444 lines
14 KiB
Python
444 lines
14 KiB
Python
from test.test_support import verify, verbose, TestFailed, fcmp
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from string import join
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from random import random, randint
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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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# ------------------------------------------------------------ utilities
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# Use check instead of assert so the test still does something
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# under -O.
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def check(ok, *args):
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if not ok:
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raise TestFailed, join(map(str, args), " ")
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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(ndigits):
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verify(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() * (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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verify(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() * (SHIFT * 2))
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verify(nbits_lo <= nbits <= nbits_hi)
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if 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 range(ndigits):
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answer = (answer << SHIFT) | randint(0, MASK)
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if random() < 0.5:
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answer = -answer
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return answer
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# --------------------------------------------------------------- divmod
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def test_division_2(x, y):
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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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check(pab == pba, "multiplication does not commute for", x, y)
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check(q == q2, "divmod returns different quotient than / for", x, y)
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check(r == r2, "divmod returns different mod than % for", x, y)
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check(x == q*y + r, "x != q*y + r after divmod on", x, y)
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if y > 0:
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check(0 <= r < y, "bad mod from divmod on", x, y)
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else:
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check(y < r <= 0, "bad mod from divmod on", x, y)
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def test_division(maxdigits=MAXDIGITS):
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if verbose:
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print "long / * % divmod"
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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 = getran(lenx)
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for leny in digits:
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y = getran(leny) or 1L
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test_division_2(x, y)
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# ------------------------------------------------------------ karatsuba
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def test_karatsuba():
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if verbose:
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print "Karatsuba"
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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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check(x == y, "bad result for", a, "*", b, x, y)
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# -------------------------------------------------------------- ~ & | ^
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def test_bitop_identities_1(x):
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check(x & 0 == 0, "x & 0 != 0 for", x)
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check(x | 0 == x, "x | 0 != x for", x)
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check(x ^ 0 == x, "x ^ 0 != x for", x)
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check(x & -1 == x, "x & -1 != x for", x)
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check(x | -1 == -1, "x | -1 != -1 for", x)
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check(x ^ -1 == ~x, "x ^ -1 != ~x for", x)
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check(x == ~~x, "x != ~~x for", x)
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check(x & x == x, "x & x != x for", x)
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check(x | x == x, "x | x != x for", x)
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check(x ^ x == 0, "x ^ x != 0 for", x)
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check(x & ~x == 0, "x & ~x != 0 for", x)
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check(x | ~x == -1, "x | ~x != -1 for", x)
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check(x ^ ~x == -1, "x ^ ~x != -1 for", x)
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check(-x == 1 + ~x == ~(x-1), "not -x == 1 + ~x == ~(x-1) for", x)
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for n in range(2*SHIFT):
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p2 = 2L ** n
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check(x << n >> n == x, "x << n >> n != x for", x, n)
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check(x // p2 == x >> n, "x // p2 != x >> n for x n p2", x, n, p2)
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check(x * p2 == x << n, "x * p2 != x << n for x n p2", x, n, p2)
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check(x & -p2 == x >> n << n == x & ~(p2 - 1),
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"not x & -p2 == x >> n << n == x & ~(p2 - 1) for x n p2",
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x, n, p2)
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def test_bitop_identities_2(x, y):
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check(x & y == y & x, "x & y != y & x for", x, y)
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check(x | y == y | x, "x | y != y | x for", x, y)
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check(x ^ y == y ^ x, "x ^ y != y ^ x for", x, y)
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check(x ^ y ^ x == y, "x ^ y ^ x != y for", x, y)
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check(x & y == ~(~x | ~y), "x & y != ~(~x | ~y) for", x, y)
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check(x | y == ~(~x & ~y), "x | y != ~(~x & ~y) for", x, y)
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check(x ^ y == (x | y) & ~(x & y),
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"x ^ y != (x | y) & ~(x & y) for", x, y)
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check(x ^ y == (x & ~y) | (~x & y),
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"x ^ y == (x & ~y) | (~x & y) for", x, y)
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check(x ^ y == (x | y) & (~x | ~y),
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"x ^ y == (x | y) & (~x | ~y) for", x, y)
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def test_bitop_identities_3(x, y, z):
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check((x & y) & z == x & (y & z),
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"(x & y) & z != x & (y & z) for", x, y, z)
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check((x | y) | z == x | (y | z),
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"(x | y) | z != x | (y | z) for", x, y, z)
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check((x ^ y) ^ z == x ^ (y ^ z),
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"(x ^ y) ^ z != x ^ (y ^ z) for", x, y, z)
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check(x & (y | z) == (x & y) | (x & z),
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"x & (y | z) != (x & y) | (x & z) for", x, y, z)
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check(x | (y & z) == (x | y) & (x | z),
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"x | (y & z) != (x | y) & (x | z) for", x, y, z)
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def test_bitop_identities(maxdigits=MAXDIGITS):
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if verbose:
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print "long bit-operation identities"
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for x in special:
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test_bitop_identities_1(x)
