blob: cbb0b37d914fce4ba40fecf51c9189b6f6b70462 [file] [log] [blame]
Barry Warsaw04f357c2002-07-23 19:04:11 +00001from test.test_support import verify, verbose, TestFailed, fcmp
Guido van Rossum4365cab1998-08-13 14:20:17 +00002from string import join
3from random import random, randint
4
5# SHIFT should match the value in longintrepr.h for best testing.
6SHIFT = 15
7BASE = 2 ** SHIFT
8MASK = BASE - 1
Tim Peters28b0e2a2002-08-13 02:17:11 +00009KARATSUBA_CUTOFF = 35 # from longobject.c
Guido van Rossum4365cab1998-08-13 14:20:17 +000010
11# Max number of base BASE digits to use in test cases. Doubling
Tim Peters28b0e2a2002-08-13 02:17:11 +000012# this will more than double the runtime.
13MAXDIGITS = 15
Guido van Rossum4365cab1998-08-13 14:20:17 +000014
Guido van Rossum4581a0c1998-10-02 01:19:48 +000015# build some special values
16special = map(long, [0, 1, 2, BASE, BASE >> 1])
17special.append(0x5555555555555555L)
18special.append(0xaaaaaaaaaaaaaaaaL)
19# some solid strings of one bits
20p2 = 4L # 0 and 1 already added
21for i in range(2*SHIFT):
22 special.append(p2 - 1)
23 p2 = p2 << 1
24del p2
25# add complements & negations
26special = special + map(lambda x: ~x, special) + \
27 map(lambda x: -x, special)
28
Guido van Rossum4365cab1998-08-13 14:20:17 +000029# ------------------------------------------------------------ utilities
30
31# Use check instead of assert so the test still does something
32# under -O.
33
34def check(ok, *args):
35 if not ok:
36 raise TestFailed, join(map(str, args), " ")
37
Guido van Rossum4581a0c1998-10-02 01:19:48 +000038# Get quasi-random long consisting of ndigits digits (in base BASE).
39# quasi == the most-significant digit will not be 0, and the number
40# is constructed to contain long strings of 0 and 1 bits. These are
41# more likely than random bits to provoke digit-boundary errors.
42# The sign of the number is also random.
43
44def getran(ndigits):
Marc-André Lemburg36619082001-01-17 19:11:13 +000045 verify(ndigits > 0)
Guido van Rossum4581a0c1998-10-02 01:19:48 +000046 nbits_hi = ndigits * SHIFT
47 nbits_lo = nbits_hi - SHIFT + 1
48 answer = 0L
49 nbits = 0
50 r = int(random() * (SHIFT * 2)) | 1 # force 1 bits to start
51 while nbits < nbits_lo:
52 bits = (r >> 1) + 1
53 bits = min(bits, nbits_hi - nbits)
Marc-André Lemburg36619082001-01-17 19:11:13 +000054 verify(1 <= bits <= SHIFT)
Guido van Rossum4581a0c1998-10-02 01:19:48 +000055 nbits = nbits + bits
56 answer = answer << bits
57 if r & 1:
58 answer = answer | ((1 << bits) - 1)
59 r = int(random() * (SHIFT * 2))
Marc-André Lemburg36619082001-01-17 19:11:13 +000060 verify(nbits_lo <= nbits <= nbits_hi)
Guido van Rossum4581a0c1998-10-02 01:19:48 +000061 if random() < 0.5:
62 answer = -answer
63 return answer
64
Guido van Rossum4365cab1998-08-13 14:20:17 +000065# Get random long consisting of ndigits random digits (relative to base
66# BASE). The sign bit is also random.
