void test_various_float_types
(long double unrounded
,long double expected
)
{
BOOST_TEST((test_one_case(static_cast<float >(unrounded), static_cast<float >(expected))));
BOOST_TEST((test_one_case(static_cast<double >(unrounded), static_cast<double >(expected))));
BOOST_TEST((test_one_case(static_cast<long double>(unrounded), static_cast<long double>(expected))));
}
static void test_PolicyServer_IPv4()
{
// IPv4:
test_one_case( /* Set & Get */ "1.2.3.4",
/* Host,port */ NULL, NULL,
/* IP Addr */ "1.2.3.4");
test_one_case( /* Set & Get */ "255.255.255.255:80",
/* Host,port */ NULL, "80",
/* IP Addr */ "255.255.255.255");
test_one_case( /* Set & Get */ " 1.2.3.4:",
/* Host,port */ NULL, NULL,
/* IP Addr */ "1.2.3.4");
}
int
main (void)
{
/* Set up a two-page region whose first page is read-write and
whose second page is inaccessible. */
size_t pagesize = (size_t) sysconf (_SC_PAGESIZE);
char *page = mmap (0, pagesize * 2, PROT_READ|PROT_WRITE,
MAP_PRIVATE|MAP_ANON, -1, 0);
if (page == MAP_FAILED)
{
perror ("mmap");
return 1;
}
memset (page, 'x', pagesize * 2);
if (mprotect (page + pagesize, pagesize, PROT_NONE))
{
perror ("mprotect");
return 1;
}
struct crypt_data cd;
memset (&cd, 0, sizeof cd);
bool ok = true;
for (size_t i = 0; i < ARRAY_SIZE (testcases); i++)
if (!test_one_case (&testcases[i], page, pagesize, &cd))
ok = false;
return ok ? 0 : 1;
}
void test_rounding()
{
// The first several blocks of tests use values with no more than
// six significant decimal digits, six being a natural value for
// std::numeric_limits<float>::digits10
// on an IEC 60559 machine.
// Test rounding in (-1.0, 1.0).
test_various_float_types(-0.999999L, -1.0L);
test_various_float_types(-0.500001L, -1.0L);
test_various_float_types(-0.500000L, -1.0L); // Away from zero.
test_various_float_types(-0.499999L, -0.0L);
test_various_float_types(-0.000001L, -0.0L);
test_various_float_types(-0.000000L, -0.0L);
test_various_float_types( 0.000000L, 0.0L);
test_various_float_types( 0.000001L, 0.0L);
test_various_float_types( 0.499999L, 0.0L);
test_various_float_types( 0.500000L, 1.0L); // Away from zero.
test_various_float_types( 0.500001L, 1.0L);
test_various_float_types( 0.999999L, 1.0L);
// Rounding to nearest: make sure halfway cases are rounded away
// from zero.
test_various_float_types(-4.5L, -5.0L);
test_various_float_types(-3.5L, -4.0L);
test_various_float_types(-2.5L, -3.0L);
test_various_float_types(-1.5L, -2.0L);
test_various_float_types(-0.5L, -1.0L);
test_various_float_types( 0.5L, 1.0L);
test_various_float_types( 1.5L, 2.0L);
test_various_float_types( 2.5L, 3.0L);
test_various_float_types( 3.5L, 4.0L);
test_various_float_types( 4.5L, 5.0L);
// The next block of tests uses values in the open interval
// (-1E29, +1E29)
// which is well within the range of a float on an IEC 60559 machine
// that uses the natural implementation such that
// std::numeric_limits<float>::max_exponent10
// is 38.
// Rounding an already-rounded integral value shouldn't change its
// representation. Note however that some of these integers are
// deliberately outside the range that can be exactly represented,
// at least on a machine where
// std::numeric_limits<some-float-type)::digits10
// is less than twenty-eight.
test_various_float_types(-1234567890123456789012345678.0L, -1234567890123456789012345678.0L);
test_various_float_types(-9876543200000000000000000000.0L, -9876543200000000000000000000.0L);
test_various_float_types(-1000000000000000000000000000.0L, -1000000000000000000000000000.0L);
test_various_float_types(-100001.0L, -100001.0L);
test_various_float_types(-2.0L, -2.0L);
test_various_float_types(-1.0L, -1.0L);
test_various_float_types(-0.0L, -0.0L);
test_various_float_types( 0.0L, 0.0L);
test_various_float_types( 1.0L, 1.0L);
test_various_float_types( 2.0L, 2.0L);
test_various_float_types( 100001.0L, 100001.0L);
test_various_float_types( 1000000000000000000000000000.0L, 1000000000000000000000000000.0L);
test_various_float_types( 9876543200000000000000000000.0L, 9876543200000000000000000000.0L);
test_various_float_types( 1234567890123456789012345678.0L, 1234567890123456789012345678.0L);
// Test some numbers that are representable in all IEEE formats,
// but not necessarily as exact integers because they have
// FLT_DIG or DBL_DIG significant digits (and mantissae chosen
// so that no more digits are accurately representable).
test_various_float_types(987654.321L, 987654.0L);
test_various_float_types(987654321098765.375L, 987654321098765.0L);
test_various_float_types(987654321098765.500L, 987654321098766.0L);
// Note: This test
// test_various_float_types(987654321098765.4321L, 987654321098765.0L);
// produces a 'failure' with type double on an intel machine using
// ISO 60559 64-bit doubles (53-bit significand) when the rounding
// direction is toward positive infinity. This is not a failure of
// the algorithm, but rather an inherent limitation on precision.
