source: trunk/essentials/dev-lang/python/Lib/test/test_long.py

Last change on this file was 3225, checked in by bird, 19 years ago

Python 2.5
File size: 18.7 KB
Line 
1import unittest
2from test import test_support
3
4import random
5
6# Used for lazy formatting of failure messages
7class Frm(object):
8 def __init__(self, format, *args):
9 self.format = format
10 self.args = args
11
12 def __str__(self):
13 return self.format % self.args
14
15# SHIFT should match the value in longintrepr.h for best testing.
16SHIFT = 15
17BASE = 2 ** SHIFT
18MASK = BASE - 1
19KARATSUBA_CUTOFF = 70 # from longobject.c
20
21# Max number of base BASE digits to use in test cases. Doubling
22# this will more than double the runtime.
23MAXDIGITS = 15
24
25# build some special values
26special = map(long, [0, 1, 2, BASE, BASE >> 1])
27special.append(0x5555555555555555L)
28special.append(0xaaaaaaaaaaaaaaaaL)
29# some solid strings of one bits
30p2 = 4L # 0 and 1 already added
31for i in range(2*SHIFT):
32 special.append(p2 - 1)
33 p2 = p2 << 1
34del p2
35# add complements & negations
36special = special + map(lambda x: ~x, special) + \
37 map(lambda x: -x, special)
38
39
40class LongTest(unittest.TestCase):
41
42 # Get quasi-random long consisting of ndigits digits (in base BASE).
43 # quasi == the most-significant digit will not be 0, and the number
44 # is constructed to contain long strings of 0 and 1 bits. These are
45 # more likely than random bits to provoke digit-boundary errors.
46 # The sign of the number is also random.
47
48 def getran(self, ndigits):
49 self.assert_(ndigits > 0)
50 nbits_hi = ndigits * SHIFT
51 nbits_lo = nbits_hi - SHIFT + 1
52 answer = 0L
53 nbits = 0
54 r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start
55 while nbits < nbits_lo:
56 bits = (r >> 1) + 1
57 bits = min(bits, nbits_hi - nbits)
58 self.assert_(1 <= bits <= SHIFT)
59 nbits = nbits + bits
60 answer = answer << bits
61 if r & 1:
62 answer = answer | ((1 << bits) - 1)
63 r = int(random.random() * (SHIFT * 2))
64 self.assert_(nbits_lo <= nbits <= nbits_hi)
65 if random.random() < 0.5:
66 answer = -answer
67 return answer
68
69 # Get random long consisting of ndigits random digits (relative to base
70 # BASE). The sign bit is also random.
71
72 def getran2(ndigits):
73 answer = 0L
74 for i in xrange(ndigits):
75 answer = (answer << SHIFT) | random.randint(0, MASK)
76 if random.random() < 0.5:
77 answer = -answer
78 return answer
79
80 def check_division(self, x, y):
81 eq = self.assertEqual
82 q, r = divmod(x, y)
83 q2, r2 = x//y, x%y
84 pab, pba = x*y, y*x
85 eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y))
86 eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y))
87 eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y))
88 eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y))
89 if y > 0:
90 self.assert_(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y))
91 else:
92 self.assert_(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y))
93
94 def test_division(self):
95 digits = range(1, MAXDIGITS+1) + range(KARATSUBA_CUTOFF,
96 KARATSUBA_CUTOFF + 14)
97 digits.append(KARATSUBA_CUTOFF * 3)
98 for lenx in digits:
99 x = self.getran(lenx)
100 for leny in digits:
101 y = self.getran(leny) or 1L
102 self.check_division(x, y)
103
104 def test_karatsuba(self):
105 digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10)
106 digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100])
107
108 bits = [digit * SHIFT for digit in digits]
109
110 # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) ==
111 # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check.
