mirror of
https://github.com/Z3Prover/z3
synced 2025-04-13 12:28:44 +00:00
Move clean_denominators code to the top
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
1e362e6fec
commit
e6102a8260
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@ -2909,6 +2909,275 @@ namespace realclosure {
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neg(r);
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}
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// ---------------------------------
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//
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// Structural equality
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//
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// ---------------------------------
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/**
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\brief Values a and b are said to be "structurally" equal if:
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- a and b are 0.
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- a and b are rationals and compare(a, b) == 0
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- a and b are rational function values p_a(x)/q_a(x) and p_b(y)/q_b(y) where x and y are field extensions, and
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* x == y (pointer equality, i.e., they are the same field extension object).
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* Every coefficient of p_a is structurally equal to every coefficient of p_b
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* Every coefficient of q_a is structurally equal to every coefficient of q_b
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Clearly structural equality implies equality, but the reverse is not true.
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*/
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bool struct_eq(value * a, value * b) const {
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if (a == b)
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return true;
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else if (a == 0 || b == 0)
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return false;
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else if (is_nz_rational(a) && is_nz_rational(b))
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return qm().eq(to_mpq(a), to_mpq(b));
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else if (is_nz_rational(a) || is_nz_rational(b))
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return false;
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else {
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SASSERT(is_rational_function(a));
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SASSERT(is_rational_function(b));
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rational_function_value * rf_a = to_rational_function(a);
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rational_function_value * rf_b = to_rational_function(b);
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if (rf_a->ext() != rf_b->ext())
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return false;
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return struct_eq(rf_a->num(), rf_b->num()) && struct_eq(rf_a->den(), rf_b->den());
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}
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}
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/**
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Auxiliary method for
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bool struct_eq(value * a, value * b)
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*/
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bool struct_eq(unsigned sz_a, value * const * p_a, unsigned sz_b, value * const * p_b) const {
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if (sz_a != sz_b)
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return false;
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for (unsigned i = 0; i < sz_a; i++) {
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if (!struct_eq(p_a[i], p_b[i]))
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return false;
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}
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return true;
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}
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/**
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Auxiliary method for
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bool struct_eq(value * a, value * b)
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*/
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bool struct_eq(polynomial const & p_a, polynomial const & p_b) const {
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return struct_eq(p_a.size(), p_a.c_ptr(), p_b.size(), p_b.c_ptr());
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}
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// ---------------------------------
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//
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// Clean denominators
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//
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// ---------------------------------
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/**
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\brief We say 'a' has "clean" denominators if
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- a is 0
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- a is a rational_value that is an integer
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- a is a rational_function_value of the form p_a(x)/1 where the coefficients of p_a also have clean denominators.
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*/
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bool has_clean_denominators(value * a) const {
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if (a == 0)
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return true;
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else if (is_nz_rational(a))
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return qm().is_int(to_mpq(a));
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else {
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rational_function_value * rf_a = to_rational_function(a);
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return is_rational_one(rf_a->den()) && has_clean_denominators(rf_a->num());
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}
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}
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/**
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\brief See comment at has_clean_denominators(value * a)
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*/
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bool has_clean_denominators(polynomial const & p) const {
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unsigned sz = p.size();
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for (unsigned i = 0; i < sz; i++) {
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if (!has_clean_denominators(p[i]))
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return false;
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}
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return true;
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}
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/**
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\brief "Clean" the denominators of 'a'. That is, return p and q s.t.
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a == p/q
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and
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has_clean_denominators(p) and has_clean_denominators(q)
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*/
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void clean_denominators_core(value * a, value_ref & p, value_ref & q) {
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INC_DEPTH();
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TRACE("rcf_clean", tout << "clean_denominators_core [" << m_exec_depth << "]\na: "; display(tout, a, false); tout << "\n";);
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p.reset(); q.reset();
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if (a == 0) {
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p = a;
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q = one();
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}
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else if (is_nz_rational(a)) {
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p = mk_rational(to_mpq(a).numerator());
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q = mk_rational(to_mpq(a).denominator());
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}
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else {
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rational_function_value * rf_a = to_rational_function(a);
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value_ref_buffer p_num(*this), p_den(*this);
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value_ref d_num(*this), d_den(*this);
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clean_denominators_core(rf_a->num(), p_num, d_num);
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clean_denominators_core(rf_a->den(), p_den, d_den);
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value_ref x(*this);
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x = mk_rational_function_value(rf_a->ext());
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mk_polynomial_value(p_num.size(), p_num.c_ptr(), x, p);
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mk_polynomial_value(p_den.size(), p_den.c_ptr(), x, q);
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if (!struct_eq(d_den, d_num)) {
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mul(p, d_den, p);
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mul(q, d_num, q);
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}
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}
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}
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/**
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\brief Clean the denominators of the polynomial p, it returns clean_p and d s.t.