67
Guido van Rossum4581a0c1998-10-02 01:19:48 +000068def getran2(ndigits):
Guido van Rossum4365cab1998-08-13 14:20:17 +000069 answer = 0L
70 for i in range(ndigits):
71 answer = (answer << SHIFT) | randint(0, MASK)
72 if random() < 0.5:
73 answer = -answer
74 return answer
75
76# --------------------------------------------------------------- divmod
77
78def test_division_2(x, y):
79 q, r = divmod(x, y)
Guido van Rossum54e54c62001-09-04 19:14:14 +000080 q2, r2 = x//y, x%y
Guido van Rossum6e277cf2000-04-10 17:41:37 +000081 pab, pba = x*y, y*x
82 check(pab == pba, "multiplication does not commute for", x, y)
Guido van Rossum4365cab1998-08-13 14:20:17 +000083 check(q == q2, "divmod returns different quotient than / for", x, y)
84 check(r == r2, "divmod returns different mod than % for", x, y)
85 check(x == q*y + r, "x != q*y + r after divmod on", x, y)
86 if y > 0:
87 check(0 <= r < y, "bad mod from divmod on", x, y)
88 else:
89 check(y < r <= 0, "bad mod from divmod on", x, y)
90
91def test_division(maxdigits=MAXDIGITS):
Tim Peters971e0692001-08-23 20:34:01 +000092 if verbose:
93 print "long / * % divmod"
Tim Peters28b0e2a2002-08-13 02:17:11 +000094 digits = range(1, maxdigits+1) + range(KARATSUBA_CUTOFF,
Tim Petersd0876b82002-08-13 02:24:25 +000095 KARATSUBA_CUTOFF + 14)
96 digits.append(KARATSUBA_CUTOFF * 3)
Guido van Rossum4365cab1998-08-13 14:20:17 +000097 for lenx in digits:
98 x = getran(lenx)
99 for leny in digits:
100 y = getran(leny) or 1L
101 test_division_2(x, y)
Tim Peters7f270ba2002-08-13 21:06:55 +0000102# ------------------------------------------------------------ karatsuba
Guido van Rossum4365cab1998-08-13 14:20:17 +0000103
Tim Peters7f270ba2002-08-13 21:06:55 +0000104def test_karatsuba():
105
106 if verbose:
107 print "Karatsuba"
108
109 digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10)
110 digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100])
111
112 bits = [digit * SHIFT for digit in digits]
113
114 # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) ==
115 # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check.
116 for abits in bits:
117 a = (1L << abits) - 1
118 for bbits in bits:
119 if bbits < abits:
120 continue
121 b = (1L << bbits) - 1
122 x = a * b
123 y = ((1L << (abits + bbits)) -
124 (1L << abits) -
125 (1L << bbits) +
126 1)
127 check(x == y, "bad result for", a, "*", b, x, y)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000128# -------------------------------------------------------------- ~ & | ^
129
130def test_bitop_identities_1(x):
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000131 check(x & 0 == 0, "x & 0 != 0 for", x)
132 check(x | 0 == x, "x | 0 != x for", x)
133 check(x ^ 0 == x, "x ^ 0 != x for", x)
134 check(x & -1 == x, "x & -1 != x for", x)
135 check(x | -1 == -1, "x | -1 != -1 for", x)
136 check(x ^ -1 == ~x, "x ^ -1 != ~x for", x)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000137 check(x == ~~x, "x != ~~x for", x)
138 check(x & x == x, "x & x != x for", x)
139 check(x | x == x, "x | x != x for", x)
140 check(x ^ x == 0, "x ^ x != 0 for", x)
141 check(x & ~x == 0, "x & ~x != 0 for", x)
142 check(x | ~x == -1, "x | ~x != -1 for", x)
143 check(x ^ ~x == -1, "x ^ ~x != -1 for", x)
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000144 check(-x == 1 + ~x == ~(x-1), "not -x == 1 + ~x == ~(x-1) for", x)
145 for n in range(2*SHIFT):
146 p2 = 2L ** n
147 check(x << n >> n == x, "x << n >> n != x for", x, n)
Guido van Rossum54e54c62001-09-04 19:14:14 +0000148 check(x // p2 == x >> n, "x // p2 != x >> n for x n p2", x, n, p2)
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000149 check(x * p2 == x << n, "x * p2 != x << n for x n p2", x, n, p2)
150 check(x & -p2 == x >> n << n == x & ~(p2 - 1),
151 "not x & -p2 == x >> n << n == x & ~(p2 - 1) for x n p2",
152 x, n, p2)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000153
154def test_bitop_identities_2(x, y):
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000155 check(x & y == y & x, "x & y != y & x for", x, y)
156 check(x | y == y | x, "x | y != y | x for", x, y)
157 check(x ^ y == y ^ x, "x ^ y != y ^ x for", x, y)
158 check(x ^ y ^ x == y, "x ^ y ^ x != y for", x, y)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000159 check(x & y == ~(~x | ~y), "x & y != ~(~x | ~y) for", x, y)
160 check(x | y == ~(~x & ~y), "x | y != ~(~x & ~y) for", x, y)
161 check(x ^ y == (x | y) & ~(x & y),
