ExecStatus
Pow<A,B>::propagate(Space& home, const ModEventDelta&) {
GECODE_ME_CHECK(x1.eq(home,pow(x0.domain(),m_n)));
if ((m_n % 2) == 0)
{
if (x0.min() >= 0)
GECODE_ME_CHECK(x0.eq(home,nth_root(x1.domain(),m_n)));
else if (x0.max() <= 0)
GECODE_ME_CHECK(x0.eq(home,-nth_root(x1.domain(),m_n)));
else
GECODE_ME_CHECK(x0.eq(home,
hull(
nth_root(x1.domain(),m_n),
-nth_root(x1.domain(),m_n)
)
));
} else
GECODE_ME_CHECK(x0.eq(home,nth_root(x1.domain(),m_n)));
return x0.assigned() ? home.ES_SUBSUMED(*this) : ES_FIX;
}
mp_int<A,T> nth_root(const mp_int<A,T>& x, const mp_int<A,T>& n)
{
if (n.is_odd() && x.is_negative())
throw std::domain_error("nth_root: argument must be positive if n is even");
if (n.size() == 1)
return nth_root(x, n[0]);
// if x is negative fudge the sign but keep track
const int neg = x.sign();
const_cast<mp_int<A,T>*>(&x)->set_sign(1);
mp_int<A,T> t1, t2, t3;
typedef typename mp_int<A,T>::size_type size_type;
static const size_type digit_bits = mp_int<A,T>::digit_bits;
const size_type result_precision = (x.precision() - 1)
/ n.template to_integral<size_type>() + 1;
t2.grow_capacity((result_precision + digit_bits - 1) / digit_bits);
t2.set_size ((result_precision + digit_bits - 1) / digit_bits);
t2[t2.size()-1] = 0;
t2.set_bits(0, result_precision + 1);
do
{
t1 = t2;
// t2 = t1 - ((t1**n - x) / (n * t1**(n-1)))
// t3 = t1**(n-1)
t3 = pow(t1, n-1);
// numerator
// t2 = t1**n
t2 = t3 * t1;
// t2 = t1**n - x
t2 -= x;
// denominator
// t3 = t1**(n-1) * n
t3 *= n;
// t3 = (t1**n - x)/(n * t1**(n-1))
t3 = t2 / t3;
t2 = t1 - t3;
} while (t1 != t2);
// result can be off by a few so check
for (;;)
{
t2 = pow(t1, n);
if (t2 > x)
--t1;
else
break;
}
// reset the sign of x first
const_cast<mp_int<A,T>*>(&x)->set_sign(neg);
// set the sign of the result
t1.set_sign(neg);
return t1;
}
ExecStatus
NthRoot<A,B>::propagate(Space& home, const ModEventDelta&) {
GECODE_ME_CHECK(x1.eq(home,nth_root(x0.domain(),m_n)));
GECODE_ME_CHECK(x0.eq(home,pow(x1.domain(),m_n)));
return x0.assigned() ? home.ES_SUBSUMED(*this) : ES_FIX;
}
