strings representing exceptions)
208	n/a	if got == expected:
209	n/a	return None
210	n/a
211	n/a	failure = "not equal"
212	n/a
213	n/a	# Turn mixed float and int comparison (e.g. floor()) to all-float
214	n/a	if isinstance(expected, float) and isinstance(got, int):
215	n/a	got = float(got)
216	n/a	elif isinstance(got, float) and isinstance(expected, int):
217	n/a	expected = float(expected)
218	n/a
219	n/a	if isinstance(expected, float) and isinstance(got, float):
220	n/a	if math.isnan(expected) and math.isnan(got):
221	n/a	# Pass, since both nan
222	n/a	failure = None
223	n/a	elif math.isinf(expected) or math.isinf(got):
224	n/a	# We already know they're not equal, drop through to failure
225	n/a	pass
226	n/a	else:
227	n/a	# Both are finite floats (now). Are they close enough?
228	n/a	failure = ulp_abs_check(expected, got, ulp_tol, abs_tol)
229	n/a
230	n/a	# arguments are not equal, and if numeric, are too far apart
231	n/a	if failure is not None:
232	n/a	fail_fmt = "expected {!r}, got {!r}"
233	n/a	fail_msg = fail_fmt.format(expected, got)
234	n/a	fail_msg += ' ({})'.format(failure)
235	n/a	return fail_msg
236	n/a	else:
237	n/a	return None
238	n/a
239	n/a	# Class providing an __index__ method.
240	n/a	class MyIndexable(object):
241	n/a	def __init__(self, value):
242	n/a	self.value = value
243	n/a
244	n/a	def __index__(self):
245	n/a	return self.value
246	n/a
247	n/a	class MathTests(unittest.TestCase):
248	n/a
249	n/a	def ftest(self, name, got, expected, ulp_tol=5, abs_tol=0.0):
250	n/a	"""Compare arguments expected and got, as floats, if either
251	n/a	is a float, using a tolerance expressed in multiples of
252	n/a	ulp(expected) or absolutely, whichever is greater.
253	n/a
254	n/a	As a convenience, when neither argument is a float, and for
255	n/a	non-finite floats, exact equality is demanded. Also, nan==nan
256	n/a	in this function.
257	n/a	"""
258	n/a	failure = result_check(expected, got, ulp_tol, abs_tol)
259	n/a	if failure is not None:
260	n/a	self.fail("{}: {}".format(name, failure))
261	n/a
262	n/a	def testConstants(self):
263	n/a	# Ref: Abramowitz & Stegun (Dover, 1965)
264	n/a	self.ftest('pi', math.pi, 3.141592653589793238462643)
265	n/a	self.ftest('e', math.e, 2.718281828459045235360287)
266	n/a	self.assertEqual(math.tau, 2*math.pi)
267	n/a
268	n/a	def testAcos(self):
269	n/a	self.assertRaises(TypeError, math.acos)
270	n/a	self.ftest('acos(-1)', math.acos(-1), math.pi)
271	n/a	self.ftest('acos(0)', math.acos(0), math.pi/2)
272	n/a	self.ftest('acos(1)', math.acos(1), 0)
273	n/a	self.assertRaises(ValueError, math.acos, INF)
274	n/a	self.assertRaises(ValueError, math.acos, NINF)
275	n/a	self.assertRaises(ValueError, math.acos, 1 + eps)
276	n/a	self.assertRaises(ValueError, math.acos, -1 - eps)
277	n/a	self.assertTrue(math.isnan(math.acos(NAN)))
278	n/a
279	n/a	def testAcosh(self):
280	n/a	self.assertRaises(TypeError, math.acosh)
281	n/a	self.ftest('acosh(1)', math.acosh(1), 0)
282	n/a	self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
283	n/a	self.assertRaises(ValueError, math.acosh, 0)
284	n/a	self.assertRaises(ValueError, math.acosh, -1)
285	n/a	self.assertEqual(math.acosh(INF), INF)
286	n/a	self.assertRaises(ValueError, math.acosh, NINF)
287	n/a	self.assertTrue(math.isnan(math.acosh(NAN)))
288	n/a
289	n/a	def testAsin(self):
290	n/a	self.assertRaises(TypeError, math.asin)
291	n/a	self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
292	n/a	self.ftest('asin(0)', math.asin(0), 0)
293	n/a	self.ftest('asin(1)', math.asin(1), math.pi/2)
294	n/a	self.assertRaises(ValueError, math.asin, INF)
295	n/a	self.assertRaises(ValueError, math.asin, NINF)
296	n/a	self.assertRaises(ValueError, math.asin, 1 + eps)
297	n/a	self.assertRaises(ValueError, math.asin, -1 - eps)
298	n/a	self.assertTrue(math.isnan(math.asin(NAN)))
299	n/a
300	n/a	def testAsinh(self):
301	n/a	self.assertRaises(TypeError, math.asinh)
302	n/a	self.ftest('asinh(0)', math.asinh(0), 0)
303	n/a	self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
304	n/a	self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
305	n/a	self.assertEqual(math.asinh(INF), INF)
306	n/a	self.assertEqual(math.asinh(NINF), NINF)
307	n/a	self.assertTrue(math.isnan(math.asinh(NAN)))
308	n/a
309	n/a	def testAtan(self):
310	n/a	self.assertRaises(TypeError, math.atan)
311	n/a	self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
312	n/a	self.ftest('atan(0)', math.atan(0), 0)
313	n/a	self.ftest('atan(1)', math.atan(1), math.pi/4)
314	n/a	self.ftest('atan(inf)', math.atan(INF), math.pi/2)
315	n/a	self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
316	n/a	self.assertTrue(math.isnan(math.atan(NAN)))
317	n/a
318	n/a	def testAtanh(self):
319	n/a	self.assertRaises(TypeError, math.atan)
320	n/a	self.ftest('atanh(0)', math.atanh(0), 0)
321	n/a	self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
322	n/a	self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
323	n/a	self.assertRaises(ValueError, math.atanh, 1)
324	n/a	self.assertRaises(ValueError, math.atanh, -1)
325	n/a	self.assertRaises(ValueError, math.atanh, INF)
326	n/a	self.assertRaises(ValueError, math.atanh, NINF)
327	n/a	self.assertTrue(math.isnan(math.atanh(NAN)))
328	n/a
329	n/a	def testAtan2(self):
330	n/a	self.assertRaises(TypeError, math.atan2)
331	n/a	self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
332	n/a	self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
333	n/a	self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
334	n/a	self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
335	n/a	self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
336	n/a
337	n/a	# math.atan2(0, x)
338	n/a	self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
339	n/a	self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
340	n/a	self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
341	n/a	self.assertEqual(math.atan2(0., 0.), 0.)
342	n/a	self.assertEqual(math.atan2(0., 2.3), 0.)
343	n/a	self.assertEqual(math.atan2(0., INF), 0.)
344	n/a	self.assertTrue(math.isnan(math.atan2(0., NAN)))
345	n/a	# math.atan2(-0, x)
346	n/a	self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
347	n/a	self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
348	n/a	self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
349	n/a	self.assertEqual(math.atan2(-0., 0.), -0.)
350	n/a	self.assertEqual(math.atan2(-0., 2.3), -0.)
351	n/a	self.assertEqual(math.atan2(-0., INF), -0.)
352	n/a	self.assertTrue(math.isnan(math.atan2(-0., NAN)))
353	n/a	# math.atan2(INF, x)
354	n/a	self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
355	n/a	self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
356	n/a	self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
357	n/a	self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
358	n/a	self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
359	n/a	self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
360	n/a	self.assertTrue(math.isnan(math.atan2(INF, NAN)))
361	n/a	# math.atan2(NINF, x)
362	n/a	self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
363	n/a	self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
364	n/a	self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
365	n/a	self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
366	n/a	self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
367	n/a	self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
368	n/a	self.assertTrue(math.isnan(math.atan2(NINF, NAN)))
369	n/a	# math.atan2(+finite, x)
370	n/a	self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
371	n/a	self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
372	n/a	self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
373	n/a	self.assertEqual(math.atan2(2.3, INF), 0.)
374	n/a	self.assertTrue(math.isnan(math.atan2(2.3, NAN)))
375	n/a	# math.atan2(-finite, x)
376	n/a	self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
377	n/a	self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
378	n/a	self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
379	n/a	self.assertEqual(math.atan2(-2.3, INF), -0.)