162 "x ^ y != (x | y) & ~(x & y) for", x, y)
163 check(x ^ y == (x & ~y) | (~x & y),
164 "x ^ y == (x & ~y) | (~x & y) for", x, y)
165 check(x ^ y == (x | y) & (~x | ~y),
166 "x ^ y == (x | y) & (~x | ~y) for", x, y)
167
168def test_bitop_identities_3(x, y, z):
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000169 check((x & y) & z == x & (y & z),
170 "(x & y) & z != x & (y & z) for", x, y, z)
171 check((x | y) | z == x | (y | z),
172 "(x | y) | z != x | (y | z) for", x, y, z)
173 check((x ^ y) ^ z == x ^ (y ^ z),
174 "(x ^ y) ^ z != x ^ (y ^ z) for", x, y, z)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000175 check(x & (y | z) == (x & y) | (x & z),
176 "x & (y | z) != (x & y) | (x & z) for", x, y, z)
177 check(x | (y & z) == (x | y) & (x | z),
178 "x | (y & z) != (x | y) & (x | z) for", x, y, z)
179
180def test_bitop_identities(maxdigits=MAXDIGITS):
Tim Peters971e0692001-08-23 20:34:01 +0000181 if verbose:
182 print "long bit-operation identities"
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000183 for x in special:
184 test_bitop_identities_1(x)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000185 digits = range(1, maxdigits+1)
186 for lenx in digits:
187 x = getran(lenx)
188 test_bitop_identities_1(x)
189 for leny in digits:
190 y = getran(leny)
191 test_bitop_identities_2(x, y)
Guido van Rossum54e54c62001-09-04 19:14:14 +0000192 test_bitop_identities_3(x, y, getran((lenx + leny)//2))
Guido van Rossum4365cab1998-08-13 14:20:17 +0000193
Fred Drakedb1bd5c1999-12-23 15:36:42 +0000194# ------------------------------------------------- hex oct repr str atol
Guido van Rossum4365cab1998-08-13 14:20:17 +0000195
196def slow_format(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
Guido van Rossum4365cab1998-08-13 14:20:17 +0000204 while x:
205 x, r = divmod(x, base)
206 digits.append(int(r))
207 digits.reverse()
208 digits = digits or [0]
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000209 return '-'[:sign] + \
Guido van Rossum4365cab1998-08-13 14:20:17 +0000210 {8: '0', 10: '', 16: '0x'}[base] + \
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000211 join(map(lambda i: "0123456789ABCDEF"[i], digits), '') + \
Guido van Rossum4365cab1998-08-13 14:20:17 +0000212 "L"
213
214def test_format_1(x):
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000215 from string import atol
Fred Drakedb1bd5c1999-12-23 15:36:42 +0000216 for base, mapper in (8, oct), (10, repr), (16, hex):
Guido van Rossum4365cab1998-08-13 14:20:17 +0000217 got = mapper(x)
218 expected = slow_format(x, base)
219 check(got == expected, mapper.__name__, "returned",
220 got, "but expected", expected, "for", x)
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000221 check(atol(got, 0) == x, 'atol("%s", 0) !=' % got, x)
Fred Drakedb1bd5c1999-12-23 15:36:42 +0000222 # str() has to be checked a little differently since there's no
223 # trailing "L"
224 got = str(x)
225 expected = slow_format(x, 10)[:-1]
226 check(got == expected, mapper.__name__, "returned",
227 got, "but expected", expected, "for", x)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000228
229def test_format(maxdigits=MAXDIGITS):
Tim Peters971e0692001-08-23 20:34:01 +0000230 if verbose:
231 print "long str/hex/oct/atol"
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000232 for x in special:
233 test_format_1(x)
Guido van Rossum4365cab1998-08-13 14:20:17 +0000234 for i in range(10):
235 for lenx in range(1, maxdigits+1):
236 x = getran(lenx)
237 test_format_1(x)
238
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000239# ----------------------------------------------------------------- misc
240
241def test_misc(maxdigits=MAXDIGITS):
Tim Peters971e0692001-08-23 20:34:01 +0000242 if verbose:
243 print "long miscellaneous operations"
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000244 import sys
245
246 # check the extremes in int<->long conversion
247 hugepos = sys.maxint
248 hugeneg = -hugepos - 1
249 hugepos_aslong = long(hugepos)
250 hugeneg_aslong = long(hugeneg)
251 check(hugepos == hugepos_aslong, "long(sys.maxint) != sys.maxint")
252 check(hugeneg == hugeneg_aslong,
253 "long(-sys.maxint-1) != -sys.maxint-1")
254
255 # long -> int should not fail for hugepos_aslong or hugeneg_aslong
256 try:
257 check(int(hugepos_aslong) == hugepos,
258 "converting sys.maxint to long and back to int fails")
259 except OverflowError:
260 raise TestFailed, "int(long(sys.maxint)) overflowed!"