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p = clean_p/d
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and has_clean_denominators(clean_p) && has_clean_denominators(d)
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*/
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void clean_denominators_core(polynomial const & p, value_ref_buffer & norm_p, value_ref & d) {
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value_ref_buffer nums(*this), dens(*this);
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value_ref a_n(*this), a_d(*this);
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bool all_one = true;
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for (unsigned i = 0; i < p.size(); i++) {
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if (p[i]) {
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clean_denominators_core(p[i], a_n, a_d);
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nums.push_back(a_n);
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if (!is_rational_one(a_d))
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all_one = false;
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dens.push_back(a_d);
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}
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else {
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nums.push_back(0);
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dens.push_back(0);
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}
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}
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if (all_one) {
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norm_p = nums;
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d = one();
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}
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else {
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// Compute lcm of the integer elements in dens.
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// This is a little trick to control the coefficient growth.
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// We don't compute lcm of the other elements of dens because it is too expensive.
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scoped_mpq lcm_z(qm());
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bool found_z = false;
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SASSERT(nums.size() == p.size());
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SASSERT(dens.size() == p.size());
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for (unsigned i = 0; i < p.size(); i++) {
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if (!dens[i])
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continue;
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if (is_nz_rational(dens[i])) {
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mpq const & _d = to_mpq(dens[i]);
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SASSERT(qm().is_int(_d));
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if (!found_z) {
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found_z = true;
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qm().set(lcm_z, _d);
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}
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else {
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qm().lcm(lcm_z, _d, lcm_z);
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}
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}
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}
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value_ref lcm(*this);
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if (found_z) {
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lcm = mk_rational(lcm_z);
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}
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else {
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lcm = one();
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}
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// Compute the multipliers for nums.
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// Compute norm_p and d
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//
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// We do NOT use GCD to compute the LCM of the denominators of non-rational values.
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// However, we detect structurally equivalent denominators.
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//
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// Thus a/(b+1) + c/(b+1) is converted into a*c/(b+1) instead of (a*(b+1) + c*(b+1))/(b+1)^2
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norm_p.reset();
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d = lcm;
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value_ref_buffer multipliers(*this);
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value_ref m(*this);
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for (unsigned i = 0; i < p.size(); i++) {
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if (!nums[i]) {
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norm_p.push_back(0);
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}
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else {
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SASSERT(dens[i]);
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bool is_z;
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if (!is_nz_rational(dens[i])) {
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m = lcm;
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is_z = false;
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}
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else {
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scoped_mpq num_z(qm());
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qm().div(lcm_z, to_mpq(dens[i]), num_z);
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SASSERT(qm().is_int(num_z));
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m = mk_rational_and_swap(num_z);
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is_z = true;
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}
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bool found_lt_eq = false;
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for (unsigned j = 0; j < p.size(); j++) {
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TRACE("rcf_clean_bug", tout << "j: " << j << " "; display(tout, m, false); tout << "\n";);
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if (!dens[j])
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continue;
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if (i != j && !is_nz_rational(dens[j])) {
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if (struct_eq(dens[i], dens[j])) {
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if (j < i)
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found_lt_eq = true;
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}
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else {
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mul(m, dens[j], m);
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}
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}
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}
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if (!is_z && !found_lt_eq) {
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mul(dens[i], d, d);
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}
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mul(m, nums[i], m);
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norm_p.push_back(m);
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}
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}
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}
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SASSERT(norm_p.size() == p.size());
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}
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void clean_denominators(value * a, value_ref & p, value_ref & q) {
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if (has_clean_denominators(a)) {
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p = a;
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q = one();
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}
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else {
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clean_denominators_core(a, p, q);
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}
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}
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void clean_denominators(polynomial const & p, value_ref_buffer & norm_p, value_ref & d) {
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if (has_clean_denominators(p)) {
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norm_p.append(p.size(), p.c_ptr());
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d = one();
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}
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else {
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clean_denominators_core(p, norm_p, d);
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}
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}
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void clean_denominators(numeral const & a, numeral & p, numeral & q) {
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value_ref _p(*this), _q(*this);
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clean_denominators(a.m_value, _p, _q);
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set(p, _p);
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set(q, _q);
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}
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// ---------------------------------
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//
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// GCD
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@ -4837,274 +5106,6 @@ namespace realclosure {
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return compare(a.m_value, b.m_value);
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}
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// ---------------------------------
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//
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// Structural equality
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//
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// ---------------------------------
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/**
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\brief Values a and b are said to be "structurally" equal if:
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- a and b are 0.
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- a and b are rationals and compare(a, b) == 0
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- a and b are rational function values p_a(x)/q_a(x) and p_b(y)/q_b(y) where x and y are field extensions, and
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* x == y (pointer equality, i.e., they are the same field extension object).
