mirror of
https://github.com/Z3Prover/z3
synced 2025-04-16 22:05:36 +00:00
301 lines
8.5 KiB
C++
301 lines
8.5 KiB
C++
#include "math/dd/dd_pdd.h"
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namespace dd {
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class test {
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public :
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static void hello_world() {
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pdd_manager m(3);
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pdd v0 = m.mk_var(0);
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pdd v1 = m.mk_var(1);
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pdd v2 = m.mk_var(2);
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std::cout << v0 << "\n";
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std::cout << v1 << "\n";
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std::cout << v2 << "\n";
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pdd c1 = v0 * v1 * v2;
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pdd c2 = v2 * v0 * v1;
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std::cout << c1 << "\n";
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VERIFY(c1 == c2);
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c1 = v0 + v1 + v2;
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c2 = v2 + v1 + v0;
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std::cout << c1 << "\n";
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VERIFY(c1 == c2);
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c1 = (v0+v1) * v2;
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c2 = (v0*v2) + (v1*v2);
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std::cout << c1 << "\n";
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VERIFY(c1 == c2);
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c1 = (c1 + 3) + 1;
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c2 = (c2 + 1) + 3;
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std::cout << c1 << "\n";
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VERIFY(c1 == c2);
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c1 = v0 - v1;
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c2 = v1 - v0;
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std::cout << c1 << " " << c2 << "\n";
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c1 = v1*v2;
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c2 = (v0*v2) + (v2*v2);
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pdd c3 = m.zero();
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VERIFY(m.try_spoly(c1, c2, c3));
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std::cout << c1 << " " << c2 << " spoly: " << c3 << "\n";
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c1 = v1*v2;
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c2 = (v0*v2) + (v1*v1);
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VERIFY(m.try_spoly(c1, c2, c3));
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std::cout << c1 << " " << c2 << " spoly: " << c3 << "\n";
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c1 = (v0*v1) - (v0*v0);
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c2 = (v0*v1*(v2 + v0)) + v2;
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c3 = c2.reduce(c1);
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std::cout << c1 << " " << c2 << " reduce: " << c3 << "\n";
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VERIFY(c3 == c3.reduce(c1));
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}
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static void reduce() {
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std::cout << "\nreduce\n";
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// a(b^2)cd + abc + bcd + bc + cd + 3 reduce by bc
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pdd_manager m(4);
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pdd a = m.mk_var(0);
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pdd b = m.mk_var(1);
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pdd c = m.mk_var(2);
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pdd d = m.mk_var(3);
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pdd e = (a * b * b * c * d) + (2*a*b*c) + (b*c*d) + (b*c) + (c*d) + 3;
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std::cout << e << "\n";
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pdd f = b * c;
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pdd r_ef = m.reduce(e, f);
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m.display(std::cout);
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std::cout << "result of reduce " << e << " by " << f << " is " << r_ef << "\n";
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VERIFY(r_ef == (c*d) + 3);
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pdd r_fe = m.reduce(f, e);
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std::cout << "result of reduce " << f << " by " << e << " is " << r_fe << "\n" ;
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VERIFY(r_fe == f);
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// test that b*c*d is treated as the leading monomial
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f = b*c*d - d*d;
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r_ef = m.reduce(e, f);
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std::cout << "result of reduce " << e << " by " << f << " is " << r_ef << "\n";
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VERIFY(r_ef == (a*b*d*d) + (2*a*b*c) + (d*d) + (b*c) + (c*d) + 3);
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pdd k = d*d + 3*b;
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VERIFY(m.reduce(f, k) == b*c*d + 3*b);
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}
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static void large_product() {
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std::cout << "\nlarge_product\n";
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pdd_manager m(4);
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pdd a = m.mk_var(0);
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pdd b = m.mk_var(1);
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pdd c = m.mk_var(2);
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pdd d = m.mk_var(3);
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pdd e = a + c;
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for (unsigned i = 0; i < 5; i++) {
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e = e * e;
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}
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e = e * b;
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std::cout << e << "\n";
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}
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static void reset() {
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std::cout << "\ntest reset\n";
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pdd_manager m(4);
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pdd a = m.mk_var(0);
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pdd b = m.mk_var(1);
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pdd c = m.mk_var(2);
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pdd d = m.mk_var(3);
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std::cout << (a + b)*(c + d) << "\n";
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unsigned_vector l2v;
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for (unsigned i = 0; i < 4; ++i)
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l2v.push_back(3 - i);
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m.reset(l2v);
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a = m.mk_var(0);
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b = m.mk_var(1);
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c = m.mk_var(2);
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d = m.mk_var(3);
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std::cout << (a + b)*(c + d) << "\n";
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}
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static void canonize() {
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std::cout << "\ncanonize\n";
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pdd_manager m(2);
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pdd a = m.mk_var(0);
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pdd b = m.mk_var(1);
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pdd e = (a - b) * ( a + b);
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pdd f = a * a - b * b;
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VERIFY(e == f);
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e = (a - b)* (a - b);
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f = a * a - 2 * a * b + b * b;
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VERIFY(e == f);
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e = a - 3;
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e = e * e;
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f = a * a - 6 * a + 9;
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VERIFY(e == f);
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e = 2 * a - 3;
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e = e * e;
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f = 4 * a * a - 12 * a + 9;
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VERIFY(e == f);
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}
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static void iterator() {
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std::cout << "test iterator\n";
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pdd_manager m(4);
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pdd a = m.mk_var(0);
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pdd b = m.mk_var(1);
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pdd c = m.mk_var(2);
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pdd d = m.mk_var(3);
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pdd p = (a + b)*(c + 3*d) + 2;
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std::cout << p << "\n";
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for (auto const& m : p) {