112 for abits in bits:
113 a = (1L << abits) - 1
114 for bbits in bits:
115 if bbits < abits:
116 continue
117 b = (1L << bbits) - 1
118 x = a * b
119 y = ((1L << (abits + bbits)) -
120 (1L << abits) -
121 (1L << bbits) +
122 1)
123 self.assertEqual(x, y,
124 Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y))
125
126 def check_bitop_identities_1(self, x):
127 eq = self.assertEqual
128 eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x))
129 eq(x | 0, x, Frm("x | 0 != x for x=%r", x))
130 eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x))
131 eq(x & -1, x, Frm("x & -1 != x for x=%r", x))
132 eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x))
133 eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x))
134 eq(x, ~~x, Frm("x != ~~x for x=%r", x))
135 eq(x & x, x, Frm("x & x != x for x=%r", x))
136 eq(x | x, x, Frm("x | x != x for x=%r", x))
137 eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x))
138 eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x))
139 eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x))
140 eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x))
141 eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x))
142 eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x))
143 for n in xrange(2*SHIFT):
144 p2 = 2L ** n
145 eq(x << n >> n, x,
146 Frm("x << n >> n != x for x=%r, n=%r", (x, n)))
147 eq(x // p2, x >> n,
148 Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2)))
149 eq(x * p2, x << n,
150 Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2)))
151 eq(x & -p2, x >> n << n,
152 Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2)))
153 eq(x & -p2, x & ~(p2 - 1),
154 Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2)))
155
156 def check_bitop_identities_2(self, x, y):
157 eq = self.assertEqual
158 eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y)))
159 eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y)))
160 eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y)))
161 eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y)))
162 eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y)))
163 eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y)))
164 eq(x ^ y, (x | y) & ~(x & y),
165 Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y)))
166 eq(x ^ y, (x & ~y) | (~x & y),
167 Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y)))
168 eq(x ^ y, (x | y) & (~x | ~y),
169 Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y)))
170
171 def check_bitop_identities_3(self, x, y, z):
172 eq = self.assertEqual
173 eq((x & y) & z, x & (y & z),
174 Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z)))
175 eq((x | y) | z, x | (y | z),
176 Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z)))
177 eq((x ^ y) ^ z, x ^ (y ^ z),
178 Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z)))
179 eq(x & (y | z), (x & y) | (x & z),
180 Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z)))
181 eq(x | (y & z), (x | y) & (x | z),
182 Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z)))
183
184 def test_bitop_identities(self):
185 for x in special:
186 self.check_bitop_identities_1(x)
187 digits = xrange(1, MAXDIGITS+1)
188 for lenx in digits:
189 x = self.getran(lenx)
190 self.check_bitop_identities_1(x)
191 for leny in digits:
192 y = self.getran(leny)
193 self.check_bitop_identities_2(x, y)
194 self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2))
195
196 def slow_format(self, x, base):
197 if (x, base) == (0, 8):
198 # this is an oddball!
199 return "0L"
200 digits = []
201 sign = 0
202 if x < 0:
203 sign, x = 1, -x
204 while x:
205 x, r = divmod(x, base)
206 digits.append(int(r))
207 digits.reverse()
208 digits = digits or [0]
209 return '-'[:sign] + \
210 {8: '0', 10: '', 16: '0x'}[base] + \
211 "".join(map(lambda i: "0123456789abcdef"[i], digits)) + "L"
212
213 def check_format_1(self, x):
214 for base, mapper in (8, oct), (10, repr), (16, hex):
215 got = mapper(x)
216 expected = self.slow_format(x, base)
217 msg = Frm("%s returned %r but expected %r for %r",
218 mapper.__name__, got, expected, x)
219 self.assertEqual(got, expected, msg)
220 self.assertEqual(long(got, 0), x, Frm('long("%s", 0) != %r', got, x))
221 # str() has to be checked a little differently since there's no
222 # trailing "L"
223 got = str(x)
224 expected = self.slow_format(x, 10)[:-1]
225 msg = Frm("%s returned %r but expected %r for %r",
226 mapper.__name__, got, expected, x)
227 self.assertEqual(got, expected, msg)
228
229 def test_format(self):
230 for x in special:
231 self.check_format_1(x)
232 for i in xrange(10):
233 for lenx in xrange(1, MAXDIGITS+1):
234 x = self.getran(lenx)
235 self.check_format_1(x)
236
237 def test_misc(self):
238 import sys
239
240 # check the extremes in int<->long conversion
241 hugepos = sys.maxint
242 hugeneg = -hugepos - 1
243 hugepos_aslong = long(hugepos)
244 hugeneg_aslong = long(hugeneg)
245 self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxint) != sys.maxint")
246 self.assertEqual(hugeneg, hugeneg_aslong,
247 "long(-sys.maxint-1) != -sys.maxint-1")
248
249 # long -> int should not fail for hugepos_aslong or hugeneg_aslong
250 try:
251 self.assertEqual(int(hugepos_aslong), hugepos,
252 "converting sys.maxint to long and back to int fails")
253 except OverflowError:
254 self.fail("int(long(sys.maxint)) overflowed!")
