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Add lazy normalization for algebraic extension values. Increase default max_precision to 128.

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-15 16:35:36 -08:00
parent 217c8375ce
commit eea3384106
2 changed files with 35 additions and 4 deletions
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4
src/math/realclosure/rcf.pyg
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@ -5,4 +5,6 @@ def_module_params('rcf',
('clean_denominators', BOOL, True, "clean denominators before root isolation"),
('initial_precision', UINT, 24, "a value k that is the initial interval size (as 1/2^k) when creating transcendentals and approximated division"),
('inf_precision', UINT, 24, "a value k that is the initial interval size (i.e., (0, 1/2^l)) used as an approximation for infinitesimal values"),
('max_precision', UINT, 64, "during sign determination we switch from interval arithmetic to complete methods when the interval size is less than 1/2^k, where k is the max_precision")))
('max_precision', UINT, 128, "during sign determination we switch from interval arithmetic to complete methods when the interval size is less than 1/2^k, where k is the max_precision"),
('lazy_algebraic_normalization', BOOL, True, "during sturm-seq and square-free polynomial computations, only normalize algebraic polynomial expressions when the definining polynomial is monic")
))

35
src/math/realclosure/realclosure.cpp
View file

@ -378,11 +378,13 @@ namespace realclosure {
unsigned m_inf_precision; //!< 2^m_inf_precision is used as the lower bound of oo and -2^m_inf_precision is used as the upper_bound of -oo
scoped_mpbq m_plus_inf_approx; // lower bound for binary rational intervals used to approximate an infinite positive value
scoped_mpbq m_minus_inf_approx; // upper bound for binary rational intervals used to approximate an infinite negative value
bool m_lazy_algebraic_normalization;
// Tracing
unsigned m_exec_depth;
bool m_in_aux_values; // True if we are computing SquareFree polynomials or Sturm sequences. That is, the values being computed will be discarded.
volatile bool m_cancel;
struct scoped_polynomial_seq {
@ -495,6 +497,8 @@ namespace realclosure {
m_exec_depth = 0;
m_in_aux_values = false;
m_cancel = false;
updt_params(p);
@ -723,6 +727,7 @@ namespace realclosure {
m_ini_precision = p.initial_precision();
m_inf_precision = p.inf_precision();
m_max_precision = p.max_precision();
m_lazy_algebraic_normalization = p.lazy_algebraic_normalization();
bqm().power(mpbq(2), m_inf_precision, m_plus_inf_approx);
bqm().set(m_minus_inf_approx, m_plus_inf_approx);
bqm().neg(m_minus_inf_approx);
@ -3454,6 +3459,10 @@ namespace realclosure {
return p.size() > 0 && is_rational_one(p[p.size() - 1]);
}
bool is_monic(polynomial const & p) {
return p.size() > 0 && is_rational_one(p[p.size() - 1]);
}
/**
\brief Force the leading coefficient of p to be 1.
*/
@ -3589,6 +3598,7 @@ namespace realclosure {
Store in r the square free factors of p.
*/
void square_free(unsigned sz, value * const * p, value_ref_buffer & r) {
flet<bool> set(m_in_aux_values, true);
if (sz <= 1) {
r.append(sz, p);
}
@ -3616,6 +3626,8 @@ namespace realclosure {
*/
void sturm_seq_core(scoped_polynomial_seq & seq) {
INC_DEPTH();
flet<bool> set(m_in_aux_values, true);
SASSERT(seq.size() >= 2);
TRACE("rcf_sturm_seq",
unsigned sz = seq.size();
@ -3788,6 +3800,8 @@ namespace realclosure {
\brief Evaluate the sign of p(b) by computing a value object.
*/
int expensive_eval_sign_at(unsigned n, value * const * p, mpbq const & b) {
flet<bool> set(m_in_aux_values, true);
SASSERT(n > 1);
SASSERT(p[n - 1] != 0);
// Actually, given b = c/2^k, we compute the sign of (2^k)^n*p(c)
@ -4877,7 +4891,13 @@ namespace realclosure {
*/
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);
if (!m_lazy_algebraic_normalization || !m_in_aux_values || is_monic(p)) {
rem(sz1, p1, p.size(), p.c_ptr(), new_p1);
}
else {
new_p1.reset();
new_p1.append(sz1, p1);
}
}
/**
@ -5693,7 +5713,16 @@ namespace realclosure {
}
void display_poly(std::ostream & out, unsigned n, value * const * p) const {
display_polynomial(out, n, p, display_free_var_proc(), false);
collect_algebraic_refs c;
for (unsigned i = 0; i < n; i++)
c.mark(p[i]);
display_polynomial(out, n, p, display_free_var_proc(), true);
std::sort(c.m_found.begin(), c.m_found.end(), rank_lt_proc());
for (unsigned i = 0; i < c.m_found.size(); i++) {
algebraic * ext = c.m_found[i];
out << "\n r!" << ext->idx() << " := ";
display_algebraic_def(out, ext, true);
}
}
void display_ext(std::ostream & out, extension * r, bool compact) const {