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Add prem to avoid rational function values

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-12 16:27:56 -08:00
parent 09d3686d58
commit e6a35c6241
1 changed files with 78 additions and 1 deletions
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79
src/math/realclosure/realclosure.cpp
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@ -366,11 +366,13 @@ namespace realclosure {
ptr_vector<value> m_to_restore; //!< Set of values v s.t. v->m_old_interval != 0
// Parameters
bool m_use_prem; //!< use pseudo-remainder when computing sturm sequences
unsigned m_ini_precision; //!< initial precision for transcendentals, infinitesimals, etc.
unsigned m_max_precision; //!< Maximum precision for interval arithmetic techniques, it switches to complete methods after that
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
// Tracing
unsigned m_exec_depth;
@ -675,6 +677,7 @@ namespace realclosure {
}
void updt_params(params_ref const & p) {
m_use_prem = p.get_bool("use_prem", true);
m_ini_precision = p.get_uint("initial_precision", 24);
m_inf_precision = p.get_uint("inf_precision", 24);
m_max_precision = p.get_uint("max_precision", 64); // == 1/2^64 for interval arithmetic methods, it switches to complete methods after that.
@ -2825,6 +2828,63 @@ namespace realclosure {
}
}
/**
\brief r <- prem(p1, p2) Pseudo-remainder
We are working on a field, but it is useful to use the pseudo-remainder algorithm because
it does not create rational function values.
That is, if has_clean_denominators(p1) and has_clean_denominators(p2) then has_clean_denominators(r).
*/
void prem(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, unsigned & d, value_ref_buffer & r) {
SASSERT(p1 != r.c_ptr());
SASSERT(p2 != r.c_ptr());
TRACE("rcf_prem",
tout << "prem\n";
display_poly(tout, sz1, p1); tout << "\n";
display_poly(tout, sz2, p2); tout << "\n";);
d = 0;
r.reset();
SASSERT(sz2 > 0);
if (sz2 == 1)
return;
r.append(sz1, p1);
if (sz1 <= 1)
return; // r is p1
value * b_n = p2[sz2 - 1];
SASSERT(b_n != 0);
value_ref a_m(*this);
value_ref new_a(*this);
while (true) {
checkpoint();
sz1 = r.size();
if (sz1 < sz2) {
TRACE("rcf_prem", tout << "prem result\n"; display_poly(tout, r.size(), r.c_ptr()); tout << "\n";);
return;
}
unsigned m_n = sz1 - sz2;
// r: a_m * x^m + a_{m-1} * x^{m-1} + ... + a_0
// p2: b_n * x^n + b_{n-1} * x^{n-1} + ... + b_0
d++;
a_m = r[sz1 - 1];
// don't need to update position sz1 - 1, since it will become 0
if (!is_rational_one(b_n)) {
for (unsigned i = 0; i < sz1 - 1; i++) {
mul(r[i], b_n, new_a);
r.set(i, new_a);
}
}
// buffer: a_m * x^m + b_n * a_{m-1} * x^{m-1} + ... + b_n * a_0
// don't need to process i = sz2 - 1, because r[sz1 - 1] will become 0.
for (unsigned i = 0; i < sz2 - 1; i++) {
mul(a_m, p2[i], new_a);
sub(r[i + m_n], new_a, new_a);
r.set(i + m_n, new_a);
}
r.shrink(sz1 - 1);
adjust_size(r);
}
}
/**
\brief r <- -p
*/
@ -2874,6 +2934,20 @@ namespace realclosure {
rem(sz1, p1, sz2, p2, r);
neg(r);
}
/**
\brief r <- sprem(p1, p2)
Signed pseudo remainder
*/
void sprem(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & r) {
SASSERT(p1 != r.c_ptr());
SASSERT(p2 != r.c_ptr());
unsigned d;
prem(sz1, p1, sz2, p2, d, r);
// We should not flip the sign if d is odd and leading coefficient of p2 is negative.
if (d % 2 == 0 || (sz2 > 0 && sign(p2[sz2-1]) < 0))
neg(r);
}
/**
\brief Force the leading coefficient of p to be 1.
@ -2986,7 +3060,10 @@ namespace realclosure {
value_ref_buffer r(*this);
while (true) {
unsigned sz = seq.size();
srem(seq.size(sz-2), seq.coeffs(sz-2), seq.size(sz-1), seq.coeffs(sz-1), r);
if (m_use_prem)
sprem(seq.size(sz-2), seq.coeffs(sz-2), seq.size(sz-1), seq.coeffs(sz-1), r);
else
srem(seq.size(sz-2), seq.coeffs(sz-2), seq.size(sz-1), seq.coeffs(sz-1), r);
TRACE("rcf_sturm_seq",
tout << "sturm_seq_core [" << m_exec_depth << "], new polynomial\n";
display_poly(tout, r.size(), r.c_ptr()); tout << "\n";);