void t5()
{
//
// Now integer functions:
//
ref_type z1, z2;
test_type t1, t2;
divide_qr(a, b, z1, z2);
divide_qr(a1, b1, t1, t2);
BOOST_TEST_EQ(z1.str(), t1.str());
BOOST_TEST_EQ(z2.str(), t2.str());
BOOST_TEST_EQ(integer_modulus(a, si), integer_modulus(a1, si));
BOOST_TEST_EQ(lsb(a), lsb(a1));
for(unsigned i = 0; i < 1000; i += 13)
{
BOOST_TEST_EQ(bit_test(a, i), bit_test(a1, i));
}
// We have to take care that our powers don't grow too large, otherwise this takes "forever",
// also don't test for modulo types, as these may give a different result from arbitrary
// precision types:
BOOST_TEST_EQ(ref_type(pow(d, ui % 19)).str(), test_type(pow(d1, ui % 19)).str());
BOOST_TEST_EQ(ref_type(powm(a, b, c)).str(), test_type(powm(a1, b1, c1)).str());
BOOST_TEST_EQ(ref_type(powm(a, b, ui)).str(), test_type(powm(a1, b1, ui)).str());
BOOST_TEST_EQ(ref_type(powm(a, ui, c)).str(), test_type(powm(a1, ui, c1)).str());
}
typename enable_if_c<is_integral<I1>::value && is_unsigned<I2>::value && is_integral<I3>::value, I1>::type
powm(const I1& a, I2 b, I3 c)
{
typedef typename detail::double_integer<I1>::type double_type;
I1 x(1), y(a);
double_type result;
while(b > 0)
{
if(b & 1)
{
multiply(result, x, y);
x = integer_modulus(result, c);
}
multiply(result, y, y);
y = integer_modulus(result, c);
b >>= 1;
}
return x % c;
}
bool check_small_factors(const I& n)
{
static const boost::uint32_t small_factors1[] = {
3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u };
static const boost::uint32_t pp1 = 223092870u;
boost::uint32_t m1 = integer_modulus(n, pp1);
for(unsigned i = 0; i < sizeof(small_factors1) / sizeof(small_factors1[0]); ++i)
{
BOOST_ASSERT(pp1 % small_factors1[i] == 0);
if(m1 % small_factors1[i] == 0)
return false;
}
static const boost::uint32_t small_factors2[] = {
29u, 31u, 37u, 41u, 43u, 47u };
static const boost::uint32_t pp2 = 2756205443u;
m1 = integer_modulus(n, pp2);
for(unsigned i = 0; i < sizeof(small_factors2) / sizeof(small_factors2[0]); ++i)
{
BOOST_ASSERT(pp2 % small_factors2[i] == 0);
if(m1 % small_factors2[i] == 0)
return false;
}
static const boost::uint32_t small_factors3[] = {
53u, 59u, 61u, 67u, 71u };
static const boost::uint32_t pp3 = 907383479u;
m1 = integer_modulus(n, pp3);
for(unsigned i = 0; i < sizeof(small_factors3) / sizeof(small_factors3[0]); ++i)
{
BOOST_ASSERT(pp3 % small_factors3[i] == 0);
if(m1 % small_factors3[i] == 0)
return false;
}
static const boost::uint32_t small_factors4[] = {
73u, 79u, 83u, 89u, 97u };
static const boost::uint32_t pp4 = 4132280413u;
m1 = integer_modulus(n, pp4);
for(unsigned i = 0; i < sizeof(small_factors4) / sizeof(small_factors4[0]); ++i)
{
BOOST_ASSERT(pp4 % small_factors4[i] == 0);
if(m1 % small_factors4[i] == 0)
return false;
}
static const boost::uint32_t small_factors5[6][4] = {
{ 101u, 103u, 107u, 109u },
{ 113u, 127u, 131u, 137u },
{ 139u, 149u, 151u, 157u },
{ 163u, 167u, 173u, 179u },
{ 181u, 191u, 193u, 197u },
{ 199u, 211u, 223u, 227u }
};
static const boost::uint32_t pp5[6] =
{
121330189u,
113u * 127u * 131u * 137u,
139u * 149u * 151u * 157u,
163u * 167u * 173u * 179u,
181u * 191u * 193u * 197u,
199u * 211u * 223u * 227u
};
for(unsigned k = 0; k < sizeof(pp5) / sizeof(*pp5); ++k)
{
m1 = integer_modulus(n, pp5[k]);
for(unsigned i = 0; i < 4; ++i)
{
BOOST_ASSERT(pp5[k] % small_factors5[k][i] == 0);
if(m1 % small_factors5[k][i] == 0)
return false;
}
}
return true;
}
