mirror of
https://github.com/Z3Prover/z3
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121 lines
3.4 KiB
C++
121 lines
3.4 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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<name>
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Abstract:
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<abstract>
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Author:
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Nikolaj Bjorner (nbjorner)
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Lev Nachmanson (levnach)
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Revision History:
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--*/
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#include "math/lp/nla_basics_lemmas.h"
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#include "math/lp/nla_core.h"
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// #include "math/lp/factorization_factory_imp.h"
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namespace nla {
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monotone::monotone(core * c) : common(c) {}
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void monotone::monotonicity_lemma() {
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unsigned shift = random();
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unsigned size = c().m_to_refine.size();
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for(unsigned i = 0; i < size && !done(); i++) {
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lpvar v = c().m_to_refine[(i + shift) % size];
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monotonicity_lemma(c().m_emons[v]);
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}
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}
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void monotone::negate_abs_a_le_abs_b(lpvar a, lpvar b, bool strict) {
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rational av = val(a);
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rational as = rational(nla::rat_sign(av));
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rational bv = val(b);
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rational bs = rational(nla::rat_sign(bv));
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TRACE("nla_solver", tout << "av = " << av << ", bv = " << bv << "\n";);
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SASSERT(as*av <= bs*bv);
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llc mod_s = strict? (llc::LE): (llc::LT);
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mk_ineq(as, a, mod_s); // |a| <= 0 || |a| < 0
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if (a != b) {
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mk_ineq(bs, b, mod_s); // |b| <= 0 || |b| < 0
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mk_ineq(as, a, -bs, b, llc::GT); // negate |aj| <= |bj|
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}
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}
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void monotone::assert_abs_val_a_le_abs_var_b(
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const monomial& a,
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const monomial& b,
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bool strict) {
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lpvar aj = var(a);
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lpvar bj = var(b);
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rational av = val(aj);
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rational as = rational(nla::rat_sign(av));
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rational bv = val(bj);
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rational bs = rational(nla::rat_sign(bv));
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// TRACE("nla_solver", tout << "rmv = " << rmv << ", jv = " << jv << "\n";);
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mk_ineq(as, aj, llc::LT); // |aj| < 0
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mk_ineq(bs, bj, llc::LT); // |bj| < 0
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mk_ineq(as, aj, -bs, bj, strict? llc::LT : llc::LE); // |aj| < |bj|
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}
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void monotone::negate_abs_a_lt_abs_b(lpvar a, lpvar b) {
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rational av = val(a);
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rational as = rational(nla::rat_sign(av));
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rational bv = val(b);
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rational bs = rational(nla::rat_sign(bv));
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TRACE("nla_solver", tout << "av = " << av << ", bv = " << bv << "\n";);
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SASSERT(as*av < bs*bv);
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mk_ineq(as, a, llc::LT); // |aj| < 0
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mk_ineq(bs, b, llc::LT); // |bj| < 0
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mk_ineq(as, a, -bs, b, llc::GE); // negate |aj| < |bj|
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}
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void monotone::monotonicity_lemma(monomial const& m) {
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SASSERT(!check_monomial(m));
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if (c().mon_has_zero(m.vars()))
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return;
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const rational prod_val = abs(c().product_value(m.vars()));
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const rational m_val = abs(val(m));
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if (m_val < prod_val)
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monotonicity_lemma_lt(m, prod_val);
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else if (m_val > prod_val)
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monotonicity_lemma_gt(m, prod_val);
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}
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void monotone::monotonicity_lemma_gt(const monomial& m, const rational& prod_val) {
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TRACE("nla_solver", tout << "prod_val = " << prod_val << "\n";);
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add_empty_lemma();
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for (lpvar j : m.vars()) {
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c().add_abs_bound(j, llc::GT);
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}
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lpvar m_j = m.var();
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c().add_abs_bound(m_j, llc::LE, prod_val);
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TRACE("nla_solver", print_lemma(tout););
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}
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/** \brief enforce the inequality |m| >= product |m[i]| .
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/\_i |m[i]| >= |val(m[i])| => |m| >= |product_i val(m[i])|
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<=>
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\/_i |m[i]| < |val(m[i])} or |m| >= |product_i val(m[i])|
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*/
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void monotone::monotonicity_lemma_lt(const monomial& m, const rational& prod_val) {
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add_empty_lemma();
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for (lpvar j : m.vars()) {
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c().add_abs_bound(j, llc::LT);
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}
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lpvar m_j = m.var();
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c().add_abs_bound(m_j, llc::GE, prod_val);
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TRACE("nla_solver", print_lemma(tout););
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}
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}
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