261 try:
262 check(int(hugeneg_aslong) == hugeneg,
263 "converting -sys.maxint-1 to long and back to int fails")
264 except OverflowError:
265 raise TestFailed, "int(long(-sys.maxint-1)) overflowed!"
266
267 # but long -> int should overflow for hugepos+1 and hugeneg-1
268 x = hugepos_aslong + 1
269 try:
Walter Dörwaldf1715402002-11-19 20:49:15 +0000270 y = int(x)
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000271 except OverflowError:
Walter Dörwaldf1715402002-11-19 20:49:15 +0000272 raise TestFailed, "int(long(sys.maxint) + 1) mustn't overflow"
273 if not isinstance(y, long):
274 raise TestFailed("int(long(sys.maxint) + 1) should have returned long")
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000275
276 x = hugeneg_aslong - 1
277 try:
Walter Dörwaldf1715402002-11-19 20:49:15 +0000278 y = int(x)
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000279 except OverflowError:
Walter Dörwaldf1715402002-11-19 20:49:15 +0000280 raise TestFailed, "int(long(-sys.maxint-1) - 1) mustn't overflow"
281 if not isinstance(y, long):
282 raise TestFailed("int(long(-sys.maxint-1) - 1) should have returned long")
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000283
Walter Dörwaldf1715402002-11-19 20:49:15 +0000284 class long2(long):
285 pass
286 x = long2(1L<<100)
287 y = int(x)
288 if type(y) is not long:
289 raise TestFailed("overflowing int conversion must return long not long subtype")
Tim Peters26c7fa32001-08-23 22:56:21 +0000290# ----------------------------------- tests of auto int->long conversion
291
292def test_auto_overflow():
293 import math, sys
294
295 if verbose:
296 print "auto-convert int->long on overflow"
297
298 special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1]
299 sqrt = int(math.sqrt(sys.maxint))
300 special.extend([sqrt-1, sqrt, sqrt+1])
301 special.extend([-i for i in special])
302
303 def checkit(*args):
304 # Heavy use of nested scopes here!
