import unittest from test import test_support import random # Used for lazy formatting of failure messages class Frm(object): def __init__(self, format, *args): self.format = format self.args = args def __str__(self): return self.format % self.args # SHIFT should match the value in longintrepr.h for best testing. SHIFT = 15 BASE = 2 ** SHIFT MASK = BASE - 1 KARATSUBA_CUTOFF = 70 # from longobject.c # Max number of base BASE digits to use in test cases. Doubling # this will more than double the runtime. MAXDIGITS = 15 # build some special values special = map(long, [0, 1, 2, BASE, BASE >> 1]) special.append(0x5555555555555555L) special.append(0xaaaaaaaaaaaaaaaaL) # some solid strings of one bits p2 = 4L # 0 and 1 already added for i in range(2*SHIFT): special.append(p2 - 1) p2 = p2 << 1 del p2 # add complements & negations special = special + map(lambda x: ~x, special) + \ map(lambda x: -x, special) class LongTest(unittest.TestCase): # Get quasi-random long consisting of ndigits digits (in base BASE). # quasi == the most-significant digit will not be 0, and the number # is constructed to contain long strings of 0 and 1 bits. These are # more likely than random bits to provoke digit-boundary errors. # The sign of the number is also random. def getran(self, ndigits): self.assert_(ndigits > 0) nbits_hi = ndigits * SHIFT nbits_lo = nbits_hi - SHIFT + 1 answer = 0L nbits = 0 r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start while nbits < nbits_lo: bits = (r >> 1) + 1 bits = min(bits, nbits_hi - nbits) self.assert_(1 <= bits <= SHIFT) nbits = nbits + bits answer = answer << bits if r & 1: answer = answer | ((1 << bits) - 1) r = int(random.random() * (SHIFT * 2)) self.assert_(nbits_lo <= nbits <= nbits_hi) if random.random() < 0.5: answer = -answer return answer # Get random long consisting of ndigits random digits (relative to base # BASE). The sign bit is also random. def getran2(ndigits): answer = 0L for i in xrange(ndigits): answer = (answer << SHIFT) | random.randint(0, MASK) if random.random() < 0.5: answer = -answer return answer def check_division(self, x, y): eq = self.assertEqual q, r = divmod(x, y) q2, r2 = x//y, x%y pab, pba = x*y, y*x eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y)) eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y)) eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y)) eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y)) if y > 0: self.assert_(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y)) else: self.assert_(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y)) def test_division(self): digits = range(1, MAXDIGITS+1) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 14) digits.append(KARATSUBA_CUTOFF * 3) for lenx in digits: x = self.getran(lenx) for leny in digits: y = self.getran(leny) or 1L self.check_division(x, y) def test_karatsuba(self): digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10) digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100]) bits = [digit * SHIFT for digit in digits] # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) == # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check. for abits in bits: a = (1L << abits) - 1 for bbits in bits: if bbits < abits: continue b = (1L << bbits) - 1 x = a * b y = ((1L << (abits + bbits)) - (1L << abits) - (1L << bbits) + 1) self.assertEqual(x, y, Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y)) def check_bitop_identities_1(self, x): eq = self.assertEqual eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x)) eq(x | 0, x, Frm("x | 0 != x for x=%r", x)) eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x)) eq(x & -1, x, Frm("x & -1 != x for x=%r", x)) eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x)) eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x)) eq(x, ~~x, Frm("x != ~~x for x=%r", x)) eq(x & x, x, Frm("x & x != x for x=%r", x)) eq(x | x, x, Frm("x | x != x for x=%r", x)) eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x)) eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x)) eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x)) eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x)) eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x)) eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x)) for n in xrange(2*SHIFT): p2 = 2L ** n eq(x << n >> n, x, Frm("x << n >> n != x for x=%r, n=%r", (x, n))) eq(x // p2, x >> n, Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2))) eq(x * p2, x << n, Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2))) eq(x & -p2, x >> n << n, Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2))) eq(x & -p2, x & ~(p2 - 1), Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2))) def