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