380	n/a	self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))
381	n/a	# math.atan2(NAN, x)
382	n/a	self.assertTrue(math.isnan(math.atan2(NAN, NINF)))
383	n/a	self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))
384	n/a	self.assertTrue(math.isnan(math.atan2(NAN, -0.)))
385	n/a	self.assertTrue(math.isnan(math.atan2(NAN, 0.)))
386	n/a	self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))
387	n/a	self.assertTrue(math.isnan(math.atan2(NAN, INF)))
388	n/a	self.assertTrue(math.isnan(math.atan2(NAN, NAN)))
389	n/a
390	n/a	def testCeil(self):
391	n/a	self.assertRaises(TypeError, math.ceil)
392	n/a	self.assertEqual(int, type(math.ceil(0.5)))
393	n/a	self.ftest('ceil(0.5)', math.ceil(0.5), 1)
394	n/a	self.ftest('ceil(1.0)', math.ceil(1.0), 1)
395	n/a	self.ftest('ceil(1.5)', math.ceil(1.5), 2)
396	n/a	self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
397	n/a	self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
398	n/a	self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
399	n/a	#self.assertEqual(math.ceil(INF), INF)
400	n/a	#self.assertEqual(math.ceil(NINF), NINF)
401	n/a	#self.assertTrue(math.isnan(math.ceil(NAN)))
402	n/a
403	n/a	class TestCeil:
404	n/a	def __ceil__(self):
405	n/a	return 42
406	n/a	class TestNoCeil:
407	n/a	pass
408	n/a	self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
409	n/a	self.assertRaises(TypeError, math.ceil, TestNoCeil())
410	n/a
411	n/a	t = TestNoCeil()
412	n/a	t.__ceil__ = lambda *args: args
413	n/a	self.assertRaises(TypeError, math.ceil, t)
414	n/a	self.assertRaises(TypeError, math.ceil, t, 0)
415	n/a
416	n/a	@requires_IEEE_754
417	n/a	def testCopysign(self):
418	n/a	self.assertEqual(math.copysign(1, 42), 1.0)
419	n/a	self.assertEqual(math.copysign(0., 42), 0.0)
420	n/a	self.assertEqual(math.copysign(1., -42), -1.0)
421	n/a	self.assertEqual(math.copysign(3, 0.), 3.0)
422	n/a	self.assertEqual(math.copysign(4., -0.), -4.0)
423	n/a
424	n/a	self.assertRaises(TypeError, math.copysign)
425	n/a	# copysign should let us distinguish signs of zeros
426	n/a	self.assertEqual(math.copysign(1., 0.), 1.)
427	n/a	self.assertEqual(math.copysign(1., -0.), -1.)
428	n/a	self.assertEqual(math.copysign(INF, 0.), INF)
429	n/a	self.assertEqual(math.copysign(INF, -0.), NINF)
430	n/a	self.assertEqual(math.copysign(NINF, 0.), INF)
431	n/a	self.assertEqual(math.copysign(NINF, -0.), NINF)
432	n/a	# and of infinities
433	n/a	self.assertEqual(math.copysign(1., INF), 1.)
434	n/a	self.assertEqual(math.copysign(1., NINF), -1.)
435	n/a	self.assertEqual(math.copysign(INF, INF), INF)
436	n/a	self.assertEqual(math.copysign(INF, NINF), NINF)
437	n/a	self.assertEqual(math.copysign(NINF, INF), INF)
438	n/a	self.assertEqual(math.copysign(NINF, NINF), NINF)
439	n/a	self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
440	n/a	self.assertTrue(math.isnan(math.copysign(NAN, INF)))
441	n/a	self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
442	n/a	self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
443	n/a	# copysign(INF, NAN) may be INF or it may be NINF, since
444	n/a	# we don't know whether the sign bit of NAN is set on any
445	n/a	# given platform.
446	n/a	self.assertTrue(math.isinf(math.copysign(INF, NAN)))
447	n/a	# similarly, copysign(2., NAN) could be 2. or -2.
448	n/a	self.assertEqual(abs(math.copysign(2., NAN)), 2.)
449	n/a
450	n/a	def testCos(self):
451	n/a	self.assertRaises(TypeError, math.cos)
452	n/a	self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0, abs_tol=ulp(1))
453	n/a	self.ftest('cos(0)', math.cos(0), 1)
454	n/a	self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=ulp(1))
455	n/a	self.ftest('cos(pi)', math.cos(math.pi), -1)
456	n/a	try:
457	n/a	self.assertTrue(math.isnan(math.cos(INF)))
458	n/a	self.assertTrue(math.isnan(math.cos(NINF)))
459	n/a	except ValueError:
460	n/a	self.assertRaises(ValueError, math.cos, INF)
461	n/a	self.assertRaises(ValueError, math.cos, NINF)
462	n/a	self.assertTrue(math.isnan(math.cos(NAN)))
463	n/a
464	n/a	def testCosh(self):
465	n/a	self.assertRaises(TypeError, math.cosh)
466	n/a	self.ftest('cosh(0)', math.cosh(0), 1)
467	n/a	self.ftest('cosh(2)-2cosh(1)2', math.cosh(2)-2math.cosh(1)**2, -1) # Thanks to Lambert
468	n/a	self.assertEqual(math.cosh(INF), INF)
469	n/a	self.assertEqual(math.cosh(NINF), INF)
470	n/a	self.assertTrue(math.isnan(math.cosh(NAN)))
471	n/a
472	n/a	def testDegrees(self):
473	n/a	self.assertRaises(TypeError, math.degrees)
474	n/a	self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
475	n/a	self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
476	n/a	self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
477	n/a	self.ftest('degrees(0)', math.degrees(0), 0)
478	n/a
479	n/a	def testExp(self):
480	n/a	self.assertRaises(TypeError, math.exp)
481	n/a	self.ftest('exp(-1)', math.exp(-1), 1/math.e)
482	n/a	self.ftest('exp(0)', math.exp(0), 1)
483	n/a	self.ftest('exp(1)', math.exp(1), math.e)
484	n/a	self.assertEqual(math.exp(INF), INF)
485	n/a	self.assertEqual(math.exp(NINF), 0.)
486	n/a	self.assertTrue(math.isnan(math.exp(NAN)))
487	n/a	self.assertRaises(OverflowError, math.exp, 1000000)
488	n/a
489	n/a	def testFabs(self):
490	n/a	self.assertRaises(TypeError, math.fabs)
491	n/a	self.ftest('fabs(-1)', math.fabs(-1), 1)
492	n/a	self.ftest('fabs(0)', math.fabs(0), 0)
493	n/a	self.ftest('fabs(1)', math.fabs(1), 1)
494	n/a
495	n/a	def testFactorial(self):
496	n/a	self.assertEqual(math.factorial(0), 1)
497	n/a	self.assertEqual(math.factorial(0.0), 1)
498	n/a	total = 1
499	n/a	for i in range(1, 1000):
500	n/a	total *= i
501	n/a	self.assertEqual(math.factorial(i), total)
502	n/a	self.assertEqual(math.factorial(float(i)), total)
503	n/a	self.assertEqual(math.factorial(i), py_factorial(i))
504	n/a	self.assertRaises(ValueError, math.factorial, -1)
505	n/a	self.assertRaises(ValueError, math.factorial, -1.0)
506	n/a	self.assertRaises(ValueError, math.factorial, -10**100)
507	n/a	self.assertRaises(ValueError, math.factorial, -1e100)
508	n/a	self.assertRaises(ValueError, math.factorial, math.pi)
509	n/a
510	n/a	# Other implementations may place different upper bounds.
511	n/a	@support.cpython_only
512	n/a	def testFactorialHugeInputs(self):
513	n/a	# Currently raises ValueError for inputs that are too large
514	n/a	# to fit into a C long.
