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Add normalize_algebraic

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-10 13:38:51 -08:00
parent 4cd2998743
commit 619e597174
1 changed files with 56 additions and 7 deletions
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63
src/math/realclosure/realclosure.cpp
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@ -3580,7 +3580,7 @@ namespace realclosure {
- new_p1 <- one; new_p2 <- p2/p1[0]; IF sz1 == 1
- new_p1 <- p1/gcd(p1, p2); new_p2 <- p2/gcd(p1, p2); Otherwise
*/
void normalize(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & new_p1, value_ref_buffer & new_p2) {
void normalize_fraction(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & new_p1, value_ref_buffer & new_p2) {
SASSERT(sz1 > 0 && sz2 > 0);
if (sz2 == 1) {
// - new_p1 <- p1/p2[0]; new_p2 <- one IF sz2 == 1
@ -3630,6 +3630,40 @@ namespace realclosure {
}
}
/**
\brief Simplify p1(x) using x's defining polynomial.
By definition of polynomial division, we have:
new_p1(x) == quotient(p1,p)(x) * p(x) + rem(p1,p)(x)
Since p(x) == 0, we have that
new_p1(x) = rem(p1,p)(x)
*/
void normalize_algebraic(algebraic * x, unsigned sz1, value * const * p1, value_ref_buffer & new_p1) {
polynomial const & p = x->p();
rem(sz1, p1, p.size(), p.c_ptr(), new_p1);
}
/**
\brief Apply normalize_algebraic (if applicable) & normalize_fraction.
*/
void normalize_all(extension * x, unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & new_p1, value_ref_buffer & new_p2) {
if (x->is_algebraic()) {
value_ref_buffer p1_norm(*this);
value_ref_buffer p2_norm(*this);
// FUTURE: we don't need to invoke normalize_algebraic if degree of p1 < degree x->p()
normalize_algebraic(to_algebraic(x), sz1, p1, p1_norm);
// FUTURE: we don't need to invoke normalize_algebraic if degree of p2 < degree x->p()
normalize_algebraic(to_algebraic(x), sz2, p2, p2_norm);
normalize_fraction(p1_norm.size(), p1_norm.c_ptr(), p2_norm.size(), p2_norm.c_ptr(), new_p1, new_p2);
}
else {
normalize_fraction(sz1, p1, sz2, p2, new_p1, new_p2);
}
}
/**
\brief Create a new value using the a->ext(), and the given numerator and denominator.
Use interval(a) + interval(b) as an initial approximation for the interval of the result, and invoke determine_sign()
@ -3692,7 +3726,7 @@ namespace realclosure {
else {
value_ref_buffer new_num(*this);
value_ref_buffer new_den(*this);
normalize(num.size(), num.c_ptr(), ad.size(), ad.c_ptr(), new_num, new_den);
normalize_all(a->ext(), num.size(), num.c_ptr(), ad.size(), ad.c_ptr(), new_num, new_den);
mk_add_value(a, b, new_num.size(), new_num.c_ptr(), new_den.size(), new_den.c_ptr(), r);
}
}
@ -3712,8 +3746,14 @@ namespace realclosure {
add(an.size(), an.c_ptr(), bn.size(), bn.c_ptr(), new_num);
if (new_num.empty())
r = 0;
else
else {
// We don't need to invoke normalize_algebraic even if x (== a->ext()) is algebraic.
// Reason: by construction the polynomials a->num() and b->num() are "normalized".
// That is, their degrees are < degree of the polynomial defining x.
// Moreover, when we add polynomials, the degree can only decrease.
// So, degree of new_num must be < degree of x's defining polynomial.
mk_add_value(a, b, new_num.size(), new_num.c_ptr(), one.size(), one.c_ptr(), r);
}
}
/**
@ -3743,7 +3783,7 @@ namespace realclosure {
mul(ad.size(), ad.c_ptr(), bd.size(), bd.c_ptr(), den);
value_ref_buffer new_num(*this);
value_ref_buffer new_den(*this);
normalize(num.size(), num.c_ptr(), den.size(), den.c_ptr(), new_num, new_den);
normalize_all(a->ext(), num.size(), num.c_ptr(), den.size(), den.c_ptr(), new_num, new_den);
mk_add_value(a, b, new_num.size(), new_num.c_ptr(), new_den.size(), new_den.c_ptr(), r);
}
}
@ -3886,7 +3926,7 @@ namespace realclosure {
SASSERT(num.size() == an.size());
value_ref_buffer new_num(*this);
value_ref_buffer new_den(*this);
normalize(num.size(), num.c_ptr(), ad.size(), ad.c_ptr(), new_num, new_den);
normalize_all(a->ext(), num.size(), num.c_ptr(), ad.size(), ad.c_ptr(), new_num, new_den);
mk_mul_value(a, b, new_num.size(), new_num.c_ptr(), new_den.size(), new_den.c_ptr(), r);
}
}
@ -3904,7 +3944,16 @@ namespace realclosure {
value_ref_buffer new_num(*this);
mul(an.size(), an.c_ptr(), bn.size(), bn.c_ptr(), new_num);
SASSERT(!new_num.empty());
mk_mul_value(a, b, new_num.size(), new_num.c_ptr(), one.size(), one.c_ptr(), r);
extension * x = a->ext();
if (x->is_algebraic()) {
// FUTURE: we don't need to invoke normalize_algebraic if degree of new_num < degree x->p()
value_ref_buffer new_num2(*this);
normalize_algebraic(to_algebraic(x), new_num.size(), new_num.c_ptr(), new_num2);
mk_mul_value(a, b, new_num2.size(), new_num2.c_ptr(), one.size(), one.c_ptr(), r);
}
else {
mk_mul_value(a, b, new_num.size(), new_num.c_ptr(), one.size(), one.c_ptr(), r);
}
}
/**
@ -3927,7 +3976,7 @@ namespace realclosure {
SASSERT(!num.empty()); SASSERT(!den.empty());
value_ref_buffer new_num(*this);
value_ref_buffer new_den(*this);
normalize(num.size(), num.c_ptr(), den.size(), den.c_ptr(), new_num, new_den);
normalize_all(a->ext(), num.size(), num.c_ptr(), den.size(), den.c_ptr(), new_num, new_den);
mk_mul_value(a, b, new_num.size(), new_num.c_ptr(), new_den.size(), new_den.c_ptr(), r);
}
}