255 try:
256 self.assertEqual(int(hugeneg_aslong), hugeneg,
257 "converting -sys.maxint-1 to long and back to int fails")
258 except OverflowError:
259 self.fail("int(long(-sys.maxint-1)) overflowed!")
260
261 # but long -> int should overflow for hugepos+1 and hugeneg-1
262 x = hugepos_aslong + 1
263 try:
264 y = int(x)
265 except OverflowError:
266 self.fail("int(long(sys.maxint) + 1) mustn't overflow")
267 self.assert_(isinstance(y, long),
268 "int(long(sys.maxint) + 1) should have returned long")
269
270 x = hugeneg_aslong - 1
271 try:
272 y = int(x)
273 except OverflowError:
274 self.fail("int(long(-sys.maxint-1) - 1) mustn't overflow")
275 self.assert_(isinstance(y, long),
276 "int(long(-sys.maxint-1) - 1) should have returned long")
277
278 class long2(long):
279 pass
280 x = long2(1L<<100)
281 y = int(x)
282 self.assert_(type(y) is long,
283 "overflowing int conversion must return long not long subtype")
284
285# ----------------------------------- tests of auto int->long conversion
286
287 def test_auto_overflow(self):
288 import math, sys
289
290 special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1]
291 sqrt = int(math.sqrt(sys.maxint))
292 special.extend([sqrt-1, sqrt, sqrt+1])
293 special.extend([-i for i in special])
294
295 def checkit(*args):
296 # Heavy use of nested scopes here!
297 self.assertEqual(got, expected,
298 Frm("for %r expected %r got %r", args, expected, got))
299
300 for x in special:
301 longx = long(x)
302
303 expected = -longx
304 got = -x
305 checkit('-', x)
306
307 for y in special:
308 longy = long(y)
309
310 expected = longx + longy
311 got = x + y
312 checkit(x, '+', y)
313
314 expected = longx - longy
315 got = x - y
316 checkit(x, '-', y)
317
318 expected = longx * longy
319 got = x * y
320 checkit(x, '*', y)
321
322 if y:
323 expected = longx / longy
324 got = x / y
325 checkit(x, '/', y)
326
327 expected = longx // longy
328 got = x // y
329 checkit(x, '//', y)
330
331 expected = divmod(longx, longy)
332 got = divmod(longx, longy)
333 checkit(x, 'divmod', y)
334
335 if abs(y) < 5 and not (x == 0 and y < 0):
336 expected = longx ** longy
337 got = x ** y
338 checkit(x, '**', y)
339
340 for z in special:
341 if z != 0 :
342 if y >= 0:
343 expected = pow(longx, longy, long(z))
344 got = pow(x, y, z)
345 checkit('pow', x, y, '%', z)
346 else:
347 self.assertRaises(TypeError, pow,longx, longy, long(z))
348
349 def test_float_overflow(self):
350 import math
351
352 for x in -2.0, -1.0, 0.0, 1.0, 2.0:
353 self.assertEqual(float(long(x)), x)
354
355 shuge = '12345' * 120
356 huge = 1L << 30000
357 mhuge = -huge
358 namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math}
359 for test in ["float(huge)", "float(mhuge)",
360 "complex(huge)", "complex(mhuge)",
361 "complex(huge, 1)", "complex(mhuge, 1)",
362 "complex(1, huge)", "complex(1, mhuge)",
363 "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.",
364 "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.",
365 "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.",
366 "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.",
367 "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.",
368 "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.",
369 "math.sin(huge)", "math.sin(mhuge)",
370 "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better
371 "math.floor(huge)", "math.floor(mhuge)"]:
372
373 self.assertRaises(OverflowError, eval, test, namespace)
374
375 # XXX Perhaps float(shuge) can raise OverflowError on some box?