515	n/a	self.assertRaises(OverflowError, math.factorial, 10**100)
516	n/a	self.assertRaises(OverflowError, math.factorial, 1e100)
517	n/a
518	n/a	def testFloor(self):
519	n/a	self.assertRaises(TypeError, math.floor)
520	n/a	self.assertEqual(int, type(math.floor(0.5)))
521	n/a	self.ftest('floor(0.5)', math.floor(0.5), 0)
522	n/a	self.ftest('floor(1.0)', math.floor(1.0), 1)
523	n/a	self.ftest('floor(1.5)', math.floor(1.5), 1)
524	n/a	self.ftest('floor(-0.5)', math.floor(-0.5), -1)
525	n/a	self.ftest('floor(-1.0)', math.floor(-1.0), -1)
526	n/a	self.ftest('floor(-1.5)', math.floor(-1.5), -2)
527	n/a	# pow() relies on floor() to check for integers
528	n/a	# This fails on some platforms - so check it here
529	n/a	self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
530	n/a	self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
531	n/a	#self.assertEqual(math.ceil(INF), INF)
532	n/a	#self.assertEqual(math.ceil(NINF), NINF)
533	n/a	#self.assertTrue(math.isnan(math.floor(NAN)))
534	n/a
535	n/a	class TestFloor:
536	n/a	def __floor__(self):
537	n/a	return 42
538	n/a	class TestNoFloor:
539	n/a	pass
540	n/a	self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
541	n/a	self.assertRaises(TypeError, math.floor, TestNoFloor())
542	n/a
543	n/a	t = TestNoFloor()
544	n/a	t.__floor__ = lambda *args: args
545	n/a	self.assertRaises(TypeError, math.floor, t)
546	n/a	self.assertRaises(TypeError, math.floor, t, 0)
547	n/a
548	n/a	def testFmod(self):
549	n/a	self.assertRaises(TypeError, math.fmod)
550	n/a	self.ftest('fmod(10, 1)', math.fmod(10, 1), 0.0)
551	n/a	self.ftest('fmod(10, 0.5)', math.fmod(10, 0.5), 0.0)
552	n/a	self.ftest('fmod(10, 1.5)', math.fmod(10, 1.5), 1.0)
553	n/a	self.ftest('fmod(-10, 1)', math.fmod(-10, 1), -0.0)
554	n/a	self.ftest('fmod(-10, 0.5)', math.fmod(-10, 0.5), -0.0)
555	n/a	self.ftest('fmod(-10, 1.5)', math.fmod(-10, 1.5), -1.0)
556	n/a	self.assertTrue(math.isnan(math.fmod(NAN, 1.)))
557	n/a	self.assertTrue(math.isnan(math.fmod(1., NAN)))
558	n/a	self.assertTrue(math.isnan(math.fmod(NAN, NAN)))
559	n/a	self.assertRaises(ValueError, math.fmod, 1., 0.)
560	n/a	self.assertRaises(ValueError, math.fmod, INF, 1.)
561	n/a	self.assertRaises(ValueError, math.fmod, NINF, 1.)
562	n/a	self.assertRaises(ValueError, math.fmod, INF, 0.)
563	n/a	self.assertEqual(math.fmod(3.0, INF), 3.0)
564	n/a	self.assertEqual(math.fmod(-3.0, INF), -3.0)
565	n/a	self.assertEqual(math.fmod(3.0, NINF), 3.0)
566	n/a	self.assertEqual(math.fmod(-3.0, NINF), -3.0)
567	n/a	self.assertEqual(math.fmod(0.0, 3.0), 0.0)
568	n/a	self.assertEqual(math.fmod(0.0, NINF), 0.0)
569	n/a
570	n/a	def testFrexp(self):
571	n/a	self.assertRaises(TypeError, math.frexp)
572	n/a
573	n/a	def testfrexp(name, result, expected):
574	n/a	(mant, exp), (emant, eexp) = result, expected
575	n/a	if abs(mant-emant) > eps or exp != eexp:
576	n/a	self.fail('%s returned %r, expected %r'%\
577	n/a	(name, result, expected))
578	n/a
579	n/a	testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
580	n/a	testfrexp('frexp(0)', math.frexp(0), (0, 0))
581	n/a	testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
582	n/a	testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
583	n/a
584	n/a	self.assertEqual(math.frexp(INF)[0], INF)
585	n/a	self.assertEqual(math.frexp(NINF)[0], NINF)
586	n/a	self.assertTrue(math.isnan(math.frexp(NAN)[0]))
587	n/a
588	n/a	@requires_IEEE_754
589	n/a	@unittest.skipIf(HAVE_DOUBLE_ROUNDING,
590	n/a	"fsum is not exact on machines with double rounding")
591	n/a	def testFsum(self):
592	n/a	# math.fsum relies on exact rounding for correct operation.
593	n/a	# There's a known problem with IA32 floating-point that causes
594	n/a	# inexact rounding in some situations, and will cause the
595	n/a	# math.fsum tests below to fail; see issue #2937. On non IEEE
596	n/a	# 754 platforms, and on IEEE 754 platforms that exhibit the
597	n/a	# problem described in issue #2937, we simply skip the whole
598	n/a	# test.
599	n/a
600	n/a	# Python version of math.fsum, for comparison. Uses a
601	n/a	# different algorithm based on frexp, ldexp and integer
602	n/a	# arithmetic.
603	n/a	from sys import float_info
604	n/a	mant_dig = float_info.mant_dig
605	n/a	etiny = float_info.min_exp - mant_dig
606	n/a
607	n/a	def msum(iterable):
608	n/a	"""Full precision summation. Compute sum(iterable) without any
609	n/a	intermediate accumulation of error. Based on the 'lsum' function
610	n/a	at http://code.activestate.com/recipes/393090/
611	n/a
612	n/a	"""
613	n/a	tmant, texp = 0, 0
614	n/a	for x in iterable:
615	n/a	mant, exp = math.frexp(x)
616	n/a	mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
617	n/a	if texp > exp:
618	n/a	tmant <<= texp-exp
619	n/a	texp = exp
620	n/a	else:
621	n/a	mant <<= exp-texp
622	n/a	tmant += mant
623	n/a	# Round tmant * 2**texp to a float. The original recipe
624	n/a	# used float(str(tmant)) * 2.0**texp for this, but that's
625	n/a	# a little unsafe because str -> float conversion can't be
626	n/a	# relied upon to do correct rounding on all platforms.