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* Every coefficient of p_a is structurally equal to every coefficient of p_b
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* Every coefficient of q_a is structurally equal to every coefficient of q_b
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Clearly structural equality implies equality, but the reverse is not true.
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*/
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bool struct_eq(value * a, value * b) const {
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if (a == b)
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return true;
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else if (a == 0 || b == 0)
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return false;
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else if (is_nz_rational(a) && is_nz_rational(b))
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return qm().eq(to_mpq(a), to_mpq(b));
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else if (is_nz_rational(a) || is_nz_rational(b))
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return false;
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else {
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SASSERT(is_rational_function(a));
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SASSERT(is_rational_function(b));
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rational_function_value * rf_a = to_rational_function(a);
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rational_function_value * rf_b = to_rational_function(b);
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if (rf_a->ext() != rf_b->ext())
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return false;
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return struct_eq(rf_a->num(), rf_b->num()) && struct_eq(rf_a->den(), rf_b->den());
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}
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}
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/**
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Auxiliary method for
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bool struct_eq(value * a, value * b)
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*/
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bool struct_eq(unsigned sz_a, value * const * p_a, unsigned sz_b, value * const * p_b) const {
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if (sz_a != sz_b)
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return false;
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for (unsigned i = 0; i < sz_a; i++) {
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if (!struct_eq(p_a[i], p_b[i]))
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return false;
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}
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return true;
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}
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/**
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Auxiliary method for
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bool struct_eq(value * a, value * b)
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*/
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bool struct_eq(polynomial const & p_a, polynomial const & p_b) const {
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return struct_eq(p_a.size(), p_a.c_ptr(), p_b.size(), p_b.c_ptr());
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}
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// ---------------------------------
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//
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// Clean denominators
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//
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// ---------------------------------
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/**
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\brief We say 'a' has "clean" denominators if
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- a is 0
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- a is a rational_value that is an integer
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- a is a rational_function_value of the form p_a(x)/1 where the coefficients of p_a also have clean denominators.
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*/
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bool has_clean_denominators(value * a) const {
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if (a == 0)
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return true;
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else if (is_nz_rational(a))
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return qm().is_int(to_mpq(a));
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else {
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rational_function_value * rf_a = to_rational_function(a);
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return is_rational_one(rf_a->den()) && has_clean_denominators(rf_a->num());
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}
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}
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/**
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\brief See comment at has_clean_denominators(value * a)
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*/
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bool has_clean_denominators(polynomial const & p) const {
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unsigned sz = p.size();
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for (unsigned i = 0; i < sz; i++) {
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if (!has_clean_denominators(p[i]))
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return false;
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}
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return true;
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}
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/**
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\brief "Clean" the denominators of 'a'. That is, return p and q s.t.
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a == p/q
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and
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has_clean_denominators(p) and has_clean_denominators(q)
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*/
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void clean_denominators_core(value * a, value_ref & p, value_ref & q) {
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INC_DEPTH();
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TRACE("rcf_clean", tout << "clean_denominators_core [" << m_exec_depth << "]\na: "; display(tout, a, false); tout << "\n";);
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p.reset(); q.reset();
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if (a == 0) {
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p = a;
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q = one();
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}
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else if (is_nz_rational(a)) {
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p = mk_rational(to_mpq(a).numerator());
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q = mk_rational(to_mpq(a).denominator());
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}
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else {
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rational_function_value * rf_a = to_rational_function(a);
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value_ref_buffer p_num(*this), p_den(*this);
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value_ref d_num(*this), d_den(*this);
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clean_denominators_core(rf_a->num(), p_num, d_num);
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clean_denominators_core(rf_a->den(), p_den, d_den);
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value_ref x(*this);
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x = mk_rational_function_value(rf_a->ext());
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mk_polynomial_value(p_num.size(), p_num.c_ptr(), x, p);
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mk_polynomial_value(p_den.size(), p_den.c_ptr(), x, q);
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if (!struct_eq(d_den, d_num)) {
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mul(p, d_den, p);
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mul(q, d_num, q);
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}
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}
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}
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/**
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\brief Clean the denominators of the polynomial p, it returns clean_p and d s.t.
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p = clean_p/d
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and has_clean_denominators(clean_p) && has_clean_denominators(d)
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*/
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void clean_denominators_core(polynomial const & p, value_ref_buffer & norm_p, value_ref & d) {
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value_ref_buffer nums(*this), dens(*this);
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value_ref a_n(*this), a_d(*this);
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bool all_one = true;
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for (unsigned i = 0; i < p.size(); i++) {
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if (p[i]) {
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clean_denominators_core(p[i], a_n, a_d);
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nums.push_back(a_n);
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if (!is_rational_one(a_d))
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all_one = false;
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dens.push_back(a_d);
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}
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else {
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nums.push_back(0);
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dens.push_back(0);
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}
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}
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if (all_one) {
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norm_p = nums;
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d = one();
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}
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else {
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// Compute lcm of the integer elements in dens.