376 # The comparison should not.
377 self.assertNotEqual(float(shuge), int(shuge),
378 "float(shuge) should not equal int(shuge)")
379
380 def test_logs(self):
381 import math
382
383 LOG10E = math.log10(math.e)
384
385 for exp in range(10) + [100, 1000, 10000]:
386 value = 10 ** exp
387 log10 = math.log10(value)
388 self.assertAlmostEqual(log10, exp)
389
390 # log10(value) == exp, so log(value) == log10(value)/log10(e) ==
391 # exp/LOG10E
392 expected = exp / LOG10E
393 log = math.log(value)
394 self.assertAlmostEqual(log, expected)
395
396 for bad in -(1L << 10000), -2L, 0L:
397 self.assertRaises(ValueError, math.log, bad)
398 self.assertRaises(ValueError, math.log10, bad)
399
400 def test_mixed_compares(self):
401 eq = self.assertEqual
402 import math
403 import sys
404
405 # We're mostly concerned with that mixing floats and longs does the
406 # right stuff, even when longs are too large to fit in a float.
407 # The safest way to check the results is to use an entirely different
408 # method, which we do here via a skeletal rational class (which
409 # represents all Python ints, longs and floats exactly).
410 class Rat:
411 def __init__(self, value):
412 if isinstance(value, (int, long)):
413 self.n = value
414 self.d = 1
415 elif isinstance(value, float):
416 # Convert to exact rational equivalent.
417 f, e = math.frexp(abs(value))
418 assert f == 0 or 0.5 <= f < 1.0
419 # |value| = f * 2**e exactly
420
421 # Suck up CHUNK bits at a time; 28 is enough so that we suck
422 # up all bits in 2 iterations for all known binary double-
423 # precision formats, and small enough to fit in an int.
424 CHUNK = 28
425 top = 0
426 # invariant: |value| = (top + f) * 2**e exactly
427 while f:
428 f = math.ldexp(f, CHUNK)
429 digit = int(f)
430 assert digit >> CHUNK == 0
431 top = (top << CHUNK) | digit
432 f -= digit
433 assert 0.0 <= f < 1.0
434 e -= CHUNK
435
436 # Now |value| = top * 2**e exactly.
437 if e >= 0:
438 n = top << e
439 d = 1
440 else:
441 n = top
442 d = 1 << -e
443 if value < 0:
444 n = -n
445 self.n = n
446 self.d = d
447 assert float(n) / float(d) == value
448 else:
449 raise TypeError("can't deal with %r" % val)
450
451 def __cmp__(self, other):
452 if not isinstance(other, Rat):
453 other = Rat(other)
454 return cmp(self.n * other.d, self.d * other.n)
455
456 cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200]
457 # 2**48 is an important boundary in the internals. 2**53 is an
458 # important boundary for IEEE double precision.
459 for t in 2.0**48, 2.0**50, 2.0**53:
460 cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0,
461 long(t-1), long(t), long(t+1)])
462 cases.extend([0, 1, 2, sys.maxint, float(sys.maxint)])
463 # 1L<<20000 should exceed all double formats. long(1e200) is to
464 # check that we get equality with 1e200 above.
465 t = long(1e200)
466 cases.extend([0L, 1L, 2L, 1L << 20000, t-1, t, t+1])
467 cases.extend([-x for x in cases])
468 for x in cases:
469 Rx = Rat(x)
470 for y in cases:
471 Ry = Rat(y)
472 Rcmp = cmp(Rx, Ry)
473 xycmp = cmp(x, y)
474 eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp))
475 eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp))
476 eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp))
477 eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp))
478 eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp))
479 eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp))
480 eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp))
481
482def test_main():
483 test_support.run_unittest(LongTest)
484
485if __name__ == "__main__":
486 test_main()
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