627	n/a	tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
628	n/a	if tail > 0:
629	n/a	h = 1 << (tail-1)
630	n/a	tmant = tmant // (2h) + bool(tmant & h and tmant & 3h-1)
631	n/a	texp += tail
632	n/a	return math.ldexp(tmant, texp)
633	n/a
634	n/a	test_values = [
635	n/a	([], 0.0),
636	n/a	([0.0], 0.0),
637	n/a	([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
638	n/a	([2.053, -0.5, -2.0-54], 2.0**53-1.0),
639	n/a	([2.053, 1.0, 2.0-100], 2.0**53+2.0),
640	n/a	([2.053+10.0, 1.0, 2.0-100], 2.0**53+12.0),
641	n/a	([2.053-4.0, 0.5, 2.0-54], 2.0**53-3.0),
642	n/a	([1./n for n in range(1, 1001)],
643	n/a	float.fromhex('0x1.df11f45f4e61ap+2')),
644	n/a	([(-1.)**n/n for n in range(1, 1001)],
645	n/a	float.fromhex('-0x1.62a2af1bd3624p-1')),
646	n/a	([1.7(i+1)-1.7i for i in range(1000)] + [-1.7**1000], -1.0),
647	n/a	([1e16, 1., 1e-16], 10000000000000002.0),
648	n/a	([1e16-2., 1.-2.-53, -(1e16-2.), -(1.-2.-53)], 0.0),
649	n/a	# exercise code for resizing partials array
650	n/a	([2.n - 2.(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
651	n/a	[-2.**1022],
652	n/a	float.fromhex('0x1.5555555555555p+970')),
653	n/a	]
654	n/a
655	n/a	for i, (vals, expected) in enumerate(test_values):
656	n/a	try:
657	n/a	actual = math.fsum(vals)
658	n/a	except OverflowError:
659	n/a	self.fail("test %d failed: got OverflowError, expected %r "
660	n/a	"for math.fsum(%.100r)" % (i, expected, vals))
661	n/a	except ValueError:
662	n/a	self.fail("test %d failed: got ValueError, expected %r "
663	n/a	"for math.fsum(%.100r)" % (i, expected, vals))
664	n/a	self.assertEqual(actual, expected)
665	n/a
666	n/a	from random import random, gauss, shuffle
667	n/a	for j in range(1000):
668	n/a	vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
669	n/a	s = 0
670	n/a	for i in range(200):
671	n/a	v = gauss(0, random()) ** 7 - s
672	n/a	s += v
673	n/a	vals.append(v)
674	n/a	shuffle(vals)
675	n/a
676	n/a	s = msum(vals)
677	n/a	self.assertEqual(msum(vals), math.fsum(vals))
678	n/a
679	n/a	def testGcd(self):
680	n/a	gcd = math.gcd
681	n/a	self.assertEqual(gcd(0, 0), 0)
682	n/a	self.assertEqual(gcd(1, 0), 1)
683	n/a	self.assertEqual(gcd(-1, 0), 1)
684	n/a	self.assertEqual(gcd(0, 1), 1)
685	n/a	self.assertEqual(gcd(0, -1), 1)
686	n/a	self.assertEqual(gcd(7, 1), 1)
687	n/a	self.assertEqual(gcd(7, -1), 1)
688	n/a	self.assertEqual(gcd(-23, 15), 1)
689	n/a	self.assertEqual(gcd(120, 84), 12)
690	n/a	self.assertEqual(gcd(84, -120), 12)
691	n/a	self.assertEqual(gcd(1216342683557601535506311712,
692	n/a	436522681849110124616458784), 32)
693	n/a	c = 652560
694	n/a	x = 434610456570399902378880679233098819019853229470286994367836600566
695	n/a	y = 1064502245825115327754847244914921553977
696	n/a	a = x * c
697	n/a	b = y * c
698	n/a	self.assertEqual(gcd(a, b), c)
699	n/a	self.assertEqual(gcd(b, a), c)
700	n/a	self.assertEqual(gcd(-a, b), c)
701	n/a	self.assertEqual(gcd(b, -a), c)
702	n/a	self.assertEqual(gcd(a, -b), c)
703	n/a	self.assertEqual(gcd(-b, a), c)
704	n/a	self.assertEqual(gcd(-a, -b), c)
705	n/a	self.assertEqual(gcd(-b, -a), c)
706	n/a	c = 576559230871654959816130551884856912003141446781646602790216406874
707	n/a	a = x * c
708	n/a	b = y * c
709	n/a	self.assertEqual(gcd(a, b), c)
710	n/a	self.assertEqual(gcd(b, a), c)
711	n/a	self.assertEqual(gcd(-a, b), c)
712	n/a	self.assertEqual(gcd(b, -a), c)
713	n/a	self.assertEqual(gcd(a, -b), c)
714	n/a	self.assertEqual(gcd(-b, a), c)
715	n/a	self.assertEqual(gcd(-a, -b), c)
716	n/a	self.assertEqual(gcd(-b, -a), c)
717	n/a
718	n/a	self.assertRaises(TypeError, gcd, 120.0, 84)
719	n/a	self.assertRaises(TypeError, gcd, 120, 84.0)
720	n/a	self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
721	n/a
722	n/a	def testHypot(self):
723	n/a	self.assertRaises(TypeError, math.hypot)
724	n/a	self.ftest('hypot(0,0)', math.hypot(0,0), 0)
725	n/a	self.ftest('hypot(3,4)', math.hypot(3,4), 5)
726	n/a	self.assertEqual(math.hypot(NAN, INF), INF)
727	n/a	self.assertEqual(math.hypot(INF, NAN), INF)
728	n/a	self.assertEqual(math.hypot(NAN, NINF), INF)
729	n/a	self.assertEqual(math.hypot(NINF, NAN), INF)
730	n/a	self.assertRaises(OverflowError, math.hypot, FLOAT_MAX, FLOAT_MAX)
731	n/a	self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
732	n/a	self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
733	n/a
734	n/a	def testLdexp(self):
735	n/a	self.assertRaises(TypeError, math.ldexp)
736	n/a	self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
737	n/a	self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
738	n/a	self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
739	n/a	self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
740	n/a	self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
741	n/a	self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
742	n/a	self.assertEqual(math.ldexp(1., -1000000), 0.)
743	n/a	self.assertEqual(math.ldexp(-1., -1000000), -0.)
744	n/a	self.assertEqual(math.ldexp(INF, 30), INF)
745	n/a	self.assertEqual(math.ldexp(NINF, -213), NINF)
746	n/a	self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
747	n/a
748	n/a	# large second argument
749	n/a	for n in [105, 1010, 1020, 1040]:
750	n/a	self.assertEqual(math.ldexp(INF, -n), INF)
751	n/a	self.assertEqual(math.ldexp(NINF, -n), NINF)
752	n/a	self.assertEqual(math.ldexp(1., -n), 0.)
753	n/a	self.assertEqual(math.ldexp(-1., -n), -0.)
754	n/a	self.assertEqual(math.ldexp(0., -n), 0.)
755	n/a	self.assertEqual(math.ldexp(-0., -n), -0.)
756	n/a	self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
757	n/a
758	n/a	self.assertRaises(OverflowError, math.ldexp, 1., n)
759	n/a	self.assertRaises(OverflowError, math.ldexp, -1., n)
760	n/a	self.assertEqual(math.ldexp(0., n), 0.)
761	n/a	self.assertEqual(math.ldexp(-0., n), -0.)
762	n/a	self.assertEqual(math.ldexp(INF, n), INF)
763	n/a	self.assertEqual(math.ldexp(NINF, n), NINF)
764	n/a	self.assertTrue(math.isnan(math.ldexp(NAN, n)))
765	n/a
766	n/a	def testLog(self):
767	n/a	self.assertRaises(TypeError, math.log)
768	n/a	self.ftest('log(1/e)', math.log(1/math.e), -1)
769	n/a	self.ftest('log(1)', math.log(1), 0)
770	n/a	self.ftest('log(e)', math.log(math.e), 1)
771	n/a	self.ftest('log(32,2)', math.log(32,2), 5)
772	n/a	self.ftest('log(1040, 10)', math.log(1040, 10), 40)
773	n/a	self.ftest('log(1040, 1020)', math.log(1040, 1020), 2)
774	n/a	self.ftest('log(101000)', math.log(101000),
775	n/a	2302.5850929940457)
776	n/a	self.assertRaises(ValueError, math.log, -1.5)
777	n/a	self.assertRaises(ValueError, math.log, -10**1000)
778	n/a	self.assertRaises(ValueError, math.log, NINF)
779	n/a	self.assertEqual(math.log(INF), INF)
780	n/a	self.assertTrue(math.isnan(math.log(NAN)))
781	n/a
782	n/a	def testLog1p(self):
783	n/a	self.assertRaises(TypeError, math.log1p)
784	n/a	for n in [2, 290, 2300]:
785	n/a	self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
786	n/a	self.assertRaises(ValueError, math.log1p, -1)
787	n/a	self.assertEqual(math.log1p(INF), INF)
788	n/a
789	n/a	@requires_IEEE_754
790	n/a	def testLog2(self):
791	n/a	self.assertRaises(TypeError, math.log2)
792	n/a
793	n/a	# Check some integer values
794	n/a	self.assertEqual(math.log2(1), 0.0)
795	n/a	self.assertEqual(math.log2(2), 1.0)
796	n/a	self.assertEqual(math.log2(4), 2.0)
797	n/a
798	n/a	# Large integer values
799	n/a	self.assertEqual(math.log2(2**1023), 1023.0)
800	n/a	self.assertEqual(math.log2(2**1024), 1024.0)
801	n/a	self.assertEqual(math.log2(2**2000), 2000.0)
802	n/a
803	n/a	self.assertRaises(ValueError, math.log2, -1.5)
804	n/a	self.assertRaises(ValueError, math.log2, NINF)
805	n/a	self.assertTrue(math.isnan(math.log2(NAN)))
806	n/a
807	n/a	@requires_IEEE_754
808	n/a	# log2() is not accurate enough on Mac OS X Tiger (10.4)
809	n/a	@support.requires_mac_ver(10, 5)
810	n/a	def testLog2Exact(self):
811	n/a	# Check that we get exact equality for log2 of powers of 2.