305 verify(got == expected, "for %r expected %r got %r" %
306 (args, expected, got))
307
308 for x in special:
309 longx = long(x)
310
311 expected = -longx
312 got = -x
313 checkit('-', x)
314
315 for y in special:
316 longy = long(y)
317
318 expected = longx + longy
319 got = x + y
320 checkit(x, '+', y)
321
322 expected = longx - longy
323 got = x - y
324 checkit(x, '-', y)
325
326 expected = longx * longy
327 got = x * y
328 checkit(x, '*', y)
329
330 if y:
Tim Peters0dad0f72001-09-04 19:48:01 +0000331 expected = longx / longy
332 got = x / y
Tim Peters26c7fa32001-08-23 22:56:21 +0000333 checkit(x, '/', y)
334
Tim Petersa3653092001-08-23 23:02:57 +0000335 expected = longx // longy
336 got = x // y
337 checkit(x, '//', y)
338
Tim Peters26c7fa32001-08-23 22:56:21 +0000339 expected = divmod(longx, longy)
340 got = divmod(longx, longy)
341 checkit(x, 'divmod', y)
342
343 if abs(y) < 5 and not (x == 0 and y < 0):
344 expected = longx ** longy
345 got = x ** y
346 checkit(x, '**', y)
347
348 for z in special:
Tim Peters32f453e2001-09-03 08:35:41 +0000349 if z != 0 :
350 if y >= 0:
351 expected = pow(longx, longy, long(z))
352 got = pow(x, y, z)
353 checkit('pow', x, y, '%', z)
354 else:
355 try:
356 pow(longx, longy, long(z))
357 except TypeError:
358 pass
359 else:
360 raise TestFailed("pow%r should have raised "
Neal Norwitz05c09d02002-04-01 19:01:39 +0000361 "TypeError" % ((longx, longy, long(z)),))
Tim Peters26c7fa32001-08-23 22:56:21 +0000362
Tim Peters9fffa3e2001-09-04 05:14:19 +0000363# ---------------------------------------- tests of long->float overflow
364
365def test_float_overflow():
366 import math
367
368 if verbose:
369 print "long->float overflow"
370
371 for x in -2.0, -1.0, 0.0, 1.0, 2.0:
372 verify(float(long(x)) == x)
373
Guido van Rossum7aa56c92003-02-03 15:25:01 +0000374 shuge = '12345' * 120
Tim Peters9fffa3e2001-09-04 05:14:19 +0000375 huge = 1L << 30000
376 mhuge = -huge
Neal Norwitzabcb0c02003-01-28 19:21:24 +0000377 namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math}
Tim Peters9fffa3e2001-09-04 05:14:19 +0000378 for test in ["float(huge)", "float(mhuge)",
379 "complex(huge)", "complex(mhuge)",
380 "complex(huge, 1)", "complex(mhuge, 1)",
381 "complex(1, huge)", "complex(1, mhuge)",
382 "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.",
383 "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.",
384 "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.",
385 "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.",
386 "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.",
387 "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.",
388 "math.sin(huge)", "math.sin(mhuge)",
Tim Peters9fffa3e2001-09-04 05:14:19 +0000389 "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better
Neal Norwitzabcb0c02003-01-28 19:21:24 +0000390 "math.floor(huge)", "math.floor(mhuge)",
391 "float(shuge) == int(shuge)"]:
Tim Peters83e7ccc2001-09-04 06:37:28 +0000392
Tim Peters9fffa3e2001-09-04 05:14:19 +0000393 try:
394 eval(test, namespace)
395 except OverflowError:
396 pass
397 else:
398 raise TestFailed("expected OverflowError from %s" % test)
Tim Peters78526162001-09-05 00:53:45 +0000399
400# ---------------------------------------------- test huge log and log10
401
402def test_logs():
403 import math
404
405 if verbose:
406 print "log and log10"
407
408 LOG10E = math.log10(math.e)
409
410 for exp in range(10) + [100, 1000, 10000]:
411 value = 10 ** exp
412 log10 = math.log10(value)
413 verify(fcmp(log10, exp) == 0)
414
415 # log10(value) == exp, so log(value) == log10(value)/log10(e) ==
416 # exp/LOG10E
417 expected = exp / LOG10E
418 log = math.log(value)
419 verify(fcmp(log, expected) == 0)
420
421 for bad in -(1L << 10000), -2L, 0L:
422 try:
423 math.log(bad)
424 raise TestFailed("expected ValueError from log(<= 0)")
425 except ValueError:
426 pass
427
428 try:
429 math.log10(bad)
430 raise TestFailed("expected ValueError from log10(<= 0)")
431 except ValueError:
432 pass
433
Guido van Rossum4365cab1998-08-13 14:20:17 +0000434# ---------------------------------------------------------------- do it
435
436test_division()
Tim Peters7f270ba2002-08-13 21:06:55 +0000437test_karatsuba()
Guido van Rossum4365cab1998-08-13 14:20:17 +0000438test_bitop_identities()
439test_format()
Guido van Rossum4581a0c1998-10-02 01:19:48 +0000440test_misc()
Tim Peters26c7fa32001-08-23 22:56:21 +0000441test_auto_overflow()
Tim Peters9fffa3e2001-09-04 05:14:19 +0000442test_float_overflow()
Tim Peters78526162001-09-05 00:53:45 +0000443test_logs()