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digits = range(1, maxdigits+1)
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for lenx in digits:
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x = getran(lenx)
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test_bitop_identities_1(x)
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for leny in digits:
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y = getran(leny)
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test_bitop_identities_2(x, y)
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test_bitop_identities_3(x, y, getran((lenx + leny)//2))
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# ------------------------------------------------- hex oct repr str atol
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def slow_format(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), '') + \
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"L"
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def test_format_1(x):
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from string import atol
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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 = slow_format(x, base)
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check(got == expected, mapper.__name__, "returned",
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got, "but expected", expected, "for", x)
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check(atol(got, 0) == x, 'atol("%s", 0) !=' % 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 = slow_format(x, 10)[:-1]
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check(got == expected, mapper.__name__, "returned",
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got, "but expected", expected, "for", x)
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def test_format(maxdigits=MAXDIGITS):
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if verbose:
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print "long str/hex/oct/atol"
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for x in special:
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test_format_1(x)
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for i in range(10):
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for lenx in range(1, maxdigits+1):
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x = getran(lenx)
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test_format_1(x)
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# ----------------------------------------------------------------- misc
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def test_misc(maxdigits=MAXDIGITS):
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if verbose:
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print "long miscellaneous operations"
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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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check(hugepos == hugepos_aslong, "long(sys.maxint) != sys.maxint")
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check(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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check(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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raise TestFailed, "int(long(sys.maxint)) overflowed!"
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try:
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check(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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raise TestFailed, "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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raise TestFailed, "int(long(sys.maxint) + 1) mustn't overflow"
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if not isinstance(y, long):
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raise TestFailed("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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raise TestFailed, "int(long(-sys.maxint-1) - 1) mustn't overflow"
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if not isinstance(y, long):
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raise TestFailed("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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if type(y) is not long:
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raise TestFailed("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():
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import math, sys
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if verbose:
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print "auto-convert int->long on overflow"
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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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verify(got == expected, "for %r expected %r got %r" %
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(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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try:
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pow(longx, longy, long(z))
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except TypeError:
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pass
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else:
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raise TestFailed("pow%r should have raised "
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"TypeError" % ((longx, longy, long(z)),))
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# ---------------------------------------- tests of long->float overflow
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def test_float_overflow():
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import math
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if verbose:
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print "long->float overflow"
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for x in -2.0, -1.0, 0.0, 1.0, 2.0:
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verify(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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"float(shuge) == int(shuge)"]:
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try:
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eval(test, namespace)
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except OverflowError:
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pass
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else:
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raise TestFailed("expected OverflowError from %s" % test)
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# ---------------------------------------------- test huge log and log10
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def test_logs():
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import math
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if verbose:
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print "log and log10"
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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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verify(fcmp(log10, exp) == 0)
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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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verify(fcmp(log, expected) == 0)
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for bad in -(1L << 10000), -2L, 0L:
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try:
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math.log(bad)
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raise TestFailed("expected ValueError from log(<= 0)")
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except ValueError:
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pass
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try:
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math.log10(bad)
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raise TestFailed("expected ValueError from log10(<= 0)")
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except ValueError:
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pass
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# ---------------------------------------------------------------- do it
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test_division()
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test_karatsuba()
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test_bitop_identities()
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test_format()
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test_misc()
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test_auto_overflow()
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test_float_overflow()
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test_logs()
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