812	n/a	actual = [math.log2(math.ldexp(1.0, n)) for n in range(-1074, 1024)]
813	n/a	expected = [float(n) for n in range(-1074, 1024)]
814	n/a	self.assertEqual(actual, expected)
815	n/a
816	n/a	def testLog10(self):
817	n/a	self.assertRaises(TypeError, math.log10)
818	n/a	self.ftest('log10(0.1)', math.log10(0.1), -1)
819	n/a	self.ftest('log10(1)', math.log10(1), 0)
820	n/a	self.ftest('log10(10)', math.log10(10), 1)
821	n/a	self.ftest('log10(101000)', math.log10(101000), 1000.0)
822	n/a	self.assertRaises(ValueError, math.log10, -1.5)
823	n/a	self.assertRaises(ValueError, math.log10, -10**1000)
824	n/a	self.assertRaises(ValueError, math.log10, NINF)
825	n/a	self.assertEqual(math.log(INF), INF)
826	n/a	self.assertTrue(math.isnan(math.log10(NAN)))
827	n/a
828	n/a	def testModf(self):
829	n/a	self.assertRaises(TypeError, math.modf)
830	n/a
831	n/a	def testmodf(name, result, expected):
832	n/a	(v1, v2), (e1, e2) = result, expected
833	n/a	if abs(v1-e1) > eps or abs(v2-e2):
834	n/a	self.fail('%s returned %r, expected %r'%\
835	n/a	(name, result, expected))
836	n/a
837	n/a	testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
838	n/a	testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
839	n/a
840	n/a	self.assertEqual(math.modf(INF), (0.0, INF))
841	n/a	self.assertEqual(math.modf(NINF), (-0.0, NINF))
842	n/a
843	n/a	modf_nan = math.modf(NAN)
844	n/a	self.assertTrue(math.isnan(modf_nan[0]))
845	n/a	self.assertTrue(math.isnan(modf_nan[1]))
846	n/a
847	n/a	def testPow(self):
848	n/a	self.assertRaises(TypeError, math.pow)
849	n/a	self.ftest('pow(0,1)', math.pow(0,1), 0)
850	n/a	self.ftest('pow(1,0)', math.pow(1,0), 1)
851	n/a	self.ftest('pow(2,1)', math.pow(2,1), 2)
852	n/a	self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
853	n/a	self.assertEqual(math.pow(INF, 1), INF)
854	n/a	self.assertEqual(math.pow(NINF, 1), NINF)
855	n/a	self.assertEqual((math.pow(1, INF)), 1.)
856	n/a	self.assertEqual((math.pow(1, NINF)), 1.)
857	n/a	self.assertTrue(math.isnan(math.pow(NAN, 1)))
858	n/a	self.assertTrue(math.isnan(math.pow(2, NAN)))
859	n/a	self.assertTrue(math.isnan(math.pow(0, NAN)))
860	n/a	self.assertEqual(math.pow(1, NAN), 1)
861	n/a
862	n/a	# pow(0., x)
863	n/a	self.assertEqual(math.pow(0., INF), 0.)
864	n/a	self.assertEqual(math.pow(0., 3.), 0.)
865	n/a	self.assertEqual(math.pow(0., 2.3), 0.)
866	n/a	self.assertEqual(math.pow(0., 2.), 0.)
867	n/a	self.assertEqual(math.pow(0., 0.), 1.)
868	n/a	self.assertEqual(math.pow(0., -0.), 1.)
869	n/a	self.assertRaises(ValueError, math.pow, 0., -2.)
870	n/a	self.assertRaises(ValueError, math.pow, 0., -2.3)
871	n/a	self.assertRaises(ValueError, math.pow, 0., -3.)
872	n/a	self.assertRaises(ValueError, math.pow, 0., NINF)
873	n/a	self.assertTrue(math.isnan(math.pow(0., NAN)))
874	n/a
875	n/a	# pow(INF, x)
876	n/a	self.assertEqual(math.pow(INF, INF), INF)
877	n/a	self.assertEqual(math.pow(INF, 3.), INF)
878	n/a	self.assertEqual(math.pow(INF, 2.3), INF)
879	n/a	self.assertEqual(math.pow(INF, 2.), INF)
880	n/a	self.assertEqual(math.pow(INF, 0.), 1.)
881	n/a	self.assertEqual(math.pow(INF, -0.), 1.)
882	n/a	self.assertEqual(math.pow(INF, -2.), 0.)
883	n/a	self.assertEqual(math.pow(INF, -2.3), 0.)
884	n/a	self.assertEqual(math.pow(INF, -3.), 0.)
885	n/a	self.assertEqual(math.pow(INF, NINF), 0.)
886	n/a	self.assertTrue(math.isnan(math.pow(INF, NAN)))
887	n/a
888	n/a	# pow(-0., x)
889	n/a	self.assertEqual(math.pow(-0., INF), 0.)
890	n/a	self.assertEqual(math.pow(-0., 3.), -0.)
891	n/a	self.assertEqual(math.pow(-0., 2.3), 0.)
892	n/a	self.assertEqual(math.pow(-0., 2.), 0.)
893	n/a	self.assertEqual(math.pow(-0., 0.), 1.)
894	n/a	self.assertEqual(math.pow(-0., -0.), 1.)
895	n/a	self.assertRaises(ValueError, math.pow, -0., -2.)
896	n/a	self.assertRaises(ValueError, math.pow, -0., -2.3)
897	n/a	self.assertRaises(ValueError, math.pow, -0., -3.)
898	n/a	self.assertRaises(ValueError, math.pow, -0., NINF)
899	n/a	self.assertTrue(math.isnan(math.pow(-0., NAN)))
900	n/a
901	n/a	# pow(NINF, x)
902	n/a	self.assertEqual(math.pow(NINF, INF), INF)
903	n/a	self.assertEqual(math.pow(NINF, 3.), NINF)
904	n/a	self.assertEqual(math.pow(NINF, 2.3), INF)
905	n/a	self.assertEqual(math.pow(NINF, 2.), INF)
906	n/a	self.assertEqual(math.pow(NINF, 0.), 1.)
907	n/a	self.assertEqual(math.pow(NINF, -0.), 1.)
908	n/a	self.assertEqual(math.pow(NINF, -2.), 0.)
909	n/a	self.assertEqual(math.pow(NINF, -2.3), 0.)
910	n/a	self.assertEqual(math.pow(NINF, -3.), -0.)
911	n/a	self.assertEqual(math.pow(NINF, NINF), 0.)
912	n/a	self.assertTrue(math.isnan(math.pow(NINF, NAN)))
913	n/a
914	n/a	# pow(-1, x)
915	n/a	self.assertEqual(math.pow(-1., INF), 1.)
916	n/a	self.assertEqual(math.pow(-1., 3.), -1.)
917	n/a	self.assertRaises(ValueError, math.pow, -1., 2.3)
918	n/a	self.assertEqual(math.pow(-1., 2.), 1.)
919	n/a	self.assertEqual(math.pow(-1., 0.), 1.)
920	n/a	self.assertEqual(math.pow(-1., -0.), 1.)
921	n/a	self.assertEqual(math.pow(-1., -2.), 1.)
922	n/a	self.assertRaises(ValueError, math.pow, -1., -2.3)
923	n/a	self.assertEqual(math.pow(-1., -3.), -1.)
924	n/a	self.assertEqual(math.pow(-1., NINF), 1.)
925	n/a	self.assertTrue(math.isnan(math.pow(-1., NAN)))
926	n/a
927	n/a	# pow(1, x)
928	n/a	self.assertEqual(math.pow(1., INF), 1.)
929	n/a	self.assertEqual(math.pow(1., 3.), 1.)
930	n/a	self.assertEqual(math.pow(1., 2.3), 1.)
931	n/a	self.assertEqual(math.pow(1., 2.), 1.)
932	n/a	self.assertEqual(math.pow(1., 0.), 1.)
933	n/a	self.assertEqual(math.pow(1., -0.), 1.)
934	n/a	self.assertEqual(math.pow(1., -2.), 1.)
935	n/a	self.assertEqual(math.pow(1., -2.3), 1.)
936	n/a	self.assertEqual(math.pow(1., -3.), 1.)
937	n/a	self.assertEqual(math.pow(1., NINF), 1.)
938	n/a	self.assertEqual(math.pow(1., NAN), 1.)
939	n/a
940	n/a	# pow(x, 0) should be 1 for any x
941	n/a	self.assertEqual(math.pow(2.3, 0.), 1.)
942	n/a	self.assertEqual(math.pow(-2.3, 0.), 1.)
943	n/a	self.assertEqual(math.pow(NAN, 0.), 1.)
944	n/a	self.assertEqual(math.pow(2.3, -0.), 1.)