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std::cout << m << "\n";
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}
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}
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static void order() {
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std::cout << "order\n";
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pdd_manager m(4);
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unsigned va = 0;
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unsigned vb = 1;
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unsigned vc = 2;
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unsigned vd = 3;
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pdd a = m.mk_var(va);
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pdd b = m.mk_var(vb);
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pdd c = m.mk_var(vc);
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pdd d = m.mk_var(vd);
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pdd p = a + b;
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std::cout << p << "\n";
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unsigned i = 0;
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for (auto const& m : p) {
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std::cout << m << "\n";
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VERIFY(i != 0 ||( m.vars.size() == 1 && m.vars[0] == vb));
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VERIFY(i != 1 ||( m.vars.size() == 1 && m.vars[0] == va));
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i++;
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}
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pdd ccbbaa = c*c*b*b*a*a;
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pdd ccbbba = c*c*b*b*b*a;
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p = ccbbaa + ccbbba;
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i = 0;
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std::cout << "p = " << p << "\n";
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for (auto const& m : p) {
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std::cout << m << "\n";
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VERIFY(i != 0 ||( m.vars.size() == 6 && m.vars[4] == vb)); // the first one has to be ccbbba
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VERIFY(i != 1 ||( m.vars.size() == 6 && m.vars[4] == va)); // the second one has to be ccbbaa
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i++;
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}
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pdd dcbba = d*c*b*b*a;
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pdd dd = d * d;
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p = dcbba + ccbbba + dd;
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vector<unsigned> v;
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std::cout << "p = " << p << "\n";
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unsigned k = p.index();
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std::cout << "pdd(k) = " << pdd(k, m) << "\n";
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k = m.first_leading(k);
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do {
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if (m.is_val(k)) {
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VERIFY(m.val(k).is_one());
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break;
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}
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v.push_back(m.var(k));
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std::cout << "pdd(k) = " << pdd(k, m) << "\n";
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std::cout << "push v" << m.var(k) << "\n";
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k = m.next_leading(k);
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} while(true);
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auto it = v.begin();
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std::cout << "v" << *it;
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it++;
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for( ; it != v.end(); it ++) {
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std::cout << "*v" << *it;
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}
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VERIFY(v.size() == 6);
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VERIFY(v[0] == vc);
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std::cout << "\n";
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v.reset();
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p = d*c*c*d + b*c*c*b + d*d*d;
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k = p.index();
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std::cout << "pdd(k) = " << pdd(k, m) << "\n";
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k = m.first_leading(k);
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do {
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if (m.is_val(k)) {
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VERIFY(m.val(k).is_one());
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break;
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}
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v.push_back(m.var(k));
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std::cout << "pdd(k) = " << pdd(k, m) << "\n";
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std::cout << "push v" << m.var(k) << "\n";
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k = m.next_leading(k);
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} while(true);
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it = v.begin();
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std::cout << "v" << *it;
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it++;
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for( ; it != v.end(); it ++) {
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std::cout << "*v" << *it;
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}
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VERIFY(v.size() == 4);
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VERIFY(v[0] == vd);
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std::cout << "\n";
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}
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static void order_lm() {
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std::cout << "order_lm\n";
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pdd_manager m(4);
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unsigned va = 0;
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unsigned vb = 1;
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unsigned vc = 2;
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unsigned vd = 3;
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pdd a = m.mk_var(va);
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pdd b = m.mk_var(vb);
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pdd c = m.mk_var(vc);
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pdd d = m.mk_var(vd);
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pdd p = a + b;
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std::cout << p << "\n";
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unsigned i = 0;
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for (auto const& m : p) {
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std::cout << m << "\n";
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VERIFY(i != 0 ||( m.vars.size() == 1 && m.vars[0] == vb));
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VERIFY(i != 1 ||( m.vars.size() == 1 && m.vars[0] == va));
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i++;
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}
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pdd ccbbaa = c*c*b*b*a*a;
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pdd ccbbba = c*c*b*b*b*a;
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p = ccbbaa + ccbbba;
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i = 0;
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std::cout << "p = " << p << "\n";
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for (auto const& m : p) {
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std::cout << m << "\n";
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VERIFY(i != 0 ||( m.vars.size() == 6 && m.vars[4] == vb)); // the first one has to be ccbbba
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VERIFY(i != 1 ||( m.vars.size() == 6 && m.vars[4] == va)); // the second one has to be ccbbaa
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i++;
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}
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pdd dcbba = d*c*b*b*a;
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pdd dd = d * d;
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pdd p0 = p + dd;
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std::cout << p0 << " > " << p << "\n";
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VERIFY(m.lm_lt(p, p0));
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VERIFY(m.lm_lt(p0 + a * b, p0 + b * b));
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}
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};
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}
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void tst_pdd() {
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dd::test::hello_world();
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dd::test::reduce();
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dd::test::large_product();
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dd::test::canonize();
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dd::test::reset();
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dd::test::iterator();
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dd::test::order();
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dd::test::order_lm();
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}
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