check_bitop_identities_2(self, x, y): eq = self.assertEqual eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y))) eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y))) eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y))) eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y))) eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y))) eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y))) eq(x ^ y, (x | y) & ~(x & y), Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y))) eq(x ^ y, (x & ~y) | (~x & y), Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y))) eq(x ^ y, (x | y) & (~x | ~y), Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y))) def check_bitop_identities_3(self, x, y, z): eq = self.assertEqual eq((x & y) & z, x & (y & z), Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z))) eq((x | y) | z, x | (y | z), Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z))) eq((x ^ y) ^ z, x ^ (y ^ z), Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z))) eq(x & (y | z), (x & y) | (x & z), Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z))) eq(x | (y & z), (x | y) & (x | z), Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z))) def test_bitop_identities(self): for x in special: self.check_bitop_identities_1(x) digits = xrange(1, MAXDIGITS+1) for lenx in digits: x = self.getran(lenx) self.check_bitop_identities_1(x) for leny in digits: y = self.getran(leny) self.check_bitop_identities_2(x, y) self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2)) def slow_format(self, x, base): if (x, base) == (0, 8): # this is an oddball! return "0" digits = [] sign = 0 if x < 0: sign, x = 1, -x while x: x, r = divmod(x, base) digits.append(int(r)) digits.reverse() digits = digits or [0] return '-'[:sign] + \ {8: '0', 10: '', 16: '0x'}[base] + \ "".join(map(lambda i: "0123456789abcdef"[i], digits)) def check_format_1(self, x): for base, mapper in (8, oct), (10, repr), (16, hex): got = mapper(x) expected = self.slow_format(x, base) msg = Frm("%s returned %r but expected %r for %r", mapper.__name__, got, expected, x) self.assertEqual(got, expected, msg) self.assertEqual(long(got, 0), x, Frm('long("%s", 0) != %r', got, x)) # str() has to be checked a little differently since there's no # trailing "L" got = str(x) expected = self.slow_format(x, 10) msg = Frm("%s returned %r but expected %r for %r", mapper.__name__, got, expected, x) self.assertEqual(got, expected, msg) def test_format(self): for x in special: self.check_format_1(x) for i in xrange(10): for lenx in xrange(1, MAXDIGITS+1): x = self.getran(lenx) self.check_format_1(x) def test_misc(self): import sys # check the extremes in int<->long conversion hugepos = sys.maxint hugeneg = -hugepos - 1 hugepos_aslong = long(hugepos) hugeneg_aslong = long(hugeneg) self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxint) != sys.maxint") self.assertEqual(hugeneg, hugeneg_aslong, "long(-sys.maxint-1) != -sys.maxint-1") # long -> int should not fail for hugepos_aslong or hugeneg_aslong try: self.assertEqual(int(hugepos_aslong), hugepos, "converting sys.maxint to long and back to int fails") except OverflowError: self.fail("int(long(sys.maxint)) overflowed!") try: self.assertEqual(int(hugeneg_aslong), hugeneg, "converting -sys.maxint-1 to long and back to int fails") except OverflowError: self.fail("int(long(-sys.maxint-1)) overflowed!") # but long -> int should overflow for hugepos+1 and hugeneg-1 x = hugepos_aslong + 1 try: y = int(x) except OverflowError: self.fail("int(long(sys.maxint) + 1) mustn't overflow") self.assert_(isinstance(y, long), "int(long(sys.maxint) + 1) should have returned long") x = hugeneg_aslong - 1 try: y = int(x) except OverflowError: self.fail("int(long(-sys.maxint-1) - 1) mustn't overflow") self.assert_(isinstance(y, long), "int(long(-sys.maxint-1) - 1) should have returned long") class long2(long): pass x = long2(1L<<100) y = int(x) self.assert_(type(y) is long, "overflowing int conversion must return long not long subtype") # ----------------------------------- tests of auto int->long conversion def test_auto_overflow(self): import math, sys special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1] sqrt = int(math.sqrt(sys.maxint)) special.extend([sqrt-1, sqrt, sqrt+1]) special.extend([-i for i in special]) def checkit(*args): # Heavy use of nested scopes here! self.assertEqual(got, expected, Frm("for %r expected %r got %r", args, expected, got)) for x in special: longx = long(x) expected = -longx got = -x checkit('-', x) for y in special: longy = long(y) expected = longx + longy got = x + y checkit(x, '+', y) expected = longx - longy got = x - y checkit(x, '-', y) expected = longx * longy got = x * y checkit(x, '*', y) if y: expected = longx / longy got = x / y checkit(x, '/', y) expected = longx // longy got = x // y checkit(x, '//', y) expected = divmod(longx, longy) got = divmod(longx, longy) checkit(x, 'divmod', y) if abs(y) < 5 and not (x == 0 and y < 0): expected = longx ** longy got = x ** y checkit(x, '**', y) for z in special: if z != 0 : if y >= 0: expected = pow(longx, longy, long(z)) got = pow(x, y, z) checkit('pow', x, y, '%', z) else: self.assertRaises(TypeError, pow,longx, longy, long(z)) def test_float_overflow(self): import math for x in -2.0, -1.0, 0.0, 1.0, 2.0: self.assertEqual(float(long(x)), x) shuge = '12345' * 120 huge = 1L << 30000 mhuge = -huge namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math} for test in ["float(huge)", "float(mhuge)", "complex(huge)", "complex(mhuge)", "complex(huge, 1)", "complex(mhuge, 1)", "complex(1, huge)", "complex(1, mhuge)", "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.", "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.", "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.", "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.", "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.", "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.", "math.sin(huge)", "math.sin(mhuge)", "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better "math.floor(huge)", "math.floor(mhuge)"]: self.assertRaises(OverflowError, eval, test, namespace) # XXX Perhaps float(shuge) can raise OverflowError on some box? # The comparison should not. self.assertNotEqual(float(shuge), int(shuge), "float(shuge) should not equal int(shuge)") def test_logs(self): import math LOG10E = math.log10(math.e) for exp in range(10) + [100, 1000, 10000]: value = 10 ** exp log10 = math.log10(value) self.assertAlmostEqual(log10, exp) # log10(value) == exp, so log(value) == log10(value)/log10(e) == # exp/LOG10E expected = exp / LOG10E log = math.log(value) self.assertAlmostEqual(log, expected) for bad in -(1L << 10000), -2L, 0L: self.assertRaises(ValueError, math.log, bad) self.assertRaises(ValueError, math.log10, bad) def test_mixed_compares(self): eq = self.assertEqual import math import sys # We're mostly concerned with that mixing floats and longs does the # right stuff, even when longs are too large to fit in a float. # The safest way to check the results is to use an entirely different # method, which we do here via a skeletal rational class (which # represents all Python ints, longs and floats exactly). class Rat: def __init__(self, value): if isinstance(value, (int, long)): self.n = value self.d = 1 elif isinstance(value, float): # Convert to exact rational equivalent. f, e = math.frexp(abs(value)) assert f == 0 or 0.5 <= f < 1.0 # |value| = f * 2**e exactly # Suck up CHUNK bits at a time; 28 is enough so that we suck # up all bits in 2 iterations for all known binary double- # precision formats, and small enough to fit in an int. CHUNK = 28 top = 0 # invariant: |value| = (top + f) * 2**e exactly while f: f = math.ldexp(f, CHUNK) digit = int(f) assert digit >> CHUNK == 0 top = (top << CHUNK) | digit f -= digit assert 0.0 <= f < 1.0 e -= CHUNK # Now |value| = top * 2**e exactly. if e >= 0: n = top << e d = 1 else: n = top d = 1 << -e if value < 0: n = -n self.n = n self.d = d assert float(n) / float(d) == value else: raise TypeError("can't deal with %r" % val) def __cmp__(self, other): if not isinstance(other, Rat): other = Rat(other) return cmp(self.n * other.d, self.d * other.n) cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200] # 2**48 is an important boundary in the internals. 2**53 is an # important boundary for IEEE double precision. for t in 2.0**48, 2.0**50, 2.0**53: cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0, long(t-1), long(t), long(t+1)]) cases.extend([0, 1, 2, sys.maxint, float(sys.maxint)]) # 1L<<20000 should exceed all double formats. long(1e200) is to # check that we get equality with 1e200 above. t = long(1e200) cases.extend([0L, 1L, 2L, 1L << 20000, t-1, t, t+1]) cases.extend([-x for x in cases]) for x in cases: Rx = Rat(x) for y in cases: Ry = Rat(y) Rcmp = cmp(Rx, Ry) xycmp = cmp(x, y) eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp)) eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp)) eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp)) eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp)) eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp)) eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp)) eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp)) def test_main(): test_support.run_unittest(LongTest) if __name__ == "__main__": test_main()