// The number to be rounded is not exactly representable as a double.
// It is between 987654321098765.375 and 987654321098765.500, which
// are exactly representable. The latter representation is chosen
// only when the rounding direction is upward, and rounding it to
// nearest correctly maps it to the next higher integer.
//
// Thus, the uncertainty due to [2.13.3/1] in the least significant
// decimal digit of a number that is not exactly representable can
// exceed four times epsilon. SOMEDAY !! It remains to establish
// rigorous bounds, both overall and for each step.
// The fifty-third Mersenne number was identified by the gnu octave
// maintainers as a difficult case. See:
// http://article.gmane.org/gmane.comp.gnu.mingw.user/26299
// [2008-04-25T00:31:26Z from Tatsuro MATSUOKA]
long double const M53 = 6361.0L * 69431.0L * 20394401.0L;
test_various_float_types( M53, 9007199254740991.0L);
test_various_float_types( -M53, -9007199254740991.0L);
test_various_float_types( 1 + M53, 9007199254740992.0L);
test_various_float_types( 1 + -M53, -9007199254740990.0L);
test_various_float_types(-1 + M53, 9007199254740990.0L);
test_various_float_types(-1 + -M53, -9007199254740992.0L);
// Here is a similar testcase from François-Xavier Coudert,
// who refers to:
// http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00917.html
// | 0.499999999999999944488848768742172978818416595458984375
// | 4503599627370497.0
// |
// | They should be rounded to 0.0 and 4503599627370497.0, but
// | simply adding 0.5 and truncating will round to 1.0 and
// | 4503599627370498.
//
// The number above that's very close to one-half is in fact
// nextafter(0.5, 0.0)
// both of which are ffffffffffffdf3f / 3fdfffffffffffff internally.
test_various_float_types(4503599627370497.0L, 4503599627370497.0L);
// This test:
// test_various_float_types(nextafter(0.5L, 0.0L), 0.0L);
// mustn't be run as such because, e.g., the value
// static_cast<float>(nextafter(0.5L, 0.0L))
// need not be distinct from 0.0F.
BOOST_TEST((test_one_case(nextafterf(0.5F, 0.0F), 0.0F)));
BOOST_TEST((test_one_case(nextafter (0.5 , 0.0 ), 0.0 )));
BOOST_TEST((test_one_case(nextafterl(0.5L, 0.0L), 0.0L)));
}
static void test_PolicyServer_IPv6()
{
// IPv6 with square brackets:
test_one_case( /* Set & Get */ "[ffff::dd:12:34]",
/* Host,port */ NULL, NULL,
/* IP Addr */ "ffff::dd:12:34");
test_one_case( /* Set & Get */ "[2001:0db8:85a3:0000:0000:8a2e:0370:7334]:64000",
/* Host,port */ NULL, "64000",
/* IP Addr */ "2001:0db8:85a3:0000:0000:8a2e:0370:7334");
test_one_case( /* Set & Get */ "[ffff::dd:12:34]:",
/* Host,port */ NULL, NULL,
/* IP Addr */ "ffff::dd:12:34");
test_one_case( /* Set & Get */ "[FF01:0:0:0:0:0:0:FB]:12345",
/* Host,port */ NULL, "12345",
/* IP Addr */ "FF01:0:0:0:0:0:0:FB");
// IPv6 without square brackets:
test_one_case( /* Set & Get */ "ffff::dd:12:34",
/* Host,port */ NULL, NULL,
/* IP Addr */ "ffff::dd:12:34");
test_one_case( /* Set & Get */ "FF01:0:0:0:0:0:0:FB",
/* Host,port */ NULL, NULL,
/* IP Addr */ "FF01:0:0:0:0:0:0:FB");
test_one_case( /* Set & Get */ "::",
/* Host,port */ NULL, NULL,
/* IP Addr */ "::");
// IPv4 mapped IPv6 addresses:
test_one_case( /* Set & Get */ "::ffff:192.0.2.128",
/* Host,port */ NULL, NULL,
/* IP Addr */ "::ffff:192.0.2.128");
test_one_case( /* Set & Get */ "[::ffff:192.0.2.128]",
/* Host,port */ NULL, NULL,
/* IP Addr */ "::ffff:192.0.2.128");
// Other:
test_one_case( /* Set & Get */ "ff02::1:ff00:0/104",
/* Host,port */ NULL, NULL,
/* IP Addr */ "ff02::1:ff00:0/104");
test_one_case( /* Set & Get */ "[ff02::1:ff00:0/104]:9",
/* Host,port */ NULL, "9",
/* IP Addr */ "ff02::1:ff00:0/104");
}