945	n/a	self.assertEqual(math.pow(-2.3, -0.), 1.)
946	n/a	self.assertEqual(math.pow(NAN, -0.), 1.)
947	n/a
948	n/a	# pow(x, y) is invalid if x is negative and y is not integral
949	n/a	self.assertRaises(ValueError, math.pow, -1., 2.3)
950	n/a	self.assertRaises(ValueError, math.pow, -15., -3.1)
951	n/a
952	n/a	# pow(x, NINF)
953	n/a	self.assertEqual(math.pow(1.9, NINF), 0.)
954	n/a	self.assertEqual(math.pow(1.1, NINF), 0.)
955	n/a	self.assertEqual(math.pow(0.9, NINF), INF)
956	n/a	self.assertEqual(math.pow(0.1, NINF), INF)
957	n/a	self.assertEqual(math.pow(-0.1, NINF), INF)
958	n/a	self.assertEqual(math.pow(-0.9, NINF), INF)
959	n/a	self.assertEqual(math.pow(-1.1, NINF), 0.)
960	n/a	self.assertEqual(math.pow(-1.9, NINF), 0.)
961	n/a
962	n/a	# pow(x, INF)
963	n/a	self.assertEqual(math.pow(1.9, INF), INF)
964	n/a	self.assertEqual(math.pow(1.1, INF), INF)
965	n/a	self.assertEqual(math.pow(0.9, INF), 0.)
966	n/a	self.assertEqual(math.pow(0.1, INF), 0.)
967	n/a	self.assertEqual(math.pow(-0.1, INF), 0.)
968	n/a	self.assertEqual(math.pow(-0.9, INF), 0.)
969	n/a	self.assertEqual(math.pow(-1.1, INF), INF)
970	n/a	self.assertEqual(math.pow(-1.9, INF), INF)
971	n/a
972	n/a	# pow(x, y) should work for x negative, y an integer
973	n/a	self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
974	n/a	self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
975	n/a	self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
976	n/a	self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
977	n/a	self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
978	n/a	self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
979	n/a	self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
980	n/a	self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
981	n/a	self.assertRaises(ValueError, math.pow, -2.0, -0.5)
982	n/a	self.assertRaises(ValueError, math.pow, -2.0, 0.5)
983	n/a
984	n/a	# the following tests have been commented out since they don't
985	n/a	# really belong here: the implementation of ** for floats is
986	n/a	# independent of the implementation of math.pow
987	n/a	#self.assertEqual(1**NAN, 1)
988	n/a	#self.assertEqual(1**INF, 1)
989	n/a	#self.assertEqual(1**NINF, 1)
990	n/a	#self.assertEqual(1**0, 1)
991	n/a	#self.assertEqual(1.**NAN, 1)
992	n/a	#self.assertEqual(1.**INF, 1)
993	n/a	#self.assertEqual(1.**NINF, 1)
994	n/a	#self.assertEqual(1.**0, 1)
995	n/a
996	n/a	def testRadians(self):
997	n/a	self.assertRaises(TypeError, math.radians)
998	n/a	self.ftest('radians(180)', math.radians(180), math.pi)
999	n/a	self.ftest('radians(90)', math.radians(90), math.pi/2)
1000	n/a	self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
1001	n/a	self.ftest('radians(0)', math.radians(0), 0)
1002	n/a
1003	n/a	def testSin(self):
1004	n/a	self.assertRaises(TypeError, math.sin)
1005	n/a	self.ftest('sin(0)', math.sin(0), 0)
1006	n/a	self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
1007	n/a	self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
1008	n/a	try:
1009	n/a	self.assertTrue(math.isnan(math.sin(INF)))
1010	n/a	self.assertTrue(math.isnan(math.sin(NINF)))
1011	n/a	except ValueError:
1012	n/a	self.assertRaises(ValueError, math.sin, INF)
1013	n/a	self.assertRaises(ValueError, math.sin, NINF)
1014	n/a	self.assertTrue(math.isnan(math.sin(NAN)))
1015	n/a
1016	n/a	def testSinh(self):
1017	n/a	self.assertRaises(TypeError, math.sinh)
1018	n/a	self.ftest('sinh(0)', math.sinh(0), 0)
1019	n/a	self.ftest('sinh(1)2-cosh(1)2', math.sinh(1)2-math.cosh(1)2, -1)
1020	n/a	self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
1021	n/a	self.assertEqual(math.sinh(INF), INF)
1022	n/a	self.assertEqual(math.sinh(NINF), NINF)
1023	n/a	self.assertTrue(math.isnan(math.sinh(NAN)))
1024	n/a
1025	n/a	def testSqrt(self):
1026	n/a	self.assertRaises(TypeError, math.sqrt)
1027	n/a	self.ftest('sqrt(0)', math.sqrt(0), 0)
1028	n/a	self.ftest('sqrt(1)', math.sqrt(1), 1)
1029	n/a	self.ftest('sqrt(4)', math.sqrt(4), 2)
1030	n/a	self.assertEqual(math.sqrt(INF), INF)
1031	n/a	self.assertRaises(ValueError, math.sqrt, -1)
1032	n/a	self.assertRaises(ValueError, math.sqrt, NINF)
1033	n/a	self.assertTrue(math.isnan(math.sqrt(NAN)))
1034	n/a
1035	n/a	def testTan(self):
1036	n/a	self.assertRaises(TypeError, math.tan)
1037	n/a	self.ftest('tan(0)', math.tan(0), 0)
1038	n/a	self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
1039	n/a	self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
1040	n/a	try:
1041	n/a	self.assertTrue(math.isnan(math.tan(INF)))
1042	n/a	self.assertTrue(math.isnan(math.tan(NINF)))
1043	n/a	except:
1044	n/a	self.assertRaises(ValueError, math.tan, INF)
1045	n/a	self.assertRaises(ValueError, math.tan, NINF)
1046	n/a	self.assertTrue(math.isnan(math.tan(NAN)))
1047	n/a
1048	n/a	def testTanh(self):
1049	n/a	self.assertRaises(TypeError, math.tanh)
1050	n/a	self.ftest('tanh(0)', math.tanh(0), 0)
1051	n/a	self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0,
1052	n/a	abs_tol=ulp(1))
1053	n/a	self.ftest('tanh(inf)', math.tanh(INF), 1)
1054	n/a	self.ftest('tanh(-inf)', math.tanh(NINF), -1)
1055	n/a	self.assertTrue(math.isnan(math.tanh(NAN)))
1056	n/a
1057	n/a	@requires_IEEE_754
1058	n/a	@unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0,
1059	n/a	"system tanh() function doesn't copy the sign")
1060	n/a	def testTanhSign(self):
1061	n/a	# check that tanh(-0.) == -0. on IEEE 754 systems
1062	n/a	self.assertEqual(math.tanh(-0.), -0.)
1063	n/a	self.assertEqual(math.copysign(1., math.tanh(-0.)),
1064	n/a	math.copysign(1., -0.))
1065	n/a
1066	n/a	def test_trunc(self):
1067	n/a	self.assertEqual(math.trunc(1), 1)
1068	n/a	self.assertEqual(math.trunc(-1), -1)
1069	n/a	self.assertEqual(type(math.trunc(1)), int)
1070	n/a	self.assertEqual(type(math.trunc(1.5)), int)
1071	n/a	self.assertEqual(math.trunc(1.5), 1)
1072	n/a	self.assertEqual(math.trunc(-1.5), -1)
1073	n/a	self.assertEqual(math.trunc(1.999999), 1)
1074	n/a	self.assertEqual(math.trunc(-1.999999), -1)
1075	n/a	self.assertEqual(math.trunc(-0.999999), -0)
1076	n/a	self.assertEqual(math.trunc(-100.999), -100)
1077	n/a
1078	n/a	class TestTrunc(object):
1079	n/a	def __trunc__(self):
1080	n/a	return 23
1081	n/a
1082	n/a	class TestNoTrunc(object):
1083	n/a	pass
1084	n/a
1085	n/a	self.assertEqual(math.trunc(TestTrunc()), 23)
1086	n/a
1087	n/a	self.assertRaises(TypeError, math.trunc)
1088	n/a	self.assertRaises(TypeError, math.trunc, 1, 2)
1089	n/a	self.assertRaises(TypeError, math.trunc, TestNoTrunc())
1090	n/a
1091	n/a	def testIsfinite(self):
1092	n/a	self.assertTrue(math.isfinite(0.0))
1093	n/a	self.assertTrue(math.isfinite(-0.0))
1094	n/a	self.assertTrue(math.isfinite(1.0))
1095	n/a	self.assertTrue(math.isfinite(-1.0))
1096	n/a	self.assertFalse(math.isfinite(float("nan")))
1097	n/a	self.assertFalse(math.isfinite(float("inf")))
1098	n/a	self.assertFalse(math.isfinite(float("-inf")))
1099	n/a
1100	n/a	def testIsnan(self):
1101	n/a	self.assertTrue(math.isnan(float("nan")))
1102	n/a	self.assertTrue(math.isnan(float("-nan")))
1103	n/a	self.assertTrue(math.isnan(float("inf") * 0.))