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// This is a little trick to control the coefficient growth.
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// We don't compute lcm of the other elements of dens because it is too expensive.
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scoped_mpq lcm_z(qm());
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bool found_z = false;
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SASSERT(nums.size() == p.size());
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SASSERT(dens.size() == p.size());
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for (unsigned i = 0; i < p.size(); i++) {
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if (!dens[i])
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continue;
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if (is_nz_rational(dens[i])) {
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mpq const & _d = to_mpq(dens[i]);
|
||||
SASSERT(qm().is_int(_d));
|
||||
if (!found_z) {
|
||||
found_z = true;
|
||||
qm().set(lcm_z, _d);
|
||||
}
|
||||
else {
|
||||
qm().lcm(lcm_z, _d, lcm_z);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
value_ref lcm(*this);
|
||||
if (found_z) {
|
||||
lcm = mk_rational(lcm_z);
|
||||
}
|
||||
else {
|
||||
lcm = one();
|
||||
}
|
||||
|
||||
// Compute the multipliers for nums.
|
||||
// Compute norm_p and d
|
||||
//
|
||||
// We do NOT use GCD to compute the LCM of the denominators of non-rational values.
|
||||
// However, we detect structurally equivalent denominators.
|
||||
//
|
||||
// Thus a/(b+1) + c/(b+1) is converted into a*c/(b+1) instead of (a*(b+1) + c*(b+1))/(b+1)^2
|
||||
norm_p.reset();
|
||||
d = lcm;
|
||||
value_ref_buffer multipliers(*this);
|
||||
value_ref m(*this);
|
||||
for (unsigned i = 0; i < p.size(); i++) {
|
||||
if (!nums[i]) {
|
||||
norm_p.push_back(0);
|
||||
}
|
||||
else {
|
||||
SASSERT(dens[i]);
|
||||
bool is_z;
|
||||
if (!is_nz_rational(dens[i])) {
|
||||
m = lcm;
|
||||
is_z = false;
|
||||
}
|
||||
else {
|
||||
scoped_mpq num_z(qm());
|
||||
qm().div(lcm_z, to_mpq(dens[i]), num_z);
|
||||
SASSERT(qm().is_int(num_z));
|
||||
m = mk_rational_and_swap(num_z);
|
||||
is_z = true;
|
||||
}
|
||||
bool found_lt_eq = false;
|
||||
for (unsigned j = 0; j < p.size(); j++) {
|
||||
TRACE("rcf_clean_bug", tout << "j: " << j << " "; display(tout, m, false); tout << "\n";);
|
||||
if (!dens[j])
|
||||
continue;
|
||||
if (i != j && !is_nz_rational(dens[j])) {
|
||||
if (struct_eq(dens[i], dens[j])) {
|
||||
if (j < i)
|
||||
found_lt_eq = true;
|
||||
}
|
||||
else {
|
||||
mul(m, dens[j], m);
|
||||
}
|
||||
}
|
||||
}
|
||||
if (!is_z && !found_lt_eq) {
|
||||
mul(dens[i], d, d);
|
||||
}
|
||||
mul(m, nums[i], m);
|
||||
norm_p.push_back(m);
|
||||
}
|
||||
}
|
||||
}
|
||||
SASSERT(norm_p.size() == p.size());
|
||||
}
|
||||
|
||||
void clean_denominators(value * a, value_ref & p, value_ref & q) {
|
||||
if (has_clean_denominators(a)) {
|
||||
p = a;
|
||||
q = one();
|
||||
}
|
||||
else {
|
||||
clean_denominators_core(a, p, q);
|
||||
}
|
||||
}
|
||||
|
||||
void clean_denominators(polynomial const & p, value_ref_buffer & norm_p, value_ref & d) {
|
||||
if (has_clean_denominators(p)) {
|
||||
norm_p.append(p.size(), p.c_ptr());
|
||||
d = one();
|
||||
}
|
||||
else {
|
||||
clean_denominators_core(p, norm_p, d);
|
||||
}
|
||||
}
|
||||
|
||||
void clean_denominators(numeral const & a, numeral & p, numeral & q) {
|
||||
value_ref _p(*this), _q(*this);
|
||||
clean_denominators(a.m_value, _p, _q);
|
||||
set(p, _p);
|
||||
set(q, _q);
|
||||
}
|
||||
|
||||
// ---------------------------------
|
||||
//
|
||||
// "Pretty printing"
|
||||
|
|
|
|||
Loading…
Reference in a new issue