1104	n/a	self.assertFalse(math.isnan(float("inf")))
1105	n/a	self.assertFalse(math.isnan(0.))
1106	n/a	self.assertFalse(math.isnan(1.))
1107	n/a
1108	n/a	def testIsinf(self):
1109	n/a	self.assertTrue(math.isinf(float("inf")))
1110	n/a	self.assertTrue(math.isinf(float("-inf")))
1111	n/a	self.assertTrue(math.isinf(1E400))
1112	n/a	self.assertTrue(math.isinf(-1E400))
1113	n/a	self.assertFalse(math.isinf(float("nan")))
1114	n/a	self.assertFalse(math.isinf(0.))
1115	n/a	self.assertFalse(math.isinf(1.))
1116	n/a
1117	n/a	@requires_IEEE_754
1118	n/a	def test_nan_constant(self):
1119	n/a	self.assertTrue(math.isnan(math.nan))
1120	n/a
1121	n/a	@requires_IEEE_754
1122	n/a	def test_inf_constant(self):
1123	n/a	self.assertTrue(math.isinf(math.inf))
1124	n/a	self.assertGreater(math.inf, 0.0)
1125	n/a	self.assertEqual(math.inf, float("inf"))
1126	n/a	self.assertEqual(-math.inf, float("-inf"))
1127	n/a
1128	n/a	# RED_FLAG 16-Oct-2000 Tim
1129	n/a	# While 2.0 is more consistent about exceptions than previous releases, it
1130	n/a	# still fails this part of the test on some platforms. For now, we only
1131	n/a	# run test_exceptions() in verbose mode, so that this isn't normally
1132	n/a	# tested.
1133	n/a	@unittest.skipUnless(verbose, 'requires verbose mode')
1134	n/a	def test_exceptions(self):
1135	n/a	try:
1136	n/a	x = math.exp(-1000000000)
1137	n/a	except:
1138	n/a	# mathmodule.c is failing to weed out underflows from libm, or
1139	n/a	# we've got an fp format with huge dynamic range
1140	n/a	self.fail("underflowing exp() should not have raised "
1141	n/a	"an exception")
1142	n/a	if x != 0:
1143	n/a	self.fail("underflowing exp() should have returned 0")
1144	n/a
1145	n/a	# If this fails, probably using a strict IEEE-754 conforming libm, and x
1146	n/a	# is +Inf afterwards. But Python wants overflows detected by default.
1147	n/a	try:
1148	n/a	x = math.exp(1000000000)
1149	n/a	except OverflowError:
1150	n/a	pass
1151	n/a	else:
1152	n/a	self.fail("overflowing exp() didn't trigger OverflowError")
1153	n/a
1154	n/a	# If this fails, it could be a puzzle. One odd possibility is that
1155	n/a	# mathmodule.c's macros are getting confused while comparing
1156	n/a	# Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
1157	n/a	# as a result (and so raising OverflowError instead).
1158	n/a	try:
1159	n/a	x = math.sqrt(-1.0)
1160	n/a	except ValueError:
1161	n/a	pass
1162	n/a	else:
1163	n/a	self.fail("sqrt(-1) didn't raise ValueError")
1164	n/a
1165	n/a	@requires_IEEE_754
1166	n/a	def test_testfile(self):
1167	n/a	# Some tests need to be skipped on ancient OS X versions.
1168	n/a	# See issue #27953.
1169	n/a	SKIP_ON_TIGER = {'tan0064'}
1170	n/a
1171	n/a	osx_version = None
1172	n/a	if sys.platform == 'darwin':
1173	n/a	version_txt = platform.mac_ver()[0]
1174	n/a	try:
1175	n/a	osx_version = tuple(map(int, version_txt.split('.')))
1176	n/a	except ValueError:
1177	n/a	pass
1178	n/a
1179	n/a	fail_fmt = "{}: {}({!r}): {}"
1180	n/a
1181	n/a	failures = []
1182	n/a	for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
1183	n/a	# Skip if either the input or result is complex
1184	n/a	if ai != 0.0 or ei != 0.0:
1185	n/a	continue
1186	n/a	if fn in ['rect', 'polar']:
1187	n/a	# no real versions of rect, polar
1188	n/a	continue
1189	n/a	# Skip certain tests on OS X 10.4.
1190	n/a	if osx_version is not None and osx_version < (10, 5):
1191	n/a	if id in SKIP_ON_TIGER:
1192	n/a	continue
1193	n/a
1194	n/a	func = getattr(math, fn)
1195	n/a
1196	n/a	if 'invalid' in flags or 'divide-by-zero' in flags:
1197	n/a	er = 'ValueError'
1198	n/a	elif 'overflow' in flags:
1199	n/a	er = 'OverflowError'
1200	n/a
1201	n/a	try:
1202	n/a	result = func(ar)
1203	n/a	except ValueError:
1204	n/a	result = 'ValueError'
1205	n/a	except OverflowError:
1206	n/a	result = 'OverflowError'
1207	n/a
1208	n/a	# Default tolerances
1209	n/a	ulp_tol, abs_tol = 5, 0.0
1210	n/a
1211	n/a	failure = result_check(er, result, ulp_tol, abs_tol)
1212	n/a	if failure is None:
1213	n/a	continue
1214	n/a
1215	n/a	msg = fail_fmt.format(id, fn, ar, failure)
1216	n/a	failures.append(msg)
1217	n/a
1218	n/a	if failures:
1219	n/a	self.fail('Failures in test_testfile:\n ' +
1220	n/a	'\n '.join(failures))
1221	n/a
1222	n/a	@requires_IEEE_754
1223	n/a	def test_mtestfile(self):
1224	n/a	fail_fmt = "{}: {}({!r}): {}"
1225	n/a
1226	n/a	failures = []
1227	n/a	for id, fn, arg, expected, flags in parse_mtestfile(math_testcases):
1228	n/a	func = getattr(math, fn)
1229	n/a
1230	n/a	if 'invalid' in flags or 'divide-by-zero' in flags:
1231	n/a	expected = 'ValueError'
1232	n/a	elif 'overflow' in flags:
1233	n/a	expected = 'OverflowError'
1234	n/a
1235	n/a	try:
1236	n/a	got = func(arg)
1237	n/a	except ValueError:
1238	n/a	got = 'ValueError'
1239	n/a	except OverflowError:
1240	n/a	got = 'OverflowError'
1241	n/a
1242	n/a	# Default tolerances
1243	n/a	ulp_tol, abs_tol = 5, 0.0
1244	n/a
1245	n/a	# Exceptions to the defaults
1246	n/a	if fn == 'gamma':
1247	n/a	# Experimental results on one platform gave
1248	n/a	# an accuracy of <= 10 ulps across the entire float
1249	n/a	# domain. We weaken that to require 20 ulp accuracy.
1250	n/a	ulp_tol = 20
1251	n/a
1252	n/a	elif fn == 'lgamma':
1253	n/a	# we use a weaker accuracy test for lgamma;
1254	n/a	# lgamma only achieves an absolute error of
1255	n/a	# a few multiples of the machine accuracy, in
1256	n/a	# general.
1257	n/a	abs_tol = 1e-15
1258	n/a
1259	n/a	elif fn == 'erfc' and arg >= 0.0:
1260	n/a	# erfc has less-than-ideal accuracy for large
1261	n/a	# arguments (x ~ 25 or so), mainly due to the
1262	n/a	# error involved in computing exp(-x*x).
1263	n/a	#
1264	n/a	# Observed between CPython and mpmath at 25 dp:
1265	n/a	# x < 0 : err <= 2 ulp
1266	n/a	# 0 <= x < 1 : err <= 10 ulp
1267	n/a	# 1 <= x < 10 : err <= 100 ulp
1268	n/a	# 10 <= x < 20 : err <= 300 ulp
1269	n/a	# 20 <= x : < 600 ulp
1270	n/a	#
1271	n/a	if arg < 1.0:
1272	n/a	ulp_tol = 10
1273	n/a	elif arg < 10.0:
1274	n/a	ulp_tol = 100
1275	n/a	else:
1276	n/a	ulp_tol = 1000
1277	n/a
1278	n/a	failure = result_check(expected, got, ulp_tol, abs_tol)
1279	n/a	if failure is None:
1280	n/a	continue
1281	n/a
1282	n/a	msg = fail_fmt.format(id, fn, arg, failure)
1283	n/a	failures.append(msg)
1284	n/a
1285	n/a	if failures:
1286	n/a	self.fail('Failures in test_mtestfile:\n ' +
1287	n/a	'\n '.join(failures))
1288	n/a
1289	n/a
1290	n/a	class IsCloseTests(unittest.TestCase):
1291	n/a	isclose = math.isclose # sublcasses should override this
1292	n/a
1293	n/a	def assertIsClose(self, a, b, args, *kwargs):
1294	n/a	self.assertTrue(self.isclose(a, b, args, *kwargs),
1295	n/a	msg="%s and %s should be close!" % (a, b))
1296	n/a
1297	n/a	def assertIsNotClose(self, a, b, args, *kwargs):
1298	n/a	self.assertFalse(self.isclose(a, b, args, *kwargs),
1299	n/a	msg="%s and %s should not be close!" % (a, b))
1300	n/a
1301	n/a	def assertAllClose(self, examples, args, *kwargs):
1302	n/a	for a, b in examples:
1303	n/a	self.assertIsClose(a, b, args, *kwargs)
1304	n/a
1305	n/a	def assertAllNotClose(self, examples, args, *kwargs):
1306	n/a	for a, b in examples:
1307	n/a	self.assertIsNotClose(a, b, args, *kwargs)
1308	n/a
1309	n/a	def test_negative_tolerances(self):
1310	n/a	# ValueError should be raised if either tolerance is less than zero
1311	n/a	with self.assertRaises(ValueError):
1312	n/a	self.assertIsClose(1, 1, rel_tol=-1e-100)
1313	n/a	with self.assertRaises(ValueError):
1314	n/a	self.assertIsClose(1, 1, rel_tol=1e-100, abs_tol=-1e10)
1315	n/a
1316	n/a	def test_identical(self):
1317	n/a	# identical values must test as close
1318	n/a	identical_examples = [(2.0, 2.0),
1319	n/a	(0.1e200, 0.1e200),
1320	n/a	(1.123e-300, 1.123e-300),
1321	n/a	(12345, 12345.0),
1322	n/a	(0.0, -0.0),
1323	n/a	(345678, 345678)]
1324	n/a	self.assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0)
1325	n/a
1326	n/a	def test_eight_decimal_places(self):
1327	n/a	# examples that are close to 1e-8, but not 1e-9
1328	n/a	eight_decimal_places_examples = [(1e8, 1e8 + 1),
1329	n/a	(-1e-8, -1.000000009e-8),
1330	n/a	(1.12345678, 1.12345679)]
1331	n/a	self.assertAllClose(eight_decimal_places_examples, rel_tol=1e-8)
1332	n/a	self.assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-9)
1333	n/a
1334	n/a	def test_near_zero(self):
1335	n/a	# values close to zero
1336	n/a	near_zero_examples = [(1e-9, 0.0),
1337	n/a	(-1e-9, 0.0),
1338	n/a	(-1e-150, 0.0)]
1339	n/a	# these should not be close to any rel_tol
1340	n/a	self.assertAllNotClose(near_zero_examples, rel_tol=0.9)
1341	n/a	# these should be close to abs_tol=1e-8
1342	n/a	self.assertAllClose(near_zero_examples, abs_tol=1e-8)
1343	n/a
1344	n/a	def test_identical_infinite(self):
1345	n/a	# these are close regardless of tolerance -- i.e. they are equal
1346	n/a	self.assertIsClose(INF, INF)
1347	n/a	self.assertIsClose(INF, INF, abs_tol=0.0)
1348	n/a	self.assertIsClose(NINF, NINF)
1349	n/a	self.assertIsClose(NINF, NINF, abs_tol=0.0)
1350	n/a
1351	n/a	def test_inf_ninf_nan(self):
1352	n/a	# these should never be close (following IEEE 754 rules for equality)
1353	n/a	not_close_examples = [(NAN, NAN),
1354	n/a	(NAN, 1e-100),
1355	n/a	(1e-100, NAN),
1356	n/a	(INF, NAN),
1357	n/a	(NAN, INF),
1358	n/a	(INF, NINF),
1359	n/a	(INF, 1.0),
1360	n/a	(1.0, INF),
1361	n/a	(INF, 1e308),
1362	n/a	(1e308, INF)]
1363	n/a	# use largest reasonable tolerance
1364	n/a	self.assertAllNotClose(not_close_examples, abs_tol=0.999999999999999)
1365	n/a
1366	n/a	def test_zero_tolerance(self):
1367	n/a	# test with zero tolerance
1368	n/a	zero_tolerance_close_examples = [(1.0, 1.0),
1369	n/a	(-3.4, -3.4),
1370	n/a	(-1e-300, -1e-300)]
1371	n/a	self.assertAllClose(zero_tolerance_close_examples, rel_tol=0.0)
1372	n/a
1373	n/a	zero_tolerance_not_close_examples = [(1.0, 1.000000000000001),
1374	n/a	(0.99999999999999, 1.0),
1375	n/a	(1.0e200, .999999999999999e200)]
1376	n/a	self.assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0)
1377	n/a
1378	n/a	def test_asymmetry(self):
1379	n/a	# test the asymmetry example from PEP 485
1380	n/a	self.assertAllClose([(9, 10), (10, 9)], rel_tol=0.1)
1381	n/a
1382	n/a	def test_integers(self):
1383	n/a	# test with integer values
1384	n/a	integer_examples = [(100000001, 100000000),
1385	n/a	(123456789, 123456788)]
1386	n/a
1387	n/a	self.assertAllClose(integer_examples, rel_tol=1e-8)
1388	n/a	self.assertAllNotClose(integer_examples, rel_tol=1e-9)
1389	n/a
1390	n/a	def test_decimals(self):
1391	n/a	# test with Decimal values
1392	n/a	from decimal import Decimal
1393	n/a
1394	n/a	decimal_examples = [(Decimal('1.00000001'), Decimal('1.0')),
1395	n/a	(Decimal('1.00000001e-20'), Decimal('1.0e-20')),
1396	n/a	(Decimal('1.00000001e-100'), Decimal('1.0e-100')),
1397	n/a	(Decimal('1.00000001e20'), Decimal('1.0e20'))]
1398	n/a	self.assertAllClose(decimal_examples, rel_tol=1e-8)
1399	n/a	self.assertAllNotClose(decimal_examples, rel_tol=1e-9)
1400	n/a
1401	n/a	def test_fractions(self):
1402	n/a	# test with Fraction values
1403	n/a	from fractions import Fraction
1404	n/a
1405	n/a	fraction_examples = [
1406	n/a	(Fraction(1, 100000000) + 1, Fraction(1)),
1407	n/a	(Fraction(100000001), Fraction(100000000)),
1408	n/a	(Fraction(108 + 1, 1028), Fraction(1, 10**20))]
1409	n/a	self.assertAllClose(fraction_examples, rel_tol=1e-8)
1410	n/a	self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
1411	n/a
1412	n/a
1413	n/a	def test_main():
1414	n/a	from doctest import DocFileSuite
1415	n/a	suite = unittest.TestSuite()
1416	n/a	suite.addTest(unittest.makeSuite(MathTests))
1417	n/a	suite.addTest(unittest.makeSuite(IsCloseTests))
1418	n/a	suite.addTest(DocFileSuite("ieee754.txt"))
1419	n/a	run_unittest(suite)
1420	n/a
1421	n/a	if __name__ == '__main__':
1422	n/a	test_main()